Exploration properties of biased evanescent random walkers on a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Esguerra, Jose Perico; Reyes, Jelian

2017-08-01

We investigate the combined effects of bias and evanescence on the characteristics of random walks on a one-dimensional lattice. We calculate the time-dependent return probability, eventual return probability, conditional mean return time, and the time-dependent mean number of visited sites of biased immortal and evanescent discrete-time random walkers on a one-dimensional lattice. We then extend the calculations to the case of a continuous-time step-coupled biased evanescent random walk on a one-dimensional lattice with an exponential waiting time distribution.

Stochastic resetting in backtrack recovery by RNA polymerases

NASA Astrophysics Data System (ADS)

Roldán, Édgar; Lisica, Ana; Sánchez-Taltavull, Daniel; Grill, Stephan W.

2016-06-01

Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random walk along the DNA template. Recovery of polymerases from the transcriptionally inactive backtracked state is determined by a kinetic competition between one-dimensional diffusion and RNA cleavage. Here we describe backtrack recovery as a continuous-time random walk, where the time for a polymerase to recover from a backtrack of a given depth is described as a first-passage time of a random walker to reach an absorbing state. We represent RNA cleavage as a stochastic resetting process and derive exact expressions for the recovery time distributions and mean recovery times from a given initial backtrack depth for both continuous and discrete-lattice descriptions of the random walk. We show that recovery time statistics do not depend on the discreteness of the DNA lattice when the rate of one-dimensional diffusion is large compared to the rate of cleavage.

Non-linear continuous time random walk models★

NASA Astrophysics Data System (ADS)

Stage, Helena; Fedotov, Sergei

2017-11-01

A standard assumption of continuous time random walk (CTRW) processes is that there are no interactions between the random walkers, such that we obtain the celebrated linear fractional equation either for the probability density function of the walker at a certain position and time, or the mean number of walkers. The question arises how one can extend this equation to the non-linear case, where the random walkers interact. The aim of this work is to take into account this interaction under a mean-field approximation where the statistical properties of the random walker depend on the mean number of walkers. The implementation of these non-linear effects within the CTRW integral equations or fractional equations poses difficulties, leading to the alternative methodology we present in this work. We are concerned with non-linear effects which may either inhibit anomalous effects or induce them where they otherwise would not arise. Inhibition of these effects corresponds to a decrease in the waiting times of the random walkers, be this due to overcrowding, competition between walkers or an inherent carrying capacity of the system. Conversely, induced anomalous effects present longer waiting times and are consistent with symbiotic, collaborative or social walkers, or indirect pinpointing of favourable regions by their attractiveness. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

The continuous time random walk, still trendy: fifty-year history, state of art and outlook

NASA Astrophysics Data System (ADS)

Kutner, Ryszard; Masoliver, Jaume

2017-03-01

In this article we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism, the numerous modifications permitted by its flexibility, its various applications, and the promising perspectives in the various fields of knowledge. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We focused on a pivotal role of CTRWs mainly in anomalous stochastic processes discovered in physics and beyond. This article plays the role of an extended announcement of the Eur. Phys. J. B Special Issue [http://epjb.epj.org/open-calls-for-papers/123-epj-b/1090-ctrw-50-years-on] containing articles which show incredible possibilities of the CTRWs. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Continuous-time random walks with reset events. Historical background and new perspectives

NASA Astrophysics Data System (ADS)

Montero, Miquel; Masó-Puigdellosas, Axel; Villarroel, Javier

2017-09-01

In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.

Alzheimer random walk

NASA Astrophysics Data System (ADS)

Odagaki, Takashi; Kasuya, Keisuke

2017-09-01

Using the Monte Carlo simulation, we investigate a memory-impaired self-avoiding walk on a square lattice in which a random walker marks each of sites visited with a given probability p and makes a random walk avoiding the marked sites. Namely, p = 0 and p = 1 correspond to the simple random walk and the self-avoiding walk, respectively. When p> 0, there is a finite probability that the walker is trapped. We show that the trap time distribution can well be fitted by Stacy's Weibull distribution b(a/b){a+1}/{b}[Γ({a+1}/{b})]-1x^a\\exp(-a/bx^b)} where a and b are fitting parameters depending on p. We also find that the mean trap time diverges at p = 0 as p- α with α = 1.89. In order to produce sufficient number of long walks, we exploit the pivot algorithm and obtain the mean square displacement and its Flory exponent ν(p) as functions of p. We find that the exponent determined for 1000 step walks interpolates both limits ν(0) for the simple random walk and ν(1) for the self-avoiding walk as [ ν(p) - ν(0) ] / [ ν(1) - ν(0) ] = pβ with β = 0.388 when p ≪ 0.1 and β = 0.0822 when p ≫ 0.1. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case

NASA Astrophysics Data System (ADS)

Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L.

2010-06-01

Continuous-time random walks, or compound renewal processes, are pure-jump stochastic processes with several applications in insurance, finance, economics and physics. Based on heuristic considerations, a definition is given for stochastic integrals driven by continuous-time random walks, which includes the Itô and Stratonovich cases. It is then shown how the definition can be used to compute these two stochastic integrals by means of Monte Carlo simulations. Our example is based on the normal compound Poisson process, which in the diffusive limit converges to the Wiener process.

Continuous Time Random Walk and Migration-Proliferation Dichotomy of Brain Cancer

NASA Astrophysics Data System (ADS)

Iomin, A.

A theory of fractional kinetics of glial cancer cells is presented. A role of the migration-proliferation dichotomy in the fractional cancer cell dynamics in the outer-invasive zone is discussed and explained in the framework of a continuous time random walk. The main suggested model is based on a construction of a 3D comb model, where the migration-proliferation dichotomy becomes naturally apparent and the outer-invasive zone of glioma cancer is considered as a fractal composite with a fractal dimension Dfr < 3.

Continuous time random walk with local particle-particle interaction

NASA Astrophysics Data System (ADS)

Xu, Jianping; Jiang, Guancheng

2018-05-01

The continuous time random walk (CTRW) is often applied to the study of particle motion in disordered media. Yet most such applications do not allow for particle-particle (walker-walker) interaction. In this paper, we consider a CTRW with particle-particle interaction; however, for simplicity, we restrain the interaction to be local. The generalized Chapman-Kolmogorov equation is modified by introducing a perturbation function that fluctuates around 1, which models the effect of interaction. Subsequently, a time-fractional nonlinear advection-diffusion equation is derived from this walking system. Under the initial condition of condensed particles at the origin and the free-boundary condition, we numerically solve this equation with both attractive and repulsive particle-particle interactions. Moreover, a Monte Carlo simulation is devised to verify the results of the above numerical work. The equation and the simulation unanimously predict that this walking system converges to the conventional one in the long-time limit. However, for systems where the free-boundary condition and long-time limit are not simultaneously satisfied, this convergence does not hold.

A Random Walk Picture of Basketball

NASA Astrophysics Data System (ADS)

Gabel, Alan; Redner, Sidney

2012-02-01

We analyze NBA basketball play-by-play data and found that scoring is well described by a weakly-biased, anti-persistent, continuous-time random walk. The time between successive scoring events follows an exponential distribution, with little memory between events. We account for a wide variety of statistical properties of scoring, such as the distribution of the score difference between opponents and the fraction of game time that one team is in the lead.

Quantum walk on a chimera graph

NASA Astrophysics Data System (ADS)

Xu, Shu; Sun, Xiangxiang; Wu, Jizhou; Zhang, Wei-Wei; Arshed, Nigum; Sanders, Barry C.

2018-05-01

We analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study continuous-time quantum walk on enhanced variants of the chimera graph and on diminished chimera graph with a random removal of vertices. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.

Heterogeneous continuous-time random walks

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.; Tupikina, Liubov

2018-01-01

We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.

Fluid limit of nonintegrable continuous-time random walks in terms of fractional differential equations.

PubMed

Sánchez, R; Carreras, B A; van Milligen, B Ph

2005-01-01

The fluid limit of a recently introduced family of nonintegrable (nonlinear) continuous-time random walks is derived in terms of fractional differential equations. In this limit, it is shown that the formalism allows for the modeling of the interaction between multiple transport mechanisms with not only disparate spatial scales but also different temporal scales. For this reason, the resulting fluid equations may find application in the study of a large number of nonlinear multiscale transport problems, ranging from the study of self-organized criticality to the modeling of turbulent transport in fluids and plasmas.

Parsimonious Continuous Time Random Walk Models and Kurtosis for Diffusion in Magnetic Resonance of Biological Tissue

NASA Astrophysics Data System (ADS)

Ingo, Carson; Sui, Yi; Chen, Yufen; Parrish, Todd; Webb, Andrew; Ronen, Itamar

2015-03-01

In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.

Phylogeography Takes a Relaxed Random Walk in Continuous Space and Time

PubMed Central

Lemey, Philippe; Rambaut, Andrew; Welch, John J.; Suchard, Marc A.

2010-01-01

Research aimed at understanding the geographic context of evolutionary histories is burgeoning across biological disciplines. Recent endeavors attempt to interpret contemporaneous genetic variation in the light of increasingly detailed geographical and environmental observations. Such interest has promoted the development of phylogeographic inference techniques that explicitly aim to integrate such heterogeneous data. One promising development involves reconstructing phylogeographic history on a continuous landscape. Here, we present a Bayesian statistical approach to infer continuous phylogeographic diffusion using random walk models while simultaneously reconstructing the evolutionary history in time from molecular sequence data. Moreover, by accommodating branch-specific variation in dispersal rates, we relax the most restrictive assumption of the standard Brownian diffusion process and demonstrate increased statistical efficiency in spatial reconstructions of overdispersed random walks by analyzing both simulated and real viral genetic data. We further illustrate how drawing inference about summary statistics from a fully specified stochastic process over both sequence evolution and spatial movement reveals important characteristics of a rabies epidemic. Together with recent advances in discrete phylogeographic inference, the continuous model developments furnish a flexible statistical framework for biogeographical reconstructions that is easily expanded upon to accommodate various landscape genetic features. PMID:20203288

Continuous Positive Airway Pressure During Exercise Improves Walking Time in Patients Undergoing Inpatient Cardiac Rehabilitation After Coronary Artery Bypass Graft Surgery: A RANDOMIZED CONTROLLED TRIAL.

PubMed

Pantoni, Camila Bianca Falasco; Di Thommazo-Luporini, Luciana; Mendes, Renata Gonçalves; Caruso, Flávia Cristina Rossi; Mezzalira, Daniel; Arena, Ross; Amaral-Neto, Othon; Catai, Aparecida Maria; Borghi-Silva, Audrey

2016-01-01

Continuous positive airway pressure (CPAP) has been used as an effective support to decrease the negative pulmonary effects of coronary artery bypass graft (CABG) surgery. However, it is unknown whether CPAP can positively influence patients undergoing CABG during exercise. This study evaluated the effectiveness of CPAP on the first day of ambulation after CABG in patients undergoing inpatient cardiac rehabilitation (CR). Fifty-four patients after CABG surgery were randomly assigned to receive either inpatient CR and CPAP (CPG) or standard CR without CPAP (CG). Cardiac rehabilitation included walking and CPAP pressures were set between 10 to 12 cmH2O. Participants were assessed on the first day of walking at rest and during walking. Outcome measures included breathing pattern variables, exercise time in seconds (ETs), dyspnea/leg effort ratings, and peripheral oxygen saturation (SpO2). Twenty-seven patients (13 CPG vs 14 CG) completed the study. Compared with walking without noninvasive ventilation assistance, CPAP increased ETs by 43.4 seconds (P = .040) during walking, promoted better thoracoabdominal coordination, increased ventilation during walking by 12.5 L/min (P = .001), increased SpO2 values at the end of walking by 2.6% (P = .016), and reduced dyspnea ratings by 1 point (P = .008). Continuous positive airway pressure can positively influence exercise tolerance, ventilatory function, and breathing pattern in response to a single bout of exercise after CABG.

Interrelations between random walks on diagrams (graphs) with and without cycles.

PubMed

Hill, T L

1988-05-01

Three topics are discussed. A discrete-state, continuous-time random walk with one or more absorption states can be studied by a presumably new method: some mean properties, including the mean time to absorption, can be found from a modified diagram (graph) in which each absorption state is replaced by a one-way cycle back to the starting state. The second problem is a random walk on a diagram (graph) with cycles. The walk terminates on completion of the first cycle. This walk can be replaced by an equivalent walk on a modified diagram with absorption. This absorption diagram can in turn be replaced by another modified diagram with one-way cycles back to the starting state, just as in the first problem. The third problem, important in biophysics, relates to a long-time continuous walk on a diagram with cycles. This diagram can be transformed (in two steps) to a modified, more-detailed, diagram with one-way cycles only. Thus, the one-way cycle fluxes of the original diagram can be found from the state probabilities of the modified diagram. These probabilities can themselves be obtained by simple matrix inversion (the probabilities are determined by linear algebraic steady-state equations). Thus, a simple method is now available to find one-way cycle fluxes exactly (previously Monte Carlo simulation was required to find these fluxes, with attendant fluctuations, for diagrams of any complexity). An incidental benefit of the above procedure is that it provides a simple proof of the one-way cycle flux relation Jn +/- = IIn +/- sigma n/sigma, where n is any cycle of the original diagram.

Random walk of passive tracers among randomly moving obstacles.

PubMed

Gori, Matteo; Donato, Irene; Floriani, Elena; Nardecchia, Ilaria; Pettini, Marco

2016-04-14

This study is mainly motivated by the need of understanding how the diffusion behavior of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target. By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle among randomly moving and interacting obstacles. The relevant physical quantity which is worked out is the diffusion coefficient of the passive tracer which is computed as a function of the average inter-obstacles distance. The results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its motion can be considerably slowed down.

Efficient quantum walk on a quantum processor

PubMed Central

Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L.; Wang, Jingbo B.; Matthews, Jonathan C. F.

2016-01-01

The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor. PMID:27146471

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Correlated continuous time random walk and option pricing

NASA Astrophysics Data System (ADS)

Lv, Longjin; Xiao, Jianbin; Fan, Liangzhong; Ren, Fuyao

2016-04-01

In this paper, we study a correlated continuous time random walk (CCTRW) with averaged waiting time, whose probability density function (PDF) is proved to follow stretched Gaussian distribution. Then, we apply this process into option pricing problem. Supposing the price of the underlying is driven by this CCTRW, we find this model captures the subdiffusive characteristic of financial markets. By using the mean self-financing hedging strategy, we obtain the closed-form pricing formulas for a European option with and without transaction costs, respectively. At last, comparing the obtained model with the classical Black-Scholes model, we find the price obtained in this paper is higher than that obtained from the Black-Scholes model. A empirical analysis is also introduced to confirm the obtained results can fit the real data well.

Continuous-Time Finance and the Waiting Time Distribution: Multiple Characteristic Times

NASA Astrophysics Data System (ADS)

Fa, Kwok Sau

2012-09-01

In this paper, we model the tick-by-tick dynamics of markets by using the continuous-time random walk (CTRW) model. We employ a sum of products of power law and stretched exponential functions for the waiting time probability distribution function; this function can fit well the waiting time distribution for BUND futures traded at LIFFE in 1997.

Solvable continuous-time random walk model of the motion of tracer particles through porous media.

PubMed

Fouxon, Itzhak; Holzner, Markus

2016-08-01

We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)PLEEE81539-375510.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ, length l, and velocity v. We solve our model with independent l and v. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ. Universality of tracer diffusion in the porous medium is considered.

Continuous time random walk model with asymptotical probability density of waiting times via inverse Mittag-Leffler function

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen

2018-04-01

The mean squared displacement (MSD) of the traditional ultraslow diffusion is a logarithmic function of time. Recently, the continuous time random walk model is employed to characterize this ultraslow diffusion dynamics by connecting the heavy-tailed logarithmic function and its variation as the asymptotical waiting time density. In this study we investigate the limiting waiting time density of a general ultraslow diffusion model via the inverse Mittag-Leffler function, whose special case includes the traditional logarithmic ultraslow diffusion model. The MSD of the general ultraslow diffusion model is analytically derived as an inverse Mittag-Leffler function, and is observed to increase even more slowly than that of the logarithmic function model. The occurrence of very long waiting time in the case of the inverse Mittag-Leffler function has the largest probability compared with the power law model and the logarithmic function model. The Monte Carlo simulations of one dimensional sample path of a single particle are also performed. The results show that the inverse Mittag-Leffler waiting time density is effective in depicting the general ultraslow random motion.

Fluorescence correlation spectroscopy: the case of subdiffusion.

PubMed

Lubelski, Ariel; Klafter, Joseph

2009-03-18

The theory of fluorescence correlation spectroscopy is revisited here for the case of subdiffusing molecules. Subdiffusion is assumed to stem from a continuous-time random walk process with a fat-tailed distribution of waiting times and can therefore be formulated in terms of a fractional diffusion equation (FDE). The FDE plays the central role in developing the fluorescence correlation spectroscopy expressions, analogous to the role played by the simple diffusion equation for regular systems. Due to the nonstationary nature of the continuous-time random walk/FDE, some interesting properties emerge that are amenable to experimental verification and may help in discriminating among subdiffusion mechanisms. In particular, the current approach predicts 1), a strong dependence of correlation functions on the initial time (aging); 2), sensitivity of correlation functions to the averaging procedure, ensemble versus time averaging (ergodicity breaking); and 3), that the basic mean-squared displacement observable depends on how the mean is taken.

Dynamical continuous time random Lévy flights

NASA Astrophysics Data System (ADS)

Liu, Jian; Chen, Xiaosong

2016-03-01

The Lévy flights' diffusive behavior is studied within the framework of the dynamical continuous time random walk (DCTRW) method, while the nonlinear friction is introduced in each step. Through the DCTRW method, Lévy random walker in each step flies by obeying the Newton's Second Law while the nonlinear friction f(v) = - γ0v - γ2v3 being considered instead of Stokes friction. It is shown that after introducing the nonlinear friction, the superdiffusive Lévy flights converges, behaves localization phenomenon with long time limit, but for the Lévy index μ = 2 case, it is still Brownian motion.

Asymptotic properties of a bold random walk

NASA Astrophysics Data System (ADS)

Serva, Maurizio

2014-08-01

In a recent paper we proposed a non-Markovian random walk model with memory of the maximum distance ever reached from the starting point (home). The behavior of the walker is different from the simple symmetric random walk only when she is at this maximum distance, where, having the choice to move either farther or closer, she decides with different probabilities. If the probability of a forward step is higher than the probability of a backward step, the walker is bold and her behavior turns out to be superdiffusive; otherwise she is timorous and her behavior turns out to be subdiffusive. The scaling behavior varies continuously from subdiffusive (timorous) to superdiffusive (bold) according to a single parameter γ ∈R. We investigate here the asymptotic properties of the bold case in the nonballistic region γ ∈[0,1/2], a problem which was left partially unsolved previously. The exact results proved in this paper require new probabilistic tools which rely on the construction of appropriate martingales of the random walk and its hitting times.

Bridging the gulf between correlated random walks and Lévy walks: autocorrelation as a source of Lévy walk movement patterns.

PubMed

Reynolds, Andy M

2010-12-06

For many years, the dominant conceptual framework for describing non-oriented animal movement patterns has been the correlated random walk (CRW) model in which an individual's trajectory through space is represented by a sequence of distinct, independent randomly oriented 'moves'. It has long been recognized that the transformation of an animal's continuous movement path into a broken line is necessarily arbitrary and that probability distributions of move lengths and turning angles are model artefacts. Continuous-time analogues of CRWs that overcome this inherent shortcoming have appeared in the literature and are gaining prominence. In these models, velocities evolve as a Markovian process and have exponential autocorrelation. Integration of the velocity process gives the position process. Here, through a simple scaling argument and through an exact analytical analysis, it is shown that autocorrelation inevitably leads to Lévy walk (LW) movement patterns on timescales less than the autocorrelation timescale. This is significant because over recent years there has been an accumulation of evidence from a variety of experimental and theoretical studies that many organisms have movement patterns that can be approximated by LWs, and there is now intense debate about the relative merits of CRWs and LWs as representations of non-orientated animal movement patterns.

Movement patterns of Tenebrio beetles demonstrate empirically that correlated-random-walks have similitude with a Lévy walk.

PubMed

Reynolds, Andy M; Leprêtre, Lisa; Bohan, David A

2013-11-07

Correlated random walks are the dominant conceptual framework for modelling and interpreting organism movement patterns. Recent years have witnessed a stream of high profile publications reporting that many organisms perform Lévy walks; movement patterns that seemingly stand apart from the correlated random walk paradigm because they are discrete and scale-free rather than continuous and scale-finite. Our new study of the movement patterns of Tenebrio molitor beetles in unchanging, featureless arenas provides the first empirical support for a remarkable and deep theoretical synthesis that unites correlated random walks and Lévy walks. It demonstrates that the two models are complementary rather than competing descriptions of movement pattern data and shows that correlated random walks are a part of the Lévy walk family. It follows from this that vast numbers of Lévy walkers could be hiding in plain sight.

Continuous time quantum random walks in free space

NASA Astrophysics Data System (ADS)

Eichelkraut, Toni; Vetter, Christian; Perez-Leija, Armando; Christodoulides, Demetrios; Szameit, Alexander

2014-05-01

We show theoretically and experimentally that two-dimensional continuous time coherent random walks are possible in free space, that is, in the absence of any external potential, by properly tailoring the associated initial wave function. These effects are experimentally demonstrated using classical paraxial light. Evidently, the usage of classical beams to explore the dynamics of point-like quantum particles is possible since both phenomena are mathematically equivalent. This in turn makes our approach suitable for the realization of random walks using different quantum particles, including electrons and photons. To study the spatial evolution of a wavefunction theoretically, we consider the one-dimensional paraxial wave equation (i∂z +1/2 ∂x2) Ψ = 0 . Starting with the initially localized wavefunction Ψ (x , 0) = exp [ -x2 / 2σ2 ] J0 (αx) , one can show that the evolution of such Gaussian-apodized Bessel envelopes within a region of validity resembles the probability pattern of a quantum walker traversing a uniform lattice. In order to generate the desired input-field in our experimental setting we shape the amplitude and phase of a collimated light beam originating from a classical HeNe-Laser (633 nm) utilizing a spatial light modulator.

The stochastic dynamics of intermittent porescale particle motion

NASA Astrophysics Data System (ADS)

Dentz, Marco; Morales, Veronica; Puyguiraud, Alexandre; Gouze, Philippe; Willmann, Matthias; Holzner, Markus

2017-04-01

Numerical and experimental data for porescale particle dynamics show intermittent patterns in Lagrangian velocities and accelerations, which manifest in long time intervals of low and short durations of high velocities [1, 2]. This phenomenon is due to the spatial persistence of particle velocities on characteristic heterogeneity length scales. In order to systematically quantify these behaviors and extract the stochastic dynamics of particle motion, we focus on the analysis of Lagrangian velocities sampled equidistantly along trajectories [3]. This method removes the intermittency observed under isochrone sampling. The space-Lagrangian velocity series can be quantified by a Markov process that is continuous in distance along streamline. It is fully parameterized in terms of the flux-weighted Eulerian velocity PDF and the characteristic pore-length. The resulting stochastic particle motion describes a continuous time random walk (CTRW). This approach allows for the process based interpretation of experimental and numerical porescale velocity, acceleration and displacement data. It provides a framework for the characterization and upscaling of particle transport and dispersion from the pore to the Darcy-scale based on the medium geometry and Eulerian flow attributes. [1] P. De Anna, T. Le Borgne, M. Dentz, A.M. Tartakovsky, D. Bolster, and P. Davy, "Flow intermittency, dispersion, and correlated continuous time random walks in porous media," Phys. Rev. Lett. 110, 184502 (2013). [2] M. Holzner, V. L. Morales, M. Willmann, and M. Dentz, "Intermittent Lagrangian velocities and accelerations in three- dimensional porous medium flow," Phys. Rev. E 92, 013015 (2015). [3] M. Dentz, P. K. Kang, A. Comolli, T. Le Borgne, and D. R. Lester, "Continuous time random walks for the evolution of Lagrangian velocities," Phys. Rev. Fluids (2016).

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.

PubMed

Henry, B I; Langlands, T A M; Wearne, S L

2006-09-01

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

Fluctuations around equilibrium laws in ergodic continuous-time random walks.

PubMed

Schulz, Johannes H P; Barkai, Eli

2015-06-01

We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.

Continuous Time Random Walk (CTRW) put to work

NASA Astrophysics Data System (ADS)

Scher, Harvey

2017-12-01

A personal history of the first applications of CTRW to the physics of transport and diffusion in disordered media is presented. The sequence of steps leading to the introduction of novel ψ(t), the probability density of particle-transfer times, without moments is briefly outlined. The key concept that emerged from those early applications is anomalous or non-Fickian transport. The latter involved spatial moments of the particle propagator with completely different time behavior, e.g., the mean ∝ tβ, 0 < β < 1 and likewise σ the rms spreading, i.e., /σ = constant. With these results many puzzling experimental data were explained. The data ranged from electronic dynamics of amorphous films to chemical migration and interaction in the subsurface of the Earth. These were not anticipated results but a consequence of the CTRW with these special ψ(t). Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

The effects of free-living interval-walking training on glycemic control, body composition, and physical fitness in type 2 diabetic patients: a randomized, controlled trial.

PubMed

Karstoft, Kristian; Winding, Kamilla; Knudsen, Sine H; Nielsen, Jens S; Thomsen, Carsten; Pedersen, Bente K; Solomon, Thomas P J

2013-02-01

To evaluate the feasibility of free-living walking training in type 2 diabetic patients and to investigate the effects of interval-walking training versus continuous-walking training upon physical fitness, body composition, and glycemic control. Subjects with type 2 diabetes were randomized to a control (n = 8), continuous-walking (n = 12), or interval-walking group (n = 12). Training groups were prescribed five sessions per week (60 min/session) and were controlled with an accelerometer and a heart-rate monitor. Continuous walkers performed all training at moderate intensity, whereas interval walkers alternated 3-min repetitions at low and high intensity. Before and after the 4-month intervention, the following variables were measured: VO(2)max, body composition, and glycemic control (fasting glucose, HbA(1c), oral glucose tolerance test, and continuous glucose monitoring [CGM]). Training adherence was high (89 ± 4%), and training energy expenditure and mean intensity were comparable. VO(2)max increased 16.1 ± 3.7% in the interval-walking group (P < 0.05), whereas no changes were observed in the continuous-walking or control group. Body mass and adiposity (fat mass and visceral fat) decreased in the interval-walking group only (P < 0.05). Glycemic control (elevated mean CGM glucose levels and increased fasting insulin) worsened in the control group (P < 0.05), whereas mean (P = 0.05) and maximum (P < 0.05) CGM glucose levels decreased in the interval-walking group. The continuous walkers showed no changes in glycemic control. Free-living walking training is feasible in type 2 diabetic patients. Continuous walking offsets the deterioration in glycemia seen in the control group, and interval walking is superior to energy expenditure-matched continuous walking for improving physical fitness, body composition, and glycemic control.

Random walks of colloidal probes in viscoelastic materials

NASA Astrophysics Data System (ADS)

Khan, Manas; Mason, Thomas G.

2014-04-01

To overcome limitations of using a single fixed time step in random walk simulations, such as those that rely on the classic Wiener approach, we have developed an algorithm for exploring random walks based on random temporal steps that are uniformly distributed in logarithmic time. This improvement enables us to generate random-walk trajectories of probe particles that span a highly extended dynamic range in time, thereby facilitating the exploration of probe motion in soft viscoelastic materials. By combining this faster approach with a Maxwell-Voigt model (MVM) of linear viscoelasticity, based on a slowly diffusing harmonically bound Brownian particle, we rapidly create trajectories of spherical probes in soft viscoelastic materials over more than 12 orders of magnitude in time. Appropriate windowing of these trajectories over different time intervals demonstrates that random walk for the MVM is neither self-similar nor self-affine, even if the viscoelastic material is isotropic. We extend this approach to spatially anisotropic viscoelastic materials, using binning to calculate the anisotropic mean square displacements and creep compliances along different orthogonal directions. The elimination of a fixed time step in simulations of random processes, including random walks, opens up interesting possibilities for modeling dynamics and response over a highly extended temporal dynamic range.

Random walk, diffusion and mixing in simulations of scalar transport in fluid flows

NASA Astrophysics Data System (ADS)

Klimenko, A. Y.

2008-12-01

Physical similarity and mathematical equivalence of continuous diffusion and particle random walk form one of the cornerstones of modern physics and the theory of stochastic processes. In many applied models used in simulation of turbulent transport and turbulent combustion, mixing between particles is used to reflect the influence of the continuous diffusion terms in the transport equations. We show that the continuous scalar transport and diffusion can be accurately specified by means of mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme. This gives an alternative formulation for the stochastic process which is selected to represent the continuous diffusion. This paper focuses on statistical errors and deals with relatively simple cases, where one-particle distributions are sufficient for a complete description of the problem.

Stock market context of the Lévy walks with varying velocity

NASA Astrophysics Data System (ADS)

Kutner, Ryszard

2002-11-01

We developed the most general Lévy walks with varying velocity, shorter called the Weierstrass walks (WW) model, by which one can describe both stationary and non-stationary stochastic time series. We considered a non-Brownian random walk where the walker moves, in general, with a velocity that assumes a different constant value between the successive turning points, i.e., the velocity is a piecewise constant function. This model is a kind of Lévy walks where we assume a hierarchical, self-similar in a stochastic sense, spatio-temporal representation of the main quantities such as waiting-time distribution and sojourn probability density (which are principal quantities in the continuous-time random walk formalism). The WW model makes possible to analyze both the structure of the Hurst exponent and the power-law behavior of kurtosis. This structure results from the hierarchical, spatio-temporal coupling between the walker displacement and the corresponding time of the walks. The analysis uses both the fractional diffusion and the super Burnett coefficients. We constructed the diffusion phase diagram which distinguishes regions occupied by classes of different universality. We study only such classes which are characteristic for stationary situations. We thus have a model ready for describing the data presented, e.g., in the form of moving averages; the operation is often used for stochastic time series, especially financial ones. The model was inspired by properties of financial time series and tested for empirical data extracted from the Warsaw stock exchange since it offers an opportunity to study in an unbiased way several features of stock exchange in its early stage.

Backward jump continuous-time random walk: An application to market trading

NASA Astrophysics Data System (ADS)

Gubiec, Tomasz; Kutner, Ryszard

2010-10-01

The backward jump modification of the continuous-time random walk model or the version of the model driven by the negative feedback was herein derived for spatiotemporal continuum in the context of a share price evolution on a stock exchange. In the frame of the model, we described stochastic evolution of a typical share price on a stock exchange with a moderate liquidity within a high-frequency time scale. The model was validated by satisfactory agreement of the theoretical velocity autocorrelation function with its empirical counterpart obtained for the continuous quotation. This agreement is mainly a result of a sharp backward correlation found and considered in this article. This correlation is a reminiscence of such a bid-ask bounce phenomenon where backward price jump has the same or almost the same length as preceding jump. We suggested that this correlation dominated the dynamics of the stock market with moderate liquidity. Although assumptions of the model were inspired by the market high-frequency empirical data, its potential applications extend beyond the financial market, for instance, to the field covered by the Le Chatelier-Braun principle of contrariness.

Backward jump continuous-time random walk: an application to market trading.

PubMed

Gubiec, Tomasz; Kutner, Ryszard

2010-10-01

The backward jump modification of the continuous-time random walk model or the version of the model driven by the negative feedback was herein derived for spatiotemporal continuum in the context of a share price evolution on a stock exchange. In the frame of the model, we described stochastic evolution of a typical share price on a stock exchange with a moderate liquidity within a high-frequency time scale. The model was validated by satisfactory agreement of the theoretical velocity autocorrelation function with its empirical counterpart obtained for the continuous quotation. This agreement is mainly a result of a sharp backward correlation found and considered in this article. This correlation is a reminiscence of such a bid-ask bounce phenomenon where backward price jump has the same or almost the same length as preceding jump. We suggested that this correlation dominated the dynamics of the stock market with moderate liquidity. Although assumptions of the model were inspired by the market high-frequency empirical data, its potential applications extend beyond the financial market, for instance, to the field covered by the Le Chatelier-Braun principle of contrariness.

Chemical Continuous Time Random Walks

NASA Astrophysics Data System (ADS)

Aquino, T.; Dentz, M.

2017-12-01

Traditional methods for modeling solute transport through heterogeneous media employ Eulerian schemes to solve for solute concentration. More recently, Lagrangian methods have removed the need for spatial discretization through the use of Monte Carlo implementations of Langevin equations for solute particle motions. While there have been recent advances in modeling chemically reactive transport with recourse to Lagrangian methods, these remain less developed than their Eulerian counterparts, and many open problems such as efficient convergence and reconstruction of the concentration field remain. We explore a different avenue and consider the question: In heterogeneous chemically reactive systems, is it possible to describe the evolution of macroscopic reactant concentrations without explicitly resolving the spatial transport? Traditional Kinetic Monte Carlo methods, such as the Gillespie algorithm, model chemical reactions as random walks in particle number space, without the introduction of spatial coordinates. The inter-reaction times are exponentially distributed under the assumption that the system is well mixed. In real systems, transport limitations lead to incomplete mixing and decreased reaction efficiency. We introduce an arbitrary inter-reaction time distribution, which may account for the impact of incomplete mixing. This process defines an inhomogeneous continuous time random walk in particle number space, from which we derive a generalized chemical Master equation and formulate a generalized Gillespie algorithm. We then determine the modified chemical rate laws for different inter-reaction time distributions. We trace Michaelis-Menten-type kinetics back to finite-mean delay times, and predict time-nonlocal macroscopic reaction kinetics as a consequence of broadly distributed delays. Non-Markovian kinetics exhibit weak ergodicity breaking and show key features of reactions under local non-equilibrium.

The Effect of Disorder on the Free-Energy for the Random Walk Pinning Model: Smoothing of the Phase Transition and Low Temperature Asymptotics

NASA Astrophysics Data System (ADS)

Berger, Quentin; Lacoin, Hubert

2011-01-01

We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in (Berger and Toninelli (Electron. J. Probab., to appear) and Birkner and Sun (Ann. Inst. Henri Poincaré Probab. Stat. 46:414-441, 2010; arXiv:0912.1663). Given a fixed realization of a random walk Y on ℤ d with jump rate ρ (that plays the role of the random medium), we modify the law of a random walk X on ℤ d with jump rate 1 by reweighting the paths, giving an energy reward proportional to the intersection time Lt(X,Y)=int0t {1}_{Xs=Ys} {d}s: the weight of the path under the new measure is exp ( βL t ( X, Y)), β∈ℝ. As β increases, the system exhibits a delocalization/localization transition: there is a critical value β c , such that if β> β c the two walks stick together for almost-all Y realizations. A natural question is that of disorder relevance, that is whether the quenched and annealed systems have the same behavior. In this paper we investigate how the disorder modifies the shape of the free energy curve: (1) We prove that, in dimension d≥3, the presence of disorder makes the phase transition at least of second order. This, in dimension d≥4, contrasts with the fact that the phase transition of the annealed system is of first order. (2) In any dimension, we prove that disorder modifies the low temperature asymptotic of the free energy.

Effective pore-scale dispersion upscaling with a correlated continuous time random walk approach

NASA Astrophysics Data System (ADS)

Le Borgne, T.; Bolster, D.; Dentz, M.; de Anna, P.; Tartakovsky, A.

2011-12-01

We investigate the upscaling of dispersion from a pore-scale analysis of Lagrangian velocities. A key challenge in the upscaling procedure is to relate the temporal evolution of spreading to the pore-scale velocity field properties. We test the hypothesis that one can represent Lagrangian velocities at the pore scale as a Markov process in space. The resulting effective transport model is a continuous time random walk (CTRW) characterized by a correlated random time increment, here denoted as correlated CTRW. We consider a simplified sinusoidal wavy channel model as well as a more complex heterogeneous pore space. For both systems, the predictions of the correlated CTRW model, with parameters defined from the velocity field properties (both distribution and correlation), are found to be in good agreement with results from direct pore-scale simulations over preasymptotic and asymptotic times. In this framework, the nontrivial dependence of dispersion on the pore boundary fluctuations is shown to be related to the competition between distribution and correlation effects. In particular, explicit inclusion of spatial velocity correlation in the effective CTRW model is found to be important to represent incomplete mixing in the pore throats.

Transmembrane protein CD93 diffuses by a continuous time random walk.

NASA Astrophysics Data System (ADS)

Goiko, Maria; de Bruyn, John; Heit, Bryan

Molecular motion within the cell membrane is a poorly-defined process. In this study, we characterized the diffusion of the transmembrane protein CD93. By careful analysis of the dependence of the ensemble-averaged mean squared displacement (EA-MSD, r2) on time t and the ensemble-averaged, time-averaged MSD (EA-TAMSD, δ2) on lag time τ and total measurement time T, we showed that the motion of CD93 is well-described by a continuous-time random walk (CTRW). CD93 tracks were acquired using single particle tracking. The tracks were classified as confined or free, and the behavior of the MSD analyzed. EA-MSDs of both populations grew non-linearly with t, indicative of anomalous diffusion. Their EA-TAMSDs were found to depend on both τ and T, indicating non-ergodicity. Free molecules had r2 tα and δ2 (τ /T 1 - α) , with α 0 . 5 , consistent with a CTRW. Mean maximal excursion analysis supported this result. Confined CD93 had r2 t0 and δ2 (τ / T) α , with α 0 . 3 , consistent with a confined CTRW. CTRWs are described by a series of random jumps interspersed with power-law distributed waiting times, and may arise due to the interactions of CD93 with the endocytic machinery. NSERC.

A new time domain random walk method for solute transport in 1-D heterogeneous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banton, O.; Delay, F.; Porel, G.

A new method to simulate solute transport in 1-D heterogeneous media is presented. This time domain random walk method (TDRW), similar in concept to the classical random walk method, calculates the arrival time of a particle cloud at a given location (directly providing the solute breakthrough curve). The main advantage of the method is that the restrictions on the space increments and the time steps which exist with the finite differences and random walk methods are avoided. In a homogeneous zone, the breakthrough curve (BTC) can be calculated directly at a given distance using a few hundred particles or directlymore » at the boundary of the zone. Comparisons with analytical solutions and with the classical random walk method show the reliability of this method. The velocity and dispersivity calculated from the simulated results agree within two percent with the values used as input in the model. For contrasted heterogeneous media, the random walk can generate high numerical dispersion, while the time domain approach does not.« less

Physical realizability of continuous-time quantum stochastic walks

NASA Astrophysics Data System (ADS)

Taketani, Bruno G.; Govia, Luke C. G.; Wilhelm, Frank K.

2018-05-01

Quantum walks are a promising methodology that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with that of a classical random walk, through open system evolution of a quantum system. Quantum stochastic walks have been shown to have applications in as far reaching fields as artificial intelligence. However, there are significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution and the physical assumptions underpinning them. We show that general direct implementations would require the complete solution of the underlying unitary dynamics and sophisticated reservoir engineering, thus weakening the benefits of experimental implementation.

Brownian dynamics simulations on a hypersphere in 4-space

NASA Astrophysics Data System (ADS)

Nissfolk, Jarl; Ekholm, Tobias; Elvingson, Christer

2003-10-01

We describe an algorithm for performing Brownian dynamics simulations of particles diffusing on S3, a hypersphere in four dimensions. The system is chosen due to recent interest in doing computer simulations in a closed space where periodic boundary conditions can be avoided. We specifically address the question how to generate a random walk on the 3-sphere, starting from the solution of the corresponding diffusion equation, and we also discuss an efficient implementation based on controlled approximations. Since S3 is a closed manifold (space), the average square displacement during a random walk is no longer proportional to the elapsed time, as in R3. Instead, its time rate of change is continuously decreasing, and approaches zero as time becomes large. We show, however, that the effective diffusion coefficient can still be obtained from the time dependence of the square displacement.

Critical spreading dynamics of parity conserving annihilating random walks with power-law branching

NASA Astrophysics Data System (ADS)

Laise, T.; dos Anjos, F. C.; Argolo, C.; Lyra, M. L.

2018-09-01

We investigate the critical spreading of the parity conserving annihilating random walks model with Lévy-like branching. The random walks are considered to perform normal diffusion with probability p on the sites of a one-dimensional lattice, annihilating in pairs by contact. With probability 1 - p, each particle can also produce two offspring which are placed at a distance r from the original site following a power-law Lévy-like distribution P(r) ∝ 1 /rα. We perform numerical simulations starting from a single particle. A finite-time scaling analysis is employed to locate the critical diffusion probability pc below which a finite density of particles is developed in the long-time limit. Further, we estimate the spreading dynamical exponents related to the increase of the average number of particles at the critical point and its respective fluctuations. The critical exponents deviate from those of the counterpart model with short-range branching for small values of α. The numerical data suggest that continuously varying spreading exponents sets up while the branching process still results in a diffusive-like spreading.

Continuous-Time Random Walk Models of DNA Electrophoresis in a Post Array: II. Mobility and Sources of Band Broadening

PubMed Central

Olson, Daniel W.; Dutta, Sarit; Laachi, Nabil; Tian, Mingwei; Dorfman, Kevin D.

2011-01-01

Using the two-state, continuous-time random walk model, we develop expressions for the mobility and the plate height during DNA electrophoresis in an ordered post array that delineate the contributions due to (i) the random distance between collisions and (ii) the random duration of a collision. These contributions are expressed in terms of the means and variances of the underlying stochastic processes, which we evaluate from a large ensemble of Brownian dynamics simulations performed using different electric fields and molecular weights in a hexagonal array of 1 μm posts with a 3 μm center-to-center distance. If we fix the molecular weight, we find that the collision frequency governs the mobility. In contrast, the average collision duration is the most important factor for predicting the mobility as a function of DNA size at constant Péclet number. The plate height is reasonably well-described by a single post rope-over-pulley model, provided that the extension of the molecule is small. Our results only account for dispersion inside the post array and thus represent a theoretical lower bound on the plate height in an actual device. PMID:21290387

Generalized run-and-turn motions: From bacteria to Lévy walks

NASA Astrophysics Data System (ADS)

Detcheverry, François

2017-07-01

Swimming bacteria exhibit a repertoire of motility patterns, in which persistent motion is interrupted by turning events. What are the statistical properties of such random walks? If some particular instances have long been studied, the general case where turning times do not follow a Poisson process has remained unsolved. We present a generic extension of the continuous time random walks formalism relying on operators and noncommutative calculus. The approach is first applied to a unimodal model of bacterial motion. We examine the existence of a minimum in velocity correlation function and discuss the maximum of diffusivity at an optimal value of rotational diffusion. The model is then extended to bimodal patterns and includes as particular cases all swimming strategies: run-and-tumble, run-stop, run-reverse and run-reverse-flick. We characterize their velocity correlation functions and investigate how bimodality affects diffusivity. Finally, the wider applicability of the method is illustrated by considering curved trajectories and Lévy walks. Our results are relevant for intermittent motion of living beings, be they swimming micro-organisms or crawling cells.

Continuous-time quantum walks on star graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salimi, S.

2009-06-15

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K{sub 2} graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.

Quantum Walk Schemes for Universal Quantum Computation

NASA Astrophysics Data System (ADS)

Underwood, Michael S.

Random walks are a powerful tool for the efficient implementation of algorithms in classical computation. Their quantum-mechanical analogues, called quantum walks, hold similar promise. Quantum walks provide a model of quantum computation that has recently been shown to be equivalent in power to the standard circuit model. As in the classical case, quantum walks take place on graphs and can undergo discrete or continuous evolution, though quantum evolution is unitary and therefore deterministic until a measurement is made. This thesis considers the usefulness of continuous-time quantum walks to quantum computation from the perspectives of both their fundamental power under various formulations, and their applicability in practical experiments. In one extant scheme, logical gates are effected by scattering processes. The results of an exhaustive search for single-qubit operations in this model are presented. It is shown that the number of distinct operations increases exponentially with the number of vertices in the scattering graph. A catalogue of all graphs on up to nine vertices that implement single-qubit unitaries at a specific set of momenta is included in an appendix. I develop a novel scheme for universal quantum computation called the discontinuous quantum walk, in which a continuous-time quantum walker takes discrete steps of evolution via perfect quantum state transfer through small 'widget' graphs. The discontinuous quantum-walk scheme requires an exponentially sized graph, as do prior discrete and continuous schemes. To eliminate the inefficient vertex resource requirement, a computation scheme based on multiple discontinuous walkers is presented. In this model, n interacting walkers inhabiting a graph with 2n vertices can implement an arbitrary quantum computation on an input of length n, an exponential savings over previous universal quantum walk schemes. This is the first quantum walk scheme that allows for the application of quantum error correction. The many-particle quantum walk can be viewed as a single quantum walk undergoing perfect state transfer on a larger weighted graph, obtained via equitable partitioning. I extend this formalism to non-simple graphs. Examples of the application of equitable partitioning to the analysis of quantum walks and many-particle quantum systems are discussed.

Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach

NASA Astrophysics Data System (ADS)

Comolli, Alessandro; Dentz, Marco

2017-09-01

We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy's law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in heterogeneous natural and engineered porous materials. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Automated time activity classification based on global positioning system (GPS) tracking data

PubMed Central

2011-01-01

Background Air pollution epidemiological studies are increasingly using global positioning system (GPS) to collect time-location data because they offer continuous tracking, high temporal resolution, and minimum reporting burden for participants. However, substantial uncertainties in the processing and classifying of raw GPS data create challenges for reliably characterizing time activity patterns. We developed and evaluated models to classify people's major time activity patterns from continuous GPS tracking data. Methods We developed and evaluated two automated models to classify major time activity patterns (i.e., indoor, outdoor static, outdoor walking, and in-vehicle travel) based on GPS time activity data collected under free living conditions for 47 participants (N = 131 person-days) from the Harbor Communities Time Location Study (HCTLS) in 2008 and supplemental GPS data collected from three UC-Irvine research staff (N = 21 person-days) in 2010. Time activity patterns used for model development were manually classified by research staff using information from participant GPS recordings, activity logs, and follow-up interviews. We evaluated two models: (a) a rule-based model that developed user-defined rules based on time, speed, and spatial location, and (b) a random forest decision tree model. Results Indoor, outdoor static, outdoor walking and in-vehicle travel activities accounted for 82.7%, 6.1%, 3.2% and 7.2% of manually-classified time activities in the HCTLS dataset, respectively. The rule-based model classified indoor and in-vehicle travel periods reasonably well (Indoor: sensitivity > 91%, specificity > 80%, and precision > 96%; in-vehicle travel: sensitivity > 71%, specificity > 99%, and precision > 88%), but the performance was moderate for outdoor static and outdoor walking predictions. No striking differences in performance were observed between the rule-based and the random forest models. The random forest model was fast and easy to execute, but was likely less robust than the rule-based model under the condition of biased or poor quality training data. Conclusions Our models can successfully identify indoor and in-vehicle travel points from the raw GPS data, but challenges remain in developing models to distinguish outdoor static points and walking. Accurate training data are essential in developing reliable models in classifying time-activity patterns. PMID:22082316

Automated time activity classification based on global positioning system (GPS) tracking data.

PubMed

Wu, Jun; Jiang, Chengsheng; Houston, Douglas; Baker, Dean; Delfino, Ralph

2011-11-14

Air pollution epidemiological studies are increasingly using global positioning system (GPS) to collect time-location data because they offer continuous tracking, high temporal resolution, and minimum reporting burden for participants. However, substantial uncertainties in the processing and classifying of raw GPS data create challenges for reliably characterizing time activity patterns. We developed and evaluated models to classify people's major time activity patterns from continuous GPS tracking data. We developed and evaluated two automated models to classify major time activity patterns (i.e., indoor, outdoor static, outdoor walking, and in-vehicle travel) based on GPS time activity data collected under free living conditions for 47 participants (N = 131 person-days) from the Harbor Communities Time Location Study (HCTLS) in 2008 and supplemental GPS data collected from three UC-Irvine research staff (N = 21 person-days) in 2010. Time activity patterns used for model development were manually classified by research staff using information from participant GPS recordings, activity logs, and follow-up interviews. We evaluated two models: (a) a rule-based model that developed user-defined rules based on time, speed, and spatial location, and (b) a random forest decision tree model. Indoor, outdoor static, outdoor walking and in-vehicle travel activities accounted for 82.7%, 6.1%, 3.2% and 7.2% of manually-classified time activities in the HCTLS dataset, respectively. The rule-based model classified indoor and in-vehicle travel periods reasonably well (Indoor: sensitivity > 91%, specificity > 80%, and precision > 96%; in-vehicle travel: sensitivity > 71%, specificity > 99%, and precision > 88%), but the performance was moderate for outdoor static and outdoor walking predictions. No striking differences in performance were observed between the rule-based and the random forest models. The random forest model was fast and easy to execute, but was likely less robust than the rule-based model under the condition of biased or poor quality training data. Our models can successfully identify indoor and in-vehicle travel points from the raw GPS data, but challenges remain in developing models to distinguish outdoor static points and walking. Accurate training data are essential in developing reliable models in classifying time-activity patterns.

Spectrum of walk matrix for Koch network and its application

NASA Astrophysics Data System (ADS)

Xie, Pinchen; Lin, Yuan; Zhang, Zhongzhi

2015-06-01

Various structural and dynamical properties of a network are encoded in the eigenvalues of walk matrix describing random walks on the network. In this paper, we study the spectra of walk matrix of the Koch network, which displays the prominent scale-free and small-world features. Utilizing the particular architecture of the network, we obtain all the eigenvalues and their corresponding multiplicities. Based on the link between the eigenvalues of walk matrix and random target access time defined as the expected time for a walker going from an arbitrary node to another one selected randomly according to the steady-state distribution, we then derive an explicit solution to the random target access time for random walks on the Koch network. Finally, we corroborate our computation for the eigenvalues by enumerating spanning trees in the Koch network, using the connection governing eigenvalues and spanning trees, where a spanning tree of a network is a subgraph of the network, that is, a tree containing all the nodes.

Path statistics, memory, and coarse-graining of continuous-time random walks on networks

PubMed Central

Kion-Crosby, Willow; Morozov, Alexandre V.

2015-01-01

Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs. PMID:26646868

Contact Time in Random Walk and Random Waypoint: Dichotomy in Tail Distribution

NASA Astrophysics Data System (ADS)

Zhao, Chen; Sichitiu, Mihail L.

Contact time (or link duration) is a fundamental factor that affects performance in Mobile Ad Hoc Networks. Previous research on theoretical analysis of contact time distribution for random walk models (RW) assume that the contact events can be modeled as either consecutive random walks or direct traversals, which are two extreme cases of random walk, thus with two different conclusions. In this paper we conduct a comprehensive research on this topic in the hope of bridging the gap between the two extremes. The conclusions from the two extreme cases will result in a power-law or exponential tail in the contact time distribution, respectively. However, we show that the actual distribution will vary between the two extremes: a power-law-sub-exponential dichotomy, whose transition point depends on the average flight duration. Through simulation results we show that such conclusion also applies to random waypoint.

Recurrence of random walks with long-range steps generated by fractional Laplacian matrices on regular networks and simple cubic lattices

NASA Astrophysics Data System (ADS)

Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.

2017-12-01

We analyze a Markovian random walk strategy on undirected regular networks involving power matrix functions of the type L\\frac{α{2}} where L indicates a ‘simple’ Laplacian matrix. We refer to such walks as ‘fractional random walks’ with admissible interval 0<α ≤slant 2 . We deduce probability-generating functions (network Green’s functions) for the fractional random walk. From these analytical results we establish a generalization of Polya’s recurrence theorem for fractional random walks on d-dimensional infinite lattices: The fractional random walk is transient for dimensions d > α (recurrent for d≤slantα ) of the lattice. As a consequence, for 0<α< 1 the fractional random walk is transient for all lattice dimensions d=1, 2, .. and in the range 1≤slantα < 2 for dimensions d≥slant 2 . Finally, for α=2 , Polya’s classical recurrence theorem is recovered, namely the walk is transient only for lattice dimensions d≥slant 3 . The generalization of Polya’s recurrence theorem remains valid for the class of random walks with Lévy flight asymptotics for long-range steps. We also analyze the mean first passage probabilities, mean residence times, mean first passage times and global mean first passage times (Kemeny constant) for the fractional random walk. For an infinite 1D lattice (infinite ring) we obtain for the transient regime 0<α<1 closed form expressions for the fractional lattice Green’s function matrix containing the escape and ever passage probabilities. The ever passage probabilities (fractional lattice Green’s functions) in the transient regime fulfil Riesz potential power law decay asymptotic behavior for nodes far from the departure node. The non-locality of the fractional random walk is generated by the non-diagonality of the fractional Laplacian matrix with Lévy-type heavy tailed inverse power law decay for the probability of long-range moves. This non-local and asymptotic behavior of the fractional random walk introduces small-world properties with the emergence of Lévy flights on large (infinite) lattices.

Occupation times and ergodicity breaking in biased continuous time random walks

NASA Astrophysics Data System (ADS)

Bel, Golan; Barkai, Eli

2005-12-01

Continuous time random walk (CTRW) models are widely used to model diffusion in condensed matter. There are two classes of such models, distinguished by the convergence or divergence of the mean waiting time. Systems with finite average sojourn time are ergodic and thus Boltzmann-Gibbs statistics can be applied. We investigate the statistical properties of CTRW models with infinite average sojourn time; in particular, the occupation time probability density function is obtained. It is shown that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point exhibits bimodal U or trimodal W shape, related to the arcsine law. The key points are as follows. (a) In a CTRW with finite or infinite mean waiting time, the distribution of the number of visits on a lattice point is determined by the probability that a member of an ensemble of particles in equilibrium occupies the lattice point. (b) The asymmetry parameter of the probability distribution function of occupation times is related to the Boltzmann probability and to the partition function. (c) The ensemble average is given by Boltzmann-Gibbs statistics for either finite or infinite mean sojourn time, when detailed balance conditions hold. (d) A non-ergodic generalization of the Boltzmann-Gibbs statistical mechanics for systems with infinite mean sojourn time is found.

Random walks on combs

NASA Astrophysics Data System (ADS)

Durhuus, Bergfinnur; Jonsson, Thordur; Wheater, John F.

2006-02-01

We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds, we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length. We also calculate exactly the spectral dimension of some fixed non-translationally invariant combs. We relate the spectral dimension to the critical exponent of the mass of the two-point function for random walks on random combs, and compute mean displacements as a function of walk duration. We prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension.

A discrete random walk on the hypercube

NASA Astrophysics Data System (ADS)

Zhang, Jingyuan; Xiang, Yonghong; Sun, Weigang

2018-03-01

In this paper, we study the scaling for mean first-passage time (MFPT) of random walks on the hypercube and obtain a closed-form formula for the MFPT over all node pairs. We also determine the exponent of scaling efficiency characterizing the random walks and compare it with those of the existing networks. Finally we study the random walks on the hypercube with a located trap and provide a solution of the Kirchhoff index of the hypercube.

Short-term and practice effects of metronome pacing in Parkinson's disease patients with gait freezing while in the 'on' state: randomized single blind evaluation.

PubMed

Cubo, Esther; Leurgans, Sue; Goetz, Christopher G

2004-12-01

In a randomized single blind parallel study, we tested the efficacy of an auditory metronome on walking speed and freezing in Parkinson's disease (PD) patients with freezing gait impairment during their 'on' function. No pharmacological treatment is effective in managing 'on' freezing in PD. Like visual cues that can help overcome freezing, rhythmic auditory pacing may provide cues that help normalize walking pace and overcome freezing. Non-demented PD patients with freezing during their 'on' state walked under two conditions, in randomized order: unassisted walking and walking with the use of an audiocassette with a metronome recording. The walking trials were randomized and gait variables were rated from videotapes by a blinded evaluator. Outcome measures were total walking time (total trial time-total freezing time), which was considered the time over a course of specified length, freezing time, average freeze duration and number of freezes. All outcomes were averaged across trials for each person and then compared across conditions using Signed Rank tests. Twelve non-demented PD patients with a mean age of 65.8 +/- 11.2 years, and mean PD duration of 12.4 +/- 7.3 years were included. The use of the metronome slowed ambulation and increased the total walking time (P < 0.0005) only during the first visit, without affecting any freezing variable. In the nine patients who took the metronome recording home and used it daily for 1 week while walking, freezing remained unimproved. Though advocated in prior publications as a walking aid for PD patients, auditory metronome pacing slows walking and is not a beneficial intervention for freezing during their 'on' periods.

Non-Fickian dispersion of groundwater age

PubMed Central

Engdahl, Nicholas B.; Ginn, Timothy R.; Fogg, Graham E.

2014-01-01

We expand the governing equation of groundwater age to account for non-Fickian dispersive fluxes using continuous random walks. Groundwater age is included as an additional (fifth) dimension on which the volumetric mass density of water is distributed and we follow the classical random walk derivation now in five dimensions. The general solution of the random walk recovers the previous conventional model of age when the low order moments of the transition density functions remain finite at their limits and describes non-Fickian age distributions when the transition densities diverge. Previously published transition densities are then used to show how the added dimension in age affects the governing differential equations. Depending on which transition densities diverge, the resulting models may be nonlocal in time, space, or age and can describe asymptotic or pre-asymptotic dispersion. A joint distribution function of time and age transitions is developed as a conditional probability and a natural result of this is that time and age must always have identical transition rate functions. This implies that a transition density defined for age can substitute for a density in time and this has implications for transport model parameter estimation. We present examples of simulated age distributions from a geologically based, heterogeneous domain that exhibit non-Fickian behavior and show that the non-Fickian model provides better descriptions of the distributions than the Fickian model. PMID:24976651

Universal principles governing multiple random searchers on complex networks: The logarithmic growth pattern and the harmonic law

NASA Astrophysics Data System (ADS)

Weng, Tongfeng; Zhang, Jie; Small, Michael; Harandizadeh, Bahareh; Hui, Pan

2018-03-01

We propose a unified framework to evaluate and quantify the search time of multiple random searchers traversing independently and concurrently on complex networks. We find that the intriguing behaviors of multiple random searchers are governed by two basic principles—the logarithmic growth pattern and the harmonic law. Specifically, the logarithmic growth pattern characterizes how the search time increases with the number of targets, while the harmonic law explores how the search time of multiple random searchers varies relative to that needed by individual searchers. Numerical and theoretical results demonstrate these two universal principles established across a broad range of random search processes, including generic random walks, maximal entropy random walks, intermittent strategies, and persistent random walks. Our results reveal two fundamental principles governing the search time of multiple random searchers, which are expected to facilitate investigation of diverse dynamical processes like synchronization and spreading.

Influence of the random walk finite step on the first-passage probability

NASA Astrophysics Data System (ADS)

Klimenkova, Olga; Menshutin, Anton; Shchur, Lev

2018-01-01

A well known connection between first-passage probability of random walk and distribution of electrical potential described by Laplace equation is studied. We simulate random walk in the plane numerically as a discrete time process with fixed step length. We measure first-passage probability to touch the absorbing sphere of radius R in 2D. We found a regular deviation of the first-passage probability from the exact function, which we attribute to the finiteness of the random walk step.

The effect of a pedometer-based community walking intervention "Walking for Wellbeing in the West" on physical activity levels and health outcomes: a 12-week randomized controlled trial.

PubMed

Baker, Graham; Gray, Stuart R; Wright, Annemarie; Fitzsimons, Claire; Nimmo, Myra; Lowry, Ruth; Mutrie, Nanette

2008-09-05

Recent systematic reviews have suggested that pedometers may be effective motivational tools to promote walking. However, studies tend to be of a relatively short duration, with small clinical based samples. Further research is required to demonstrate their effectiveness in adequately powered, community based studies. Using a randomized controlled trial design, this study assessed the impact of a 12-week graduated pedometer-based walking intervention on daily step-counts, self-reported physical activity and health outcomes in a Scottish community sample not meeting current physical activity recommendations. Sixty-three women and 16 men (49.2 years +/- 8.8) were randomly assigned to either an intervention (physical activity consultation and 12-week pedometer-based walking program) or control (no action) group. Measures for step-counts, 7-day physical activity recall, affect, quality of life (n = 79), body mass, BMI, % body fat, waist and hip circumference (n = 76), systolic/diastolic blood pressure, total cholesterol and HDL cholesterol (n = 66) were taken at baseline and week 12. Analyses were performed on an intention to treat basis using 2-way mixed factorial analyses of variance for parametric data and Mann Whitney and Wilcoxon tests for non-parametric data. Significant increases were found in the intervention group for step-counts (p < .001), time spent in leisure walking (p = .02) and positive affect (p = .027). Significant decreases were found in this group for time spent in weekday (p = .003), weekend (p = .001) and total sitting (p = .001) with no corresponding changes in the control group. No significant changes in any other health outcomes were found in either group. In comparison with the control group at week 12, the intervention group reported a significantly greater number of minutes spent in leisure time (p = .008), occupational (p = .045) and total walking (p = .03), and significantly fewer minutes in time spent in weekend (p = .003) and total sitting (p = .022). A pedometer-based walking program, incorporating a physical activity consultation, is effective in promoting walking and improving positive affect over 12 weeks in community based individuals. The discussion examines possible explanations for the lack of significant changes in health outcomes. Continued follow-up of this study will examine adherence to the intervention and possible resulting effects on health outcomes.

Effects of the Integration of Dynamic Weight Shifting Training Into Treadmill Training on Walking Function of Children with Cerebral Palsy: A Randomized Controlled Study.

PubMed

Wu, Ming; Kim, Janis; Arora, Pooja; Gaebler-Spira, Deborah J; Zhang, Yunhui

2017-11-01

The aim of the study was to determine whether applying an assistance force to the pelvis and legs during treadmill training can improve walking function in children with cerebral palsy. Twenty-three children with cerebral palsy were randomly assigned to the robotic or treadmill only group. For participants who were assigned to the robotic group, a controlled force was applied to the pelvis and legs during treadmill walking. For participants who were assigned to the treadmill only group, manual assistance was provided as needed. Each participant trained 3 times/wk for 6 wks. Outcome measures included walking speed, 6-min walking distance, and clinical assessment of motor function, which were evaluated before, after training, and 8 wks after the end of training, and were compared between two groups. Significant increases in walking speed and 6-min walking distance were observed after robotic training (P = 0.03), but no significant change was observed after treadmill training only. A greater increase in 6-min walking distance was observed after robotic training than that after treadmill only training (P = 0.01). Applying a controlled force to the pelvis and legs, for facilitating weight-shift and leg swing, respectively, during treadmill training may improve walking speed and endurance in children with cerebral palsy. Complete the self-assessment activity and evaluation online at http://www.physiatry.org/JournalCME CME OBJECTIVES: Upon completion of this article, the reader should be able to: (1) discuss the importance of physical activity at the participation level (sports programs) for children with cerebral palsy; (2) contrast the changes in walking ability and endurance for children in GMFCS level I, II and III following sports programs; and (3) identify the impact of higher frequency of sports program attendance over time on walking ability. Advanced ACCREDITATION: The Association of Academic Physiatrists is accredited by the Accreditation Council for Continuing Medical Education to provide continuing medical education for physicians.The Association of Academic Physiatrists designates this Journal-based CME activity for a maximum of 0.5 AMA PRA Category 1 Credit(s)™. Physicians should only claim credit commensurate with the extent of their participation in the activity.

Anomalous transport in turbulent plasmas and continuous time random walks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balescu, R.

1995-05-01

The possibility of a model of anomalous transport problems in a turbulent plasma by a purely stochastic process is investigated. The theory of continuous time random walks (CTRW`s) is briefly reviewed. It is shown that a particular class, called the standard long tail CTRW`s is of special interest for the description of subdiffusive transport. Its evolution is described by a non-Markovian diffusion equation that is constructed in such a way as to yield exact values for all the moments of the density profile. The concept of a CTRW model is compared to an exact solution of a simple test problem:more » transport of charged particles in a fluctuating magnetic field in the limit of infinite perpendicular correlation length. Although the well-known behavior of the mean square displacement proportional to {ital t}{sup 1/2} is easily recovered, the exact density profile cannot be modeled by a CTRW. However, the quasilinear approximation of the kinetic equation has the form of a non-Markovian diffusion equation and can thus be generated by a CTRW.« less

Effectiveness of Long and Short Bout Walking on Increasing Physical Activity in Women

PubMed Central

Serwe, Katrina M.; Swartz, Ann M.; Hart, Teresa L.; Strath, Scott J.

2011-01-01

Abstract Background The accumulation of physical activity (PA) throughout the day has been suggested as a means to increase PA behavior. It is not known, however, if accumulated PA results in equivalent increases in PA behavior compared with one continuous session. The purpose of this investigation was to compare changes in PA between participants assigned to walk daily in accumulated shorter bouts vs. one continuous session. Methods In this 8-week randomized controlled trial, 60 inactive women were randomly assigned to one of the following: (1) control group, (2) 30 minutes a day of walking 5 days a week in one continuous long bout (LB), or (3) three short 10-minute bouts (SB) of walking a day, all at a prescribed heart rate intensity. Walking was assessed by pedometer and self-reported walking log. Before and after measures were taken of average steps/day, resting systolic and diastolic blood pressure (SBP, DBP), resting heart rate (RHR), six-minute walk test (6MWT) distance, height, weight, body mass index (BMI), and hip and waist circumference. Results Both walking groups significantly increased PA measured as steps/day compared to controls (p < 0.001), and no significant differences were found between LB and SB groups. The LB group demonstrated significant decreases in hip circumference and significant increases in 6MWT distance compared to the control group. Conclusions Both walking groups significantly increased PA participation. LB group participants completed more walking at a higher intensity than the SB and control groups, which resulted in significant increases in health benefits. PMID:21314449

Maxima of two random walks: Universal statistics of lead changes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ben-Naim, E.; Krapivsky, P. L.; Randon-Furling, J.

2016-04-18

In this study, we investigate statistics of lead changes of the maxima of two discrete-time random walks in one dimension. We show that the average number of lead changes grows asmore » $${\\pi }^{-1}\\mathrm{ln}t$$ in the long-time limit. We present theoretical and numerical evidence that this asymptotic behavior is universal. Specifically, this behavior is independent of the jump distribution: the same asymptotic underlies standard Brownian motion and symmetric Lévy flights. We also show that the probability to have at most n lead changes behaves as $${t}^{-1/4}{(\\mathrm{ln}t)}^{n}$$ for Brownian motion and as $${t}^{-\\beta (\\mu )}{(\\mathrm{ln}t)}^{n}$$ for symmetric Lévy flights with index μ. The decay exponent $$\\beta \\equiv \\beta (\\mu )$$ varies continuously with the Lévy index when $$0\\lt \\mu \\lt 2$$, and remains constant $$\\beta =1/4$$ for $$\\mu \\gt 2$$.« less

Volcano monitoring using the Global Positioning System: Filtering strategies

USGS Publications Warehouse

Larson, K.M.; Cervelli, Peter; Lisowski, M.; Miklius, Asta; Segall, P.; Owen, S.

2001-01-01

Permanent Global Positioning System (GPS) networks are routinely used for producing improved orbits and monitoring secular tectonic deformation. For these applications, data are transferred to an analysis center each day and routinely processed in 24-hour segments. To use GPS for monitoring volcanic events, which may last only a few hours, real-time or near real-time data processing and subdaily position estimates are valuable. Strategies have been researched for obtaining station coordinates every 15 min using a Kalman filter; these strategies have been tested on data collected by a GPS network on Kilauea Volcano. Data from this network are tracked continuously, recorded every 30 s, and telemetered hourly to the Hawaiian Volcano Observatory. A white noise model is heavily impacted by data outages and poor satellite geometry, but a properly constrained random walk model fits the data well. Using a borehole tiltmeter at Kilauea's summit as ground-truth, solutions using different random walk constraints were compared. This study indicates that signals on the order of 5 mm/h are resolvable using a random walk standard deviation of 0.45 cm/???h. Values lower than this suppress small signals, and values greater than this have significantly higher noise at periods of 1-6 hours. Copyright 2001 by the American Geophysical Union.

Scaling behavior for random walks with memory of the largest distance from the origin

NASA Astrophysics Data System (ADS)

Serva, Maurizio

2013-11-01

We study a one-dimensional random walk with memory. The behavior of the walker is modified with respect to the simple symmetric random walk only when he or she is at the maximum distance ever reached from his or her starting point (home). In this case, having the choice to move farther or to move closer, the walker decides with different probabilities. If the probability of a forward step is higher then the probability of a backward step, the walker is bold, otherwise he or she is timorous. We investigate the asymptotic properties of this bold-timorous random walk, showing that the scaling behavior varies continuously from subdiffusive (timorous) to superdiffusive (bold). The scaling exponents are fully determined with a new mathematical approach based on a decomposition of the dynamics in active journeys (the walker is at the maximum distance) and lazy journeys (the walker is not at the maximum distance).

Quantum walks with tuneable self-avoidance in one dimension

PubMed Central

Camilleri, Elizabeth; Rohde, Peter P.; Twamley, Jason

2014-01-01

Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Here the walker has memory of its previous locations and preferentially avoids stepping back to locations where it has previously resided. Classical self-avoiding random walks have found numerous algorithmic applications, most notably in the modelling of protein folding. We consider the analogous problem in the quantum setting – a quantum walk in one dimension with tunable levels of self-avoidance. We complement a quantum walk with a memory register that records where the walker has previously resided. The walker is then able to avoid returning back to previously visited sites or apply more general memory conditioned operations to control the walk. We characterise this walk by examining the variance of the walker's distribution against time, the standard metric for quantifying how quantum or classical a walk is. We parameterise the strength of the memory recording and the strength of the memory back-action on the walker, and investigate their effect on the dynamics of the walk. We find that by manipulating these parameters, which dictate the degree of self-avoidance, the walk can be made to reproduce ideal quantum or classical random walk statistics, or a plethora of more elaborate diffusive phenomena. In some parameter regimes we observe a close correspondence between classical self-avoiding random walks and the quantum self-avoiding walk. PMID:24762398

Pólya number and first return of bursty random walk: Rigorous solutions

NASA Astrophysics Data System (ADS)

Wan, J.; Xu, X. P.

2012-03-01

The recurrence properties of random walks can be characterized by Pólya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we investigate Pólya number and first return for bursty random walk on a line, in which the walk has different step size and moving probabilities. Using the concept of the Catalan number, we obtain exact results for first return probability, the average first return time and Pólya number for the first time. We show that Pólya number displays two different functional behavior when the walk deviates from the recurrent point. By utilizing the Lagrange inversion formula, we interpret our findings by transferring Pólya number to the closed-form solutions of an inverse function. We also calculate Pólya number using another approach, which corroborates our results and conclusions. Finally, we consider the recurrence properties and Pólya number of two variations of the bursty random walk model.

Effects of Interrupting Children's Sedentary Behaviors With Activity on Metabolic Function: A Randomized Trial.

PubMed

Belcher, Britni R; Berrigan, David; Papachristopoulou, Alexia; Brady, Sheila M; Bernstein, Shanna B; Brychta, Robert J; Hattenbach, Jacob D; Tigner, Ira L; Courville, Amber B; Drinkard, Bart E; Smith, Kevin P; Rosing, Douglas R; Wolters, Pamela L; Chen, Kong Y; Yanovski, Jack A

2015-10-01

Limited data suggest that interrupting sedentary behaviors with activity improves metabolic parameters in adults. We tested whether interrupting sitting with short, moderate-intensity walking bouts improved glucose tolerance in children. Participants underwent two experimental conditions in random order on different days: continuous sitting for 3 hours or sitting interrupted by walking (3 min of moderate-intensity walking every 30 min). Insulin, C-peptide, glucose, and free fatty acids were measured every 30 minutes for 3 hours during an oral glucose tolerance test. Area under the curve (AUC) was calculated from hormone and substrate measurements. Children were given a buffet meal after each condition. The study was conducted at the National Institutes of Health Hatfield Clinical Research Center. Twenty-eight normal-weight 7-11 year olds participated. Patterns of substrate/hormone secretion and AUC, as well as energy intake, were examined by experimental condition. Interrupting sitting resulted in a 32% lower insulin AUC (P < .001), 17% lower C-peptide AUC (P < .001), and 7% lower glucose AUC (P = .018) vs continuous sitting. Mixed model results indicated that insulin (P = .036) and free fatty acid concentrations (P = .009) were significantly lower in the interrupted vs the continuous sitting condition. Lunchtime buffet meal energy intake did not significantly differ between the conditions (975 ± 387 vs 963 ± 309 kcal; P = .85). Interrupting sedentary time with brief moderate-intensity walking improved short-term metabolic function in non-overweight children without increasing subsequent energy intake. These findings suggest that interrupting sedentary behavior may be a promising prevention strategy for reducing cardiometabolic risk in children.

Random Walks on Homeo( S 1)

NASA Astrophysics Data System (ADS)

Malicet, Dominique

2017-12-01

In this paper, we study random walks {g_n=f_{n-1}\\ldots f_0} on the group Homeo ( S 1) of the homeomorphisms of the circle, where the homeomorphisms f k are chosen randomly, independently, with respect to a same probability measure {ν}. We prove that under the only condition that there is no probability measure invariant by {ν}-almost every homeomorphism, the random walk almost surely contracts small intervals. It generalizes what has been known on this subject until now, since various conditions on {ν} were imposed in order to get the phenomenon of contractions. Moreover, we obtain the surprising fact that the rate of contraction is exponential, even in the lack of assumptions of smoothness on the f k 's. We deduce various dynamical consequences on the random walk ( g n ): finiteness of ergodic stationary measures, distribution of the trajectories, asymptotic law of the evaluations, etc. The proof of the main result is based on a modification of the Ávila-Viana's invariance principle, working for continuous cocycles on a space fibred in circles.

Phenomenological picture of fluctuations in branching random walks

NASA Astrophysics Data System (ADS)

Mueller, A. H.; Munier, S.

2014-10-01

We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the 1 /√{t } correction to the average position of the rightmost particle of a branching random walk for large times t ≫1 , computed by Ebert and Van Saarloos, as fluctuations on top of the mean-field approximation of this process with a Brunet-Derrida cutoff at the tip that simulates discreteness. Our analytical formulas successfully compare to numerical simulations of a particular model of a branching random walk.

Estimating rate uncertainty with maximum likelihood: differences between power-law and flicker–random-walk models

USGS Publications Warehouse

Langbein, John O.

2012-01-01

Recent studies have documented that global positioning system (GPS) time series of position estimates have temporal correlations which have been modeled as a combination of power-law and white noise processes. When estimating quantities such as a constant rate from GPS time series data, the estimated uncertainties on these quantities are more realistic when using a noise model that includes temporal correlations than simply assuming temporally uncorrelated noise. However, the choice of the specific representation of correlated noise can affect the estimate of uncertainty. For many GPS time series, the background noise can be represented by either: (1) a sum of flicker and random-walk noise or, (2) as a power-law noise model that represents an average of the flicker and random-walk noise. For instance, if the underlying noise model is a combination of flicker and random-walk noise, then incorrectly choosing the power-law model could underestimate the rate uncertainty by a factor of two. Distinguishing between the two alternate noise models is difficult since the flicker component can dominate the assessment of the noise properties because it is spread over a significant portion of the measurable frequency band. But, although not necessarily detectable, the random-walk component can be a major constituent of the estimated rate uncertainty. None the less, it is possible to determine the upper bound on the random-walk noise.

The one-dimensional asymmetric persistent random walk

NASA Astrophysics Data System (ADS)

Rossetto, Vincent

2018-04-01

Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic and symmetric 1D persistent random walk is governed by the telegrapher’s equation, also called the hyperbolic heat conduction equation. These equations have been designed to resolve the paradox of the infinite speed in the heat and diffusion equations. The finiteness of both the speed and the correlation length leads to several classes of random walks: Persistent random walk in one dimension can display anomalies that cannot arise for Brownian motion such as anisotropy and asymmetries. In this work we focus on the case where the mean free path is anisotropic, the only anomaly leading to a physics that is different from the telegrapher’s case. We derive exact expression of its Green’s function, for its scattering statistics and distribution of first-passage time at the origin. The phenomenology of the latter shows a transition for quantities like the escape probability and the residence time.

The Dynamical Classification of Centaurs which Evolve into Comets

NASA Astrophysics Data System (ADS)

Wood, Jeremy R.; Horner, Jonathan; Hinse, Tobias; Marsden, Stephen; Swinburne University of Technology

2016-10-01

Centaurs are small Solar system bodies with semi-major axes between Jupiter and Neptune and perihelia beyond Jupiter. Centaurs can be further subclassified into two dynamical categories - random walk and resonance hopping. Random walk Centaurs have mean square semi-major axes (< a2 >) which vary in time according to a generalized diffusion equation where < a2 > ~t2H. H is the Hurst exponent with 0 < H < 1, and t is time. The behavior of < a2 > for resonance hopping Centaurs is not well described by generalized diffusion.The aim of this study is to determine which dynamical type of Centaur is most likely to evolve into each class of comet. 31,722 fictional massless test particles were integrated for 3 Myr in the 6-body problem (Sun, Jovian planets, test particle). Initially each test particle was a member of one of four groups. The semi-major axes of all test particles in a group were clustered within 0.27 au from a first order, interior Mean Motion resonance of Neptune. The resonances were centered at 18.94 au, 22.95 au, 24.82 au and 28.37 au.If the perihelion of a test particle reached < 4 au then the test particle was considered to be a comet and classified as either a random walk or resonance hopping Centaur. The results showed that over 4,000 test particles evolved into comets within 3 Myr. 59% of these test particles were random walk and 41% were resonance hopping. The behavior of the semi-major axis in time was usually well described by generalized diffusion for random walk Centaurs (ravg = 0.98) and poorly described for resonance hopping Centaurs (ravg = 0.52). The average Hurst exponent was 0.48 for random walk Centaurs and 0.20 for resonance hopping Centaurs. Random walk Centaurs were more likely to evolve into short period comets while resonance hopping Centaurs were more likely to evolve into long period comets. For each initial cluster, resonance hopping Centaurs took longer to evolve into comets than random walk Centaurs. Overall the population of random walk Centaurs averaged 143 kyr to evolve into comets, and the population of resonance hopping Centaurs averaged 164 kyr.

Record statistics of financial time series and geometric random walks

NASA Astrophysics Data System (ADS)

Sabir, Behlool; Santhanam, M. S.

2014-09-01

The study of record statistics of correlated series in physics, such as random walks, is gaining momentum, and several analytical results have been obtained in the past few years. In this work, we study the record statistics of correlated empirical data for which random walk models have relevance. We obtain results for the records statistics of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent α lying in the range 1.5≤α≤1.8. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that obtained from empirical stock data.

Regenerating time series from ordinal networks.

PubMed

McCullough, Michael; Sakellariou, Konstantinos; Stemler, Thomas; Small, Michael

2017-03-01

Recently proposed ordinal networks not only afford novel methods of nonlinear time series analysis but also constitute stochastic approximations of the deterministic flow time series from which the network models are constructed. In this paper, we construct ordinal networks from discrete sampled continuous chaotic time series and then regenerate new time series by taking random walks on the ordinal network. We then investigate the extent to which the dynamics of the original time series are encoded in the ordinal networks and retained through the process of regenerating new time series by using several distinct quantitative approaches. First, we use recurrence quantification analysis on traditional recurrence plots and order recurrence plots to compare the temporal structure of the original time series with random walk surrogate time series. Second, we estimate the largest Lyapunov exponent from the original time series and investigate the extent to which this invariant measure can be estimated from the surrogate time series. Finally, estimates of correlation dimension are computed to compare the topological properties of the original and surrogate time series dynamics. Our findings show that ordinal networks constructed from univariate time series data constitute stochastic models which approximate important dynamical properties of the original systems.

Regenerating time series from ordinal networks

NASA Astrophysics Data System (ADS)

McCullough, Michael; Sakellariou, Konstantinos; Stemler, Thomas; Small, Michael

2017-03-01

Recently proposed ordinal networks not only afford novel methods of nonlinear time series analysis but also constitute stochastic approximations of the deterministic flow time series from which the network models are constructed. In this paper, we construct ordinal networks from discrete sampled continuous chaotic time series and then regenerate new time series by taking random walks on the ordinal network. We then investigate the extent to which the dynamics of the original time series are encoded in the ordinal networks and retained through the process of regenerating new time series by using several distinct quantitative approaches. First, we use recurrence quantification analysis on traditional recurrence plots and order recurrence plots to compare the temporal structure of the original time series with random walk surrogate time series. Second, we estimate the largest Lyapunov exponent from the original time series and investigate the extent to which this invariant measure can be estimated from the surrogate time series. Finally, estimates of correlation dimension are computed to compare the topological properties of the original and surrogate time series dynamics. Our findings show that ordinal networks constructed from univariate time series data constitute stochastic models which approximate important dynamical properties of the original systems.

Adaptive random walks on the class of Web graphs

NASA Astrophysics Data System (ADS)

Tadić, B.

2001-09-01

We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [B. Tadić, Physica A 293, 273 (2001)], and are characterized by a pair of power-law distributions of out- and in-degree for each value of the parameter β, which measures the degree of rewiring in the graph. The walker adapts its move strategy according to locally available information both on out-degree of the visited node and in-degree of target node. A standard random walk, on the other hand, uses the out-degree only. We compute the distribution of connected subgraphs visited by an ensemble of walkers, the average access time and survival probability of the walks. We discuss these properties of the walk dynamics relative to the changes in the global graph structure when the control parameter β is varied. For β≥ 3, corresponding to the world-wide Web, the access time of the walk to a given level of hierarchy on the graph is much shorter compared to the standard random walk on the same graph. By reducing the amount of rewiring towards rigidity limit β↦βc≲ 0.1, corresponding to the range of naturally occurring biochemical networks, the survival probability of adaptive and standard random walk become increasingly similar. The adaptive random walk can be used as an efficient message-passing algorithm on this class of graphs for large degree of rewiring.

Diffusion in randomly perturbed dissipative dynamics

NASA Astrophysics Data System (ADS)

Rodrigues, Christian S.; Chechkin, Aleksei V.; de Moura, Alessandro P. S.; Grebogi, Celso; Klages, Rainer

2014-11-01

Dynamical systems having many coexisting attractors present interesting properties from both fundamental theoretical and modelling points of view. When such dynamics is under bounded random perturbations, the basins of attraction are no longer invariant and there is the possibility of transport among them. Here we introduce a basic theoretical setting which enables us to study this hopping process from the perspective of anomalous transport using the concept of a random dynamical system with holes. We apply it to a simple model by investigating the role of hyperbolicity for the transport among basins. We show numerically that our system exhibits non-Gaussian position distributions, power-law escape times, and subdiffusion. Our simulation results are reproduced consistently from stochastic continuous time random walk theory.

Improvement of walking distance by defibrotide in patients with intermittent claudication--results of a randomized, placebo-controlled study (the DICLIS study). Defibrotide Intermittent CLaudication Italian Study.

PubMed

Violi, F; Marubini, E; Coccheri, S; Nenci, G G

2000-05-01

Defibrotide is an antithrombotic drug which enhances prostacyclin production and activates fibrinolytic system. The aim of this study was to investigate the improvement of walking distance in patients with intermittent claudication treated with defibrotide. DICLIS was a double blind, placebo-controlled study which included patients with walking distance autonomy at a standardized treadmill test < or =350 > or =100 meters. A total of 310 patients were randomly allocated to placebo (n = 101), defibrotide 800 mg/day (n = 104) or defibrotide 1200 mg/day (n = 105). During a one year follow-up, the Absolute Walking Distance (AWD) was measured six times (0, 30, 60, 90, 180, 360 days). Similar improvement in walking distance was found in the three groups until the 90th day; thereafter placebo group showed no further increase, while AWD continued to increase in the defibrotide groups. Between the 180th and 360th day visits, AWD was significantly higher (P <0.01) in patients given defibrotide than in patients given placebo. No difference in efficacy was observed between the two dosages of defibrotide. No differences in side effects were observed among the three groups. The results of the present trial suggest that long-term administration of defibrotide improves walking distance in patients with intermittent claudication.

US stock market efficiency over weekly, monthly, quarterly and yearly time scales

NASA Astrophysics Data System (ADS)

Rodriguez, E.; Aguilar-Cornejo, M.; Femat, R.; Alvarez-Ramirez, J.

2014-11-01

In financial markets, the weak form of the efficient market hypothesis implies that price returns are serially uncorrelated sequences. In other words, prices should follow a random walk behavior. Recent developments in evolutionary economic theory (Lo, 2004) have tailored the concept of adaptive market hypothesis (AMH) by proposing that market efficiency is not an all-or-none concept, but rather market efficiency is a characteristic that varies continuously over time and across markets. Within the AMH framework, this work considers the Dow Jones Index Average (DJIA) for studying the deviations from the random walk behavior over time. It is found that the market efficiency also varies over different time scales, from weeks to years. The well-known detrended fluctuation analysis was used for the characterization of the serial correlations of the return sequences. The results from the empirical showed that interday and intraday returns are more serially correlated than overnight returns. Also, some insights in the presence of business cycles (e.g., Juglar and Kuznets) are provided in terms of time variations of the scaling exponent.

Long-Term Follow-up to a Randomized Controlled Trial Comparing Peroneal Nerve Functional Electrical Stimulation to an Ankle Foot Orthosis for Patients With Chronic Stroke.

PubMed

Bethoux, Francois; Rogers, Helen L; Nolan, Karen J; Abrams, Gary M; Annaswamy, Thiru; Brandstater, Murray; Browne, Barbara; Burnfield, Judith M; Feng, Wuwei; Freed, Mitchell J; Geis, Carolyn; Greenberg, Jason; Gudesblatt, Mark; Ikramuddin, Farha; Jayaraman, Arun; Kautz, Steven A; Lutsep, Helmi L; Madhavan, Sangeetha; Meilahn, Jill; Pease, William S; Rao, Noel; Seetharama, Subramani; Sethi, Pramod; Turk, Margaret A; Wallis, Roi Ann; Kufta, Conrad

2015-01-01

Evidence supports peroneal nerve functional electrical stimulation (FES) as an effective alternative to ankle foot orthoses (AFO) for treatment of foot drop poststroke, but few long-term, randomized controlled comparisons exist. Compare changes in gait quality and function between FES and AFOs in individuals with foot drop poststroke over a 12-month period. Follow-up analysis of an unblinded randomized controlled trial (ClinicalTrials.gov #NCT01087957) conducted at 30 rehabilitation centers comparing FES to AFOs over 6 months. Subjects continued to wear their randomized device for another 6 months to final 12-month assessments. Subjects used study devices for all home and community ambulation. Multiply imputed intention-to-treat analyses were utilized; primary endpoints were tested for noninferiority and secondary endpoints for superiority. Primary endpoints: 10 Meter Walk Test (10MWT) and device-related serious adverse event rate. Secondary endpoints: 6-Minute Walk Test (6MWT), GaitRite Functional Ambulation Profile, and Modified Emory Functional Ambulation Profile (mEFAP). A total of 495 subjects were randomized, and 384 completed the 12-month follow-up. FES proved noninferior to AFOs for all primary endpoints. Both FES and AFO groups showed statistically and clinically significant improvement for 10MWT compared with initial measurement. No statistically significant between-group differences were found for primary or secondary endpoints. The FES group demonstrated statistically significant improvements for 6MWT and mEFAP Stair-time subscore. At 12 months, both FES and AFOs continue to demonstrate equivalent gains in gait speed. Results suggest that long-term FES use may lead to additional improvements in walking endurance and functional ambulation; further research is needed to confirm these findings. © The Author(s) 2015.

Ages of Records in Random Walks

NASA Astrophysics Data System (ADS)

Szabó, Réka; Vető, Bálint

2016-12-01

We consider random walks with continuous and symmetric step distributions. We prove universal asymptotics for the average proportion of the age of the kth longest lasting record for k=1,2,ldots and for the probability that the record of the kth longest age is broken at step n. Due to the relation to the Chinese restaurant process, the ranked sequence of proportions of ages converges to the Poisson-Dirichlet distribution.

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

PubMed Central

Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

2013-01-01

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. PMID:24209851

In Vivo Anomalous Diffusion and Weak Ergodicity Breaking of Lipid Granules

NASA Astrophysics Data System (ADS)

Jeon, Jae-Hyung; Tejedor, Vincent; Burov, Stas; Barkai, Eli; Selhuber-Unkel, Christine; Berg-Sørensen, Kirstine; Oddershede, Lene; Metzler, Ralf

2011-01-01

Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.

Randomized Controlled Trial of a Home-Based Action Observation Intervention to Improve Walking in Parkinson Disease.

PubMed

Jaywant, Abhishek; Ellis, Terry D; Roy, Serge; Lin, Cheng-Chieh; Neargarder, Sandy; Cronin-Golomb, Alice

2016-05-01

To examine the feasibility and efficacy of a home-based gait observation intervention for improving walking in Parkinson disease (PD). Participants were randomly assigned to an intervention or control condition. A baseline walking assessment, a training period at home, and a posttraining assessment were conducted. The laboratory and participants' home and community environments. Nondemented individuals with PD (N=23) experiencing walking difficulty. In the gait observation (intervention) condition, participants viewed videos of healthy and parkinsonian gait. In the landscape observation (control) condition, participants viewed videos of moving water. These tasks were completed daily for 8 days. Spatiotemporal walking variables were assessed using accelerometers in the laboratory (baseline and posttraining assessments) and continuously at home during the training period. Variables included daily activity, walking speed, stride length, stride frequency, leg swing time, and gait asymmetry. Questionnaires including the 39-item Parkinson Disease Questionnaire (PDQ-39) were administered to determine self-reported change in walking, as well as feasibility. At posttraining assessment, only the gait observation group reported significantly improved mobility (PDQ-39). No improvements were seen in accelerometer-derived walking data. Participants found the at-home training tasks and accelerometer feasible to use. Participants found procedures feasible and reported improved mobility, suggesting that observational training holds promise in the rehabilitation of walking in PD. Observational training alone, however, may not be sufficient to enhance walking in PD. A more challenging and adaptive task, and the use of explicit perceptual learning and practice of actions, may be required to effect change. Copyright © 2016 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

NASA Astrophysics Data System (ADS)

Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.

2012-09-01

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

A fast random walk algorithm for computing the pulsed-gradient spin-echo signal in multiscale porous media.

PubMed

Grebenkov, Denis S

2011-02-01

A new method for computing the signal attenuation due to restricted diffusion in a linear magnetic field gradient is proposed. A fast random walk (FRW) algorithm for simulating random trajectories of diffusing spin-bearing particles is combined with gradient encoding. As random moves of a FRW are continuously adapted to local geometrical length scales, the method is efficient for simulating pulsed-gradient spin-echo experiments in hierarchical or multiscale porous media such as concrete, sandstones, sedimentary rocks and, potentially, brain or lungs. Copyright © 2010 Elsevier Inc. All rights reserved.

Ergodic Transition in a Simple Model of the Continuous Double Auction

PubMed Central

Radivojević, Tijana; Anselmi, Jonatha; Scalas, Enrico

2014-01-01

We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior of prices and logarithmic returns are observed. In the ergodic regime, prices are unstable and one can observe a heteroskedastic behavior in the logarithmic returns. On the contrary, non-ergodicity triggers stability of prices, even if two different regimes can be seen. PMID:24558377

Ergodic transition in a simple model of the continuous double auction.

PubMed

Radivojević, Tijana; Anselmi, Jonatha; Scalas, Enrico

2014-01-01

We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent M/M/1 queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior of prices and logarithmic returns are observed. In the ergodic regime, prices are unstable and one can observe a heteroskedastic behavior in the logarithmic returns. On the contrary, non-ergodicity triggers stability of prices, even if two different regimes can be seen.

Relation between random walks and quantum walks

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Falkner, Stefan; Portugal, Renato

2015-05-01

Based on studies of four specific networks, we conjecture a general relation between the walk dimensions dw of discrete-time random walks and quantum walks with the (self-inverse) Grover coin. In each case, we find that dw of the quantum walk takes on exactly half the value found for the classical random walk on the same geometry. Since walks on homogeneous lattices satisfy this relation trivially, our results for heterogeneous networks suggest that such a relation holds irrespective of whether translational invariance is maintained or not. To develop our results, we extend the renormalization-group analysis (RG) of the stochastic master equation to one with a unitary propagator. As in the classical case, the solution ρ (x ,t ) in space and time of this quantum-walk equation exhibits a scaling collapse for a variable xdw/t in the weak limit, which defines dw and illuminates fundamental aspects of the walk dynamics, e.g., its mean-square displacement. We confirm the collapse for ρ (x ,t ) in each case with extensive numerical simulation. The exact values for dw themselves demonstrate that RG is a powerful complementary approach to study the asymptotics of quantum walks that weak-limit theorems have not been able to access, such as for systems lacking translational symmetries beyond simple trees.

Random walks exhibiting anomalous diffusion: elephants, urns and the limits of normality

NASA Astrophysics Data System (ADS)

Kearney, Michael J.; Martin, Richard J.

2018-01-01

A random walk model is presented which exhibits a transition from standard to anomalous diffusion as a parameter is varied. The model is a variant on the elephant random walk and differs in respect of the treatment of the initial state, which in the present work consists of a given number N of fixed steps. This also links the elephant random walk to other types of history dependent random walk. As well as being amenable to direct analysis, the model is shown to be asymptotically equivalent to a non-linear urn process. This provides fresh insights into the limiting form of the distribution of the walker’s position at large times. Although the distribution is intrinsically non-Gaussian in the anomalous diffusion regime, it gradually reverts to normal form when N is large under quite general conditions.

Virtual reality-based training improves community ambulation in individuals with stroke: a randomized controlled trial.

PubMed

Yang, Yea-Ru; Tsai, Meng-Pin; Chuang, Tien-Yow; Sung, Wen-Hsu; Wang, Ray-Yau

2008-08-01

This is a single blind randomized controlled trial to examine the effect of virtual reality-based training on the community ambulation in individuals with stroke. Twenty subjects with stroke were assigned randomly to either the control group (n=9) or the experimental group (n=11). Subjects in the control group received the treadmill training. Subjects in the experimental group underwent the virtual reality-based treadmill training. Walking speed, community walking time, walking ability questionnaire (WAQ), and activities-specific balance confidence (ABC) scale were evaluated. Subjects in the experimental group improved significantly in walking speed, community walking time, and WAQ score at posttraining and 1-month follow-up periods. Their ABC score also significantly increased at posttraining but did not maintain at follow-up period. Regarding the between-group comparisons, the experimental group improved significantly more than control group in walking speed (P=0.03) and community walking time (P=0.04) at posttraining period and in WAQ score (P=0.03) at follow-up period. Our results support the perceived benefits of gait training programs that incorporate virtual reality to augment the community ambulation of individuals with stroke.

A continuous time random walk (CTRW) integro-differential equation with chemical interaction

NASA Astrophysics Data System (ADS)

Ben-Zvi, Rami; Nissan, Alon; Scher, Harvey; Berkowitz, Brian

2018-01-01

A nonlocal-in-time integro-differential equation is introduced that accounts for close coupling between transport and chemical reaction terms. The structure of the equation contains these terms in a single convolution with a memory function M ( t), which includes the source of non-Fickian (anomalous) behavior, within the framework of a continuous time random walk (CTRW). The interaction is non-linear and second-order, relevant for a bimolecular reaction A + B → C. The interaction term ΓP A ( s, t) P B ( s, t) is symmetric in the concentrations of A and B (i.e. P A and P B ); thus the source terms in the equations for A, B and C are similar, but with a change in sign for that of C. Here, the chemical rate coefficient, Γ, is constant. The fully coupled equations are solved numerically using a finite element method (FEM) with a judicious representation of M ( t) that eschews the need for the entire time history, instead using only values at the former time step. To begin to validate the equations, the FEM solution is compared, in lieu of experimental data, to a particle tracking method (CTRW-PT); the results from the two approaches, particularly for the C profiles, are in agreement. The FEM solution, for a range of initial and boundary conditions, can provide a good model for reactive transport in disordered media.

Anomalous diffusion on a random comblike structure

NASA Astrophysics Data System (ADS)

Havlin, Shlomo; Kiefer, James E.; Weiss, George H.

1987-08-01

We have recently studied a random walk on a comblike structure as an analog of diffusion on a fractal structure. In our earlier work, the comb was assumed to have a deterministic structure, the comb having teeth of infinite length. In the present paper we study diffusion on a one-dimensional random comb, the length of whose teeth are random variables with an asymptotic stable law distribution φ(L)~L-(1+γ) where 0<γ<=1. Two mean-field methods are used for the analysis, one based on the continuous-time random walk, and the second a self-consistent scaling theory. Both lead to the same conclusions. We find that the diffusion exponent characterizing the mean-square displacement along the backbone of the comb is dw=4/(1+γ) for γ<1 and dw=2 for γ>=1. The probability of being at the origin at time t is P0(t)~t-ds/2 for large t with ds=(3-γ)/2 for γ<1 and ds=1 for γ>1. When a field is applied along the backbone of the comb the diffusion exponent is dw=2/(1+γ) for γ<1 and dw=1 for γ>=1. The theoretical results are confirmed using the exact enumeration method.

Real time visualization of quantum walk

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miyazaki, Akihide; Hamada, Shinji; Sekino, Hideo

2014-02-20

Time evolution of quantum particles like electrons is described by time-dependent Schrödinger equation (TDSE). The TDSE is regarded as the diffusion equation of electrons with imaginary diffusion coefficients. And the TDSE is solved by quantum walk (QW) which is regarded as a quantum version of a classical random walk. The diffusion equation is solved in discretized space/time as in the case of classical random walk with additional unitary transformation of internal degree of freedom typical for quantum particles. We call the QW for solution of the TDSE a Schrödinger walk (SW). For observation of one quantum particle evolution under amore » given potential in atto-second scale, we attempt a successive computation and visualization of the SW. Using Pure Data programming, we observe the correct behavior of a probability distribution under the given potential in real time for observers of atto-second scale.« less

Movement measurements at home for multiple sclerosis: walking speed measured by a novel ambient measurement system.

PubMed

Smith, Victoria Mj; Varsanik, Jonathan S; Walker, Rachel A; Russo, Andrew W; Patel, Kevin R; Gabel, Wendy; Phillips, Glenn A; Kimmel, Zebadiah M; Klawiter, Eric C

2018-01-01

Gait disturbance is a major contributor to clinical disability in multiple sclerosis (MS). A sensor was developed to assess walking speed at home for people with MS using infrared technology in real-time without the use of wearables. To develop continuous in-home outcome measures to assess gait in adults with MS. Movement measurements were collected continuously for 8 months from six people with MS. Average walking speed and peak walking speed were calculated from movement data, then analyzed for variability over time, by room (location), and over the course of the day. In-home continuous gait outcomes and variability were correlated with standard in-clinic gait outcomes. Measured in-home average walking speed of participants ranged from 0.33 m/s to 0.96 m/s and peak walking speed ranged from 0.89 m/s to 1.51 m/s. Mean total within-participant coefficient of variation for daily average walking speed and peak walking speed were 10.75% and 10.93%, respectively. Average walking speed demonstrated a moderately strong correlation with baseline Timed 25-Foot Walk (r s  = 0.714, P  = 0.111). New non-wearable technology provides reliable and continuous in-home assessment of walking speed.

A scaling law for random walks on networks

PubMed Central

Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-01-01

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics. PMID:25311870

A scaling law for random walks on networks

NASA Astrophysics Data System (ADS)

Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-10-01

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

A scaling law for random walks on networks.

PubMed

Perkins, Theodore J; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-10-14

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

Return probabilities and hitting times of random walks on sparse Erdös-Rényi graphs.

PubMed

Martin, O C; Sulc, P

2010-03-01

We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdös-Rényi graphs. Using the tree approach, which is expected to be exact in the large graph limit, we show how to solve for the distribution of these quantities and we find that these distributions exhibit a form of self-similarity.

SIRRACT: An international randomized clinical trial of activity feedback during inpatient stroke rehabilitation enabled by wireless sensing

PubMed Central

Dorsch, Andrew K.; Thomas, Seth; Xu, Xiaoyu; Kaiser, William; Dobkin, Bruce H.

2014-01-01

Background Walking-related disability is the most frequent reason for inpatient stroke rehabilitation. Task-related practice is a critical component for improving patient outcomes. Objective To test the feasibility of providing quantitative feedback about daily walking performance and motivating greater skills practice via remote sensing. Methods In this phase III randomized, single blind clinical trial, patients participated in conventional therapies while wearing wireless sensors (tri-axial accelerometers) at both ankles. Activity-recognition algorithms calculated the speed, distance, and duration of walking bouts. Three times a week, therapists provided either feedback about performance on a 10-meter walk (speed-only) or walking speed feedback plus a review of walking activity recorded by the sensors (augmented). Primary outcomes at discharge included total daily walking time, derived from the sensors, and a timed 15-meter walk. Results Sixteen rehabilitation centers in 11 countries enrolled 135 participants over 15 months. Sensors recorded more than 1800 days of therapy, 37,000 individual walking bouts, and 2.5 million steps. No significant differences were found between the two feedback groups in daily walking time (15.1±13.1min vs. 16.6±14.3min, p=0.54) or 15-meter walking speed (0.93±0.47m/s vs. 0.91±0.53m/s, p=0.96). Remarkably, 30% of participants decreased their total daily walking time over their rehabilitation stay. Conclusions In this first trial of remote monitoring of inpatient stroke rehabilitation, augmented feedback beyond speed alone did not increase the time spent practicing or improve walking outcomes. Remarkably modest time was spent walking. Wireless sensing, however, allowed clinicians to audit skills practice and provided ground truth regarding changes in clinically important, mobility-related activities. PMID:25261154

An Examination of Models of Relaxation in Complex Systems. I. Continuous Time Random Walk (CTRW) Models.

DTIC Science & Technology

1986-02-04

Laberge , Phys. Chem. Glasses 14, 122 (1973); F.S. Howell, R. Bose, P.B. Macedo and C.T. Moynihan, J. Phys. Chem. 78, 639 (1974). 30. K.L. Ngai, R.W...J.R. Stevens , J. Polym. Sci.: Polym. Phys. Ed. 17, 1547 (1979); 21, 605 (1983). 41. For Polyethyl acrylate (PEA) see G. Williams and D.C. Watts in

Modelling nematode movement using time-fractional dynamics.

PubMed

Hapca, Simona; Crawford, John W; MacMillan, Keith; Wilson, Mike J; Young, Iain M

2007-09-07

We use a correlated random walk model in two dimensions to simulate the movement of the slug parasitic nematode Phasmarhabditis hermaphrodita in homogeneous environments. The model incorporates the observed statistical distributions of turning angle and speed derived from time-lapse studies of individual nematode trails. We identify strong temporal correlations between the turning angles and speed that preclude the case of a simple random walk in which successive steps are independent. These correlated random walks are appropriately modelled using an anomalous diffusion model, more precisely using a fractional sub-diffusion model for which the associated stochastic process is characterised by strong memory effects in the probability density function.

The scaling law of human travel - A message from George

NASA Astrophysics Data System (ADS)

Brockmann, Dirk; Hufnagel, Lars

The dispersal of individuals of a species is the key driving force of various spatiotemporal phenomena which occur on geographical scales. It can synchronize populations of interacting species, stabilize them, and diversify gene pools.1-3 The geographic spread of human infectious diseases such as influenza, measles and the recent severe acute respiratory syndrome (SARS) is essentially promoted by human travel which occurs on many length scales and is sustained by a variety of means of trans-portation4-8. In the light of increasing international trade, intensified human traffic, and an imminent influenza A pandemic the knowledge of dynamical and statistical properties of human dispersal is of fundamental importance and acute. 7,9,10 A quantitative statistical theory for human travel and concomitant reliable forecasts would substantially improve and extend existing prevention strategies. Despite its crucial role, a quantitative assessment of human dispersal remains elusive and the opinion that humans disperse diffusively still prevails in many models. 11 In this chapter we will report on a recently developed technique which permits a solid and quantitative assessment of human dispersal on geographical scales.12 The key idea is to infer the statistical properties of human travel by analysing the geographic circulation of individual bank notes for which comprehensive datasets are collected at online bill-tracking websites. The analysis shows that the distribution of traveling distances decays as a power law, indicating that the movement of bank notes is reminiscent of superdiffusive, scale free random walks known as Lévy flights.13 Secondly, the probability of remaining in a small, spatially confined region for a time T is dominated by heavy tails which attenuate superdiffusive dispersal. We will show that the dispersal of bank notes can be described on many spatiotemporal scales by a two parameter continuous time random walk (CTRW) model to a surprising accuracy. We will provide a brief introduction to continuous time random walk theory14 and will show that human disperal is an ambivalent, effectively superdiffusive process.

Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium.

PubMed

Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

2013-11-05

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Logical-Rule Models of Classification Response Times: A Synthesis of Mental-Architecture, Random-Walk, and Decision-Bound Approaches

ERIC Educational Resources Information Center

Fific, Mario; Little, Daniel R.; Nosofsky, Robert M.

2010-01-01

We formalize and provide tests of a set of logical-rule models for predicting perceptual classification response times (RTs) and choice probabilities. The models are developed by synthesizing mental-architecture, random-walk, and decision-bound approaches. According to the models, people make independent decisions about the locations of stimuli…

Emergence of Lévy Walks from Second-Order Stochastic Optimization

NASA Astrophysics Data System (ADS)

Kuśmierz, Łukasz; Toyoizumi, Taro

2017-12-01

In natural foraging, many organisms seem to perform two different types of motile search: directed search (taxis) and random search. The former is observed when the environment provides cues to guide motion towards a target. The latter involves no apparent memory or information processing and can be mathematically modeled by random walks. We show that both types of search can be generated by a common mechanism in which Lévy flights or Lévy walks emerge from a second-order gradient-based search with noisy observations. No explicit switching mechanism is required—instead, continuous transitions between the directed and random motions emerge depending on the Hessian matrix of the cost function. For a wide range of scenarios, the Lévy tail index is α =1 , consistent with previous observations in foraging organisms. These results suggest that adopting a second-order optimization method can be a useful strategy to combine efficient features of directed and random search.

Game story space of professional sports: Australian rules football

NASA Astrophysics Data System (ADS)

Kiley, Dilan Patrick; Reagan, Andrew J.; Mitchell, Lewis; Danforth, Christopher M.; Dodds, Peter Sheridan

2016-05-01

Sports are spontaneous generators of stories. Through skill and chance, the script of each game is dynamically written in real time by players acting out possible trajectories allowed by a sport's rules. By properly characterizing a given sport's ecology of "game stories," we are able to capture the sport's capacity for unfolding interesting narratives, in part by contrasting them with random walks. Here we explore the game story space afforded by a data set of 1310 Australian Football League (AFL) score lines. We find that AFL games exhibit a continuous spectrum of stories rather than distinct clusters. We show how coarse graining reveals identifiable motifs ranging from last-minute comeback wins to one-sided blowouts. Through an extensive comparison with biased random walks, we show that real AFL games deliver a broader array of motifs than null models, and we provide consequent insights into the narrative appeal of real games.

Simulating transient dynamics of the time-dependent time fractional Fokker-Planck systems

NASA Astrophysics Data System (ADS)

Kang, Yan-Mei

2016-09-01

For a physically realistic type of time-dependent time fractional Fokker-Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker-Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed.

Exits in order: How crowding affects particle lifetimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Penington, Catherine J.; Simpson, Matthew J.; Baker, Ruth E.

2016-06-28

Diffusive processes are often represented using stochastic random walk frameworks. The amount of time taken for an individual in a random walk to intersect with an absorbing boundary is a fundamental property that is often referred to as the particle lifetime, or the first passage time. The mean lifetime of particles in a random walk model of diffusion is related to the amount of time required for the diffusive process to reach a steady state. Mathematical analysis describing the mean lifetime of particles in a standard model of diffusion without crowding is well known. However, the lifetime of agents inmore » a random walk with crowding has received much less attention. Since many applications of diffusion in biology and biophysics include crowding effects, here we study a discrete model of diffusion that incorporates crowding. Using simulations, we show that crowding has a dramatic effect on agent lifetimes, and we derive an approximate expression for the mean agent lifetime that includes crowding effects. Our expression matches simulation results very well, and highlights the importance of crowding effects that are sometimes overlooked.« less

The Locomotion of Mouse Fibroblasts in Tissue Culture

PubMed Central

Gail, Mitchell H.; Boone, Charles W.

1970-01-01

Time-lapse cinematography was used to investigate the motion of mouse fibroblasts in tissue culture. Observations over successive short time intervals revealed a tendency for the cells to persist in their direction of motion from one 2.5 hr time interval to the next. Over 5.0-hr time intervals, however, the direction of motion appeared random. This fact suggested that D, the diffusion constant of a random walk model, might serve to characterize cellular motility if suitably long observation times were used. We therefore investigated the effect of “persistence” on the pure random walk model, and we found theoretically and confirmed experimentally that the motility of a persisting cell could indeed be characterized by an augmented diffusion constant, D*. A method for determining confidence limits on D* was also developed. Thus a random walk model, modified to comprehend the persistence effect, was found to describe the motion of fibroblasts in tissue culture and to provide a numerical measure of cellular motility. PMID:5531614

Use of Accelerometer-Based Feedback of Walking Activity for Appraising Progress With Walking-Related Goals in Inpatient Stroke Rehabilitation: A Randomized Controlled Trial.

PubMed

Mansfield, Avril; Wong, Jennifer S; Bryce, Jessica; Brunton, Karen; Inness, Elizabeth L; Knorr, Svetlana; Jones, Simon; Taati, Babak; McIlroy, William E

2015-10-01

Regaining independent ambulation is important to those with stroke. Increased walking practice during "down time" in rehabilitation could improve walking function for individuals with stroke. To determine the effect of providing physiotherapists with accelerometer-based feedback on patient activity and walking-related goals during inpatient stroke rehabilitation. Participants with stroke wore accelerometers around both ankles every weekday during inpatient rehabilitation. Participants were randomly assigned to receive daily feedback about walking activity via their physiotherapists (n = 29) or to receive no feedback (n = 28). Changes in measures of daily walking (walking time, number of steps, average cadence, longest bout duration, and number of "long" walking bouts) and changes in gait control and function assessed in-laboratory were compared between groups. There was no significant increase in walking time, number of steps, longest bout duration, or number of long walking bouts for the feedback group compared with the control group (P values > .20). However, individuals who received feedback significantly increased cadence of daily walking more than the control group (P = .013). From the in-laboratory gait assessment, individuals who received feedback had a greater increase in walking speed and decrease in step time variability than the control group (P values < .030). Feedback did not increase the amount of walking completed by individuals with stroke. However, there was a significant increase in cadence, indicating that intensity of daily walking was greater for those who received feedback than the control group. Additionally, more intense daily walking activity appeared to translate to greater improvements in walking speed. © The Author(s) 2015.

Random walk study of electron motion in helium in crossed electromagnetic fields

NASA Technical Reports Server (NTRS)

Englert, G. W.

1972-01-01

Random walk theory, previously adapted to electron motion in the presence of an electric field, is extended to include a transverse magnetic field. In principle, the random walk approach avoids mathematical complexity and concomitant simplifying assumptions and permits determination of energy distributions and transport coefficients within the accuracy of available collisional cross section data. Application is made to a weakly ionized helium gas. Time of relaxation of electron energy distribution, determined by the random walk, is described by simple expressions based on energy exchange between the electron and an effective electric field. The restrictive effect of the magnetic field on electron motion, which increases the required number of collisions per walk to reach a terminal steady state condition, as well as the effect of the magnetic field on electron transport coefficients and mean energy can be quite adequately described by expressions involving only the Hall parameter.

Noteworthy fractal features and transport properties of Cantor tartans

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.; Golmankhaneh, Alireza K.; Patiño-Ortiz, Julián; Patiño-Ortiz, Miguel

2018-06-01

This Letter is focused on the impact of fractal topology on the transport processes governed by different kinds of random walks on Cantor tartans. We establish that the spectral dimension of the infinitely ramified Cantor tartan ds is equal to its fractal (self-similarity) dimension D. Consequently, the random walk on the Cantor tartan leads to a normal diffusion. On the other hand, the fractal geometry of Cantor tartans allows for a natural definition of power-law distributions of the waiting times and step lengths of random walkers. These distributions are Lévy stable if D > 1.5. Accordingly, we found that the random walk with rests leads to sub-diffusion, whereas the Lévy walk leads to ballistic diffusion. The Lévy walk with rests leads to super-diffusion, if D >√{ 3 }, or sub-diffusion, if 1.5 < D <√{ 3 }.

A New Method of Random Environmental Walking for Assessing Behavioral Preferences for Different Lighting Applications

PubMed Central

Patching, Geoffrey R.; Rahm, Johan; Jansson, Märit; Johansson, Maria

2017-01-01

Accurate assessment of people’s preferences for different outdoor lighting applications is increasingly considered important in the development of new urban environments. Here a new method of random environmental walking is proposed to complement current methods of assessing urban lighting applications, such as self-report questionnaires. The procedure involves participants repeatedly walking between different lighting applications by random selection of a lighting application and preferred choice or by random selection of a lighting application alone. In this manner, participants are exposed to all lighting applications of interest more than once and participants’ preferences for the different lighting applications are reflected in the number of times they walk to each lighting application. On the basis of an initial simulation study, to explore the feasibility of this approach, a comprehensive field test was undertaken. The field test included random environmental walking and collection of participants’ subjective ratings of perceived pleasantness (PP), perceived quality, perceived strength, and perceived flicker of four lighting applications. The results indicate that random environmental walking can reveal participants’ preferences for different lighting applications that, in the present study, conformed to participants’ ratings of PP and perceived quality of the lighting applications. As a complement to subjectively stated environmental preferences, random environmental walking has the potential to expose behavioral preferences for different lighting applications. PMID:28337163

Global mean first-passage times of random walks on complex networks.

PubMed

Tejedor, V; Bénichou, O; Voituriez, R

2009-12-01

We present a general framework, applicable to a broad class of random walks on complex networks, which provides a rigorous lower bound for the mean first-passage time of a random walker to a target site averaged over its starting position, the so-called global mean first-passage time (GMFPT). This bound is simply expressed in terms of the equilibrium distribution at the target and implies a minimal scaling of the GMFPT with the network size. We show that this minimal scaling, which can be arbitrarily slow, is realized under the simple condition that the random walk is transient at the target site and independently of the small-world, scale-free, or fractal properties of the network. Last, we put forward that the GMFPT to a specific target is not a representative property of the network since the target averaged GMFPT satisfies much more restrictive bounds.

Covering Ground: Movement Patterns and Random Walk Behavior in Aquilonastra anomala Sea Stars.

PubMed

Lohmann, Amanda C; Evangelista, Dennis; Waldrop, Lindsay D; Mah, Christopher L; Hedrick, Tyson L

2016-10-01

The paths animals take while moving through their environments affect their likelihood of encountering food and other resources; thus, models of foraging behavior abound. To collect movement data appropriate for comparison with these models, we used time-lapse photography to track movements of a small, hardy, and easy-to-obtain organism, Aquilonastra anomala sea stars. We recorded the sea stars in a tank over many hours, with and without a food cue. With food present, they covered less distance, as predicted by theory; this strategy would allow them to remain near food. We then compared the paths of the sea stars to three common models of animal movement: Brownian motion, Lévy walks, and correlated random walks; we found that the sea stars' movements most closely resembled a correlated random walk. Additionally, we compared the search performance of models of Brownian motion, a Lévy walk, and a correlated random walk to that of a model based on the sea stars' movements. We found that the behavior of the modeled sea star walk was similar to that of the modeled correlated random walk and the Brownian motion model, but that the sea star walk was slightly more likely than the other walks to find targets at intermediate distances. While organisms are unlikely to follow an idealized random walk in all details, our data suggest that comparing the effectiveness of an organism's paths to those from theory can give insight into the organism's actual movement strategy. Finally, automated optical tracking of invertebrates proved feasible, and A. anomala was revealed to be a tractable, 2D-movement study system.

Home-based walking during pregnancy affects mood and birth outcomes among sedentary women: A randomized controlled trial.

PubMed

Taniguchi, Chie; Sato, Chifumi

2016-10-01

We examined the effects of home-based walking on sedentary Japanese women's pregnancy outcomes and mood. A randomized controlled trial was conducted, involving 118 women aged 22-36 years. Participants were randomly assigned to walking intervention (n = 60) or control (n = 58) groups. The walking group was instructed to walk briskly for 30 min, three times weekly from 30 weeks' gestation until delivery. Both groups counted their daily steps using pedometers. Pregnancy and delivery outcomes were assessed, participants completed the Profile of Mood States, and we used the intention-to-treat principle. Groups showed no differences regarding pregnancy or delivery outcomes. The walking group exhibited decreased scores on the depression-dejection and confusion subscales of the Profile of Mood States. Five of the 54 women in the intervention group who remained in the study (9.2%) completed 100% of the prescribed walking program; 32 (59.3%) women completed 80% or more. Unsupervised walking improves sedentary pregnant women's mood, indicating that regular walking during pregnancy should be promoted in this group. © 2016 John Wiley & Sons Australia, Ltd.

PoleStriding exercise and vitamin E for management of peripheral vascular disease.

PubMed

Collins, Eileen G; Edwin Langbein, W; Orebaugh, Cynthia; Bammert, Christine; Hanson, Karla; Reda, Domenic; Edwards, Lonnie C; Littooy, Fred N

2003-03-01

The purpose of this investigation was to evaluate the efficacy of PoleStriding exercise (a form of walking that uses muscles of the upper and lower body in a continuous movement similar to cross-country skiing) and vitamin E (alpha-tocopherol) to improve walking ability and perceived quality of life (QOL) of patients with claudication pain secondary to peripheral arterial disease (PAD). Fifty-two subjects were randomized into four groups: PoleStriding with vitamin E (N = 13), PoleStriding with placebo (N= 14), vitamin E without exercise (N= 13), and placebo without exercise (N = 12). The dose of vitamin E was 400 IU daily. Only the PoleStriding with vitamin E and PoleStriding with placebo groups received PoleStriding instruction and training. Assignment to vitamin E or placebo was double blind. Subjects trained three times weekly for 30-45 min (rest time excluded). Individuals in vitamin E and placebo groups came to the laboratory biweekly for ankle blood-pressure measurements. Results of this randomized clinical trial provide strong evidence that PoleStriding significantly (P< 0.001) improved exercise tolerance on the constant work-rate and incremental treadmill tests. Ratings of perceived claudication pain were significantly less after the PoleStriding training program (P= 0.02). In contrast, vitamin E did not have a statistically significant effect on the subjects' ratings of perceived leg pain (P= 0.35) or treadmill walking duration ( P= 0.36). Perceived distance and walking speed (Walking Impairment Questionnaire) and perceived physical function (Rand Short Form-36) improved in the PoleStriding trained group only (P< 0.001, 0.022 and 0.003, respectively). PoleStriding effectively improved the exercise tolerance and perceived QOL of patients with PAD. Little additional benefit to exercise capacity was realized from vitamin E supplementation.

Comparison of the Effect of Lateral and Backward Walking Training on Walking Function in Patients with Poststroke Hemiplegia: A Pilot Randomized Controlled Trial.

PubMed

Kim, Chang-Yong; Lee, Jung-Sun; Kim, Hyeong-Dong

2017-02-01

The purposes of the present study were to compare the effects of backward and lateral walking training and to identify whether additional backward or lateral walking training would be more effective in increasing the walking function of poststroke patients. Fifty-one subjects with hemiplegic stroke were randomly allocated to 3 groups, each containing 17 subjects: the control group, the backward walking training group, and the lateral walking training group. The walking abilities of each group were assessed using a 10-m walk test and the GAITRite system for spatiotemporal gait. The results show that there were significantly greater posttest increases in gait velocity (F = -12.09, P = 0.02) and stride length (F = -11.50, P = 0.02), decreases in the values of the 10-m walk test (F = -7.10, P = 0.03) (P < 0.05) and double-limb support period (F = 40.15, P = 0.000), and improvements in gait asymmetry (F = 13.88, P = 0.002) (P < 0.01) in subjects in the lateral walking training group compared with those in the other 2 groups. These findings demonstrate that asymmetric gait patterns in poststroke patients could be improved by receiving additional lateral walking training therapy rather than backward walking training. Complete the self-assessment activity and evaluation online at http://www.physiatry.org/JournalCME CME OBJECTIVES: Upon completion of this article, the reader should be able to: (1) understand the potential benefits of backward walking (BW) and lateral walking (LW) training on improving muscle strength and gait; (2) appreciate the potential value of backward and lateral walking gait training in the treatment of hemiplegic stroke patients; and (3) appropriately incorporate backward and lateral walking gait training into the treatment plan of hemiplegic stroke patients. Advanced ACCREDITATION: The Association of Academic Physiatrists is accredited by the Accreditation Council for Continuing Medical Education to provide continuing medical education for physicians.The Association of Academic Physiatrists designates this activity for a maximum of 1.5 AMA PRA Category 1 Credit(s)™. Physicians should only claim credit commensurate with the extent of their participation in the activity.

Numerical Simulation of the Anomalous Transport of High-Energy Cosmic Rays in Galactic Superbubble

NASA Technical Reports Server (NTRS)

Barghouty, A. F.; Price, E. M.; MeWaldt, R. A.

2013-01-01

A continuous-time random-walk (CTRW) model to simulate the transport and acceleration of high-energy cosmic rays in galactic superbubbles has recently been put forward (Barghouty & Schnee 2102). The new model has been developed to simulate and highlight signatures of anomalous transport on particles' evolution and their spectra in a multi-shock, collective acceleration context. The superbubble is idealized as a heterogeneous region of particle sources and sinks bounded by a random surface. This work concentrates on the effects of the bubble's assumed astrophysical characteristics (cf. geometry and roughness) on the particles' spectra.

The First Order Correction to the Exit Distribution for Some Random Walks

NASA Astrophysics Data System (ADS)

Kennedy, Tom

2016-07-01

We study three different random walk models on several two-dimensional lattices by Monte Carlo simulations. One is the usual nearest neighbor random walk. Another is the nearest neighbor random walk which is not allowed to backtrack. The final model is the smart kinetic walk. For all three of these models the distribution of the point where the walk exits a simply connected domain D in the plane converges weakly to harmonic measure on partial D as the lattice spacing δ → 0. Let ω (0,\\cdot ;D) be harmonic measure for D, and let ω _δ (0,\\cdot ;D) be the discrete harmonic measure for one of the random walk models. Our definition of the random walk models is unusual in that we average over the orientation of the lattice with respect to the domain. We are interested in the limit of (ω _δ (0,\\cdot ;D)- ω (0,\\cdot ;D))/δ . Our Monte Carlo simulations of the three models lead to the conjecture that this limit equals c_{M,L} ρ _D(z) times Lebesgue measure with respect to arc length along the boundary, where the function ρ _D(z) depends on the domain, but not on the model or lattice, and the constant c_{M,L} depends on the model and on the lattice, but not on the domain. So there is a form of universality for this first order correction. We also give an explicit formula for the conjectured density ρ _D.

A physical activity program to mobilize older people: a practical and sustainable approach.

PubMed

Jancey, Jonine M; Clarke, Ann; Howat, Peter A; Lee, Andy H; Shilton, Trevor; Fisher, John

2008-04-01

Despite the documented benefits of physical activity, it remains difficult to motivate older adults to start and maintain regular physical activity. This study tested an innovative intervention for mobilizing older adults into a neighborhood-based walking program. Researchers recruited a total of 260 healthy but insufficiently active adults aged 65 to 74 years and randomly selected from the Australian electoral roll from 30 Perth metropolitan neighborhoods. Social cognitive theory guided the design of the program. Researchers collected both qualitative and quantitative data to inform the development, together with ongoing process evaluation. A total of 65% of participants completed the program. Their mean weekly walking time for recreation increased by about 100 min, and 80% of participants reported that they would continue to walk twice per week upon program completion. This practical program is potentially effective and sustainable with respect to mobilizing physically inactive older people.

Simulating Pre-Asymptotic, Non-Fickian Transport Although Doing Simple Random Walks - Supported By Empirical Pore-Scale Velocity Distributions and Memory Effects

NASA Astrophysics Data System (ADS)

Most, S.; Jia, N.; Bijeljic, B.; Nowak, W.

2016-12-01

Pre-asymptotic characteristics are almost ubiquitous when analyzing solute transport processes in porous media. These pre-asymptotic aspects are caused by spatial coherence in the velocity field and by its heterogeneity. For the Lagrangian perspective of particle displacements, the causes of pre-asymptotic, non-Fickian transport are skewed velocity distribution, statistical dependencies between subsequent increments of particle positions (memory) and dependence between the x, y and z-components of particle increments. Valid simulation frameworks should account for these factors. We propose a particle tracking random walk (PTRW) simulation technique that can use empirical pore-space velocity distributions as input, enforces memory between subsequent random walk steps, and considers cross dependence. Thus, it is able to simulate pre-asymptotic non-Fickian transport phenomena. Our PTRW framework contains an advection/dispersion term plus a diffusion term. The advection/dispersion term produces time-series of particle increments from the velocity CDFs. These time series are equipped with memory by enforcing that the CDF values of subsequent velocities change only slightly. The latter is achieved through a random walk on the axis of CDF values between 0 and 1. The virtual diffusion coefficient for that random walk is our only fitting parameter. Cross-dependence can be enforced by constraining the random walk to certain combinations of CDF values between the three velocity components in x, y and z. We will show that this modelling framework is capable of simulating non-Fickian transport by comparison with a pore-scale transport simulation and we analyze the approach to asymptotic behavior.

The effect of walking on falls in older people: the 'Easy Steps to Health' randomized controlled trial study protocol

PubMed Central

2011-01-01

Background Falls in older people continue to be a major public health issue in industrialized countries. Extensive research into falls prevention has identified exercise as a proven fall prevention strategy. However, despite over a decade of promoting physical activity, hospitalisation rates due to falls injuries in older people are still increasing. This could be because efforts to increase physical activity amongst older people have been unsuccessful, or the physical activity that older people engage in is insufficient and/or inappropriate. The majority of older people choose walking as their predominant form of exercise. While walking has been shown to lower the risk of many chronic diseases its role in falls prevention remains unclear. This paper outlines the methodology of a study whose aims are to determine: if a home-based walking intervention will reduce the falls rate among healthy but inactive community-dwelling older adults (65 + years) compared to no intervention (usual activity) and; whether such an intervention can improve risk factors for falls, such as balance, strength and reaction time. Methods/Design This study uses a randomised controlled trial design. A total of 484 older people exercising less than 120 minutes per week will be recruited through the community and health care referrals throughout Sydney and neighboring regions. All participants are randomised into either the self-managed walking program group or the health-education waiting list group using a block randomization scheme. Outcome measures include prospective falls and falls injuries, quality of life, and physical activity levels. A subset of participants (n = 194) will also receive physical performance assessments comprising of tests of dynamic balance, strength, reaction time and lower limb functional status. Discussion Certain types of physical activity can reduce the risk of falls. As walking is already the most popular physical activity amongst older people, if walking is shown to reduce falls the public health implications could be enormous. Conversely, if walking does not reduce falls in older people, or even puts older people at greater risk, then health resources targeting falls prevention need to be invested elsewhere. Trial Registration Australia and New Zealand Clinical Trials Register (ANZCTR): ACTRN12610000380099 PMID:22115340

The effect of walking on falls in older people: the 'Easy Steps to Health' randomized controlled trial study protocol.

PubMed

Voukelatos, Alexander; Merom, Dafna; Rissel, Chris; Sherrington, Cathie; Watson, Wendy; Waller, Karen

2011-11-24

Falls in older people continue to be a major public health issue in industrialized countries. Extensive research into falls prevention has identified exercise as a proven fall prevention strategy. However, despite over a decade of promoting physical activity, hospitalisation rates due to falls injuries in older people are still increasing. This could be because efforts to increase physical activity amongst older people have been unsuccessful, or the physical activity that older people engage in is insufficient and/or inappropriate. The majority of older people choose walking as their predominant form of exercise. While walking has been shown to lower the risk of many chronic diseases its role in falls prevention remains unclear. This paper outlines the methodology of a study whose aims are to determine: if a home-based walking intervention will reduce the falls rate among healthy but inactive community-dwelling older adults (65 + years) compared to no intervention (usual activity) and; whether such an intervention can improve risk factors for falls, such as balance, strength and reaction time. This study uses a randomised controlled trial design.A total of 484 older people exercising less than 120 minutes per week will be recruited through the community and health care referrals throughout Sydney and neighboring regions. All participants are randomised into either the self-managed walking program group or the health-education waiting list group using a block randomization scheme.Outcome measures include prospective falls and falls injuries, quality of life, and physical activity levels. A subset of participants (n = 194) will also receive physical performance assessments comprising of tests of dynamic balance, strength, reaction time and lower limb functional status. Certain types of physical activity can reduce the risk of falls. As walking is already the most popular physical activity amongst older people, if walking is shown to reduce falls the public health implications could be enormous. Conversely, if walking does not reduce falls in older people, or even puts older people at greater risk, then health resources targeting falls prevention need to be invested elsewhere. Australia and New Zealand Clinical Trials Register (ANZCTR): ACTRN12610000380099.

A Random Walk Approach to Query Informative Constraints for Clustering.

PubMed

Abin, Ahmad Ali

2017-08-09

This paper presents a random walk approach to the problem of querying informative constraints for clustering. The proposed method is based on the properties of the commute time, that is the expected time taken for a random walk to travel between two nodes and return, on the adjacency graph of data. Commute time has the nice property of that, the more short paths connect two given nodes in a graph, the more similar those nodes are. Since computing the commute time takes the Laplacian eigenspectrum into account, we use this property in a recursive fashion to query informative constraints for clustering. At each recursion, the proposed method constructs the adjacency graph of data and utilizes the spectral properties of the commute time matrix to bipartition the adjacency graph. Thereafter, the proposed method benefits from the commute times distance on graph to query informative constraints between partitions. This process iterates for each partition until the stop condition becomes true. Experiments on real-world data show the efficiency of the proposed method for constraints selection.

A random walk rule for phase I clinical trials.

PubMed

Durham, S D; Flournoy, N; Rosenberger, W F

1997-06-01

We describe a family of random walk rules for the sequential allocation of dose levels to patients in a dose-response study, or phase I clinical trial. Patients are sequentially assigned the next higher, same, or next lower dose level according to some probability distribution, which may be determined by ethical considerations as well as the patient's response. It is shown that one can choose these probabilities in order to center dose level assignments unimodally around any target quantile of interest. Estimation of the quantile is discussed; the maximum likelihood estimator and its variance are derived under a two-parameter logistic distribution, and the maximum likelihood estimator is compared with other nonparametric estimators. Random walk rules have clear advantages: they are simple to implement, and finite and asymptotic distribution theory is completely worked out. For a specific random walk rule, we compute finite and asymptotic properties and give examples of its use in planning studies. Having the finite distribution theory available and tractable obviates the need for elaborate simulation studies to analyze the properties of the design. The small sample properties of our rule, as determined by exact theory, compare favorably to those of the continual reassessment method, determined by simulation.

Human mammary epithelial cells exhibit a bimodal correlated random walk pattern.

PubMed

Potdar, Alka A; Jeon, Junhwan; Weaver, Alissa M; Quaranta, Vito; Cummings, Peter T

2010-03-10

Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells) that exist in multi-cellular organisms (humans) follow a bimodal correlated random walk (BCRW). Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases) each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation). Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.

Increasing older adults’ walking through primary care: results of a pilot randomized controlled trial

PubMed Central

Mutrie, Nanette

2012-01-01

Background. Physical activity can positively influence health for older adults. Primary care is a good setting for physical activity promotion. Objective. To assess the feasibility of a pedometer-based walking programme in combination with physical activity consultations. Methods. Design: Two-arm (intervention/control) 12-week randomized controlled trial with a 12-week follow-up for the intervention group. Setting: One general practice in Glasgow, UK. Participants: Participants were aged ≥65 years. The intervention group received two 30-minute physical activity consultations from a trained practice nurse, a pedometer and a walking programme. The control group continued as normal for 12 weeks and then received the intervention. Both groups were followed up at 12 and 24 weeks. Outcome measures: Step counts were measured by sealed pedometers and an activPALTM monitor. Psychosocial variables were assessed and focus groups conducted. Results. The response rate was 66% (187/284), and 90% of those randomized (37/41) completed the study. Qualitative data suggested that the pedometer and nurse were helpful to the intervention. Step counts (activPAL) showed a significant increase from baseline to week 12 for the intervention group, while the control group showed no change. Between weeks 12 and 24, step counts were maintained in the intervention group, and increased for the control group after receiving the intervention. The intervention was associated with improved quality of life and reduced sedentary time. Conclusions. It is feasible to recruit and retain older adults from primary care and help them increase walking. A larger trial is necessary to confirm findings and consider cost-effectiveness. PMID:22843637

Randomized Trial of Intelligent Sensor System for Early Illness Alerts in Senior Housing.

PubMed

Rantz, Marilyn; Phillips, Lorraine J; Galambos, Colleen; Lane, Kari; Alexander, Gregory L; Despins, Laurel; Koopman, Richelle J; Skubic, Marjorie; Hicks, Lanis; Miller, Steven; Craver, Andy; Harris, Bradford H; Deroche, Chelsea B

2017-10-01

Measure the clinical effectiveness and cost effectiveness of using sensor data from an environmentally embedded sensor system for early illness recognition. This sensor system has demonstrated in pilot studies to detect changes in function and in chronic diseases or acute illnesses on average 10 days to 2 weeks before usual assessment methods or self-reports of illness. Prospective intervention study in 13 assisted living (AL) communities of 171 residents randomly assigned to intervention (n=86) or comparison group (n=85) receiving usual care. Intervention participants lived with the sensor system an average of one year. Continuous data collected 24 hours/7 days a week from motion sensors to measure overall activity, an under mattress bed sensor to capture respiration, pulse, and restlessness as people sleep, and a gait sensor that continuously measures gait speed, stride length and time, and automatically assess for increasing fall risk as the person walks around the apartment. Continuously running computer algorithms are applied to the sensor data and send health alerts to staff when there are changes in sensor data patterns. The randomized comparison group functionally declined more rapidly than the intervention group. Walking speed and several measures from GaitRite, velocity, step length left and right, stride length left and right, and the fall risk measure of functional ambulation profile (FAP) all had clinically significant changes. The walking speed increase (worse) and velocity decline (worse) of 0.073 m/s for comparison group exceeded 0.05 m/s, a value considered to be a minimum clinically important difference. No differences were measured in health care costs. These findings demonstrate that sensor data with health alerts and fall alerts sent to AL nursing staff can be an effective strategy to detect and intervene in early signs of illness or functional decline. Copyright © 2017 AMDA – The Society for Post-Acute and Long-Term Care Medicine. Published by Elsevier Inc. All rights reserved.

A continuous time random walk model for Darcy-scale anomalous transport in heterogeneous porous media.

NASA Astrophysics Data System (ADS)

Comolli, Alessandro; Hakoun, Vivien; Dentz, Marco

2017-04-01

Achieving the understanding of the process of solute transport in heterogeneous porous media is of crucial importance for several environmental and social purposes, ranging from aquifers contamination and remediation, to risk assessment in nuclear waste repositories. The complexity of this aim is mainly ascribable to the heterogeneity of natural media, which can be observed at all the scales of interest, from pore scale to catchment scale. In fact, the intrinsic heterogeneity of porous media is responsible for the arising of the well-known non-Fickian footprints of transport, including heavy-tailed breakthrough curves, non-Gaussian spatial density profiles and the non-linear growth of the mean squared displacement. Several studies investigated the processes through which heterogeneity impacts the transport properties, which include local modifications to the advective-dispersive motion of solutes, mass exchanges between some mobile and immobile phases (e.g. sorption/desorption reactions or diffusion into solid matrix) and spatial correlation of the flow field. In the last decades, the continuous time random walk (CTRW) model has often been used to describe solute transport in heterogenous conditions and to quantify the impact of point heterogeneity, spatial correlation and mass transfer on the average transport properties [1]. Open issues regarding this approach are the possibility to relate measurable properties of the medium to the parameters of the model, as well as its capability to provide predictive information. In a recent work [2] the authors have shed new light on understanding the relationship between Lagrangian and Eulerian dynamics as well as on their evolution from arbitrary initial conditions. On the basis of these results, we derive a CTRW model for the description of Darcy-scale transport in d-dimensional media characterized by spatially random permeability fields. The CTRW approach models particle velocities as a spatial Markov process, which is characterized by a velocity transition probability and the steady state velocity distribution. These are related to the Eulerian velocity distribution and the distribution and spatial organization of hydraulic conductivity. The CTRW model is used for the prediction of transport data (particle dispersion and breakthrough curves) from direct numerical flow and transport simulations in heterogeneous hydraulic conductivity fields. References: [1] Comolli, A., Hidalgo, J. J., Moussey, C., & Dentz, M. (2016). Non-Fickian Transport Under Heterogeneous Advection and Mobile-Immobile Mass Transfer. Transport in Porous Media, 1-25. [2] Dentz, M., Kang, P. K., Comolli, A., Le Borgne, T., & Lester, D. R. (2016). Continuous time random walks for the evolution of Lagrangian velocities. Physical Review Fluids, 1(7), 074004.

Persistent-random-walk approach to anomalous transport of self-propelled particles

NASA Astrophysics Data System (ADS)

Sadjadi, Zeinab; Shaebani, M. Reza; Rieger, Heiko; Santen, Ludger

2015-06-01

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's displacement. It is shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short-time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.

Random walk with memory enhancement and decay

NASA Astrophysics Data System (ADS)

Tan, Zhi-Jie; Zou, Xian-Wu; Huang, Sheng-You; Zhang, Wei; Jin, Zhun-Zhi

2002-04-01

A model of random walk with memory enhancement and decay was presented on the basis of the characteristics of the biological intelligent walks. In this model, the movement of the walker is determined by the difference between the remaining information at the jumping-out site and jumping-in site. The amount of the memory information si(t) at a site i is enhanced with the increment of visiting times to that site, and decays with time t by the rate e-βt, where β is the memory decay exponent. When β=0, there exists a transition from Brownian motion (BM) to the compact growth of walking trajectory with the density of information energy u increasing. But for β>0, this transition does not appear and the walk with memory enhancement and decay can be considered as the BM of the mass center of the cluster composed of remembered sites in the late stage.

First passage time: Connecting random walks to functional responses in heterogeneous environments (Invited)

NASA Astrophysics Data System (ADS)

Lewis, M. A.; McKenzie, H.; Merrill, E.

2010-12-01

In this talk I will outline first passage time analysis for animals undertaking complex movement patterns, and will demonstrate how first passage time can be used to derive functional responses in predator prey systems. The result is a new approach to understanding type III functional responses based on a random walk model. I will extend the analysis to heterogeneous environments to assess the effects of linear features on functional responses in wolves and elk using GPS tracking data.

Coordinated Search for a Random Walk Target Motion

NASA Astrophysics Data System (ADS)

El-Hadidy, Mohamed Abd Allah; Abou-Gabal, Hamdy M.

This paper presents the cooperation between two searchers at the origin to find a Random Walk moving target on the real line. No information is not available about the target’s position all the time. Rather than finding the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite, we show the existence of the optimal search strategy which minimizes this first meeting time. The effectiveness of this model is illustrated using a numerical example.

Variable order fractional Fokker-Planck equations derived from Continuous Time Random Walks

NASA Astrophysics Data System (ADS)

Straka, Peter

2018-08-01

Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied, where the anomalous exponent β(x) ∈(0 , 1) varies in space. This type of situation occurs e.g. in biophysics, where the density of the intracellular matrix varies throughout a cell. Scaling limits of CTRWs are known to have probability distributions which solve fractional Fokker-Planck type equations (FFPE). This correspondence between stochastic processes and FFPE solutions has many useful extensions e.g. to nonlinear particle interactions and reactions, but has not yet been sufficiently developed for FFPEs of the "variable order" type with non-constant β(x) . In this article, variable order FFPEs (VOFFPE) are derived from scaling limits of CTRWs. The key mathematical tool is the 1-1 correspondence of a CTRW scaling limit to a bivariate Langevin process, which tracks the cumulative sum of jumps in one component and the cumulative sum of waiting times in the other. The spatially varying anomalous exponent is modelled by spatially varying β(x) -stable Lévy noise in the waiting time component. The VOFFPE displays a spatially heterogeneous temporal scaling behaviour, with generalized diffusivity and drift coefficients whose units are length2/timeβ(x) resp. length/timeβ(x). A global change of the time scale results in a spatially varying change in diffusivity and drift. A consequence of the mathematical derivation of a VOFFPE from CTRW limits in this article is that a solution of a VOFFPE can be approximated via Monte Carlo simulations. Based on such simulations, we are able to confirm that the VOFFPE is consistent under a change of the global time scale.

Approximate scaling properties of RNA free energy landscapes

NASA Technical Reports Server (NTRS)

Baskaran, S.; Stadler, P. F.; Schuster, P.

1996-01-01

RNA free energy landscapes are analysed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe the structure of these "time series". Although they are stationary by construction, we find that their local behavior is consistent with both AR(1) and self-affine processes. Random walks confined to excursion sets (i.e., with the restriction that the fitness value exceeds a certain threshold at each step) exhibit essentially the same statistics as free random walks. We find that an AR(1) time series is in general approximately self-affine on timescales up to approximately the correlation length. We present an empirical relation between the correlation parameter rho of the AR(1) model and the exponents characterizing self-affinity.

A Spectral Analysis of Discrete-Time Quantum Walks Related to the Birth and Death Chains

NASA Astrophysics Data System (ADS)

Ho, Choon-Lin; Ide, Yusuke; Konno, Norio; Segawa, Etsuo; Takumi, Kentaro

2018-04-01

In this paper, we consider a spectral analysis of discrete time quantum walks on the path. For isospectral coin cases, we show that the time averaged distribution and stationary distributions of the quantum walks are described by the pair of eigenvalues of the coins as well as the eigenvalues and eigenvectors of the corresponding random walks which are usually referred as the birth and death chains. As an example of the results, we derive the time averaged distribution of so-called Szegedy's walk which is related to the Ehrenfest model. It is represented by Krawtchouk polynomials which is the eigenvectors of the model and includes the arcsine law.

Integrodifferential formulations of the continuous-time random walk for solute transport subject to bimolecular A +B →0 reactions: From micro- to mesoscopic

NASA Astrophysics Data System (ADS)

Hansen, Scott K.; Berkowitz, Brian

2015-03-01

We develop continuous-time random walk (CTRW) equations governing the transport of two species that annihilate when in proximity to one another. In comparison with catalytic or spontaneous transformation reactions that have been previously considered in concert with CTRW, both species have spatially variant concentrations that require consideration. We develop two distinct formulations. The first treats transport and reaction microscopically, potentially capturing behavior at sharp fronts, but at the cost of being strongly nonlinear. The second, mesoscopic, formulation relies on a separation-of-scales technique we develop to separate microscopic-scale reaction and upscaled transport. This simplifies the governing equations and allows treatment of more general reaction dynamics, but requires stronger smoothness assumptions of the solution. The mesoscopic formulation is easily tractable using an existing solution from the literature (we also provide an alternative derivation), and the generalized master equation (GME) for particles undergoing A +B →0 reactions is presented. We show that this GME simplifies, under appropriate circumstances, to both the GME for the unreactive CTRW and to the advection-dispersion-reaction equation. An additional major contribution of this work is on the numerical side: to corroborate our development, we develop an indirect particle-tracking-partial-integro-differential-equation (PIDE) hybrid verification technique which could be applicable widely in reactive anomalous transport. Numerical simulations support the mesoscopic analysis.

Quantum-like Viewpoint on the Complexity and Randomness of the Financial Market

NASA Astrophysics Data System (ADS)

Choustova, Olga

In economics and financial theory, analysts use random walk and more general martingale techniques to model behavior of asset prices, in particular share prices on stock markets, currency exchange rates and commodity prices. This practice has its basis in the presumption that investors act rationally and without bias, and that at any moment they estimate the value of an asset based on future expectations. Under these conditions, all existing information affects the price, which changes only when new information comes out. By definition, new information appears randomly and influences the asset price randomly. Corresponding continuous time models are based on stochastic processes (this approach was initiated in the thesis of [4]), see, e.g., the books of [33] and [37] for historical and mathematical details.

Anomalous diffusion and the structure of human transportation networks

NASA Astrophysics Data System (ADS)

Brockmann, D.

2008-04-01

The dispersal of individuals of a species is the key driving force of various spatiotemporal phenomena which occur on geographical scales. It can synchronise populations of interacting species, stabilise them, and diversify gene pools [1-3]. The geographic spread of human infectious diseases such as influenza, measles and the recent severe acute respiratory syndrome (SARS) is essentially promoted by human travel which occurs on many length scales and is sustained by a variety of means of transportation [4-8]. In the light of increasing international trade, intensified human traffic, and an imminent influenza A pandemic the knowledge of dynamical and statistical properties of human dispersal is of fundamental importance and acute [7,9,10]. A quantitative statistical theory for human travel and concomitant reliable forecasts would substantially improve and extend existing prevention strategies. Despite its crucial role, a quantitative assessment of human dispersal remains elusive and the opinion that humans disperse diffusively still prevails in many models [11]. In this chapter I will report on a recently developed technique which permits a solid and quantitative assessment of human dispersal on geographical scales [11]. The key idea is to infer the statistical properties of human travel by analysing the geographic circulation of individual bank notes for which comprehensive datasets are collected at the online bill-tracking website www.wheresgeorge.com. The analysis shows that the distribution of travelling distances decays as a power law, indicating that the movement of bank notes is reminiscent of superdiffusive, scale free random walks known as Lèvy flights [13]. Secondly, the probability of remaining in a small, spatially confined region for a time T is dominated by heavy tails which attenuate superdiffusive dispersal. I will show that the dispersal of bank notes can be described on many spatiotemporal scales by a two parameter continuous time random walk (CTRW) model to a surprising accuracy. To this end, I will provide a brief introduction to continuous time random walk theory [14] and will show that human dispersal is an ambivalent, effectively superdiffusive process.

Electron avalanche structure determined by random walk theory

NASA Technical Reports Server (NTRS)

Englert, G. W.

1973-01-01

A self-consistent avalanche solution which accounts for collective long range Coulomb interactions as well as short range elastic and inelastic collisions between electrons and background atoms is made possible by a random walk technique. Results show that the electric field patterns in the early formation stages of avalanches in helium are close to those obtained from theory based on constant transport coefficients. Regions of maximum and minimum induced electrostatic potential phi are located on the axis of symmetry and within the volume covered by the electron swarm. As formation time continues, however, the region of minimum phi moves to slightly higher radii and the electric field between the extrema becomes somewhat erratic. In the intermediate formation periods the avalanche growth is slightly retarded by the high concentration of ions in the tail which oppose the external electric field. Eventually the formation of ions and electrons in the localized regions of high field strength more than offset this effect causing a very abrupt increase in avalanche growth.

Diabetic Erythrocytes Test by Correlation Coefficient

PubMed Central

Korol, A.M; Foresto, P; Darrigo, M; Rosso, O.A

2008-01-01

Even when a healthy individual is studied, his/her erythrocytes in capillaries continually change their shape in a synchronized erratic fashion. In this work, the problem of characterizing the cell behavior is studied from the perspective of bounded correlated random walk, based on the assumption that diffractometric data involves both deterministic and stochastic components. The photometric readings are obtained by ektacytometry over several millions of shear elongated cells, using a home-made device called Erythrodeformeter. We have only a scalar signal and no governing equations; therefore the complete behavior has to be reconstructed in an artificial phase space. To analyze dynamics we used the technique of time delay coordinates suggested by Takens, May algorithm, and Fourier transform. The results suggest that on random-walk approach the samples from healthy controls exhibit significant differences from those from diabetic patients and these could allow us to claim that we have linked mathematical nonlinear tools with clinical aspects of diabetic erythrocytes’ rheological properties. PMID:19415139

Stochastic modelling of animal movement.

PubMed

Smouse, Peter E; Focardi, Stefano; Moorcroft, Paul R; Kie, John G; Forester, James D; Morales, Juan M

2010-07-27

Modern animal movement modelling derives from two traditions. Lagrangian models, based on random walk behaviour, are useful for multi-step trajectories of single animals. Continuous Eulerian models describe expected behaviour, averaged over stochastic realizations, and are usefully applied to ensembles of individuals. We illustrate three modern research arenas. (i) Models of home-range formation describe the process of an animal 'settling down', accomplished by including one or more focal points that attract the animal's movements. (ii) Memory-based models are used to predict how accumulated experience translates into biased movement choices, employing reinforced random walk behaviour, with previous visitation increasing or decreasing the probability of repetition. (iii) Lévy movement involves a step-length distribution that is over-dispersed, relative to standard probability distributions, and adaptive in exploring new environments or searching for rare targets. Each of these modelling arenas implies more detail in the movement pattern than general models of movement can accommodate, but realistic empiric evaluation of their predictions requires dense locational data, both in time and space, only available with modern GPS telemetry.

Emergence of an optimal search strategy from a simple random walk

PubMed Central

Sakiyama, Tomoko; Gunji, Yukio-Pegio

2013-01-01

In reports addressing animal foraging strategies, it has been stated that Lévy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths. PMID:23804445

Emergence of an optimal search strategy from a simple random walk.

PubMed

Sakiyama, Tomoko; Gunji, Yukio-Pegio

2013-09-06

In reports addressing animal foraging strategies, it has been stated that Lévy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths.

Is walking a random walk? Evidence for long-range correlations in stride interval of human gait

NASA Technical Reports Server (NTRS)

Hausdorff, Jeffrey M.; Peng, C.-K.; Ladin, Zvi; Wei, Jeanne Y.; Goldberger, Ary L.

1995-01-01

Complex fluctuation of unknown origin appear in the normal gait pattern. These fluctuations might be described as being (1) uncorrelated white noise, (2) short-range correlations, or (3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that sucessfully accounts for the experimentally observed long-range correlations.

Cardiorespiratory Kinetics Determined by Pseudo-Random Binary Sequences - Comparisons between Walking and Cycling.

PubMed

Koschate, J; Drescher, U; Thieschäfer, L; Heine, O; Baum, K; Hoffmann, U

2016-12-01

This study aims to compare cardiorespiratory kinetics as a response to a standardised work rate protocol with pseudo-random binary sequences between cycling and walking in young healthy subjects. Muscular and pulmonary oxygen uptake (V̇O 2 ) kinetics as well as heart rate kinetics were expected to be similar for walking and cycling. Cardiac data and V̇O 2 of 23 healthy young subjects were measured in response to pseudo-random binary sequences. Kinetics were assessed applying time series analysis. Higher maxima of cross-correlation functions between work rate and the respective parameter indicate faster kinetics responses. Muscular V̇O 2 kinetics were estimated from heart rate and pulmonary V̇O 2 using a circulatory model. Muscular (walking vs. cycling [mean±SD in arbitrary units]: 0.40±0.08 vs. 0.41±0.08) and pulmonary V̇O 2 kinetics (0.35±0.06 vs. 0.35±0.06) were not different, although the time courses of the cross-correlation functions of pulmonary V̇O 2 showed unexpected biphasic responses. Heart rate kinetics (0.50±0.14 vs. 0.40±0.14; P=0.017) was faster for walking. Regarding the biphasic cross-correlation functions of pulmonary V̇O 2 during walking, the assessment of muscular V̇O 2 kinetics via pseudo-random binary sequences requires a circulatory model to account for cardio-dynamic distortions. Faster heart rate kinetics for walking should be considered by comparing results from cycle and treadmill ergometry. © Georg Thieme Verlag KG Stuttgart · New York.

A simple method to calculate first-passage time densities with arbitrary initial conditions

NASA Astrophysics Data System (ADS)

Nyberg, Markus; Ambjörnsson, Tobias; Lizana, Ludvig

2016-06-01

Numerous applications all the way from biology and physics to economics depend on the density of first crossings over a boundary. Motivated by the lack of general purpose analytical tools for computing first-passage time densities (FPTDs) for complex problems, we propose a new simple method based on the independent interval approximation (IIA). We generalise previous formulations of the IIA to include arbitrary initial conditions as well as to deal with discrete time and non-smooth continuous time processes. We derive a closed form expression for the FPTD in z and Laplace-transform space to a boundary in one dimension. Two classes of problems are analysed in detail: discrete time symmetric random walks (Markovian) and continuous time Gaussian stationary processes (Markovian and non-Markovian). Our results are in good agreement with Langevin dynamics simulations.

A Telehealth Intervention Using Nintendo Wii Fit Balance Boards and iPads to Improve Walking in Older Adults With Lower Limb Amputation (Wii.n.Walk): Study Protocol for a Randomized Controlled Trial.

PubMed

Imam, Bita; Miller, William C; Finlayson, Heather C; Eng, Janice J; Payne, Michael Wc; Jarus, Tal; Goldsmith, Charles H; Mitchell, Ian M

2014-12-22

The number of older adults living with lower limb amputation (LLA) who require rehabilitation for improving their walking capacity and mobility is growing. Existing rehabilitation practices frequently fail to meet this demand. Nintendo Wii Fit may be a valuable tool to enable rehabilitation interventions. Based on pilot studies, we have developed "Wii.n.Walk", an in-home telehealth Wii Fit intervention targeted to improve walking capacity in older adults with LLA. The objective of this study is to determine whether the Wii.n.Walk intervention enhances walking capacity compared to an attention control group. This project is a multi-site (Vancouver BC, London ON), parallel, evaluator-blind randomized controlled trial. Participants include community-dwelling older adults over the age of 50 years with unilateral transtibial or transfemoral amputation. Participants will be stratified by site and block randomized in triplets to either the Wii.n.Walk intervention or an attention control group employing the Wii Big Brain cognitive software. This trial will include both supervised and unsupervised phases. During the supervised phase, both groups will receive 40-minute sessions of supervised group training three times per week for a duration of 4 weeks. Participants will complete the first week of the intervention in groups of three at their local rehabilitation center with a trainer. The remaining 3 weeks will take place at participants' homes using remote supervision by the trainer using Apple iPad technology. At the end of 4 weeks, the supervised period will end and the unsupervised period will begin. Participants will retain the Wii console and be encouraged to continue using the program for an additional 4 weeks' duration. The primary outcome measure will be the "Two-Minute Walk Test" to measure walking capacity. Outcome measures will be evaluated for all participants at baseline, after the end of both the supervised and unsupervised phases, and after 1-year follow up. Study staff have been hired and trained at both sites and recruitment is currently underway. No participants have been enrolled yet. Wii.n.Walk is a promising in-home telehealth intervention that may have useful applications for older adults with LLA who are discharged from rehabilitation or live in remote areas having limited or no access to existing rehabilitation programs. Clinicaltrial.gov NCT01942798; http://clinicaltrials.gov/ct2/show/NCT01942798 (Archived by WebCite at http://www.webcitation.org/6V0w8baKP).

Studies on energy transfer in dendrimer supermolecule using classical random walk model and Eyring model

NASA Astrophysics Data System (ADS)

Rana, Dipankar; Gangopadhyay, Gautam

2003-01-01

We have analyzed the energy transfer process in a dendrimer supermolecule using a classical random walk model and an Eyring model of membrane permeation. Here the energy transfer is considered as a multiple barrier crossing process by thermal hopping on the backbone of a cayley tree. It is shown that the mean residence time and mean first passage time, which involve explicit local escape rates, depend upon the temperature, size of the molecule, core branching, and the nature of the potential energy landscape along the cayley tree architecture. The effect of branching tries to create a uniform distribution of mean residence time over the generations and the distribution depends upon the interplay of funneling and local rates of transitions. The calculation of flux at the steady state from the Eyring model also gives a useful idea about the rate when the dendrimeric system is considered as an open system where the core is absorbing the transported energy like a photosynthetic reaction center and a continuous supply of external energy is maintained at the peripheral nodes. The effect of the above parameters of the system are shown to depend on the steady-state flux that has a qualitative resemblence with the result of the mean first passage time approach.

Mean first passage time for random walk on dual structure of dendrimer

NASA Astrophysics Data System (ADS)

Li, Ling; Guan, Jihong; Zhou, Shuigeng

2014-12-01

The random walk approach has recently been widely employed to study the relations between the underlying structure and dynamic of complex systems. The mean first-passage time (MFPT) for random walks is a key index to evaluate the transport efficiency in a given system. In this paper we study analytically the MFPT in a dual structure of dendrimer network, Husimi cactus, which has different application background and different structure (contains loops) from dendrimer. By making use of the iterative construction, we explicitly determine both the partial mean first-passage time (PMFT, the average of MFPTs to a given target) and the global mean first-passage time (GMFT, the average of MFPTs over all couples of nodes) on Husimi cactus. The obtained closed-form results show that PMFPT and EMFPT follow different scaling with the network order, suggesting that the target location has essential influence on the transport efficiency. Finally, the impact that loop structure could bring is analyzed and discussed.

Quantum Ultra-Walks: Walks on a Line with Spatial Disorder

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Falkner, Stefan

We discuss the model of a heterogeneous discrete-time walk on a line with spatial disorder in the form of a set of ultrametric barriers. Simulations show that such an quantum ultra-walk spreads with a walk exponent dw that ranges from ballistic (dw = 1) to complete confinement (dw = ∞) for increasing separation 1 <= 1 / ɛ < ∞ in barrier heights. We develop a formalism by which the classical random walk as well as the quantum walk can be treated in parallel using a coined walk with internal degrees of freedom. For the random walk, this amounts to a 2nd -order Markov process with a stochastic coin, better know as an (anti-)persistent walk. The exact analysis, based on the real-space renormalization group (RG), reproduces the results of the well-known model of ``ultradiffusion,'' dw = 1 -log2 ɛ for 0 < ɛ <= 1 / 2 . However, while the evaluation of the RG fixed-points proceeds virtually identical, for the corresponding quantum walk with a unitary coin it fails to reproduce the numerical results. A new way to analyze the RG is indicated. Supported by NSF-DMR 1207431.

Hydrotherapy vs. conventional land-based exercise for improving walking and balance after stroke: a randomized controlled trial.

PubMed

Zhu, Zhizhong; Cui, Liling; Yin, Miaomiao; Yu, Yang; Zhou, Xiaona; Wang, Hongtu; Yan, Hua

2016-06-01

To investigate the effects of hydrotherapy on walking ability and balance in patients with chronic stroke. Single-blind, randomized controlled pilot trial. Outpatient rehabilitation clinic at a tertiary neurological hospital in China. A total of 28 participants with impairments in walking and controlling balance more than six months post-stroke. After baseline evaluations, participants were randomly assigned to a land-based therapy (control group, n = 14) or hydrotherapy (study group, n = 14). Participants underwent individual sessions for four weeks, five days a week, for 45 minutes per session. After four weeks of rehabilitation, all participants were evaluated by a blinded assessor. Functional assessments included the Functional Reach Test, Berg Balance Scale, 2-minute walk test, and Timed Up and Go Test. After four weeks of treatment, the Berg Balance Scale, functional reach test, 2-minute walk test, and the Timed Up and Go Test scores had improved significantly in each group (P < 0.05). The mean improvement of the functional reach test and 2-minute walk test were significantly higher in the aquatic group than in the control group (P < 0.01). The differences in the mean values of the improvements in the Berg Balance Scale and the Timed Up and Go Test were not statistically significant. The results of this study suggest that a relatively short programme (four weeks) of hydrotherapy exercise resulted in a large improvement in a small group (n = 14) of individuals with relatively high balance and walking function following a stroke. © The Author(s) 2015.

An online social network to increase walking in dog owners: a randomized trial.

PubMed

Schneider, Kristin L; Murphy, Deirdra; Ferrara, Cynthia; Oleski, Jessica; Panza, Emily; Savage, Clara; Gada, Kimberly; Bozzella, Brianne; Olendzki, Effie; Kern, Daniel; Lemon, Stephenie C

2015-03-01

Encouraging dog walking may increase physical activity in dog owners. This cluster-randomized controlled trial investigated whether a social networking Web site (Meetup™) could be used to deliver a multicomponent dog walking intervention to increase physical activity. Sedentary dog owners (n = 102) participated. Eight neighborhoods were randomly assigned to the Meetup™ condition (Meetup™) or a condition where participants received monthly e-mails with content from the American Heart Association regarding increasing physical activity. The Meetup™ intervention was delivered over 6 months and consisted of newsletters, dog walks, community events, and an activity monitor. The primary outcome was steps; secondary outcomes included social support for walking, sense of community, perceived dog walking outcomes, barriers to dog walking, and feasibility of the intervention. Mixed-model analyses examined change from baseline to postintervention (6 months) and whether change in outcomes differed by condition. Daily steps increased over time (P = 0.04, d = 0.28), with no differences by condition. The time-condition interaction was significant for the perceived outcomes of dog walking (P = 0.04, d = 0.40), such that the Meetup™ condition reported an increase in the perceived positive outcomes of dog walking, whereas the American Heart Association condition did not. Social support, sense of community, and dog walking barriers did not significantly change. Meetup™ logins averaged 58.38 per week (SD, 11.62). Within 2 months of the intervention ending, organization of the Meetup™ groups transitioned from the study staff to Meetup™ members. Results suggest that a Meetup™ group is feasible for increasing physical activity in dog owners. Further research is needed to understand how to increase participation in the Meetup™ group and facilitate greater connection among dog owners.

An Online Social Network to Increase Walking in Dog Owners: A Randomized Trial

PubMed Central

Schneider, Kristin L.; Murphy, Deirdra; Ferrara, Cynthia; Oleski, Jessica; Panza, Emily; Savage, Clara; Gada, Kimberly; Bozzella, Brianne; Olendzki, Effie; Kern, Daniel; Lemon, Stephenie C.

2014-01-01

PURPOSE Encouraging dog walking may increase physical activity in dog owners. This cluster randomized controlled trial investigated whether a social networking website (Meetup™) could be used to deliver a multi-component dog walking intervention to increase physical activity. METHODS Sedentary dog owners (n=102) participated. Eight neighborhoods were randomly assigned to the Meetup condition (Meetup) or a condition where participants received monthly emails with content from the American Heart Association on increasing physical activity (AHA). The Meetup intervention was delivered over 6 months and consisted of newsletters, dog walks, community events and an activity monitor. The primary outcome was steps; secondary outcomes included social support for walking, sense of community, perceived dog walking outcomes, barriers to dog walking and feasibility of the intervention. RESULTS Mixed model analyses examined change from baseline to post-intervention (6 months) and whether change in outcomes differed by condition. Daily steps increased over time (p=0.04, d=0.28), with no differences by condition. The time x condition interaction was significant for the perceived outcomes of dog walking (p=0.04, d=0.40), such that the Meetup condition reported an increase in the perceived positive outcomes of dog walking, whereas the AHA condition did not. Social support, sense of community and dog walking barriers did not significantly change. Meetup logins averaged 58.38 per week (SD=11.62). Within two months of the intervention ending, organization of the Meetup groups transitioned from study staff to Meetup members. CONCLUSION Results suggest that a Meetup group is feasible for increasing physical activity in dog owners. Further research is needed to understand how to increase participation in the Meetup group and facilitate greater connection among dog owners. PMID:25003777

Bayesian dynamic modeling of time series of dengue disease case counts.

PubMed

Martínez-Bello, Daniel Adyro; López-Quílez, Antonio; Torres-Prieto, Alexander

2017-07-01

The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model's short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order random walk time-varying coefficients. We applied Markov Chain Monte Carlo simulations for parameter estimation, and deviance information criterion statistic (DIC) for model selection. We assessed the short-term predictive performance of the selected final model, at several time points within the study period using the mean absolute percentage error. The results showed the best model including first-order random walk time-varying coefficients for calendar trend and first-order random walk time-varying coefficients for the meteorological variables. Besides the computational challenges, interpreting the results implies a complete analysis of the time series of dengue with respect to the parameter estimates of the meteorological effects. We found small values of the mean absolute percentage errors at one or two weeks out-of-sample predictions for most prediction points, associated with low volatility periods in the dengue counts. We discuss the advantages and limitations of the dynamic Poisson models for studying the association between time series of dengue disease and meteorological variables. The key conclusion of the study is that dynamic Poisson models account for the dynamic nature of the variables involved in the modeling of time series of dengue disease, producing useful models for decision-making in public health.

Large Deviations for Stationary Probabilities of a Family of Continuous Time Markov Chains via Aubry-Mather Theory

NASA Astrophysics Data System (ADS)

Lopes, Artur O.; Neumann, Adriana

2015-05-01

In the present paper, we consider a family of continuous time symmetric random walks indexed by , . For each the matching random walk take values in the finite set of states ; notice that is a subset of , where is the unitary circle. The infinitesimal generator of such chain is denoted by . The stationary probability for such process converges to the uniform distribution on the circle, when . Here we want to study other natural measures, obtained via a limit on , that are concentrated on some points of . We will disturb this process by a potential and study for each the perturbed stationary measures of this new process when . We disturb the system considering a fixed potential and we will denote by the restriction of to . Then, we define a non-stochastic semigroup generated by the matrix , where is the infinifesimal generator of . From the continuous time Perron's Theorem one can normalized such semigroup, and, then we get another stochastic semigroup which generates a continuous time Markov Chain taking values on . This new chain is called the continuous time Gibbs state associated to the potential , see (Lopes et al. in J Stat Phys 152:894-933, 2013). The stationary probability vector for such Markov Chain is denoted by . We assume that the maximum of is attained in a unique point of , and from this will follow that . Thus, here, our main goal is to analyze the large deviation principle for the family , when . The deviation function , which is defined on , will be obtained from a procedure based on fixed points of the Lax-Oleinik operator and Aubry-Mather theory. In order to obtain the associated Lax-Oleinik operator we use the Varadhan's Lemma for the process . For a careful analysis of the problem we present full details of the proof of the Large Deviation Principle, in the Skorohod space, for such family of Markov Chains, when . Finally, we compute the entropy of the invariant probabilities on the Skorohod space associated to the Markov Chains we analyze.

One Model Fits All: Explaining Many Aspects of Number Comparison within a Single Coherent Model-A Random Walk Account

ERIC Educational Resources Information Center

Reike, Dennis; Schwarz, Wolf

2016-01-01

The time required to determine the larger of 2 digits decreases with their numerical distance, and, for a given distance, increases with their magnitude (Moyer & Landauer, 1967). One detailed quantitative framework to account for these effects is provided by random walk models. These chronometric models describe how number-related noisy…

Finite Memory Walk and Its Application to Small-World Network

NASA Astrophysics Data System (ADS)

Oshima, Hiraku; Odagaki, Takashi

2012-07-01

In order to investigate the effects of cycles on the dynamical process on both regular lattices and complex networks, we introduce a finite memory walk (FMW) as an extension of the simple random walk (SRW), in which a walker is prohibited from moving to sites visited during m steps just before the current position. This walk interpolates the simple random walk (SRW), which has no memory (m = 0), and the self-avoiding walk (SAW), which has an infinite memory (m = ∞). We investigate the FMW on regular lattices and clarify the fundamental characteristics of the walk. We find that (1) the mean-square displacement (MSD) of the FMW shows a crossover from the SAW at a short time step to the SRW at a long time step, and the crossover time is approximately equivalent to the number of steps remembered, and that the MSD can be rescaled in terms of the time step and the size of memory; (2) the mean first-return time (MFRT) of the FMW changes significantly at the number of remembered steps that corresponds to the size of the smallest cycle in the regular lattice, where ``smallest'' indicates that the size of the cycle is the smallest in the network; (3) the relaxation time of the first-return time distribution (FRTD) decreases as the number of cycles increases. We also investigate the FMW on the Watts--Strogatz networks that can generate small-world networks, and show that the clustering coefficient of the Watts--Strogatz network is strongly related to the MFRT of the FMW that can remember two steps.

The feasibility and effectiveness of high-intensity boxing training versus moderate-intensity brisk walking in adults with abdominal obesity: a pilot study.

PubMed

Cheema, Birinder S; Davies, Timothy B; Stewart, Matthew; Papalia, Shona; Atlantis, Evan

2015-01-01

High-intensity interval training (HIIT) performed on exercise cycle or treadmill is considered safe and often more beneficial for fat loss and cardiometabolic health than moderate-intensity continuous training (MICT). The aim of this pilot study was to assess the feasibility and effectiveness of a 12-week boxing training (HIIT) intervention compared with an equivalent dose of brisk walking (MICT) in obese adults. Men and women with abdominal obesity and body mass index >25 kg/m(2) were randomized to either a boxing group or a brisk walking (control) group for 12 weeks. Each group engaged in 4 training sessions per week, equated for total physical activity. Feasibility outcomes included recruitment rates, assessment of training intensities, adherence and adverse events. Effectiveness was assessed pre and post intervention via pertinent obesity-, cardiovascular-, and health-related quality of life (HRQoL) outcomes. Nineteen individuals expressed an interest and 63% (n = 12) consented. Recruitment was slower than anticipated (1.3 participants/week). The boxing group trained at a significantly higher intensity each week versus the brisk walking group (p < 0.05). Two participants in the boxing group experienced an adverse event; both continued to exercise with modifications to the exercise program. No other adverse events were noted. The boxing group attended more sessions (79% vs. 55%) and had a lower attrition rate (n = 0 vs. n = 2) than the walking group. Analysis of covariance revealed that the boxing group significantly improved body fat percentage (p = 0.047), systolic blood pressure (p = 0.026), augmentation index (AIx; p < 0.001), absolute VO2max (p = 0.015), and Physical Functioning (p = 0.042) and Vitality (p = 0.024) domains of HRQoL over time. The walking group did not improve any clinical outcomes, and experienced a worsening of Vitality (p = 0.043). Boxing training (HIIT) in adults with abdominal obesity is feasible and may elicit a better therapeutic effect on obesity, cardiovascular, and HRQoL outcomes than an equivalent dose of brisk walking (MICT). Robustly designed randomized controlled trials are required to confirm these findings and inform clinical guidelines and practice for obesity treatment. ACTRN12615000007538.

Clearing out a maze: A model of chemotactic motion in porous media

NASA Astrophysics Data System (ADS)

Schilling, Tanja; Voigtmann, Thomas

2017-12-01

We study the anomalous dynamics of a biased "hungry" (or "greedy") random walk on a percolating cluster. The model mimics chemotaxis in a porous medium: In close resemblance to the 1980s arcade game PAC-MA N ®, the hungry random walker consumes food, which is initially distributed in the maze, and biases its movement towards food-filled sites. We observe that the mean-squared displacement of the process follows a power law with an exponent that is different from previously known exponents describing passive or active microswimmer dynamics. The change in dynamics is well described by a dynamical exponent that depends continuously on the propensity to move towards food. It results in slower differential growth when compared to the unbiased random walk.

Effects of a Flexibility and Relaxation Programme, Walking, and Nordic Walking on Parkinson's Disease

PubMed Central

Reuter, I.; Mehnert, S.; Leone, P.; Kaps, M.; Oechsner, M.; Engelhardt, M.

2011-01-01

Symptoms of Parkinson's disease (PD) progress despite optimized medical treatment. The present study investigated the effects of a flexibility and relaxation programme, walking, and Nordic walking (NW) on walking speed, stride length, stride length variability, Parkinson-specific disability (UPDRS), and health-related quality of life (PDQ 39). 90 PD patients were randomly allocated to the 3 treatment groups. Patients participated in a 6-month study with 3 exercise sessions per week, each lasting 70 min. Assessment after completion of the training showed that pain was reduced in all groups, and balance and health-related quality of life were improved. Furthermore, walking, and Nordic walking improved stride length, gait variability, maximal walking speed, exercise capacity at submaximal level, and PD disease-specific disability on the UPDRS in addition. Nordic walking was superior to the flexibility and relaxation programme and walking in improving postural stability, stride length, gait pattern and gait variability. No significant injuries occurred during the training. All patients of the Nordic walking group continued Nordic walking after completing the study. PMID:21603199

Self-Trapping Self-Repelling Random Walks

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2017-10-01

Although the title seems self-contradictory, it does not contain a misprint. The model we study is a seemingly minor modification of the "true self-avoiding walk" model of Amit, Parisi, and Peliti in two dimensions. The walks in it are self-repelling up to a characteristic time T* (which depends on various parameters), but spontaneously (i.e., without changing any control parameter) become self-trapping after that. For free walks, T* is astronomically large, but on finite lattices the transition is easily observable. In the self-trapped regime, walks are subdiffusive and intermittent, spending longer and longer times in small areas until they escape and move rapidly to a new area. In spite of this, these walks are extremely efficient in covering finite lattices, as measured by average cover times.

Anomalous diffusion and dynamics of fluorescence recovery after photobleaching in the random-comb model

NASA Astrophysics Data System (ADS)

Yuste, S. B.; Abad, E.; Baumgaertner, A.

2016-07-01

We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ ,P (ℓ ) ˜ℓ-(1 +α ) (α >0 ). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems.

Persistent random walk of cells involving anomalous effects and random death

NASA Astrophysics Data System (ADS)

Fedotov, Sergei; Tan, Abby; Zubarev, Andrey

2015-04-01

The purpose of this paper is to implement a random death process into a persistent random walk model which produces sub-ballistic superdiffusion (Lévy walk). We develop a stochastic two-velocity jump model of cell motility for which the switching rate depends upon the time which the cell has spent moving in one direction. It is assumed that the switching rate is a decreasing function of residence (running) time. This assumption leads to the power law for the velocity switching time distribution. This describes the anomalous persistence of cell motility: the longer the cell moves in one direction, the smaller the switching probability to another direction becomes. We derive master equations for the cell densities with the generalized switching terms involving the tempered fractional material derivatives. We show that the random death of cells has an important implication for the transport process through tempering of the superdiffusive process. In the long-time limit we write stationary master equations in terms of exponentially truncated fractional derivatives in which the rate of death plays the role of tempering of a Lévy jump distribution. We find the upper and lower bounds for the stationary profiles corresponding to the ballistic transport and diffusion with the death-rate-dependent diffusion coefficient. Monte Carlo simulations confirm these bounds.

Patterns of particle distribution in multiparticle systems by random walks with memory enhancement and decay

NASA Astrophysics Data System (ADS)

Tan, Zhi-Jie; Zou, Xian-Wu; Huang, Sheng-You; Zhang, Wei; Jin, Zhun-Zhi

2002-07-01

We investigate the pattern of particle distribution and its evolution with time in multiparticle systems using the model of random walks with memory enhancement and decay. This model describes some biological intelligent walks. With decrease in the memory decay exponent α, the distribution of particles changes from a random dispersive pattern to a locally dense one, and then returns to the random one. Correspondingly, the fractal dimension Df,p characterizing the distribution of particle positions increases from a low value to a maximum and then decreases to the low one again. This is determined by the degree of overlap of regions consisting of sites with remanent information. The second moment of the density ρ(2) was introduced to investigate the inhomogeneity of the particle distribution. The dependence of ρ(2) on α is similar to that of Df,p on α. ρ(2) increases with time as a power law in the process of adjusting the particle distribution, and then ρ(2) tends to a stable equilibrium value.

The effect of atrial-based pacing on exercise capacity as measured by the 6-minute walk test: a substudy of the Canadian Trial of Physiological Pacing (CTOPP).

PubMed

Baranchuk, Adrian; Healey, Jeff S; Thorpe, Kevin E; Morillo, Carlos A; Nair, Girish; Crystal, Eugene; Kerr, Charles R; Connolly, Stuart J

2007-08-01

Although several randomized trials have detected no reduction in major cardiovascular events with the routine use of dual-chamber as opposed to ventricular pacemakers, many individuals continue to advocate their use as a means of improving exercise capacity. The Canadian Trial of Physiological Pacing (CTOPP) trial is the largest trial comparing ventricular pacing to atrial-based pacing (atrial or dual-chamber) in patients with bradycardia. All patients in this trial were asked to complete a 6-minute hall walk test (6MWT) at the time of their first study follow-up. The distance walked in 6 minutes and the patient's heart rate before and immediately after the walk were recorded. Of the 2568 patients in the CTOPP, 76% completed the 6MWT. The mean distance walked was 350 +/- 127 m in the ventricular pacing group and 356 +/- 127 m in the atrial-based group (P = NS). Similarly, there was no difference in the change in heart rate between the two groups (17 +/- 13 vs. 18 +/- 12 bpm: P = NS). However, among patients with an unpaced heart rate of

Origins and nature of non-Fickian transport through fractures

NASA Astrophysics Data System (ADS)

Wang, L.; Cardenas, M. B.

2014-12-01

Non-Fickian transport occurs across all scales within fractured and porous geological media. Fundamental understanding and appropriate characterization of non-Fickian transport through fractures is critical for understanding and prediction of the fate of solutes and other scalars. We use both analytical and numerical modeling, including direct numerical simulation and particle tracking random walk, to investigate the origin of non-Fickian transport through both homogeneous and heterogeneous fractures. For the simple homogenous fracture case, i.e., parallel plates, we theoretically derived a formula for dynamic longitudinal dispersion (D) within Poiseuille flow. Using the closed-form expression for the theoretical D, we quantified the time (T) and length (L) scales separating preasymptotic and asymptotic dispersive transport, with T and L proportional to aperture (b) of parallel plates to second and fourth orders, respectively. As for heterogeneous fractures, the fracture roughness and correlation length are closely associated with the T and L, and thus indicate the origin for non-Fickian transport. Modeling solute transport through 2D rough-walled fractures with continuous time random walk with truncated power shows that the degree of deviation from Fickian transport is proportional to fracture roughness. The estimated L for 2D rough-walled fractures is significantly longer than that derived from the formula within Poiseuille flow with equivalent b. Moreover, we artificially generated normally distributed 3D fractures with fixed correlation length but different fracture dimensions. Solute transport through 3D fractures was modeled with a particle tracking random walk algorithm. We found that transport transitions from non-Fickian to Fickian with increasing fracture dimensions, where the estimated L for the studied 3D fractures is related to the correlation length.

The influence of dog ownership on objective measures of free-living physical activity and sedentary behaviour in community-dwelling older adults: a longitudinal case-controlled study.

PubMed

Dall, Philippa Margaret; Ellis, Sarah Lesley Helen; Ellis, Brian Martin; Grant, P Margaret; Colyer, Alison; Gee, Nancy Renee; Granat, Malcolm Howard; Mills, Daniel Simon

2017-06-09

There is some evidence to suggest that dog ownership may improve physical activity (PA) among older adults, but to date, studies examining this, have either depended on self-report or incomplete datasets due to the type of activity monitor used to record physical activity. Additionally, the effect of dog ownership on sedentary behaviour (SB) has not been explored. The aim of the current study was to address these issues by using activPAL monitors to evaluate the influence of dog ownership on health enhancing PA and SB in a longitudinal study of independently-mobile, community-dwelling older adults. Study participants (43 pairs of dog owners and non-dog owners, matched on a range of demographic variables) wore an activPAL monitor continuously for three, one-week data collection periods over the course of a year. Participants also reported information about their own and their dog demographics, caring responsibilities, and completed a diary of wake times. Diary data was used to isolate waking times, and outcome measures of time spent walking, time spent walking at a moderate cadence (>100 steps/min), time spent standing, time spent sitting, number of sitting events (continuous periods of sitting), and the number of and of time spent sitting in prolonged events (>30 min). For each measure, a linear mixed effects model with dog ownership as a fixed effect, and a random effects structure of measurement point nested in participant nested in pair was used to assess the effect of dog ownership. Owning a dog indicated a large, potentially health improving, average effect of 22 min additional time spent walking, 95%CI (12, 34), and 2760 additional steps per day, 95%CI (1667, 3991), with this additional walking undertaken at a moderate intensity cadence. Dog owners had significantly fewer sitting events. However, there were no significant differences between the groups for either the total time spent sitting, or the number or duration of prolonged sedentary events. The scale of the influence of dog ownership on PA found in this study, indicates that future research regarding PA in older adults should assess and report dog ownership and/or dog walking status.

Discrete-time Quantum Walks via Interchange Framework and Memory in Quantum Evolution

NASA Astrophysics Data System (ADS)

Dimcovic, Zlatko

One of the newer and rapidly developing approaches in quantum computing is based on "quantum walks," which are quantum processes on discrete space that evolve in either discrete or continuous time and are characterized by mixing of components at each step. The idea emerged in analogy with the classical random walks and stochastic techniques, but these unitary processes are very different even as they have intriguing similarities. This thesis is concerned with study of discrete-time quantum walks. The original motivation from classical Markov chains required for discrete-time quantum walks that one adds an auxiliary Hilbert space, unrelated to the one in which the system evolves, in order to be able to mix components in that space and then take the evolution steps accordingly (based on the state in that space). This additional, "coin," space is very often an internal degree of freedom like spin. We have introduced a general framework for construction of discrete-time quantum walks in a close analogy with the classical random walks with memory that is rather different from the standard "coin" approach. In this method there is no need to bring in a different degree of freedom, while the full state of the system is still described in the direct product of spaces (of states). The state can be thought of as an arrow pointing from the previous to the current site in the evolution, representing the one-step memory. The next step is then controlled by a single local operator assigned to each site in the space, acting quite like a scattering operator. This allows us to probe and solve some problems of interest that have not had successful approaches with "coined" walks. We construct and solve a walk on the binary tree, a structure of great interest but until our result without an explicit discrete time quantum walk, due to difficulties in managing coin spaces necessary in the standard approach. Beyond algorithmic interests, the model based on memory allows one to explore effects of history on the quantum evolution and the subtle emergence of classical features as "memory" is explicitly kept for additional steps. We construct and solve a walk with an additional correlation step, finding interesting new features. On the other hand, the fact that the evolution is driven entirely by a local operator, not involving additional spaces, enables us to choose the Fourier transform as an operator completely controlling the evolution. This in turn allows us to combine the quantum walk approach with Fourier transform based techniques, something decidedly not possible in classical computational physics. We are developing a formalism for building networks manageable by walks constructed with this framework, based on the surprising efficiency of our framework in discovering internals of a simple network that we so far solved. Finally, in line with our expectation that the field of quantum walks can take cues from the rich history of development of the classical stochastic techniques, we establish starting points for the work on non-Abelian quantum walks, with a particular quantum-walk analog of the classical "card shuffling," the walk on the permutation group. In summary, this thesis presents a new framework for construction of discrete time quantum walks, employing and exploring memoried nature of unitary evolution. It is applied to fully solving the problems of: A walk on the binary tree and exploration of the quantum-to-classical transition with increased correlation length (history). It is then used for simple network discovery, and to lay the groundwork for analysis of complex networks, based on combined power of efficient exploration of the Hilbert space (as a walk mixing components) and Fourier transformation (since we can choose this for the evolution operator). We hope to establish this as a general technique as its power would be unmatched by any approaches available in the classical computing. We also looked at the promising and challenging prospect of walks on non-Abelian structures by setting up the problem of "quantum card shuffling," a quantum walk on the permutation group. Relation to other work is thoroughly discussed throughout, along with examination of the context of our work and overviews of our current and future work.

The immediate and long-term effects of a walking-skill program compared to usual physiotherapy care in patients who have undergone total knee arthroplasty (TKA): a randomized controlled trial.

PubMed

Bruun-Olsen, Vigdis; Heiberg, Kristi Elisabeth; Wahl, Astrid Klopstad; Mengshoel, Anne Marit

2013-01-01

To examine the immediate and long-term effects of a walking-skill program compared with usual physiotherapy on physical function, pain and perceived self-efficacy in patients after total knee arthroplasty (TKA). A single blind randomized controlled trial design was applied. Fifty-seven patients with primary TKA, mean age of 69 years (SD ± 9), were randomly assigned to a walking-skill program emphasizing weight-bearing exercises or usual physiotherapy. Outcomes were assessed before the interventions started at 6 weeks postoperatively (T1), directly after the interventions at 12-14 weeks (T2) and 9 months after the interventions (T3). Walking was the primary outcome, assessed by the 6 min walk test (6MWT). The secondary outcomes were timed stair climbing, timed stands, Figure-of-eight test, Index of muscle function, active knee range of motion, Knee Injury and Osteoarthritis Outcome Score and self-efficacy score. From T1 to T2, a better 6MWT score was found in favor of the walking-skill program of 39 m (2-76), p = 0.04. The difference between the groups in 6MWT persisted at T3, 44 m (8-80), p = 0.02. No differences in other outcome measures were found. The walking-skill program had better effect on walking than usual physiotherapy. Weight bearing was tolerated. Implications for Rehabilitation Weight-bearing exercises are tolerated by the patients in the early stage after TKA. Physiotherapy that focuses on learning different ways of walking through practice may be a plausible way to train patients after TKA.

Logical-rule models of classification response times: a synthesis of mental-architecture, random-walk, and decision-bound approaches.

PubMed

Fific, Mario; Little, Daniel R; Nosofsky, Robert M

2010-04-01

We formalize and provide tests of a set of logical-rule models for predicting perceptual classification response times (RTs) and choice probabilities. The models are developed by synthesizing mental-architecture, random-walk, and decision-bound approaches. According to the models, people make independent decisions about the locations of stimuli along a set of component dimensions. Those independent decisions are then combined via logical rules to determine the overall categorization response. The time course of the independent decisions is modeled via random-walk processes operating along individual dimensions. Alternative mental architectures are used as mechanisms for combining the independent decisions to implement the logical rules. We derive fundamental qualitative contrasts for distinguishing among the predictions of the rule models and major alternative models of classification RT. We also use the models to predict detailed RT-distribution data associated with individual stimuli in tasks of speeded perceptual classification. PsycINFO Database Record (c) 2010 APA, all rights reserved.

Single-particle dispersion in stably stratified turbulence

NASA Astrophysics Data System (ADS)

Sujovolsky, N. E.; Mininni, P. D.; Rast, M. P.

2018-03-01

We present models for single-particle dispersion in vertical and horizontal directions of stably stratified flows. The model in the vertical direction is based on the observed Lagrangian spectrum of the vertical velocity, while the model in the horizontal direction is a combination of a continuous-time eddy-constrained random walk process with a contribution to transport from horizontal winds. Transport at times larger than the Lagrangian turnover time is not universal and dependent on these winds. The models yield results in good agreement with direct numerical simulations of stratified turbulence, for which single-particle dispersion differs from the well-studied case of homogeneous and isotropic turbulence.

Improving Motor Control in Walking: A Randomized Clinical Trial in Older Adults with Subclinical Walking Difficulty

PubMed Central

Brach, Jennifer S.; Lowry, Kristin; Perera, Subashan; Hornyak, Victoria; Wert, David; Studenski, Stephanie A.; VanSwearingen, Jessie M.

2016-01-01

Objective The objective was to test the proposed mechanism of action of a task-specific motor learning intervention by examining its effect on measures of the motor control of gait. Design Single blinded randomized clinical trial. Setting University research laboratory. Participants Forty older adults 65 years of age and older, with gait speed >1.0 m/s and impaired motor skill (Figure of 8 walk time > 8 secs). Interventions The two interventions included a task-oriented motor learning and a standard exercise program. Both interventions lasted 12 weeks, with twice weekly one hour physical therapist supervised sessions. Main Outcome Measures Two measure of the motor control of gait, gait variability and smoothness of walking, were assessed pre and post intervention by assessors masked to treatment arm. Results Of 40 randomized subjects; 38 completed the trial (mean age 77.1±6.0 years). Motor control group improved more than standard group in double support time variability (0.13 vs. 0.05 m/s; adjusted difference, AD=0.006, p=0.03). Smoothness of walking in the anterior/posterior direction improved more in motor control than standard for all conditions (usual: AD=0.53, p=0.05; narrow: AD=0.56, p=0.01; dual task: AD=0.57, p=0.04). Conclusions Among older adults with subclinical walking difficulty, there is initial evidence that task-oriented motor learning exercise results in gains in the motor control of walking, while standard exercise does not. Task-oriented motor learning exercise is a promising intervention for improving timing and coordination deficits related to mobility difficulties in older adults, and needs to be evaluated in a definitive larger trial. PMID:25448244

Narrow log-periodic modulations in non-Markovian random walks

NASA Astrophysics Data System (ADS)

Diniz, R. M. B.; Cressoni, J. C.; da Silva, M. A. A.; Mariz, A. M.; de Araújo, J. M.

2017-12-01

What are the necessary ingredients for log-periodicity to appear in the dynamics of a random walk model? Can they be subtle enough to be overlooked? Previous studies suggest that long-range damaged memory and negative feedback together are necessary conditions for the emergence of log-periodic oscillations. The role of negative feedback would then be crucial, forcing the system to change direction. In this paper we show that small-amplitude log-periodic oscillations can emerge when the system is driven by positive feedback. Due to their very small amplitude, these oscillations can easily be mistaken for numerical finite-size effects. The models we use consist of discrete-time random walks with strong memory correlations where the decision process is taken from memory profiles based either on a binomial distribution or on a delta distribution. Anomalous superdiffusive behavior and log-periodic modulations are shown to arise in the large time limit for convenient choices of the models parameters.

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

NASA Astrophysics Data System (ADS)

Zhang, Hong; Li, Guo-Hua

2016-11-01

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. Project supported by the Foundation for Young Key Teachers of Chengdu University of Technology, China (Grant No. KYGG201414) and the Opening Foundation of Geomathematics Key Laboratory of Sichuan Province, China (Grant No. scsxdz2013009).

Open quantum random walk in terms of quantum Bernoulli noise

NASA Astrophysics Data System (ADS)

Wang, Caishi; Wang, Ce; Ren, Suling; Tang, Yuling

2018-03-01

In this paper, we introduce an open quantum random walk, which we call the QBN-based open walk, by means of quantum Bernoulli noise, and study its properties from a random walk point of view. We prove that, with the localized ground state as its initial state, the QBN-based open walk has the same limit probability distribution as the classical random walk. We also show that the probability distributions of the QBN-based open walk include those of the unitary quantum walk recently introduced by Wang and Ye (Quantum Inf Process 15:1897-1908, 2016) as a special case.

Unexpected perturbations training improves balance control and voluntary stepping times in older adults - a double blind randomized control trial.

PubMed

Kurz, Ilan; Gimmon, Yoav; Shapiro, Amir; Debi, Ronen; Snir, Yoram; Melzer, Itshak

2016-03-04

Falls are common among elderly, most of them occur while slipping or tripping during walking. We aimed to explore whether a training program that incorporates unexpected loss of balance during walking able to improve risk factors for falls. In a double-blind randomized controlled trial 53 community dwelling older adults (age 80.1±5.6 years), were recruited and randomly allocated to an intervention group (n = 27) or a control group (n = 26). The intervention group received 24 training sessions over 3 months that included unexpected perturbation of balance exercises during treadmill walking. The control group performed treadmill walking with no perturbations. The primary outcome measures were the voluntary step execution times, traditional postural sway parameters and Stabilogram-Diffusion Analysis. The secondary outcome measures were the fall efficacy Scale (FES), self-reported late life function (LLFDI), and Performance-Oriented Mobility Assessment (POMA). Compared to control, participation in intervention program that includes unexpected loss of balance during walking led to faster Voluntary Step Execution Times under single (p = 0.002; effect size [ES] =0.75) and dual task (p = 0.003; [ES] = 0.89) conditions; intervention group subjects showed improvement in Short-term Effective diffusion coefficients in the mediolateral direction of the Stabilogram-Diffusion Analysis under eyes closed conditions (p = 0.012, [ES] = 0.92). Compared to control there were no significant changes in FES, LLFDI, and POMA. An intervention program that includes unexpected loss of balance during walking can improve voluntary stepping times and balance control, both previously reported as risk factors for falls. This however, did not transferred to a change self-reported function and FES. ClinicalTrials.gov NCT01439451 .

Promoting Activity in Geriatric Rehabilitation: A Randomized Controlled Trial of Accelerometry.

PubMed

Peel, Nancye M; Paul, Sanjoy K; Cameron, Ian D; Crotty, Maria; Kurrle, Susan E; Gray, Leonard C

2016-01-01

Low activity levels in inpatient rehabilitation are associated with adverse outcomes. The study aimed to test whether activity levels can be increased by the provision of monitored activity data to patients and clinicians in the context of explicit goal setting. A randomized controlled trial in three sites in Australia included 255 inpatients aged 60 and older who had a rehabilitation goal to become ambulant. The primary outcome was patients' walking time measured by accelerometers during the rehabilitation admission. Walking times from accelerometry were made available daily to treating therapists and intervention participants to motivate patients to improve incidental activity levels and reach set goals. For the control group, 'usual care' was followed, including the setting of mobility goals; however, for this group, neither staff nor patients received data on walking times to aid the setting of daily walking time targets. The median daily walking time in the intervention group increased from 10.3 minutes at baseline to 32.1 minutes at day 28, compared with an increase from 9.5 to 26.5 minutes per day in the control group. Subjects in the intervention group had significantly higher non-therapy walking time by about 7 minutes [mean (95% CI): 24.6 (21.7, 27.4)] compared to those in the control group [mean(95% CI): 17.3 (14.4, 20.3)] (p = 0.001). Daily feedback to patients and therapists using an accelerometer increased walking times during rehabilitation admissions. The results of this study suggest objective monitoring of activity levels could provide clinicians with information on clinically important, mobility-related activities to assist goal setting. Australian New Zealand Clinical Trials Registry ACTRN12611000034932 http://www.ANZCTR.org.au/.

Why the null matters: statistical tests, random walks and evolution.

PubMed

Sheets, H D; Mitchell, C E

2001-01-01

A number of statistical tests have been developed to determine what type of dynamics underlie observed changes in morphology in evolutionary time series, based on the pattern of change within the time series. The theory of the 'scaled maximum', the 'log-rate-interval' (LRI) method, and the Hurst exponent all operate on the same principle of comparing the maximum change, or rate of change, in the observed dataset to the maximum change expected of a random walk. Less change in a dataset than expected of a random walk has been interpreted as indicating stabilizing selection, while more change implies directional selection. The 'runs test' in contrast, operates on the sequencing of steps, rather than on excursion. Applications of these tests to computer generated, simulated time series of known dynamical form and various levels of additive noise indicate that there is a fundamental asymmetry in the rate of type II errors of the tests based on excursion: they are all highly sensitive to noise in models of directional selection that result in a linear trend within a time series, but are largely noise immune in the case of a simple model of stabilizing selection. Additionally, the LRI method has a lower sensitivity than originally claimed, due to the large range of LRI rates produced by random walks. Examination of the published results of these tests show that they have seldom produced a conclusion that an observed evolutionary time series was due to directional selection, a result which needs closer examination in light of the asymmetric response of these tests.

Exploration and Trapping of Mortal Random Walkers

NASA Astrophysics Data System (ADS)

Yuste, S. B.; Abad, E.; Lindenberg, Katja

2013-05-01

Exploration and trapping properties of random walkers that may evanesce at any time as they walk have seen very little treatment in the literature, and yet a finite lifetime is a frequent occurrence, and its effects on a number of random walk properties may be profound. For instance, whereas the average number of distinct sites visited by an immortal walker grows with time without bound, that of a mortal walker may, depending on dimensionality and rate of evanescence, remain finite or keep growing with the passage of time. This number can in turn be used to calculate other classic quantities such as the survival probability of a target surrounded by diffusing traps. If the traps are immortal, the survival probability will vanish with increasing time. However, if the traps are evanescent, the target may be spared a certain death. We analytically calculate a number of basic and broadly used quantities for evanescent random walkers.

Record statistics for biased random walks, with an application to financial data

NASA Astrophysics Data System (ADS)

Wergen, Gregor; Bogner, Miro; Krug, Joachim

2011-05-01

We consider the occurrence of record-breaking events in random walks with asymmetric jump distributions. The statistics of records in symmetric random walks was previously analyzed by Majumdar and Ziff [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.101.050601 101, 050601 (2008)] and is well understood. Unlike the case of symmetric jump distributions, in the asymmetric case the statistics of records depends on the choice of the jump distribution. We compute the record rate Pn(c), defined as the probability for the nth value to be larger than all previous values, for a Gaussian jump distribution with standard deviation σ that is shifted by a constant drift c. For small drift, in the sense of c/σ≪n-1/2, the correction to Pn(c) grows proportional to arctan(n) and saturates at the value (c)/(2σ). For large n the record rate approaches a constant, which is approximately given by 1-(σ/2πc)exp(-c2/2σ2) for c/σ≫1. These asymptotic results carry over to other continuous jump distributions with finite variance. As an application, we compare our analytical results to the record statistics of 366 daily stock prices from the Standard & Poor's 500 index. The biased random walk accounts quantitatively for the increase in the number of upper records due to the overall trend in the stock prices, and after detrending the number of upper records is in good agreement with the symmetric random walk. However the number of lower records in the detrended data is significantly reduced by a mechanism that remains to be identified.

Different Patterns of Walking and Postprandial Triglycerides in Older Women

PubMed Central

KASHIWABARA, KYOKO; KIDOKORO, TETSUHIRO; YANAOKA, TAKUMA; BURNS, STEPHEN F.; STENSEL, DAVID J.; MIYASHITA, MASASHI

2018-01-01

ABSTRACT Purpose Although a single bout of continuous exercise (≥30 min) reduces postprandial triglyceride (TG), little evidence is available regarding the effect of multiple short (≤10 min) bouts of exercise on postprandial TG in individuals at increased risk for cardiovascular diseases. This study compared the effects of different patterns of walking on postprandial TG in postmenopausal, older women with hypertriglyceridemia. Methods Twelve inactive women (mean age ± SD, 71 ± 5 yr) with hypertriglyceridemia (fasting TG ≥1.70 mmol·L−1) completed three, 1-d laboratory-based trials in a random order: 1) control, 2) continuous walking, and 3) multiple short bouts of walking. On the control trial, participants sat in a chair for 8 h. For the walking trials, participants walked briskly in either one 30-min bout in the morning (0900–0930 h) or twenty 90-s bouts over 8 h. Except for walking, both exercise trials mimicked the control trial. In each trial, participants consumed a standardized breakfast (0800 h) and lunch (1100 h). Venous blood samples were collected in the fasted state and at 2, 4, 6, and 8 h after breakfast. Results The serum TG incremental area under the curve was 35% and 33% lower on the continuous and multiple short bouts of walking trials than that on the control trial (8.2 ± 3.1 vs 8.5 ± 5.4 vs 12.7 ± 5.8 mmol per 8 h·L−1, respectively; main effect of trial: effect size = 0.459, P = 0.001). Conclusions Accumulating walking in short bouts limits postprandial TG in at-risk, inactive older women with fasting hypertriglyceridemia. PMID:28857839

Reheating-volume measure for random-walk inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Winitzki, Sergei; Yukawa Institute of Theoretical Physics, Kyoto University, Kyoto

2008-09-15

The recently proposed 'reheating-volume' (RV) measure promises to solve the long-standing problem of extracting probabilistic predictions from cosmological multiverse scenarios involving eternal inflation. I give a detailed description of the new measure and its applications to generic models of eternal inflation of random-walk type. For those models I derive a general formula for RV-regulated probability distributions that is suitable for numerical computations. I show that the results of the RV cutoff in random-walk type models are always gauge invariant and independent of the initial conditions at the beginning of inflation. In a toy model where equal-time cutoffs lead to themore » 'youngness paradox', the RV cutoff yields unbiased results that are distinct from previously proposed measures.« less

Pores-scale hydrodynamics in a progressively bio-clogged three-dimensional porous medium: 3D particle tracking experiments and stochastic transport modelling

NASA Astrophysics Data System (ADS)

Morales, V. L.; Carrel, M.; Dentz, M.; Derlon, N.; Morgenroth, E.; Holzner, M.

2017-12-01

Biofilms are ubiquitous bacterial communities growing in various porous media including soils, trickling and sand filters and are relevant for applications such as the degradation of pollutants for bioremediation, waste water or drinking water production purposes. By their development, biofilms dynamically change the structure of porous media, increasing the heterogeneity of the pore network and the non-Fickian or anomalous dispersion. In this work, we use an experimental approach to investigate the influence of biofilm growth on pore scale hydrodynamics and transport processes and propose a correlated continuous time random walk model capturing these observations. We perform three-dimensional particle tracking velocimetry at four different time points from 0 to 48 hours of biofilm growth. The biofilm growth notably impacts pore-scale hydrodynamics, as shown by strong increase of the average velocity and in tailing of Lagrangian velocity probability density functions. Additionally, the spatial correlation length of the flow increases substantially. This points at the formation of preferential flow pathways and stagnation zones, which ultimately leads to an increase of anomalous transport in the porous media considered, characterized by non-Fickian scaling of mean-squared displacements and non-Gaussian distributions of the displacement probability density functions. A gamma distribution provides a remarkable approximation of the bulk and the high tail of the Lagrangian pore-scale velocity magnitude, indicating a transition from a parallel pore arrangement towards a more serial one. Finally, a correlated continuous time random walk based on a stochastic relation velocity model accurately reproduces the observations and could be used to predict transport beyond the time scales accessible to the experiment.

Analytic method for calculating properties of random walks on networks

NASA Technical Reports Server (NTRS)

Goldhirsch, I.; Gefen, Y.

1986-01-01

A method for calculating the properties of discrete random walks on networks is presented. The method divides complex networks into simpler units whose contribution to the mean first-passage time is calculated. The simplified network is then further iterated. The method is demonstrated by calculating mean first-passage times on a segment, a segment with a single dangling bond, a segment with many dangling bonds, and a looplike structure. The results are analyzed and related to the applicability of the Einstein relation between conductance and diffusion.

Prolonged Walking with a Wearable System Providing Intelligent Auditory Input in People with Parkinson's Disease.

PubMed

Ginis, Pieter; Heremans, Elke; Ferrari, Alberto; Dockx, Kim; Canning, Colleen G; Nieuwboer, Alice

2017-01-01

Rhythmic auditory cueing is a well-accepted tool for gait rehabilitation in Parkinson's disease (PD), which can now be applied in a performance-adapted fashion due to technological advance. This study investigated the immediate differences on gait during a prolonged, 30 min, walk with performance-adapted (intelligent) auditory cueing and verbal feedback provided by a wearable sensor-based system as alternatives for traditional cueing. Additionally, potential effects on self-perceived fatigue were assessed. Twenty-eight people with PD and 13 age-matched healthy elderly (HE) performed four 30 min walks with a wearable cue and feedback system. In randomized order, participants received: (1) continuous auditory cueing; (2) intelligent cueing (10 metronome beats triggered by a deviating walking rhythm); (3) intelligent feedback (verbal instructions triggered by a deviating walking rhythm); and (4) no external input. Fatigue was self-scored at rest and after walking during each session. The results showed that while HE were able to maintain cadence for 30 min during all conditions, cadence in PD significantly declined without input. With continuous cueing and intelligent feedback people with PD were able to maintain cadence ( p  = 0.04), although they were more physically fatigued than HE. Furthermore, cadence deviated significantly more in people with PD than in HE without input and particularly with intelligent feedback (both: p  = 0.04). In PD, continuous and intelligent cueing induced significantly less deviations of cadence ( p  = 0.006). Altogether, this suggests that intelligent cueing is a suitable alternative for the continuous mode during prolonged walking in PD, as it induced similar effects on gait without generating levels of fatigue beyond that of HE.

From samples to populations in retinex models

NASA Astrophysics Data System (ADS)

Gianini, Gabriele

2017-05-01

Some spatial color algorithms, such as Brownian Milano retinex (MI-retinex) and random spray retinex (RSR), are based on sampling. In Brownian MI-retinex, memoryless random walks (MRWs) explore the neighborhood of a pixel and are then used to compute its output. Considering the relative redundancy and inefficiency of MRW exploration, the algorithm RSR replaced the walks by samples of points (the sprays). Recent works point to the fact that a mapping from the sampling formulation to the probabilistic formulation of the corresponding sampling process can offer useful insights into the models, at the same time featuring intrinsically noise-free outputs. The paper continues the development of this concept and shows that the population-based versions of RSR and Brownian MI-retinex can be used to obtain analytical expressions for the outputs of some test images. The comparison of the two analytic expressions from RSR and from Brownian MI-retinex demonstrates not only that the two outputs are, in general, different but also that they depend in a qualitatively different way upon the features of the image.

Monte Carlo random walk simulation of electron transport in confined porous TiO{sub 2} as a promising candidate for photo-electrode of nano-crystalline solar cells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Javadi, M.; Abdi, Y., E-mail: y.abdi@ut.ac.ir

2015-08-14

Monte Carlo continuous time random walk simulation is used to study the effects of confinement on electron transport, in porous TiO{sub 2}. In this work, we have introduced a columnar structure instead of the thick layer of porous TiO{sub 2} used as anode in conventional dye solar cells. Our simulation results show that electron diffusion coefficient in the proposed columnar structure is significantly higher than the diffusion coefficient in the conventional structure. It is shown that electron diffusion in the columnar structure depends both on the cross section area of the columns and the porosity of the structure. Also, wemore » demonstrate that such enhanced electron diffusion can be realized in the columnar photo-electrodes with a cross sectional area of ∼1 μm{sup 2} and porosity of 55%, by a simple and low cost fabrication process. Our results open up a promising approach to achieve solar cells with higher efficiencies by engineering the photo-electrode structure.« less

Monte Carlo random walk simulation of electron transport in confined porous TiO2 as a promising candidate for photo-electrode of nano-crystalline solar cells

NASA Astrophysics Data System (ADS)

Javadi, M.; Abdi, Y.

2015-08-01

Monte Carlo continuous time random walk simulation is used to study the effects of confinement on electron transport, in porous TiO2. In this work, we have introduced a columnar structure instead of the thick layer of porous TiO2 used as anode in conventional dye solar cells. Our simulation results show that electron diffusion coefficient in the proposed columnar structure is significantly higher than the diffusion coefficient in the conventional structure. It is shown that electron diffusion in the columnar structure depends both on the cross section area of the columns and the porosity of the structure. Also, we demonstrate that such enhanced electron diffusion can be realized in the columnar photo-electrodes with a cross sectional area of ˜1 μm2 and porosity of 55%, by a simple and low cost fabrication process. Our results open up a promising approach to achieve solar cells with higher efficiencies by engineering the photo-electrode structure.

Effect of Body Weight-supported Walking on Exercise Capacity and Walking Speed in Patients with Knee Osteoarthritis: A Randomized Controlled Trial

PubMed Central

Someya, Fujiko

2013-01-01

Abstract Objective: To compare the effect of body-weight-supported treadmill training (BWSTT) and full-body-weight treadmill training (FBWTT) on patients with knee osteoarthritis (OA). Methods: Design was Randomized controlled trial. Patients with knee osteoarthritis (n = 30; mean age, 76.0±7.5 y) were randomly assigned to BWSTT or FBWTT group. All patients performed 20 min walking exercise twice a week for 6 weeks under the supervision of the therapist. Main measures were 10-meter walking test (10MWT), functional reach test (FRT), timed get up and go test (TUG), one-leg standing test, 6-minute walking test (6MWT), the parameters set on the treadmill, MOS Short-Form 36-Item Health Survey (SF36), Japanese Knee Osteoarthritis Measure (JKOM). Results: Twenty-five patients (10 men, 15 women; mean age, 76.5 ± 8.0 y) completed the experiment. Exercise capacity, indicated by the heart rate, was similar in both groups. After 3 weeks of BWSTT, the patients performed significantly better in the 10-m and 6-min walking tests. This was not the case with FBWTT even after 6 weeks training. Pain levels assessed were significantly improved after 3 weeks of BWSTT and 6 weeks of FBWTT. There were no significant improvements in either group assessed by the FRT, one-leg standing time test, TUG, or SF -36 questionnaire. Conclusions: BWSTT enhanced exercise capacity in terms of walking speed and pain reduction after 3 weeks; however, there was no significant improvement in patients' functional abilities or quality of life. PMID:25792901

Locally adaptive methods for KDE-based random walk models of reactive transport in porous media

NASA Astrophysics Data System (ADS)

Sole-Mari, G.; Fernandez-Garcia, D.

2017-12-01

Random Walk Particle Tracking (RWPT) coupled with Kernel Density Estimation (KDE) has been recently proposed to simulate reactive transport in porous media. KDE provides an optimal estimation of the area of influence of particles which is a key element to simulate nonlinear chemical reactions. However, several important drawbacks can be identified: (1) the optimal KDE method is computationally intensive and thereby cannot be used at each time step of the simulation; (2) it does not take advantage of the prior information about the physical system and the previous history of the solute plume; (3) even if the kernel is optimal, the relative error in RWPT simulations typically increases over time as the particle density diminishes by dilution. To overcome these problems, we propose an adaptive branching random walk methodology that incorporates the physics, the particle history and maintains accuracy with time. The method allows particles to efficiently split and merge when necessary as well as to optimally adapt their local kernel shape without having to recalculate the kernel size. We illustrate the advantage of the method by simulating complex reactive transport problems in randomly heterogeneous porous media.

Aerobic treadmill plus Bobath walking training improves walking in subacute stroke: a randomized controlled trial.

PubMed

Eich, H-J; Mach, H; Werner, C; Hesse, S

2004-09-01

To evaluate the immediate and long-term effects of aerobic treadmill plus Bobath walking training in subacute stroke survivors compared with Bobath walking training alone. Randomized controlled trial. Rehabilitation unit. Fifty patients, first-time supratentorial stroke, stroke interval less than six weeks, Barthel Index (0-100) from 50 to 80, able to walk a minimum distance of 12 m with either intermittent help or stand-by while walking, cardiovascular stable, minimum 50 W in the bicycle ergometry, randomly allocated to two groups, A and B. Group A 30 min of treadmill training, harness secured and minimally supported according to patients' needs, and 30 min of physiotherapy, every workday for six weeks, speed and inclination of the treadmill were adjusted to achieve a heart rate of HR: (Hrmax-HRrest)*0.6+HRrest; in group B 60 min of daily physiotherapy for six weeks. Primary outcome variables were the absolute improvement of walking velocity (m/s) and capacity (m), secondary were gross motor function including walking ability (score out of 13) and walking quality (score out of 41), blindly assessed before and after the intervention, and at follow-up three months later. Patients tolerated the aerobic training well with no side-effects, significantly greater improvement of walking velocity and capacity both at study end (p =0.001 versus p =0.002) and at follow-up (p <0.001 versus p <0.001) in the experimental group. Between weeks 0 and 6, the experimental group improved walking speed and capacity by a mean of.31 m/s and 91 m, the control group by a mean of 0.16 m/s and 56 m. Between weeks 0 and 18, the experimental group improved walking speed and capacity by a mean of 0.36 m/s and 111 m, the control group by a mean of 0.15 m/s and 57 m. Gross motor function and walking quality did not differ at any time. Aerobic treadmill plus Bobath walking training in moderately affected stroke patients was better than Bobath walking training alone with respect to the improvement of walking velocity and capacity. The treatment approach is recommended in patients meeting the inclusion criteria. A multicentre trial should follow to strengthen the evidence.

Effects of a wearable exoskeleton stride management assist system (SMA®) on spatiotemporal gait characteristics in individuals after stroke: a randomized controlled trial.

PubMed

Buesing, Carolyn; Fisch, Gabriela; O'Donnell, Megan; Shahidi, Ida; Thomas, Lauren; Mummidisetty, Chaithanya K; Williams, Kenton J; Takahashi, Hideaki; Rymer, William Zev; Jayaraman, Arun

2015-08-20

Robots offer an alternative, potentially advantageous method of providing repetitive, high-dosage, and high-intensity training to address the gait impairments caused by stroke. In this study, we compared the effects of the Stride Management Assist (SMA®) System, a new wearable robotic device developed by Honda R&D Corporation, Japan, with functional task specific training (FTST) on spatiotemporal gait parameters in stroke survivors. A single blinded randomized control trial was performed to assess the effect of FTST and task-specific walking training with the SMA® device on spatiotemporal gait parameters. Participants (n=50) were randomly assigned to FTST or SMA. Subjects in both groups received training 3 times per week for 6-8 weeks for a maximum of 18 training sessions. The GAITRite® system was used to collect data on subjects' spatiotemporal gait characteristics before training (baseline), at mid-training, post-training, and at a 3-month follow-up. After training, significant improvements in gait parameters were observed in both training groups compared to baseline, including an increase in velocity and cadence, a decrease in swing time on the impaired side, a decrease in double support time, an increase in stride length on impaired and non-impaired sides, and an increase in step length on impaired and non-impaired sides. No significant differences were observed between training groups; except for SMA group, step length on the impaired side increased significantly during self-selected walking speed trials and spatial asymmetry decreased significantly during fast-velocity walking trials. SMA and FTST interventions provided similar, significant improvements in spatiotemporal gait parameters; however, the SMA group showed additional improvements across more parameters at various time points. These results indicate that the SMA® device could be a useful therapeutic tool to improve spatiotemporal parameters and contribute to improved functional mobility in stroke survivors. Further research is needed to determine the feasibility of using this device in a home setting vs a clinic setting, and whether such home use provides continued benefits. This study is registered under the title "Development of walk assist device to improve community ambulation" and can be located in clinicaltrials.gov with the study identifier: NCT01994395 .

Wheeled and standard walkers in Parkinson's disease patients with gait freezing.

PubMed

Cubo, Esther; Moore, Charity G; Leurgans, Sue; Goetz, Christopher G

2003-10-01

Compare the efficacy of two walking assistance devices (wheeled walker and standard walker) to unassisted walking for patients with PD and gait freezing. Although numerous walking devices are used clinically, their relative effects on freezing and walking speed have never been systematically tested. Nineteen PD patients (14 non-demented) walked under three conditions in randomized order: unassisted walking, standard walker, and wheeled walker. Patients walked up to three times in each condition through a standard course that included rising from a chair, walking through a doorway, straightway walking, pivoting, and return. Total walking time, freezing time and number of freezes were compared for the three conditions using mixed models (walking time) and Friedman's test (freezing). The wheeled walker was further studied by comparing the effect of an attached laser that projected a bar of light on the floor as a visual walking cue. Use of either type of device significantly slowed walking compared to unassisted walking. Neither walker reduced any index of freezing, nor the laser attachment offered any advantage to the wheeled walker. The standard walker increased freezing, and the wheeled walker had no effect on freezing. Among the non-demented subjects (n=14), the same patterns occurred, although the walking speed was less impaired by the wheeled walker than the standard walker in this group. Though walkers may stabilize patients and increase confidence, PD patients walk more slowly when using them, without reducing freezing. Because the wheeled walker was intermediate for walking time and does not aggravate freezing, if walkers are used for these subjects, this type of walker should be favored.

Effectiveness of an innovative hip energy storage walking orthosis for improving paraplegic walking: A pilot randomized controlled study.

PubMed

Yang, Mingliang; Li, Jianjun; Guan, Xinyu; Gao, Lianjun; Gao, Feng; Du, Liangjie; Zhao, Hongmei; Yang, Degang; Yu, Yan; Wang, Qimin; Wang, Rencheng; Ji, Linhong

2017-09-01

The high energy cost of paraplegic walking using a reciprocating gait orthosis (RGO) is attributed to limited hip motion and excessive upper limb loading for support. To address the limitation, we designed the hip energy storage walking orthosis (HESWO) which uses a spring assembly on the pelvic shell to store energy from the movements of the healthy upper limbs and flexion-extension of the lumbar spine and hip and returns this energy to lift the pelvis and lower limb to assist with the swing and stance components of a stride. Our aim was to evaluate gait and energy cost indices for the HESWO compared to the RGO in patients with paraplegia. The cross-over design was used in the pilot study. Twelve patients with a complete T4-L5 chronic spinal cord injury underwent gait training using the HESWO and RGO. Gait performance (continuous walking distance, as well as the maximum and comfortable walking speeds) and energy expenditure (at a walking speed of 3.3m/min on a treadmill) were measured at the end of the 4-week training session. Compared to the RGO, the HESWO increased continuous walking distance by 24.7% (P<0.05), maximum walking speed by 20.4% (P<0.05) and the comfortable walking speed by 15.3% (P<0.05), as well as decreasing energy expenditure by 13.9% (P<0.05). Our preliminary results provide support for the use of the HESWO as an alternative support for paraplegic walking. Copyright © 2017. Published by Elsevier B.V.

Individual analyses of Lévy walk in semi-free ranging Tonkean macaques (Macaca tonkeana).

PubMed

Sueur, Cédric; Briard, Léa; Petit, Odile

2011-01-01

Animals adapt their movement patterns to their environment in order to maximize their efficiency when searching for food. The Lévy walk and the Brownian walk are two types of random movement found in different species. Studies have shown that these random movements can switch from a Brownian to a Lévy walk according to the size distribution of food patches. However no study to date has analysed how characteristics such as sex, age, dominance or body mass affect the movement patterns of an individual. In this study we used the maximum likelihood method to examine the nature of the distribution of step lengths and waiting times and assessed how these distributions are influenced by the age and the sex of group members in a semi free-ranging group of ten Tonkean macaques. Individuals highly differed in their activity budget and in their movement patterns. We found an effect of age and sex of individuals on the power distribution of their step lengths and of their waiting times. The males and old individuals displayed a higher proportion of longer trajectories than females and young ones. As regards waiting times, females and old individuals displayed higher rates of long stationary periods than males and young individuals. These movement patterns resembling random walks can probably be explained by the animals moving from one location to other known locations. The power distribution of step lengths might be due to a power distribution of food patches in the enclosure while the power distribution of waiting times might be due to the power distribution of the patch sizes.

In the eye of the beholder: Inhomogeneous distribution of high-resolution shapes within the random-walk ensemble

NASA Astrophysics Data System (ADS)

Müller, Christian L.; Sbalzarini, Ivo F.; van Gunsteren, Wilfred F.; Žagrović, Bojan; Hünenberger, Philippe H.

2009-06-01

The concept of high-resolution shapes (also referred to as folds or states, depending on the context) of a polymer chain plays a central role in polymer science, structural biology, bioinformatics, and biopolymer dynamics. However, although the idea of shape is intuitively very useful, there is no unambiguous mathematical definition for this concept. In the present work, the distributions of high-resolution shapes within the ideal random-walk ensembles with N =3,…,6 beads (or up to N =10 for some properties) are investigated using a systematic (grid-based) approach based on a simple working definition of shapes relying on the root-mean-square atomic positional deviation as a metric (i.e., to define the distance between pairs of structures) and a single cutoff criterion for the shape assignment. Although the random-walk ensemble appears to represent the paramount of homogeneity and randomness, this analysis reveals that the distribution of shapes within this ensemble, i.e., in the total absence of interatomic interactions characteristic of a specific polymer (beyond the generic connectivity constraint), is significantly inhomogeneous. In particular, a specific (densest) shape occurs with a local probability that is 1.28, 1.79, 2.94, and 10.05 times (N =3,…,6) higher than the corresponding average over all possible shapes (these results can tentatively be extrapolated to a factor as large as about 1028 for N =100). The qualitative results of this analysis lead to a few rather counterintuitive suggestions, namely, that, e.g., (i) a fold classification analysis applied to the random-walk ensemble would lead to the identification of random-walk "folds;" (ii) a clustering analysis applied to the random-walk ensemble would also lead to the identification random-walk "states" and associated relative free energies; and (iii) a random-walk ensemble of polymer chains could lead to well-defined diffraction patterns in hypothetical fiber or crystal diffraction experiments. The inhomogeneous nature of the shape probability distribution identified here for random walks may represent a significant underlying baseline effect in the analysis of real polymer chain ensembles (i.e., in the presence of specific interatomic interactions). As a consequence, a part of what is called a polymer shape may actually reside just "in the eye of the beholder" rather than in the nature of the interactions between the constituting atoms, and the corresponding observation-related bias should be taken into account when drawing conclusions from shape analyses as applied to real structural ensembles.

In the eye of the beholder: Inhomogeneous distribution of high-resolution shapes within the random-walk ensemble.

PubMed

Müller, Christian L; Sbalzarini, Ivo F; van Gunsteren, Wilfred F; Zagrović, Bojan; Hünenberger, Philippe H

2009-06-07

The concept of high-resolution shapes (also referred to as folds or states, depending on the context) of a polymer chain plays a central role in polymer science, structural biology, bioinformatics, and biopolymer dynamics. However, although the idea of shape is intuitively very useful, there is no unambiguous mathematical definition for this concept. In the present work, the distributions of high-resolution shapes within the ideal random-walk ensembles with N=3,...,6 beads (or up to N=10 for some properties) are investigated using a systematic (grid-based) approach based on a simple working definition of shapes relying on the root-mean-square atomic positional deviation as a metric (i.e., to define the distance between pairs of structures) and a single cutoff criterion for the shape assignment. Although the random-walk ensemble appears to represent the paramount of homogeneity and randomness, this analysis reveals that the distribution of shapes within this ensemble, i.e., in the total absence of interatomic interactions characteristic of a specific polymer (beyond the generic connectivity constraint), is significantly inhomogeneous. In particular, a specific (densest) shape occurs with a local probability that is 1.28, 1.79, 2.94, and 10.05 times (N=3,...,6) higher than the corresponding average over all possible shapes (these results can tentatively be extrapolated to a factor as large as about 10(28) for N=100). The qualitative results of this analysis lead to a few rather counterintuitive suggestions, namely, that, e.g., (i) a fold classification analysis applied to the random-walk ensemble would lead to the identification of random-walk "folds;" (ii) a clustering analysis applied to the random-walk ensemble would also lead to the identification random-walk "states" and associated relative free energies; and (iii) a random-walk ensemble of polymer chains could lead to well-defined diffraction patterns in hypothetical fiber or crystal diffraction experiments. The inhomogeneous nature of the shape probability distribution identified here for random walks may represent a significant underlying baseline effect in the analysis of real polymer chain ensembles (i.e., in the presence of specific interatomic interactions). As a consequence, a part of what is called a polymer shape may actually reside just "in the eye of the beholder" rather than in the nature of the interactions between the constituting atoms, and the corresponding observation-related bias should be taken into account when drawing conclusions from shape analyses as applied to real structural ensembles.

From coupled elementary units to the complexity of the glass transition.

PubMed

Rehwald, Christian; Rubner, Oliver; Heuer, Andreas

2010-09-10

Supercooled liquids display fascinating properties upon cooling such as the emergence of dynamic length scales. Different models strongly vary with respect to the choice of the elementary subsystems as well as their mutual coupling. Here we show via computer simulations of a glass former that both ingredients can be identified via analysis of finite-size effects within the continuous-time random walk framework. The subsystems already contain complete information about thermodynamics and diffusivity, whereas the coupling determines structural relaxation and the emergence of dynamic length scales.

Bayesian dynamic modeling of time series of dengue disease case counts

PubMed Central

López-Quílez, Antonio; Torres-Prieto, Alexander

2017-01-01

The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model’s short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order random walk time-varying coefficients. We applied Markov Chain Monte Carlo simulations for parameter estimation, and deviance information criterion statistic (DIC) for model selection. We assessed the short-term predictive performance of the selected final model, at several time points within the study period using the mean absolute percentage error. The results showed the best model including first-order random walk time-varying coefficients for calendar trend and first-order random walk time-varying coefficients for the meteorological variables. Besides the computational challenges, interpreting the results implies a complete analysis of the time series of dengue with respect to the parameter estimates of the meteorological effects. We found small values of the mean absolute percentage errors at one or two weeks out-of-sample predictions for most prediction points, associated with low volatility periods in the dengue counts. We discuss the advantages and limitations of the dynamic Poisson models for studying the association between time series of dengue disease and meteorological variables. The key conclusion of the study is that dynamic Poisson models account for the dynamic nature of the variables involved in the modeling of time series of dengue disease, producing useful models for decision-making in public health. PMID:28671941

Applications of a general random-walk theory for confined diffusion.

PubMed

Calvo-Muñoz, Elisa M; Selvan, Myvizhi Esai; Xiong, Ruichang; Ojha, Madhusudan; Keffer, David J; Nicholson, Donald M; Egami, Takeshi

2011-01-01

A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.

On Convergent Probability of a Random Walk

ERIC Educational Resources Information Center

Lee, Y.-F.; Ching, W.-K.

2006-01-01

This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.

Cardiac Patients’ Walking Activity Determined by a Step Counter in Cardiac Telerehabilitation: Data From the Intervention Arm of a Randomized Controlled Trial

PubMed Central

Hansen, John; Grønkjær, Mette; Andreasen, Jan Jesper; Nielsen, Gitte; Sørensen, Erik Elgaard; Dinesen, Birthe Irene

2016-01-01

Background Walking represents a large part of daily physical activity. It reduces both overall and cardiovascular diseases and mortality and is suitable for cardiac patients. A step counter measures walking activity and might be a motivational tool to increase and maintain physical activity. There is a lack of knowledge about both cardiac patients’ adherence to step counter use in a cardiac telerehabilitation program and how many steps cardiac patients walk up to 1 year after a cardiac event. Objective The purpose of this substudy was to explore cardiac patients’ walking activity. The walking activity was analyzed in relation to duration of pedometer use to determine correlations between walking activity, demographics, and medical and rehabilitation data. Methods A total of 64 patients from a randomized controlled telerehabilitation trial (Teledi@log) from Aalborg University Hospital and Hjoerring Hospital, Denmark, from December 2012 to March 2014 were included in this study. Inclusion criteria were patients hospitalized with acute coronary syndrome, heart failure, and coronary artery bypass grafting or valve surgery. In Teledi@log, the patients received telerehabilitation technology and selected one of three telerehabilitation settings: a call center, a community health care center, or a hospital. Monitoring of steps continued for 12 months and a step counter (Fitbit Zip) was used to monitor daily steps. Results Cardiac patients walked a mean 5899 (SD 3274) steps per day, increasing from mean 5191 (SD 3198) steps per day in the first week to mean 7890 (SD 2629) steps per day after 1 year. Adherence to step counter use lasted for a mean 160 (SD 100) days. The patients who walked significantly more were younger (P=.01) and continued to use the pedometer for a longer period (P=.04). Furthermore, less physically active patients weighed more. There were no significant differences in mean steps per day for patients in the three rehabilitation settings or in the disease groups. Conclusions This study indicates that cardiac telerehabilitation at a call center can support walking activity just as effectively as telerehabilitation at either a hospital or a health care center. In this study, the patients tended to walk fewer steps per day than cardiac patients in comparable studies, but our study may represent a more realistic picture of walking activity due to the continuation of step counter use. Qualitative studies on patients’ behavior and motivation regarding step counter use are needed to shed light on adherence to and motivation to use step counters. Trial Registration ClinicalTrails.gov NCT01752192; https://clinicaltrials.gov/ct2/show/NCT01752192 (Archived by WebCite at http://www.webcitation.org/6fgigfUyV) PMID:27044310

Scaling Limit of Symmetric Random Walk in High-Contrast Periodic Environment

NASA Astrophysics Data System (ADS)

Piatnitski, A.; Zhizhina, E.

2017-11-01

The paper deals with the asymptotic properties of a symmetric random walk in a high contrast periodic medium in Z^d, d≥1. From the existing homogenization results it follows that under diffusive scaling the limit behaviour of this random walk need not be Markovian. The goal of this work is to show that if in addition to the coordinate of the random walk in Z^d we introduce an extra variable that characterizes the position of the random walk inside the period then the limit dynamics of this two-component process is Markov. We describe the limit process and observe that the components of the limit process are coupled. We also prove the convergence in the path space for the said random walk.

Phase I/II randomized trial of aerobic exercise in Parkinson disease in a community setting.

PubMed

Uc, Ergun Y; Doerschug, Kevin C; Magnotta, Vincent; Dawson, Jeffrey D; Thomsen, Teri R; Kline, Joel N; Rizzo, Matthew; Newman, Sara R; Mehta, Sonya; Grabowski, Thomas J; Bruss, Joel; Blanchette, Derek R; Anderson, Steven W; Voss, Michelle W; Kramer, Arthur F; Darling, Warren G

2014-07-29

To (1) investigate effects of aerobic walking on motor function, cognition, and quality of life in Parkinson disease (PD), and (2) compare safety, tolerability, and fitness benefits of different forms of exercise intervention: continuous/moderate intensity vs interval/alternating between low and vigorous intensity, and individual/neighborhood vs group/facility setting. Initial design was a 6-month, 2 × 2 randomized trial of different exercise regimens in independently ambulatory patients with PD. All arms were required to exercise 3 times per week, 45 minutes per session. Randomization to group/facility setting was not feasible because of logistical factors. Over the first 2 years, we randomized 43 participants to continuous or interval training. Because preliminary analyses suggested higher musculoskeletal adverse events in the interval group and lack of difference between training methods in improving fitness, the next 17 participants were allocated only to continuous training. Eighty-one percent of 60 participants completed the study with a mean attendance of 83.3% (95% confidence interval: 77.5%-89.0%), exercising at 46.8% (44.0%-49.7%) of their heart rate reserve. There were no serious adverse events. Across all completers, we observed improvements in maximum oxygen consumption, gait speed, Unified Parkinson's Disease Rating Scale sections I and III scores (particularly axial functions and rigidity), fatigue, depression, quality of life (e.g., psychological outlook), and flanker task scores (p < 0.05 to p < 0.001). Increase in maximum oxygen consumption correlated with improvements on the flanker task and quality of life (p < 0.05). Our preliminary study suggests that aerobic walking in a community setting is safe, well tolerated, and improves aerobic fitness, motor function, fatigue, mood, executive control, and quality of life in mild to moderate PD. This study provides Class IV evidence that in patients with PD, an aerobic exercise program improves aerobic fitness, motor function, fatigue, mood, and cognition. © 2014 American Academy of Neurology.

A Telehealth Intervention Using Nintendo Wii Fit Balance Boards and iPads to Improve Walking in Older Adults With Lower Limb Amputation (Wii.n.Walk): Study Protocol for a Randomized Controlled Trial

PubMed Central

Imam, Bita; Finlayson, Heather C; Eng, Janice J; Payne, Michael WC; Jarus, Tal; Goldsmith, Charles H; Mitchell, Ian M

2014-01-01

Background The number of older adults living with lower limb amputation (LLA) who require rehabilitation for improving their walking capacity and mobility is growing. Existing rehabilitation practices frequently fail to meet this demand. Nintendo Wii Fit may be a valuable tool to enable rehabilitation interventions. Based on pilot studies, we have developed “Wii.n.Walk”, an in-home telehealth Wii Fit intervention targeted to improve walking capacity in older adults with LLA. Objective The objective of this study is to determine whether the Wii.n.Walk intervention enhances walking capacity compared to an attention control group. Methods This project is a multi-site (Vancouver BC, London ON), parallel, evaluator-blind randomized controlled trial. Participants include community-dwelling older adults over the age of 50 years with unilateral transtibial or transfemoral amputation. Participants will be stratified by site and block randomized in triplets to either the Wii.n.Walk intervention or an attention control group employing the Wii Big Brain cognitive software. This trial will include both supervised and unsupervised phases. During the supervised phase, both groups will receive 40-minute sessions of supervised group training three times per week for a duration of 4 weeks. Participants will complete the first week of the intervention in groups of three at their local rehabilitation center with a trainer. The remaining 3 weeks will take place at participants’ homes using remote supervision by the trainer using Apple iPad technology. At the end of 4 weeks, the supervised period will end and the unsupervised period will begin. Participants will retain the Wii console and be encouraged to continue using the program for an additional 4 weeks’ duration. The primary outcome measure will be the “Two-Minute Walk Test” to measure walking capacity. Outcome measures will be evaluated for all participants at baseline, after the end of both the supervised and unsupervised phases, and after 1-year follow up. Results Study staff have been hired and trained at both sites and recruitment is currently underway. No participants have been enrolled yet. Conclusions Wii.n.Walk is a promising in-home telehealth intervention that may have useful applications for older adults with LLA who are discharged from rehabilitation or live in remote areas having limited or no access to existing rehabilitation programs. Trial Registration Clinicaltrial.gov NCT01942798; http://clinicaltrials.gov/ct2/show/NCT01942798 (Archived by WebCite at http://www.webcitation.org/6V0w8baKP). PMID:25533902

Graphic matching based on shape contexts and reweighted random walks

NASA Astrophysics Data System (ADS)

Zhang, Mingxuan; Niu, Dongmei; Zhao, Xiuyang; Liu, Mingjun

2018-04-01

Graphic matching is a very critical issue in all aspects of computer vision. In this paper, a new graphics matching algorithm combining shape contexts and reweighted random walks was proposed. On the basis of the local descriptor, shape contexts, the reweighted random walks algorithm was modified to possess stronger robustness and correctness in the final result. Our main process is to use the descriptor of the shape contexts for the random walk on the iteration, of which purpose is to control the random walk probability matrix. We calculate bias matrix by using descriptors and then in the iteration we use it to enhance random walks' and random jumps' accuracy, finally we get the one-to-one registration result by discretization of the matrix. The algorithm not only preserves the noise robustness of reweighted random walks but also possesses the rotation, translation, scale invariance of shape contexts. Through extensive experiments, based on real images and random synthetic point sets, and comparisons with other algorithms, it is confirmed that this new method can produce excellent results in graphic matching.

Diffusion limit of Lévy-Lorentz gas is Brownian motion

NASA Astrophysics Data System (ADS)

Magdziarz, Marcin; Szczotka, Wladyslaw

2018-07-01

In this paper we analyze asymptotic behaviour of a stochastic process called Lévy-Lorentz gas. This process is aspecial kind of continuous-time random walk in which walker moves in the fixed environment composed of scattering points. Upon each collision the walker performs a flight to the nearest scattering point. This type of dynamics is observed in Lévy glasses or long quenched polymers. We show that the diffusion limit of Lévy-Lorentz gas with finite mean distance between scattering centers is the standard Brownian motion. Thus, for long times the behaviour of the Lévy-Lorentz gas is close to the diffusive regime.

Random walk-percolation-based modeling of two-phase flow in porous media: Breakthrough time and net to gross ratio estimation

NASA Astrophysics Data System (ADS)

Ganjeh-Ghazvini, Mostafa; Masihi, Mohsen; Ghaedi, Mojtaba

2014-07-01

Fluid flow modeling in porous media has many applications in waste treatment, hydrology and petroleum engineering. In any geological model, flow behavior is controlled by multiple properties. These properties must be known in advance of common flow simulations. When uncertainties are present, deterministic modeling often produces poor results. Percolation and Random Walk (RW) methods have recently been used in flow modeling. Their stochastic basis is useful in dealing with uncertainty problems. They are also useful in finding the relationship between porous media descriptions and flow behavior. This paper employs a simple methodology based on random walk and percolation techniques. The method is applied to a well-defined model reservoir in which the breakthrough time distributions are estimated. The results of this method and the conventional simulation are then compared. The effect of the net to gross ratio on the breakthrough time distribution is studied in terms of Shannon entropy. Use of the entropy plot allows one to assign the appropriate net to gross ratio to any porous medium.

Multicomponent physical exercise with simultaneous cognitive training to enhance dual-task walking of older adults: a secondary analysis of a 6-month randomized controlled trial with 1-year follow-up.

PubMed

Eggenberger, Patrick; Theill, Nathan; Holenstein, Stefan; Schumacher, Vera; de Bruin, Eling D

2015-01-01

About one-third of people older than 65 years fall at least once a year. Physical exercise has been previously demonstrated to improve gait, enhance physical fitness, and prevent falls. Nonetheless, the addition of cognitive training components may potentially increase these effects, since cognitive impairment is related to gait irregularities and fall risk. We hypothesized that simultaneous cognitive-physical training would lead to greater improvements in dual-task (DT) gait compared to exclusive physical training. Elderly persons older than 70 years and without cognitive impairment were randomly assigned to the following groups: 1) virtual reality video game dancing (DANCE), 2) treadmill walking with simultaneous verbal memory training (MEMORY), or 3) treadmill walking (PHYS). Each program was complemented with strength and balance exercises. Two 1-hour training sessions per week over 6 months were applied. Gait variables, functional fitness (Short Physical Performance Battery, 6-minute walk), and fall frequencies were assessed at baseline, after 3 months and 6 months, and at 1-year follow-up. Multiple regression analyses with planned comparisons were carried out. Eighty-nine participants were randomized to three groups initially; 71 completed the training and 47 were available at 1-year follow-up. DANCE/MEMORY showed a significant advantage compared to PHYS in DT costs of step time variability at fast walking (P=0.044). Training-specific gait adaptations were found on comparing DANCE and MEMORY: DANCE reduced step time at fast walking (P=0.007) and MEMORY reduced gait variability in DT and DT costs at preferred walking speed (both trend P=0.062). Global linear time effects showed improved gait (P<0.05), functional fitness (P<0.05), and reduced fall frequency (-77%, P<0.001). Only single-task fast walking, gait variability at preferred walking speed, and Short Physical Performance Battery were reduced at follow-up (all P<0.05 or trend). Long-term multicomponent cognitive-physical and exclusive physical training programs demonstrated similar potential to counteract age-related decline in physical functioning.

Multicomponent physical exercise with simultaneous cognitive training to enhance dual-task walking of older adults: a secondary analysis of a 6-month randomized controlled trial with 1-year follow-up

PubMed Central

Eggenberger, Patrick; Theill, Nathan; Holenstein, Stefan; Schumacher, Vera; de Bruin, Eling D

2015-01-01

Background About one-third of people older than 65 years fall at least once a year. Physical exercise has been previously demonstrated to improve gait, enhance physical fitness, and prevent falls. Nonetheless, the addition of cognitive training components may potentially increase these effects, since cognitive impairment is related to gait irregularities and fall risk. We hypothesized that simultaneous cognitive–physical training would lead to greater improvements in dual-task (DT) gait compared to exclusive physical training. Methods Elderly persons older than 70 years and without cognitive impairment were randomly assigned to the following groups: 1) virtual reality video game dancing (DANCE), 2) treadmill walking with simultaneous verbal memory training (MEMORY), or 3) treadmill walking (PHYS). Each program was complemented with strength and balance exercises. Two 1-hour training sessions per week over 6 months were applied. Gait variables, functional fitness (Short Physical Performance Battery, 6-minute walk), and fall frequencies were assessed at baseline, after 3 months and 6 months, and at 1-year follow-up. Multiple regression analyses with planned comparisons were carried out. Results Eighty-nine participants were randomized to three groups initially; 71 completed the training and 47 were available at 1-year follow-up. DANCE/MEMORY showed a significant advantage compared to PHYS in DT costs of step time variability at fast walking (P=0.044). Training-specific gait adaptations were found on comparing DANCE and MEMORY: DANCE reduced step time at fast walking (P=0.007) and MEMORY reduced gait variability in DT and DT costs at preferred walking speed (both trend P=0.062). Global linear time effects showed improved gait (P<0.05), functional fitness (P<0.05), and reduced fall frequency (−77%, P<0.001). Only single-task fast walking, gait variability at preferred walking speed, and Short Physical Performance Battery were reduced at follow-up (all P<0.05 or trend). Conclusion Long-term multicomponent cognitive–physical and exclusive physical training programs demonstrated similar potential to counteract age-related decline in physical functioning. PMID:26604719

A random walk approach to quantum algorithms.

PubMed

Kendon, Vivien M

2006-12-15

The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The outcome of a quantum random walk is very different from the corresponding classical random walk owing to the interference between the different possible paths. The upshot is that quantum walkers find themselves further from their starting point than a classical walker on average, and this forms the basis of a quantum speed up, which can be exploited to solve problems faster. Surprisingly, the effect of making the walk slightly less than perfectly quantum can optimize the properties of the quantum walk for algorithmic applications. Looking to the future, even with a small quantum computer available, the development of quantum walk algorithms might proceed more rapidly than it has, especially for solving real problems.

Open quantum random walks: Bistability on pure states and ballistically induced diffusion

NASA Astrophysics Data System (ADS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2013-12-01

Open quantum random walks (OQRWs) deal with quantum random motions on a line for systems with internal and orbital degrees of freedom. The internal system behaves as a quantum random gyroscope coding for the direction of the orbital moves. We reveal the existence of a transition, depending on OQRW moduli, in the internal system behaviors from simple oscillations to random flips between two unstable pure states. This induces a transition in the orbital motions from the usual diffusion to ballistically induced diffusion with a large mean free path and large effective diffusion constant at large times. We also show that mixed states of the internal system are converted into random pure states during the process. We touch upon possible experimental realizations.

Efficient sampling of complex network with modified random walk strategies

NASA Astrophysics Data System (ADS)

Xie, Yunya; Chang, Shuhua; Zhang, Zhipeng; Zhang, Mi; Yang, Lei

2018-02-01

We present two novel random walk strategies, choosing seed node (CSN) random walk and no-retracing (NR) random walk. Different from the classical random walk sampling, the CSN and NR strategies focus on the influences of the seed node choice and path overlap, respectively. Three random walk samplings are applied in the Erdös-Rényi (ER), Barabási-Albert (BA), Watts-Strogatz (WS), and the weighted USAir networks, respectively. Then, the major properties of sampled subnets, such as sampling efficiency, degree distributions, average degree and average clustering coefficient, are studied. The similar conclusions can be reached with these three random walk strategies. Firstly, the networks with small scales and simple structures are conducive to the sampling. Secondly, the average degree and the average clustering coefficient of the sampled subnet tend to the corresponding values of original networks with limited steps. And thirdly, all the degree distributions of the subnets are slightly biased to the high degree side. However, the NR strategy performs better for the average clustering coefficient of the subnet. In the real weighted USAir networks, some obvious characters like the larger clustering coefficient and the fluctuation of degree distribution are reproduced well by these random walk strategies.

pyCTQW: A continuous-time quantum walk simulator on distributed memory computers

NASA Astrophysics Data System (ADS)

Izaac, Josh A.; Wang, Jingbo B.

2015-01-01

In the general field of quantum information and computation, quantum walks are playing an increasingly important role in constructing physical models and quantum algorithms. We have recently developed a distributed memory software package pyCTQW, with an object-oriented Python interface, that allows efficient simulation of large multi-particle CTQW (continuous-time quantum walk)-based systems. In this paper, we present an introduction to the Python and Fortran interfaces of pyCTQW, discuss various numerical methods of calculating the matrix exponential, and demonstrate the performance behavior of pyCTQW on a distributed memory cluster. In particular, the Chebyshev and Krylov-subspace methods for calculating the quantum walk propagation are provided, as well as methods for visualization and data analysis.

Spatial Search by Quantum Walk is Optimal for Almost all Graphs.

PubMed

Chakraborty, Shantanav; Novo, Leonardo; Ambainis, Andris; Omar, Yasser

2016-03-11

The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work, we prove that for Erdös-Renyi random graphs, i.e., graphs of n vertices where each edge exists with probability p, search by CTQW is almost surely optimal as long as p≥log^{3/2}(n)/n. Consequently, we show that quantum spatial search is in fact optimal for almost all graphs, meaning that the fraction of graphs of n vertices for which this optimality holds tends to one in the asymptotic limit. We obtain this result by proving that search is optimal on graphs where the ratio between the second largest and the largest eigenvalue is bounded by a constant smaller than 1. Finally, we show that we can extend our results on search to establish high fidelity quantum communication between two arbitrary nodes of a random network of interacting qubits, namely, to perform quantum state transfer, as well as entanglement generation. Our work shows that quantum information tasks typically designed for structured systems retain performance in very disordered structures.

A randomized trial of functional electrical stimulation for walking in incomplete spinal cord injury: Effects on walking competency

PubMed Central

Kapadia, Naaz; Masani, Kei; Catharine Craven, B.; Giangregorio, Lora M.; Hitzig, Sander L.; Richards, Kieva; Popovic, Milos R.

2014-01-01

Background Multi-channel surface functional electrical stimulation (FES) for walking has been used to improve voluntary walking and balance in individuals with spinal cord injury (SCI). Objective To investigate short- and long-term benefits of 16 weeks of thrice-weekly FES-assisted walking program, while ambulating on a body weight support treadmill and harness system, versus a non-FES exercise program, on improvements in gait and balance in individuals with chronic incomplete traumatic SCI, in a randomized controlled trial design. Methods Individuals with traumatic and chronic (≥18 months) motor incomplete SCI (level C2 to T12, American Spinal Cord Injury Association Impairment Scale C or D) were recruited from an outpatient SCI rehabilitation hospital, and randomized to FES-assisted walking therapy (intervention group) or aerobic and resistance training program (control group). Outcomes were assessed at baseline, and after 4, 6, and 12 months. Gait, balance, spasticity, and functional measures were collected. Results Spinal cord independence measure (SCIM) mobility sub-score improved over time in the intervention group compared with the control group (baseline/12 months: 17.27/21.33 vs. 19.09/17.36, respectively). On all other outcome measures the intervention and control groups had similar improvements. Irrespective of group allocation walking speed, endurance, and balance during ambulation all improved upon completion of therapy, and majority of participants retained these gains at long-term follow-ups. Conclusions Task-oriented training improves walking ability in individuals with incomplete SCI, even in the chronic stage. Further randomized controlled trials, involving a large number of participants are needed, to verify if FES-assisted treadmill training is superior to aerobic and strength training. PMID:25229735

Answer (in part) blowing in the wind. Comment on "Liberating Lévy walk research from the shackles of optimal foraging" by A. Reynolds

NASA Astrophysics Data System (ADS)

Cheng, Ken

2015-09-01

In a perspective in this issue based on thorough review, Andy Reynolds [1] tackles the issue of how the by now ubiquitously found Lévy walks can be generated, by animals, by organisms other than animals, and other forms of life below the level of organisms, such as cells. The answer comes not in a single whole cloth, but rather in a patchwork of generating factors. Lévy-like movements arise in objects blowing in the wind, or from travelers encountering turbulence in the seas or being repelled by boundaries. A variety of desiderata in movements, not related to achieving optimal foraging, may also engender Lévy-like movements. These include avoiding other organisms or not crossing one's traveled path. Adding to that plethora are ways in which variations on the theme of garden-variety random walks can at least approach a Lévy walk, if not capturing the mathematical form perfectly. Such variations include executing random walks on multiple scales, a strategy exhibited by desert ants [2,3], mussels [4], and quite likely extant hunter-gatherer humans as well [5]. It is possible that fossil tracks over 50 million years old also show this strategy, as the curve fitting with multiple random walks, characterized by multiple exponential distributions, is as good or better than curve fits having the power-law distribution characteristic of Lévy walks [6]. Another variation is to have a random walk search whose scale is expanding over time. In great detail and based on extensive literature - the review has over 200 references - a range of other ways in which Lévy-like movements might come about are also discussed.

Random walk in degree space and the time-dependent Watts-Strogatz model

NASA Astrophysics Data System (ADS)

Casa Grande, H. L.; Cotacallapa, M.; Hase, M. O.

2017-01-01

In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erdős-Rényi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.

Random walk in degree space and the time-dependent Watts-Strogatz model.

PubMed

Casa Grande, H L; Cotacallapa, M; Hase, M O

2017-01-01

In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erdős-Rényi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.

Asymptotic densities from the modified Montroll-Weiss equation for coupled CTRWs

NASA Astrophysics Data System (ADS)

Aghion, Erez; Kessler, David A.; Barkai, Eli

2018-01-01

We examine the bi-scaling behavior of Lévy walks with nonlinear coupling, where χ, the particle displacement during each step, is coupled to the duration of the step, τ, by χ τβ. An example of such a process is regular Lévy walks, where β = 1. In recent years such processes were shown to be highly useful for analysis of a class of Langevin dynamics, in particular a system of Sisyphus laser-cooled atoms in an optical lattice, where β = 3/2. We discuss the well-known decoupling approximation used to describe the central part of the particles' position distribution, and use the recently introduced infinite-covariant density approach to study the large fluctuations. Since the density of the step displacements is fat-tailed, the last travel event must be treated with care for the latter. This effect requires a modification of the Montroll-Weiss equation, an equation which has proved important for the analysis of many microscopic models. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Theoretical proposal for a magnetic resonance study of charge transport in organic semiconductors

NASA Astrophysics Data System (ADS)

Mkhitaryan, Vagharsh

Charge transport in disordered organic semiconductors occurs via carrier incoherent hops in a band of localized states. In the framework of continuous-time random walk the carrier on-site waiting time distribution (WTD) is one of the basic characteristics of diffusion. Besides, WTD is fundamentally related to the density of states (DOS) of localized states, which is a key feature of a material determining the optoelectric properties. However, reliable first-principle calculations of DOS in organic materials are not yet available and experimental characterization of DOS and WTD is desirable. We theoretically study the spin dynamics of hopping carriers and propose measurement schemes directly probing WTD, based on the zero-field spin relaxation and the primary (Hahn) spin echo. The proposed schemes are possible because, as we demonstrate, the long-time behavior of the zero-field relaxation and the primary echo is determined by WTD, both for the hyperfine coupling dominated and the spin-orbit coupling dominated spin dynamics. We also examine the dispersive charge transport, which is a non-Markovian sub-diffusive process characterized by non-stationarity. We show that the proposed schemes unambiguously capture the effects of non-stationarity, e.g., the aging behavior of random walks. This work was supported by the Department of Energy-Basic Energy Sciences under Contract No. DE-AC02-07CH11358.

Quantum dynamics of nuclear spins and spin relaxation in organic semiconductors

NASA Astrophysics Data System (ADS)

Mkhitaryan, V. V.; Dobrovitski, V. V.

2017-06-01

We investigate the role of the nuclear-spin quantum dynamics in hyperfine-induced spin relaxation of hopping carriers in organic semiconductors. The fast-hopping regime, when the carrier spin does not rotate much between subsequent hops, is typical for organic semiconductors possessing long spin coherence times. We consider this regime and focus on a carrier random-walk diffusion in one dimension, where the effect of the nuclear-spin dynamics is expected to be the strongest. Exact numerical simulations of spin systems with up to 25 nuclear spins are performed using the Suzuki-Trotter decomposition of the evolution operator. Larger nuclear-spin systems are modeled utilizing the spin-coherent state P -representation approach developed earlier. We find that the nuclear-spin dynamics strongly influences the carrier spin relaxation at long times. If the random walk is restricted to a small area, it leads to the quenching of carrier spin polarization at a nonzero value at long times. If the random walk is unrestricted, the carrier spin polarization acquires a long-time tail, decaying as 1 /√{t } . Based on the numerical results, we devise a simple formula describing the effect quantitatively.

Membrane Diffusion Occurs by Continuous-Time Random Walk Sustained by Vesicular Trafficking.

PubMed

Goiko, Maria; de Bruyn, John R; Heit, Bryan

2018-06-19

Diffusion in cellular membranes is regulated by processes that occur over a range of spatial and temporal scales. These processes include membrane fluidity, interprotein and interlipid interactions, interactions with membrane microdomains, interactions with the underlying cytoskeleton, and cellular processes that result in net membrane movement. The complex, non-Brownian diffusion that results from these processes has been difficult to characterize, and moreover, the impact of factors such as membrane recycling on membrane diffusion remains largely unexplored. We have used a careful statistical analysis of single-particle tracking data of the single-pass plasma membrane protein CD93 to show that the diffusion of this protein is well described by a continuous-time random walk in parallel with an aging process mediated by membrane corrals. The overall result is an evolution in the diffusion of CD93: proteins initially diffuse freely on the cell surface but over time become increasingly trapped within diffusion-limiting membrane corrals. Stable populations of freely diffusing and corralled CD93 are maintained by an endocytic/exocytic process in which corralled CD93 is selectively endocytosed, whereas freely diffusing CD93 is replenished by exocytosis of newly synthesized and recycled CD93. This trafficking not only maintained CD93 diffusivity but also maintained the heterogeneous distribution of CD93 in the plasma membrane. These results provide insight into the nature of the biological and biophysical processes that can lead to significantly non-Brownian diffusion of membrane proteins and demonstrate that ongoing membrane recycling is critical to maintaining steady-state diffusion and distribution of proteins in the plasma membrane. Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Efficacy of gait trainer as an adjunct to traditional physical therapy on walking performance in hemiparetic cerebral palsied children: a randomized controlled trial.

PubMed

Gharib, Nevein Mm; El-Maksoud, Gehan M Abd; Rezk-Allah, Soheir S

2011-10-01

To assess the effects of additional gait trainer assisted walking exercises on walking performance in children with hemiparetic cerebral palsy. A randomized controlled study. Paediatric physical therapy outpatient clinic. Thirty spastic hemiparetic cerebral palsied children of both sexes (10-13 years - 19 girls and 11 boys). Children were randomly assigned into two equal groups; experimental and control groups. Participants in both groups received a traditional physical therapy exercise programme. Those in the experimental group received additional gait trainer based walking exercises which aimed to improve walking performance. Treatment was provided three times per week for three successive months. Children received baseline and post-treatment assessments using Biodex Gait Trainer 2 assessment device to evaluate gait parameters including: average step length, walking speed, time on each foot (% of gait cycle) and ambulation index. Children in the experimental group showed a significant improvement as compared with those in the control group. The ambulation index was 75.53±7.36 (11.93 ± 2.89 change score) for the experimental group and 66.06 ± 5.48 (2.13 ± 4.43 change score) for the control group (t = 3.99 and P = 0.0001). Time of support for the affected side was 42.4 ± 3.37 (7 ± 2.20 change score) for the experimental group and 38.06 ± 4.63 (3.33 ± 6.25 change score) for the control group (t = 2.92 and P = 0.007). Also, there was a significant improvement in step length and walking speed in both groups. Gait trainer combined with traditional physiotherapy increase the chance of improving gait performance in children with spastic hemiparetic cerebral palsy.

A New Continuous Rotation IMU Alignment Algorithm Based on Stochastic Modeling for Cost Effective North-Finding Applications

PubMed Central

Li, Yun; Wu, Wenqi; Jiang, Qingan; Wang, Jinling

2016-01-01

Based on stochastic modeling of Coriolis vibration gyros by the Allan variance technique, this paper discusses Angle Random Walk (ARW), Rate Random Walk (RRW) and Markov process gyroscope noises which have significant impacts on the North-finding accuracy. A new continuous rotation alignment algorithm for a Coriolis vibration gyroscope Inertial Measurement Unit (IMU) is proposed in this paper, in which the extended observation equations are used for the Kalman filter to enhance the estimation of gyro drift errors, thus improving the north-finding accuracy. Theoretical and numerical comparisons between the proposed algorithm and the traditional ones are presented. The experimental results show that the new continuous rotation alignment algorithm using the extended observation equations in the Kalman filter is more efficient than the traditional two-position alignment method. Using Coriolis vibration gyros with bias instability of 0.1°/h, a north-finding accuracy of 0.1° (1σ) is achieved by the new continuous rotation alignment algorithm, compared with 0.6° (1σ) north-finding accuracy for the two-position alignment and 1° (1σ) for the fixed-position alignment. PMID:27983585

Three 15-min Bouts of Moderate Postmeal Walking Significantly Improves 24-h Glycemic Control in Older People at Risk for Impaired Glucose Tolerance

PubMed Central

DiPietro, Loretta; Gribok, Andrei; Stevens, Michelle S.; Hamm, Larry F.; Rumpler, William

2013-01-01

OBJECTIVE The purpose of this study was to compare the effectiveness of three 15-min bouts of postmeal walking with 45 min of sustained walking on 24-h glycemic control in older persons at risk for glucose intolerance. RESEARCH DESIGN AND METHODS Inactive older (≥60 years of age) participants (N = 10) were recruited from the community and were nonsmoking, with a BMI <35 kg/m2 and a fasting blood glucose concentration between 105 and 125 mg dL−1. Participants completed three randomly ordered exercise protocols spaced 4 weeks apart. Each protocol comprised a 48-h stay in a whole-room calorimeter, with the first day serving as the control day. On the second day, participants engaged in either 1) postmeal walking for 15 min or 45 min of sustained walking performed at 2) 10:30 a.m. or 3) 4:30 p.m. All walking was on a treadmill at an absolute intensity of 3 METs. Interstitial glucose concentrations were determined over 48 h with a continuous glucose monitor. Substrate utilization was measured continuously by respiratory exchange (VCO2/VO2). RESULTS Both sustained morning walking (127 ± 23 vs. 118 ± 14 mg dL−1) and postmeal walking (129 ± 24 vs. 116 ± 13 mg dL−1) significantly improved 24-h glycemic control relative to the control day (P < 0.05). Moreover, postmeal walking was significantly (P < 0.01) more effective than 45 min of sustained morning or afternoon walking in lowering 3-h postdinner glucose between the control and experimental day. CONCLUSIONS Short, intermittent bouts of postmeal walking appear to be an effective way to control postprandial hyperglycemia in older people. PMID:23761134

The effects of a walking/talking program on communication, ambulation, and functional status in residents with Alzheimer disease.

PubMed

Cott, Cheryl A; Dawson, Pamela; Sidani, Souraya; Wells, Donna

2002-01-01

The purpose of this study was to investigate the effects of a walking/talking program on residents' communication, ambulation, and level of function when there were two residents to one care provider (2:1). A randomized control trial design was used. Subjects were residents with Alzheimer disease in three geriatric long-term care facilities in Metropolitan Toronto. Residents who met the inclusion criteria were randomly assigned to one of three groups: walk-and-talk group (30 min, 5 times per week for 16 weeks, walking/talking in pairs), talk-only group (30 min, 5 times per week for 16 weeks, talk only in pairs), or no intervention. The outcome measures were the Functional Assessment of Communication Skills for Adults, the 2-min walk test, and London Psychogeriatric Rating Scale. Residents who received the walk-and-talk intervention did not demonstrate statistically significant differences in the outcome variables measured posttest when compared with residents who received the talk-only intervention or no intervention, even after controlling for individual differences. Variability in the outcomes measured posttest is explained by differences in the residents' level of cognitive impairment before the study rather than by study group membership. These findings are contradictory to those of previous studies.

Open Quantum Random Walks on the Half-Line: The Karlin-McGregor Formula, Path Counting and Foster's Theorem

NASA Astrophysics Data System (ADS)

Jacq, Thomas S.; Lardizabal, Carlos F.

2017-11-01

In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability expressions for classes of walks via a matrix version of the Karlin-McGregor formula. We focus on absorbing boundary conditions and, for simpler classes of examples, we consider path counting and the corresponding combinatorial tools. A non-commutative version of the gambler's ruin is studied by obtaining the probability of reaching a certain fortune and the mean time to reach a fortune or ruin in terms of generating functions. In the case of the Hadamard coin, a counting technique for boundary restricted paths in a lattice is also presented. We discuss an open quantum version of Foster's Theorem for the expected return time together with applications.

Feasibility and Preliminary Efficacy of Visual Cue Training to Improve Adaptability of Walking after Stroke: Multi-Centre, Single-Blind Randomised Control Pilot Trial.

PubMed

Hollands, Kristen L; Pelton, Trudy A; Wimperis, Andrew; Whitham, Diane; Tan, Wei; Jowett, Sue; Sackley, Catherine M; Wing, Alan M; Tyson, Sarah F; Mathias, Jonathan; Hensman, Marianne; van Vliet, Paulette M

2015-01-01

Given the importance of vision in the control of walking and evidence indicating varied practice of walking improves mobility outcomes, this study sought to examine the feasibility and preliminary efficacy of varied walking practice in response to visual cues, for the rehabilitation of walking following stroke. This 3 arm parallel, multi-centre, assessor blind, randomised control trial was conducted within outpatient neurorehabilitation services. Community dwelling stroke survivors with walking speed <0.8m/s, lower limb paresis and no severe visual impairments. Over-ground visual cue training (O-VCT), Treadmill based visual cue training (T-VCT), and Usual care (UC) delivered by physiotherapists twice weekly for 8 weeks. Participants were randomised using computer generated random permutated balanced blocks of randomly varying size. Recruitment, retention, adherence, adverse events and mobility and balance were measured before randomisation, post-intervention and at four weeks follow-up. Fifty-six participants participated (18 T-VCT, 19 O-VCT, 19 UC). Thirty-four completed treatment and follow-up assessments. Of the participants that completed, adherence was good with 16 treatments provided over (median of) 8.4, 7.5 and 9 weeks for T-VCT, O-VCT and UC respectively. No adverse events were reported. Post-treatment improvements in walking speed, symmetry, balance and functional mobility were seen in all treatment arms. Outpatient based treadmill and over-ground walking adaptability practice using visual cues are feasible and may improve mobility and balance. Future studies should continue a carefully phased approach using identified methods to improve retention. Clinicaltrials.gov NCT01600391.

Generalized master equation via aging continuous-time random walks.

PubMed

Allegrini, Paolo; Aquino, Gerardo; Grigolini, Paolo; Palatella, Luigi; Rosa, Angelo

2003-11-01

We discuss the problem of the equivalence between continuous-time random walk (CTRW) and generalized master equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site for extended times. The sojourn times have a distribution density psi(t) that is assumed to be an inverse power law with the power index micro. We assume that the Onsager principle is fulfilled, and we use this assumption to establish a complete equivalence between GME and the Montroll-Weiss CTRW. We prove that this equivalence is confined to the case where psi(t) is an exponential. We argue that is so because the Montroll-Weiss CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)], is nonstationary, thereby implying aging, while the Onsager principle is valid only in the case of fully aged systems. The case of a Poisson distribution of sojourn times is the only one with no aging associated to it, and consequently with no need to establish special initial conditions to fulfill the Onsager principle. We consider the case of a dichotomous fluctuation, and we prove that the Onsager principle is fulfilled for any form of regression to equilibrium provided that the stationary condition holds true. We set the stationary condition on both the CTRW and the GME, thereby creating a condition of total equivalence, regardless of the nature of the waiting-time distribution. As a consequence of this procedure we create a GME that is a bona fide master equation, in spite of being non-Markov. We note that the memory kernel of the GME affords information on the interaction between system of interest and its bath. The Poisson case yields a bath with infinitely fast fluctuations. We argue that departing from the Poisson form has the effect of creating a condition of infinite memory and that these results might be useful to shed light on the problem of how to unravel non-Markov quantum master equations.

Quantum random walks on congested lattices and the effect of dephasing.

PubMed

Motes, Keith R; Gilchrist, Alexei; Rohde, Peter P

2016-01-27

We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled on lattices that contain static defects which reverse the walker's direction. We implement a dephasing process after each step which allows us to smoothly interpolate between classical and quantum random walks as well as study the effect of dephasing on the quantum walk. Our key results show that a quantum walker escapes a finite boundary dramatically faster than a classical walker and that this advantage remains in the presence of heavily congested lattices.

Evaluation of the Dogs, Physical Activity, and Walking (Dogs PAW) Intervention: A Randomized Controlled Trial.

PubMed

Richards, Elizabeth A; Ogata, Niwako; Cheng, Ching-Wei

2016-01-01

To facilitate physical activity (PA) adoption and maintenance, promotion of innovative population-level strategies that focus on incorporating moderate-intensity lifestyle PAs are needed. The purpose of this randomized controlled trial was to evaluate the Dogs, Physical Activity, and Walking intervention, a 3-month, social cognitive theory (SCT), e-mail-based PA intervention. In a longitudinal, repeated-measures design, 49 dog owners were randomly assigned to a control (n = 25) or intervention group (n = 24). The intervention group received e-mail messages (twice weekly for 4 weeks and weekly for 8 weeks) designed to influence SCT constructs of self-efficacy, self-regulation, outcome expectations and expectancies, and social support. At baseline and every 3 months through 1 year, participants completed self-reported questionnaires of individual, interpersonal, and PA variables. Linear mixed models were used to assess for significant differences in weekly minutes of dog walking and theoretical constructs between groups (intervention and control) across time. To test self-efficacy as a mediator of social support for dog walking, tests for mediation were conducted using the bootstrapping technique. With the exception of Month 9, participants in the intervention group accumulated significantly more weekly minutes of dog walking than the control group. On average, the intervention group accumulated 58.4 more minutes (SD = 18.1) of weekly dog walking than the control group (p < .05). Self-efficacy partially mediated the effect of social support variables on dog walking. Results indicate that a simple SCT-based e-mail intervention is effective in increasing and maintaining an increase in dog walking among dog owners at 12-month follow-up. In light of these findings, it may be advantageous to design dog walking interventions that focus on increasing self-efficacy for dog walking by fostering social support.

Early or delayed provision of an ankle-foot orthosis in patients with acute and subacute stroke: a randomized controlled trial.

PubMed

Nikamp, Corien Dm; Buurke, Jaap H; van der Palen, Job; Hermens, Hermie J; Rietman, Johan S

2017-06-01

(1) To study the effects of providing ankle-foot orthoses in subjects with (sub)acute stroke; and (2) to study whether the point in time at which an ankle-foot orthosis is provided post-stroke (early or delayed) influences these effects. Randomized controlled trial. Rehabilitation centre. Unilateral hemiparetic stroke subjects with indication for use of an ankle-foot orthosis and maximal six weeks post-stroke. Subjects were randomly assigned to: early provision (at inclusion; Week 1) or delayed provision (eight weeks later; Week 9). 10-metre walk test, 6-minute walk test, Timed Up and Go Test, stairs test, Functional Ambulation Categories, Berg Balance Scale, Rivermead Mobility Index and Barthel Index; assessed in Weeks 1, 3, 9 and 11. A total of 33 subjects were randomized (16 early, 17 delayed). Positive effects of ankle-foot orthoses were found two weeks after provision, both when provided early (significant effects on all outcomes) or delayed (Berg Balance Scale p = 0.011, Functional Ambulation Categories p = 0.008, 6-minute walk test p = 0.005, Timed Up and Go Test p = 0.028). Comparing effects after early and delayed provision showed that early provision resulted in increased levels of improvement on Berg Balance Scale (+5.1 points, p = 0.002), Barthel Index (+1.9 points, p = 0.002) and non-significant improvements on 10-metre walk test (+0.14 m/s, p = 0.093) and Timed Up and Go Test (-5.4 seconds, p = 0.087), compared with delayed provision. We found positive effects of providing ankle-foot orthoses in (sub)acute stroke subjects that had not used these orthoses before.

Lagrangian particles with mixing. I. Simulating scalar transport

NASA Astrophysics Data System (ADS)

Klimenko, A. Y.

2009-06-01

The physical similarity and mathematical equivalence of continuous diffusion and particle random walk forms one of the cornerstones of modern physics and the theory of stochastic processes. The randomly walking particles do not need to posses any properties other than location in physical space. However, particles used in many models dealing with simulating turbulent transport and turbulent combustion do posses a set of scalar properties and mixing between particle properties is performed to reflect the dissipative nature of the diffusion processes. We show that the continuous scalar transport and diffusion can be accurately specified by means of localized mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme. Particles with scalar properties and localized mixing represent an alternative formulation for the process, which is selected to represent the continuous diffusion. Simulating diffusion by Lagrangian particles with mixing involves three main competing requirements: minimizing stochastic uncertainty, minimizing bias introduced by numerical diffusion, and preserving independence of particles. These requirements are analyzed for two limited cases of mixing between two particles and mixing between a large number of particles. The problem of possible dependences between particles is most complicated. This problem is analyzed using a coupled chain of equations that has similarities with Bogolubov-Born-Green-Kirkwood-Yvon chain in statistical physics. Dependences between particles can be significant in close proximity of the particles resulting in a reduced rate of mixing. This work develops further ideas introduced in the previously published letter [Phys. Fluids 19, 031702 (2007)]. Paper I of this work is followed by Paper II [Phys. Fluids 19, 065102 (2009)] where modeling of turbulent reacting flows by Lagrangian particles with localized mixing is specifically considered.

FAST TRACK COMMUNICATION: Suppressing anomalous diffusion by cooperation

NASA Astrophysics Data System (ADS)

Dybiec, Bartłomiej

2010-08-01

Within a continuous time random walk scenario we consider a motion of a complex of particles which moves coherently. The motion of every particle is characterized by the waiting time and jump length distributions which are of the power-law type. Due to the interactions between particles it is assumed that the waiting time is adjusted to the shortest or to the longest waiting time. Analogously, the jump length is adjusted to the shortest or to the longest jump length. We show that adjustment to the shortest waiting time can suppress the subdiffusive behavior even in situations when the exponent characterizing the waiting time distribution assures subdiffusive motion of a single particle. Finally, we demonstrate that the characteristic of the motion depends on the number of particles building a complex.

Mean-Potential Law in Evolutionary Games

NASA Astrophysics Data System (ADS)

Nałecz-Jawecki, Paweł; Miekisz, Jacek

2018-01-01

The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of a potential function for discrete-space stochastic systems. It is based on a correspondence between one-dimensional stochastic differential equations and random walks, which may be exact not only in the continuous limit but also in finite-state spaces. Our method is useful for computation of fixation probabilities in discrete stochastic dynamical systems with two absorbing states. We apply it to evolutionary games, formulating two simple and intuitive criteria for evolutionary stability of pure Nash equilibria in finite populations. In particular, we show that the 1 /3 law of evolutionary games, introduced by Nowak et al. [Nature, 2004], follows from a more general mean-potential law.

A Perron-Frobenius type of theorem for quantum operations

NASA Astrophysics Data System (ADS)

Lagro, Matthew

Quantum random walks are a generalization of classical Markovian random walks to a quantum mechanical or quantum computing setting. Quantum walks have promising applications but are complicated by quantum decoherence. We prove that the long-time limiting behavior of the class of quantum operations which are the convex combination of norm one operators is governed by the eigenvectors with norm one eigenvalues which are shared by the operators. This class includes all operations formed by a coherent operation with positive probability of orthogonal measurement at each step. We also prove that any operation that has range contained in a low enough dimension subspace of the space of density operators has limiting behavior isomorphic to an associated Markov chain. A particular class of such operations are coherent operations followed by an orthogonal measurement. Applications of the convergence theorems to quantum walks are given.

Markov-switching multifractal models as another class of random-energy-like models in one-dimensional space

NASA Astrophysics Data System (ADS)

Saakian, David B.

2012-03-01

We map the Markov-switching multifractal model (MSM) onto the random energy model (REM). The MSM is, like the REM, an exactly solvable model in one-dimensional space with nontrivial correlation functions. According to our results, four different statistical physics phases are possible in random walks with multifractal behavior. We also introduce the continuous branching version of the model, calculate the moments, and prove multiscaling behavior. Different phases have different multiscaling properties.

Hierarchical structure of the energy landscape of proteins revisited by time series analysis. I. Mimicking protein dynamics in different time scales

NASA Astrophysics Data System (ADS)

Alakent, Burak; Camurdan, Mehmet C.; Doruker, Pemra

2005-10-01

Time series models, which are constructed from the projections of the molecular-dynamics (MD) runs on principal components (modes), are used to mimic the dynamics of two proteins: tendamistat and immunity protein of colicin E7 (ImmE7). Four independent MD runs of tendamistat and three independent runs of ImmE7 protein in vacuum are used to investigate the energy landscapes of these proteins. It is found that mean-square displacements of residues along the modes in different time scales can be mimicked by time series models, which are utilized in dividing protein dynamics into different regimes with respect to the dominating motion type. The first two regimes constitute the dominance of intraminimum motions during the first 5ps and the random walk motion in a hierarchically higher-level energy minimum, which comprise the initial time period of the trajectories up to 20-40ps for tendamistat and 80-120ps for ImmE7. These are also the time ranges within which the linear nonstationary time series are completely satisfactory in explaining protein dynamics. Encountering energy barriers enclosing higher-level energy minima constrains the random walk motion of the proteins, and pseudorelaxation processes at different levels of minima are detected in tendamistat, depending on the sampling window size. Correlation (relaxation) times of 30-40ps and 150-200ps are detected for two energy envelopes of successive levels for tendamistat, which gives an overall idea about the hierarchical structure of the energy landscape. However, it should be stressed that correlation times of the modes are highly variable with respect to conformational subspaces and sampling window sizes, indicating the absence of an actual relaxation. The random-walk step sizes and the time length of the second regime are used to illuminate an important difference between the dynamics of the two proteins, which cannot be clarified by the investigation of relaxation times alone: ImmE7 has lower-energy barriers enclosing the higher-level energy minimum, preventing the protein to relax and letting it move in a random-walk fashion for a longer period of time.

Lévy walks

NASA Astrophysics Data System (ADS)

Zaburdaev, V.; Denisov, S.; Klafter, J.

2015-04-01

Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The Lévy-walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, biophysics, and behavioral science demonstrate that this particular type of random walk provides significant insight into complex transport phenomena. This review gives a self-consistent introduction to Lévy walks, surveys their existing applications, including latest advances, and outlines further perspectives.

Search for Directed Networks by Different Random Walk Strategies

NASA Astrophysics Data System (ADS)

Zhu, Zi-Qi; Jin, Xiao-Ling; Huang, Zhi-Long

2012-03-01

A comparative study is carried out on the efficiency of five different random walk strategies searching on directed networks constructed based on several typical complex networks. Due to the difference in search efficiency of the strategies rooted in network clustering, the clustering coefficient in a random walker's eye on directed networks is defined and computed to be half of the corresponding undirected networks. The search processes are performed on the directed networks based on Erdös—Rényi model, Watts—Strogatz model, Barabási—Albert model and clustered scale-free network model. It is found that self-avoiding random walk strategy is the best search strategy for such directed networks. Compared to unrestricted random walk strategy, path-iteration-avoiding random walks can also make the search process much more efficient. However, no-triangle-loop and no-quadrangle-loop random walks do not improve the search efficiency as expected, which is different from those on undirected networks since the clustering coefficient of directed networks are smaller than that of undirected networks.

Descriptive parameter for photon trajectories in a turbid medium

NASA Astrophysics Data System (ADS)

Gandjbakhche, Amir H.; Weiss, George H.

2000-06-01

In many applications of laser techniques for diagnostic or therapeutic purposes it is necessary to be able to characterize photon trajectories to know which parts of the tissue are being interrogated. In this paper, we consider the cw reflectance experiment on a semi-infinite medium with uniform optical parameters and having a planar interface. The analysis is carried out in terms of a continuous-time random walk and the relation between the occupancy of a plane parallel to the surface to the maximum depth reached by the random walker is studied. The first moment of the ratio of average depth to the average maximum depth yields information about the volume of tissue interrogated as well as giving some indication of the region of tissue that gets the most light. We have also calculated the standard deviation of this random variable. It is not large enough to qualitatively affect information contained in the first moment.

Quantum random walks on congested lattices and the effect of dephasing

PubMed Central

Motes, Keith R.; Gilchrist, Alexei; Rohde, Peter P.

2016-01-01

We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled on lattices that contain static defects which reverse the walker’s direction. We implement a dephasing process after each step which allows us to smoothly interpolate between classical and quantum random walks as well as study the effect of dephasing on the quantum walk. Our key results show that a quantum walker escapes a finite boundary dramatically faster than a classical walker and that this advantage remains in the presence of heavily congested lattices. PMID:26812924

Walking adaptability therapy after stroke: study protocol for a randomized controlled trial.

PubMed

Timmermans, Celine; Roerdink, Melvyn; van Ooijen, Marielle W; Meskers, Carel G; Janssen, Thomas W; Beek, Peter J

2016-08-26

Walking in everyday life requires the ability to adapt walking to the environment. This adaptability is often impaired after stroke, and this might contribute to the increased fall risk after stroke. To improve safe community ambulation, walking adaptability training might be beneficial after stroke. This study is designed to compare the effects of two interventions for improving walking speed and walking adaptability: treadmill-based C-Mill therapy (therapy with augmented reality) and the overground FALLS program (a conventional therapy program). We hypothesize that C-Mill therapy will result in better outcomes than the FALLS program, owing to its expected greater amount of walking practice. This is a single-center parallel group randomized controlled trial with pre-intervention, post-intervention, retention, and follow-up tests. Forty persons after stroke (≥3 months) with deficits in walking or balance will be included. Participants will be randomly allocated to either C-Mill therapy or the overground FALLS program for 5 weeks. Both interventions will incorporate practice of walking adaptability and will be matched in terms of frequency, duration, and therapist attention. Walking speed, as determined by the 10 Meter Walking Test, will be the primary outcome measure. Secondary outcome measures will pertain to walking adaptability (10 Meter Walking Test with context or cognitive dual-task and Interactive Walkway assessments). Furthermore, commonly used clinical measures to determine walking ability (Timed Up-and-Go test), walking independence (Functional Ambulation Category), balance (Berg Balance Scale), and balance confidence (Activities-specific Balance Confidence scale) will be used, as well as a complementary set of walking-related assessments. The amount of walking practice (the number of steps taken per session) will be registered using the treadmill's inbuilt step counter (C-Mill therapy) and video recordings (FALLS program). This process measure will be compared between the two interventions. This study will assess the effects of treadmill-based C-Mill therapy compared with the overground FALLS program and thereby the relative importance of the amount of walking practice as a key aspect of effective intervention programs directed at improving walking speed and walking adaptability after stroke. Netherlands Trial Register NTR4030 . Registered on 11 June 2013, amendment filed on 17 June 2016.

The hydrogen diffusion in liquid aluminum alloys from ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Jakse, N.; Pasturel, A.

2014-09-01

We study the hydrogen diffusion in liquid aluminum alloys through extensive ab initio molecular dynamics simulations. At the microscopic scale, we show that the hydrogen motion is characterized by a broad distribution of spatial jumps that does not correspond to a Brownian motion. To determine the self-diffusion coefficient of hydrogen in liquid aluminum alloys, we use a generalized continuous time random walk model recently developed to describe the hydrogen diffusion in pure aluminum. In particular, we show that the model successfully accounts the effects of alloying elements on the hydrogen diffusion in agreement with experimental features.

Effects of Standing and Light-Intensity Walking and Cycling on 24-h Glucose.

PubMed

Crespo, Noe C; Mullane, Sarah L; Zeigler, Zachary S; Buman, Matthew P; Gaesser, Glenn A

2016-12-01

This study aimed to compare 24-h and postprandial glucose responses to incremental intervals of standing (STAND), walking (WALK), and cycling (CYCLE) to a sit-only (SIT) condition. Nine overweight/obese (body mass index = 29 ± 3 kg·m) adults (30 ± 15 yr) participated in this randomized crossover full-factorial study, with each condition performed 1 wk apart. STAND, CYCLE, and WALK intervals increased from 10 to 30 min·h (2.5 h total) during an 8-h workday. WALK (1.0 mph) and STAND were matched for upright time, and WALK and CYCLE were matched for energy expenditure (~2 METs). Continuous interstitial glucose monitoring was performed for 24 h to include the 8-h workday (LAB), after-work evening hours (EVE), and sleep (SLEEP). Three 2-h postprandial periods were also analyzed. Linear mixed models were used to test for condition differences. Compared with SIT (5.7 ± 1.0 mmol·L), mean 24-h glucose during STAND (5.4 ± 0.9 mmol·L) and WALK (5.3 ± 0.9 mmol·L) were lower, and CYCLE (5.1 ± 1.0 mmol·L) was lower than all other conditions (all P < 0.001). During LAB and EVE, mean glucose was lower for STAND, WALK, and CYCLE compared with SIT (P < 0.001). During SLEEP, the mean glucose for CYCLE was lower than all other conditions (P < 0.001). Compared with SIT, cumulative 6-h postprandial mean glucose was 5%-12% lower (P < 0.001) during STAND, WALK, and CYCLE, and 6-h postprandial glucose integrated area under the curve was 24% lower during WALK (P < 0.05) and 44% lower during CYCLE (P < 0.001). Replacing sitting with regular intervals of standing or light-intensity activity during an 8-h workday reduces 24-h and postprandial glucose. These effects persist during evening hours, with CYCLE having the largest and most sustained effect.

Quantum walks on the chimera graph and its variants

NASA Astrophysics Data System (ADS)

Sanders, Barry; Sun, Xiangxiang; Xu, Shu; Wu, Jizhou; Zhang, Wei-Wei; Arshed, Nigum

We study quantum walks on the chimera graph, which is an important graph for performing quantum annealing, and we explore the nature of quantum walks on variants of the chimera graph. Features of these quantum walks provide profound insights into the nature of the chimera graph, including effects of greater and lesser connectivity, strong differences between quantum and classical random walks, isotropic spreading and localization only in the quantum case, and random graphs. We analyze finite-size effects due to limited width and length of the graph, and we explore the effect of different boundary conditions such as periodic and reflecting. Effects are explained via spectral analysis and the properties of stationary states, and spectral analysis enables us to characterize asymptotic behavior of the quantum walker in the long-time limit. Supported by China 1000 Talent Plan, National Science Foundation of China, Hefei National Laboratory for Physical Sciences at Microscale Fellowship, and the Chinese Academy of Sciences President's International Fellowship Initiative.

Limited capacity of working memory in unihemispheric random walks implies conceivable slow dispersal.

PubMed

Wei, Kun; Zhong, Suchuan

2017-08-01

Phenomenologically inspired by dolphins' unihemispheric sleep, we introduce a minimal model for random walks with physiological memory. The physiological memory consists of long-term memory which includes unconscious implicit memory and conscious explicit memory, and working memory which serves as a multi-component system for integrating, manipulating and managing short-term storage. The model assumes that the sleeping state allows retrievals of episodic objects merely from the episodic buffer where these memory objects are invoked corresponding to the ambient objects and are thus object-oriented, together with intermittent but increasing use of implicit memory in which decisions are unconsciously picked up from historical time series. The process of memory decay and forgetting is constructed in the episodic buffer. The walker's risk attitude, as a product of physiological heuristics according to the performance of objected-oriented decisions, is imposed on implicit memory. The analytical results of unihemispheric random walks with the mixture of object-oriented and time-oriented memory, as well as the long-time behavior which tends to the use of implicit memory, are provided, indicating the common sense that a conservative risk attitude is inclinable to slow movement.

How fast does a random walk cover a torus?

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2017-07-01

We present high statistics simulation data for the average time that a random walk needs to cover completely a two-dimensional torus of size L ×L . They confirm the mathematical prediction that ˜(LlnL ) 2 for large L , but the prefactor seems to deviate significantly from the supposedly exact result 4 /π derived by Dembo et al. [Ann. Math. 160, 433 (2004), 10.4007/annals.2004.160.433], if the most straightforward extrapolation is used. On the other hand, we find that this scaling does hold for the time TN (t )=1(L ) at which the average number of yet unvisited sites is 1, as also predicted previously. This might suggest (wrongly) that and TN (t )=1(L ) scale differently, although the distribution of rescaled cover times becomes sharp in the limit L →∞ . But our results can be reconciled with those of Dembo et al. by a very slow and nonmonotonic convergence of /(LlnL ) 2 , as had been indeed proven by Belius et al. [Probab. Theory Relat. Fields 167, 461 (2017), 10.1007/s00440-015-0689-6] for Brownian walks, and was conjectured by them to hold also for lattice walks.

Impact of Pilates Exercise in Multiple Sclerosis: A Randomized Controlled Trial.

PubMed

Duff, Whitney R D; Andrushko, Justin W; Renshaw, Doug W; Chilibeck, Philip D; Farthing, Jonathan P; Danielson, Jana; Evans, Charity D

2018-01-01

Pilates is a series of exercises based on whole-body movement and may improve mobility in people with multiple sclerosis (MS). The purpose of this study was to determine the effect of Pilates on walking performance in people with MS. 30 individuals with MS who were not restricted to a wheelchair or scooter (Patient-Determined Disease Steps scale score <7) were randomized to receive Pilates (twice weekly) and massage therapy (once weekly) or once-weekly massage therapy only (control group). The Pilates was delivered in a group setting (five to ten participants per session). The primary outcome was change in walking performance (6-Minute Walk Test) after 12 weeks. Secondary outcomes included functional ability (Timed Up and Go test), balance (Fullerton Advanced Balance Scale), flexibility (sit and reach test), body composition (dual-energy X-ray absorptiometry), core endurance (plank-hold test), and muscle strength and voluntary activation (quadriceps). Intention-to-treat analysis was performed using a two-factor repeated-measures analysis of variance. Walking distance increased by a mean (SD) of 52.4 (40.2) m in the Pilates group versus 15.0 (34.1) m in the control group (group × time, P = .01). Mean (SD) time to complete the Timed Up and Go test decreased by 1.5 (2.8) seconds in the Pilates group versus an increase of 0.3 (0.9) seconds in the control group (group × time, P = .03). There were no other significant differences between groups over time. Pilates improved walking performance and functional ability in persons with MS and is a viable exercise option to help manage the disease.

Body weight-supported treadmill training vs. overground walking training for persons with chronic stroke: a pilot randomized controlled trial.

PubMed

Combs-Miller, Stephanie A; Kalpathi Parameswaran, Anu; Colburn, Dawn; Ertel, Tara; Harmeyer, Amanda; Tucker, Lindsay; Schmid, Arlene A

2014-09-01

To compare the effects of body weight-supported treadmill training and overground walking training when matched for task and dose (duration/frequency/intensity) on improving walking function, activity, and participation after stroke. Single-blind, pilot randomized controlled trial with three-month follow-up. University and community settings. A convenience sample of participants (N = 20) at least six months post-stroke and able to walk independently were recruited. Thirty-minute walking interventions (body weight-supported treadmill training or overground walking training) were administered five times a week for two weeks. Intensity was monitored with the Borg Rating of Perceived Exertion Scale at five-minute increments to maintain a moderate training intensity. Walking speed (comfortable/fast 10-meter walk), walking endurance (6-minute walk), spatiotemporal symmetry, and the ICF Measure of Participation and ACTivity were assessed before, immediately after, and three months following the intervention. The overground walking training group demonstrated significantly greater improvements in comfortable walking speed compared with the body weight-supported treadmill training group immediately (change of 0.11 m/s vs. 0.06 m/s, respectively; p = 0.047) and three months (change of 0.14 m/s vs. 0.08 m/s, respectively; p = 0.029) after training. Only the overground walking training group significantly improved comfortable walking speed (p = 0.001), aspects of gait symmetry (p = 0.032), and activity (p = 0.003) immediately after training. Gains were maintained at the three-month follow-up (p < 0.05) for all measures except activity. Improvements in participation were not demonstrated. Overgound walking training was more beneficial than body weight-supported treadmill training at improving self-selected walking speed for the participants in this study. © The Author(s) 2014.

Combinatorial approximation algorithms for MAXCUT using random walks.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seshadhri, Comandur; Kale, Satyen

We give the first combinatorial approximation algorithm for MaxCut that beats the trivial 0.5 factor by a constant. The main partitioning procedure is very intuitive, natural, and easily described. It essentially performs a number of random walks and aggregates the information to provide the partition. We can control the running time to get an approximation factor-running time tradeoff. We show that for any constant b > 1.5, there is an {tilde O}(n{sup b}) algorithm that outputs a (0.5 + {delta})-approximation for MaxCut, where {delta} = {delta}(b) is some positive constant. One of the components of our algorithm is a weakmore » local graph partitioning procedure that may be of independent interest. Given a starting vertex i and a conductance parameter {phi}, unless a random walk of length {ell} = O(log n) starting from i mixes rapidly (in terms of {phi} and {ell}), we can find a cut of conductance at most {phi} close to the vertex. The work done per vertex found in the cut is sublinear in n.« less

Faster quantum walk search on a weighted graph

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2015-09-01

A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ (N3 /4) . We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ (√{N }) . To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

An Ambulatory System for Gait Monitoring Based on Wireless Sensorized Insoles.

PubMed

González, Iván; Fontecha, Jesús; Hervás, Ramón; Bravo, José

2015-07-09

A new gait phase detection system for continuous monitoring based on wireless sensorized insoles is presented. The system can be used in gait analysis mobile applications, and it is designed for real-time demarcation of gait phases. The system employs pressure sensors to assess the force exerted by each foot during walking. A fuzzy rule-based inference algorithm is implemented on a smartphone and used to detect each of the gait phases based on the sensor signals. Additionally, to provide a solution that is insensitive to perturbations caused by non-walking activities, a probabilistic classifier is employed to discriminate walking forward from other low-level activities, such as turning, walking backwards, lateral walking, etc. The combination of these two algorithms constitutes the first approach towards a continuous gait assessment system, by means of the avoidance of non-walking influences.

Elephant random walks and their connection to Pólya-type urns

NASA Astrophysics Data System (ADS)

Baur, Erich; Bertoin, Jean

2016-11-01

In this paper, we explain the connection between the elephant random walk (ERW) and an urn model à la Pólya and derive functional limit theorems for the former. The ERW model was introduced in [Phys. Rev. E 70, 045101 (2004), 10.1103/PhysRevE.70.045101] to study memory effects in a highly non-Markovian setting. More specifically, the ERW is a one-dimensional discrete-time random walk with a complete memory of its past. The influence of the memory is measured in terms of a memory parameter p between zero and one. In the past years, a considerable effort has been undertaken to understand the large-scale behavior of the ERW, depending on the choice of p . Here, we use known results on urns to explicitly solve the ERW in all memory regimes. The method works as well for ERWs in higher dimensions and is widely applicable to related models.

Effective degrees of freedom of a random walk on a fractal

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.

2015-12-01

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence.

PubMed

Rossi, Luca; Torsello, Andrea; Hancock, Edwin R

2015-02-01

In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous-time quantum walks. In order to analyze the behavior of the walks without causing wave function collapse, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic. We also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the Hamiltonians associated with the two original graphs have an empty intersection.

Pilates exercise training vs. physical therapy for improving walking and balance in people with multiple sclerosis: a randomized controlled trial.

PubMed

Kalron, Alon; Rosenblum, Uri; Frid, Lior; Achiron, Anat

2017-03-01

Evaluate the effects of a Pilates exercise programme on walking and balance in people with multiple sclerosis and compare this exercise approach to conventional physical therapy sessions. Randomized controlled trial. Multiple Sclerosis Center, Sheba Medical Center, Tel-Hashomer, Israel. Forty-five people with multiple sclerosis, 29 females, mean age (SD) was 43.2 (11.6) years; mean Expanded Disability Status Scale (S.D) was 4.3 (1.3). Participants received 12 weekly training sessions of either Pilates ( n=22) or standardized physical therapy ( n=23) in an outpatient basis. Spatio-temporal parameters of walking and posturography parameters during static stance. Functional tests included the Time Up and Go Test, 2 and 6-minute walk test, Functional Reach Test, Berg Balance Scale and the Four Square Step Test. In addition, the following self-report forms included the Multiple Sclerosis Walking Scale and Modified Fatigue Impact Scale. At the termination, both groups had significantly increased their walking speed ( P=0.021) and mean step length ( P=0.023). According to the 2-minute and 6-minute walking tests, both groups at the end of the intervention program had increased their walking speed. Mean (SD) increase in the Pilates and physical therapy groups were 39.1 (78.3) and 25.3 (67.2) meters, respectively. There was no effect of group X time in all instrumented and clinical balance and gait measures. Pilates is a possible treatment option for people with multiple sclerosis in order to improve their walking and balance capabilities. However, this approach does not have any significant advantage over standardized physical therapy.

Nonlocal operators, parabolic-type equations, and ultrametric random walks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacón-Cortes, L. F., E-mail: fchaconc@math.cinvestav.edu.mx; Zúñiga-Galindo, W. A., E-mail: wazuniga@math.cinvestav.edu.mx

2013-11-15

In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the numbermore » of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.« less

Feasibility and Preliminary Efficacy of Visual Cue Training to Improve Adaptability of Walking after Stroke: Multi-Centre, Single-Blind Randomised Control Pilot Trial

PubMed Central

Hollands, Kristen L.; Pelton, Trudy A.; Wimperis, Andrew; Whitham, Diane; Tan, Wei; Jowett, Sue; Sackley, Catherine M.; Wing, Alan M.; Tyson, Sarah F.; Mathias, Jonathan; Hensman, Marianne; van Vliet, Paulette M.

2015-01-01

Objectives Given the importance of vision in the control of walking and evidence indicating varied practice of walking improves mobility outcomes, this study sought to examine the feasibility and preliminary efficacy of varied walking practice in response to visual cues, for the rehabilitation of walking following stroke. Design This 3 arm parallel, multi-centre, assessor blind, randomised control trial was conducted within outpatient neurorehabilitation services Participants Community dwelling stroke survivors with walking speed <0.8m/s, lower limb paresis and no severe visual impairments Intervention Over-ground visual cue training (O-VCT), Treadmill based visual cue training (T-VCT), and Usual care (UC) delivered by physiotherapists twice weekly for 8 weeks. Main outcome measures: Participants were randomised using computer generated random permutated balanced blocks of randomly varying size. Recruitment, retention, adherence, adverse events and mobility and balance were measured before randomisation, post-intervention and at four weeks follow-up. Results Fifty-six participants participated (18 T-VCT, 19 O-VCT, 19 UC). Thirty-four completed treatment and follow-up assessments. Of the participants that completed, adherence was good with 16 treatments provided over (median of) 8.4, 7.5 and 9 weeks for T-VCT, O-VCT and UC respectively. No adverse events were reported. Post-treatment improvements in walking speed, symmetry, balance and functional mobility were seen in all treatment arms. Conclusions Outpatient based treadmill and over-ground walking adaptability practice using visual cues are feasible and may improve mobility and balance. Future studies should continue a carefully phased approach using identified methods to improve retention. Trial Registration Clinicaltrials.gov NCT01600391 PMID:26445137

A CTRW-based model of time-resolved fluorescence lifetime imaging in a turbid medium

NASA Astrophysics Data System (ADS)

Chernomordik, Victor; Gandjbakhche, Amir H.; Hassan, Moinuddin; Pajevic, Sinisa; Weiss, George H.

2010-12-01

We develop an analytic model of time-resolved fluorescent imaging of photons migrating through a semi-infinite turbid medium bounded by an infinite plane in the presence of a single stationary point fluorophore embedded in the medium. In contrast to earlier models of fluorescent imaging in which photon motion is assumed to be some form of continuous diffusion process, the present analysis is based on a continuous-time random walk (CTRW) on a simple cubic lattice, the objective being to estimate the position and lifetime of the fluorophore. This can provide information related to local variations in pH and temperature with potential medical significance. Aspects of the theory were tested using time-resolved measurements of the fluorescence from small inclusions inside tissue-like phantoms. The experimental results were found to be in good agreement with theoretical predictions provided that the fluorophore was not located too close to the planar boundary, a common problem in many diffusive systems.

Gradient-free MCMC methods for dynamic causal modelling

DOE PAGES

Sengupta, Biswa; Friston, Karl J.; Penny, Will D.

2015-03-14

Here, we compare the performance of four gradient-free MCMC samplers (random walk Metropolis sampling, slice-sampling, adaptive MCMC sampling and population-based MCMC sampling with tempering) in terms of the number of independent samples they can produce per unit computational time. For the Bayesian inversion of a single-node neural mass model, both adaptive and population-based samplers are more efficient compared with random walk Metropolis sampler or slice-sampling; yet adaptive MCMC sampling is more promising in terms of compute time. Slice-sampling yields the highest number of independent samples from the target density -- albeit at almost 1000% increase in computational time, in comparisonmore » to the most efficient algorithm (i.e., the adaptive MCMC sampler).« less

Synthesis of Polyferrocenylsilane Block Copolymers and their Crystallization-Driven Self-Assembly in Protic Solvents

NASA Astrophysics Data System (ADS)

Zhou, Hang

Quantum walks are the quantum mechanical analogue of classical random walks. Discrete-time quantum walks have been introduced and studied mostly on the line Z or higher dimensional space Zd but rarely defined on graphs with fractal dimensions because the coin operator depends on the position and the Fourier transform on the fractals is not defined. Inspired by its nature of classical walks, different quantum walks will be defined by choosing different shift and coin operators. When the coin operator is uniform, the results of classical walks will be obtained upon measurement at each step. Moreover, with measurement at each step, our results reveal more information about the classical random walks. In this dissertation, two graphs with fractal dimensions will be considered. The first one is Sierpinski gasket, a degree-4 regular graph with Hausdorff dimension of df = ln 3/ ln 2. The second is the Cantor graph derived like Cantor set, with Hausdorff dimension of df = ln 2/ ln 3. The definitions and amplitude functions of the quantum walks will be introduced. The main part of this dissertation is to derive a recursive formula to compute the amplitude Green function. The exiting probability will be computed and compared with the classical results. When the generation of graphs goes to infinity, the recursion of the walks will be investigated and the convergence rates will be obtained and compared with the classical counterparts.

Mean-Potential Law in Evolutionary Games.

PubMed

Nałęcz-Jawecki, Paweł; Miękisz, Jacek

2018-01-12

The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of a potential function for discrete-space stochastic systems. It is based on a correspondence between one-dimensional stochastic differential equations and random walks, which may be exact not only in the continuous limit but also in finite-state spaces. Our method is useful for computation of fixation probabilities in discrete stochastic dynamical systems with two absorbing states. We apply it to evolutionary games, formulating two simple and intuitive criteria for evolutionary stability of pure Nash equilibria in finite populations. In particular, we show that the 1/3 law of evolutionary games, introduced by Nowak et al. [Nature, 2004], follows from a more general mean-potential law.

A New Random Walk for Replica Detection in WSNs.

PubMed

Aalsalem, Mohammed Y; Khan, Wazir Zada; Saad, N M; Hossain, Md Shohrab; Atiquzzaman, Mohammed; Khan, Muhammad Khurram

2016-01-01

Wireless Sensor Networks (WSNs) are vulnerable to Node Replication attacks or Clone attacks. Among all the existing clone detection protocols in WSNs, RAWL shows the most promising results by employing Simple Random Walk (SRW). More recently, RAND outperforms RAWL by incorporating Network Division with SRW. Both RAND and RAWL have used SRW for random selection of witness nodes which is problematic because of frequently revisiting the previously passed nodes that leads to longer delays, high expenditures of energy with lower probability that witness nodes intersect. To circumvent this problem, we propose to employ a new kind of constrained random walk, namely Single Stage Memory Random Walk and present a distributed technique called SSRWND (Single Stage Memory Random Walk with Network Division). In SSRWND, single stage memory random walk is combined with network division aiming to decrease the communication and memory costs while keeping the detection probability higher. Through intensive simulations it is verified that SSRWND guarantees higher witness node security with moderate communication and memory overheads. SSRWND is expedient for security oriented application fields of WSNs like military and medical.

A New Random Walk for Replica Detection in WSNs

PubMed Central

Aalsalem, Mohammed Y.; Saad, N. M.; Hossain, Md. Shohrab; Atiquzzaman, Mohammed; Khan, Muhammad Khurram

2016-01-01

Wireless Sensor Networks (WSNs) are vulnerable to Node Replication attacks or Clone attacks. Among all the existing clone detection protocols in WSNs, RAWL shows the most promising results by employing Simple Random Walk (SRW). More recently, RAND outperforms RAWL by incorporating Network Division with SRW. Both RAND and RAWL have used SRW for random selection of witness nodes which is problematic because of frequently revisiting the previously passed nodes that leads to longer delays, high expenditures of energy with lower probability that witness nodes intersect. To circumvent this problem, we propose to employ a new kind of constrained random walk, namely Single Stage Memory Random Walk and present a distributed technique called SSRWND (Single Stage Memory Random Walk with Network Division). In SSRWND, single stage memory random walk is combined with network division aiming to decrease the communication and memory costs while keeping the detection probability higher. Through intensive simulations it is verified that SSRWND guarantees higher witness node security with moderate communication and memory overheads. SSRWND is expedient for security oriented application fields of WSNs like military and medical. PMID:27409082

Effects of various boundary conditions on the response of Poisson-Nernst-Planck impedance spectroscopy analysis models and comparison with a continuous-time random-walk model.

PubMed

Macdonald, J Ross

2011-11-24

Various electrode reaction rate boundary conditions suitable for mean-field Poisson-Nernst-Planck (PNP) mobile charge frequency response continuum models are defined and incorporated in the resulting Chang-Jaffe (CJ) CJPNP model, the ohmic OHPNP one, and a simplified GPNP one in order to generalize from full to partial blocking of mobile charges at the two plane parallel electrodes. Model responses using exact synthetic PNP data involving only mobile negative charges are discussed and compared for a wide range of CJ dimensionless reaction rate values. The CJPNP and OHPNP ones are shown to be fully equivalent, except possibly for the analysis of nanomaterial structures. The dielectric strengths associated with the CJPNP diffuse double layers at the electrodes were found to decrease toward 0 as the reaction rate increased, consistent with fewer blocked charges and more reacting ones. Parameter estimates from GPNP fits of CJPNP data were shown to lead to accurate calculated values of the CJ reaction rate and of some other CJPNP parameters. Best fits of CaCu(3)Ti(4)O(12) (CCTO) single-crystal data, an electronic conductor, at 80 and 140 K, required the anomalous diffusion model, CJPNPA, and led to medium-size rate estimates of about 0.12 and 0.03, respectively, as well as good estimates of the values of other important CJPNPA parameters such as the independently verified concentration of neutral dissociable centers. These continuum-fit results were found to be only somewhat comparable to those obtained from a composite continuous-time random-walk hopping/trapping semiuniversal UN model.

Benefits of home-based rocking-chair exercise for physical performance in community-dwelling elderly women: a randomized controlled trial.

PubMed

Niemelä, Kristiina; Väänänen, Ilkka; Leinonen, Raija; Laukkanen, Pia

2011-08-01

Home-based exercise is a viable alternative for older adults with difficulties in exercise opportunities outside the home. The aim of this study was to investigate the benefits of home-based rocking-chair training, and its effects on the physical performance of elderly women. Community- dwelling women (n=51) aged 73-87 years were randomly assigned to the rocking-chair group (RCG, n=26) or control group (CG, n=25) by drawing lots. Baseline and outcome measurements were hand grip strength, maximal isometric knee extension, maximal walking speed over 10 meters, rising from a chair five times, and the Berg Balance Scale (BBS). The RCG carried out a six-week rocking-chair training program at home, involving ten sessions per week, twice a day for 15 minutes per session, and ten different movements. The CG continued their usual daily lives. After three months, the RCG responded to a mail questionnaire. After the intervention, the RCG improved and the CG declined. The data showed significant interactions of group by time in the BBS score (p=0.001), maximal knee extension strength (p=0.006) and maximal walking speed (p=0.046), which indicates that the change between groups during the follow-up period was significant. Adherence to the training protocol was high (96%). After three months, the exercise program had become a regular home exercise habit for 88.5% of the subjects. Results indicate that home-based elderly women benefit from this easily implemented rocking-chair exercise program. The subjects became motivated to participate in training and continued the exercises. This is a promising alternative exercise method for maintaining physical activity and leads to improvements in physical performance.

The Shark Random Swim - (Lévy Flight with Memory)

NASA Astrophysics Data System (ADS)

Businger, Silvia

2018-05-01

The Elephant Random Walk (ERW), first introduced by Schütz and Trimper (Phys Rev E 70:045101, 2004), is a one-dimensional simple random walk on Z having a memory about the whole past. We study the Shark Random Swim, a random walk with memory about the whole past, whose steps are α -stable distributed with α \\in (0,2] . Our aim in this work is to study the impact of the heavy tailed step distributions on the asymptotic behavior of the random walk. We shall see that, as for the ERW, the asymptotic behavior of the Shark Random Swim depends on its memory parameter p, and that a phase transition can be observed at the critical value p=1/α.

Optimal Quantum Spatial Search on Random Temporal Networks

NASA Astrophysics Data System (ADS)

Chakraborty, Shantanav; Novo, Leonardo; Di Giorgio, Serena; Omar, Yasser

2017-12-01

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs G (n ,p ), where p is the probability that any two given nodes are connected: After every time interval τ , a new graph G (n ,p ) replaces the previous one. We prove analytically that, for any given p , there is always a range of values of τ for which the running time of the algorithm is optimal, i.e., O (√{n }), even when search on the individual static graphs constituting the temporal network is suboptimal. On the other hand, there are regimes of τ where the algorithm is suboptimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the nontrivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.

Do walking strategies to increase physical activity reduce reported sitting in workplaces: a randomized control trial

PubMed Central

Gilson, Nicholas D; Puig-Ribera, Anna; McKenna, Jim; Brown, Wendy J; Burton, Nicola W; Cooke, Carlton B

2009-01-01

Background Interventions designed to increase workplace physical activity may not automatically reduce high volumes of sitting, a behaviour independently linked to chronic diseases such as obesity and type II diabetes. This study compared the impact two different walking strategies had on step counts and reported sitting times. Methods Participants were white-collar university employees (n = 179; age 41.3 ± 10.1 years; 141 women), who volunteered and undertook a standardised ten-week intervention at three sites. Pre-intervention step counts (Yamax SW-200) and self-reported sitting times were measured over five consecutive workdays. Using pre-intervention step counts, employees at each site were randomly allocated to a control group (n = 60; maintain normal behaviour), a route-based walking group (n = 60; at least 10 minutes sustained walking each workday) or an incidental walking group (n = 59; walking in workday tasks). Workday step counts and reported sitting times were re-assessed at the beginning, mid- and endpoint of intervention and group mean± SD steps/day and reported sitting times for pre-intervention and intervention measurement points compared using a mixed factorial ANOVA; paired sample-t-tests were used for follow-up, simple effect analyses. Results A significant interactive effect (F = 3.5; p < 0.003) was found between group and step counts. Daily steps for controls decreased over the intervention period (-391 steps/day) and increased for route (968 steps/day; t = 3.9, p < 0.000) and incidental (699 steps/day; t = 2.5, p < 0.014) groups. There were no significant changes for reported sitting times, but average values did decrease relative to the control (routes group = 7 minutes/day; incidental group = 15 minutes/day). Reductions were most evident for the incidental group in the first week of intervention, where reported sitting decreased by an average of 21 minutes/day (t = 1.9; p < 0.057). Conclusion Compared to controls, both route and incidental walking increased physical activity in white-collar employees. Our data suggests that workplace walking, particularly through incidental movement, also has the potential to decrease employee sitting times, but there is a need for on-going research using concurrent and objective measures of sitting, standing and walking. PMID:19619295

Directional Migration of Recirculating Lymphocytes through Lymph Nodes via Random Walks

PubMed Central

Thomas, Niclas; Matejovicova, Lenka; Srikusalanukul, Wichat; Shawe-Taylor, John; Chain, Benny

2012-01-01

Naive T lymphocytes exhibit extensive antigen-independent recirculation between blood and lymph nodes, where they may encounter dendritic cells carrying cognate antigen. We examine how long different T cells may spend in an individual lymph node by examining data from long term cannulation of blood and efferent lymphatics of a single lymph node in the sheep. We determine empirically the distribution of transit times of migrating T cells by applying the Least Absolute Shrinkage & Selection Operator () or regularised to fit experimental data describing the proportion of labelled infused cells in blood and efferent lymphatics over time. The optimal inferred solution reveals a distribution with high variance and strong skew. The mode transit time is typically between 10 and 20 hours, but a significant number of cells spend more than 70 hours before exiting. We complement the empirical machine learning based approach by modelling lymphocyte passage through the lymph node . On the basis of previous two photon analysis of lymphocyte movement, we optimised distributions which describe the transit times (first passage times) of discrete one dimensional and continuous (Brownian) three dimensional random walks with drift. The optimal fit is obtained when drift is small, i.e. the ratio of probabilities of migrating forward and backward within the node is close to one. These distributions are qualitatively similar to the inferred empirical distribution, with high variance and strong skew. In contrast, an optimised normal distribution of transit times (symmetrical around mean) fitted the data poorly. The results demonstrate that the rapid recirculation of lymphocytes observed at a macro level is compatible with predominantly randomised movement within lymph nodes, and significant probabilities of long transit times. We discuss how this pattern of migration may contribute to facilitating interactions between low frequency T cells and antigen presenting cells carrying cognate antigen. PMID:23028891

Effects of aquatic walking exercise using a walker in a chronic stroke patient.

PubMed

Matsuda, Tadashi; Akezaki, Yoshiteru

2017-07-01

[Purpose] The aim of this study was to examine the usefulness of aquatic walking exercise using a walker for chronic stroke patients. We also examined the psychological effects on the study subject and the primary caregiver before and after aquatic walking exercise. [Subject and Methods] The subject was a 60-year-old male with bilateral paralysis after a cerebrovascular accident. The Fugl-Meyer Assessment (FMA) total score was 116 on the right and 115 on the left. The intervention combined aquatic and land walking exercise. A U-shaped walker was used for both water and land exercise. Continuous walking distance was the measure used to evaluate land walking ability. The psychological effects on the study subject and the primary caregiver were examined with the questionnaire. [Results] In aquatic walking, the mean time to walk 5 m showed an increase from the intervention after two months. After the aquatic walking and land walking combination, continuous walking distance also showed a prolonged trend. In the survey given to the main caregivers, improvements were observed. [Conclusion] Aquatic walking practice using a walker improved motivation in a chronic stroke patient, leading to improved walking ability, with a positive psychological influence on the participant and family caregiver.

Effects of aquatic walking exercise using a walker in a chronic stroke patient

PubMed Central

Matsuda, Tadashi; Akezaki, Yoshiteru

2017-01-01

[Purpose] The aim of this study was to examine the usefulness of aquatic walking exercise using a walker for chronic stroke patients. We also examined the psychological effects on the study subject and the primary caregiver before and after aquatic walking exercise. [Subject and Methods] The subject was a 60-year-old male with bilateral paralysis after a cerebrovascular accident. The Fugl-Meyer Assessment (FMA) total score was 116 on the right and 115 on the left. The intervention combined aquatic and land walking exercise. A U-shaped walker was used for both water and land exercise. Continuous walking distance was the measure used to evaluate land walking ability. The psychological effects on the study subject and the primary caregiver were examined with the questionnaire. [Results] In aquatic walking, the mean time to walk 5 m showed an increase from the intervention after two months. After the aquatic walking and land walking combination, continuous walking distance also showed a prolonged trend. In the survey given to the main caregivers, improvements were observed. [Conclusion] Aquatic walking practice using a walker improved motivation in a chronic stroke patient, leading to improved walking ability, with a positive psychological influence on the participant and family caregiver. PMID:28744062

An Ambulatory System for Gait Monitoring Based on Wireless Sensorized Insoles

PubMed Central

González, Iván; Fontecha, Jesús; Hervás, Ramón; Bravo, José

2015-01-01

A new gait phase detection system for continuous monitoring based on wireless sensorized insoles is presented. The system can be used in gait analysis mobile applications, and it is designed for real-time demarcation of gait phases. The system employs pressure sensors to assess the force exerted by each foot during walking. A fuzzy rule-based inference algorithm is implemented on a smartphone and used to detect each of the gait phases based on the sensor signals. Additionally, to provide a solution that is insensitive to perturbations caused by non-walking activities, a probabilistic classifier is employed to discriminate walking forward from other low-level activities, such as turning, walking backwards, lateral walking, etc. The combination of these two algorithms constitutes the first approach towards a continuous gait assessment system, by means of the avoidance of non-walking influences. PMID:26184199

Establishing the kinetics of ballistic-to-diffusive transition using directional statistics

NASA Astrophysics Data System (ADS)

Liu, Pai; Heinson, William R.; Sumlin, Benjamin J.; Shen, Kuan-Yu; Chakrabarty, Rajan K.

2018-04-01

We establish the kinetics of ballistic-to-diffusive (BD) transition observed in two-dimensional random walk using directional statistics. Directional correlation is parameterized using the walker's turning angle distribution, which follows the commonly adopted wrapped Cauchy distribution (WCD) function. During the BD transition, the concentration factor (ρ) governing the WCD shape is observed to decrease from its initial value. We next analytically derive the relationship between effective ρ and time, which essentially quantifies the BD transition rate. The prediction of our kinetic expression agrees well with the empirical datasets obtained from correlated random walk simulation. We further connect our formulation with the conventionally used scaling relationship between the walker's mean-square displacement and time.

"You gotta try it all": Parents' Experiences with Robotic Gait Training for their Children with Cerebral Palsy.

PubMed

Beveridge, Briony; Feltracco, Deanna; Struyf, Jillian; Strauss, Emily; Dang, Saniya; Phelan, Shanon; Wright, F Virginia; Gibson, Barbara E

2015-01-01

Innovative robotic technologies hold strong promise for improving walking abilities of children with cerebral palsy (CP), but may create expectations for parents pursuing the "newest thing" in treatment. The aim of this qualitative study was to explore parents' values about walking in relation to their experiences with robotic gait training for their children. Semi-structured interviews were conducted with parents of five ambulatory children with CP participating in a randomized trial investigating robotic gait training effectiveness. Parents valued walking, especially "correct" walking, as a key component of their children's present and future well-being. They continually sought the "next best thing" in therapy and viewed the robotic gait trainer as a potentially revolutionary technology despite mixed experiences. The results can help inform rehabilitation therapists' knowledge of parents' values and perspectives, and guide effective collaborations toward meeting the therapeutic needs of children with CP.

Treadmill Training or Progressive Strength Training to Improve Walking in People with Multiple Sclerosis? A Randomized Parallel Group Trial.

PubMed

Braendvik, Siri Merete; Koret, Teija; Helbostad, Jorunn L; Lorås, Håvard; Bråthen, Geir; Hovdal, Harald Olav; Aamot, Inger Lise

2016-12-01

The most effective treatment approach to improve walking in people with multiple sclerosis (MS) is not known. The aim of this trial was to assess the efficacy of treadmill training and progressive strength training on walking in people with MS. A single blinded randomized parallel group trial was carried out. Eligible participants were adults with MS with Expanded Disability Status Scale score ≤6. A total of 29 participants were randomized and 28 received the allocated exercise intervention, treadmill (n = 13) or strength training (n = 15). Both groups exercised 30 minutes, three times a week for 8 weeks. Primary outcome was The Functional Ambulation Profile evaluated by the GAITRite walkway. Secondary outcomes were walking work economy and balance control during walking, measured by a small lightweight accelerometer connected to the lower back. Testing was performed at baseline and the subsequent week after completion of training. Two participants were lost to follow-up, and 11 (treadmill) and 15 (strength training) were left for analysis. The treadmill group increased their Functional Ambulation Profile score significantly compared with the strength training group (p = .037). A significant improvement in walking work economy (p = .024) and a reduction of root mean square of vertical acceleration (p = .047) also favoured the treadmill group. The results indicate that task-specific training by treadmill walking is a favourable approach compared with strength training to improve walking in persons with mild and moderate MS. Implications for Physiotherapy practice, this study adds knowledge for the decision of optimal treatment approaches in people with MS. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Randomized controlled trial of physical activity, cognition, and walking in multiple sclerosis.

PubMed

Sandroff, Brian M; Klaren, Rachel E; Pilutti, Lara A; Dlugonski, Deirdre; Benedict, Ralph H B; Motl, Robert W

2014-02-01

The present study adopted a randomized controlled trial design and examined the effect of a physical activity behavioral intervention on cognitive and walking performance among persons with MS who have mild or moderate disability status. A total of 82 MS patients were randomly allocated into intervention or wait-list control conditions. The intervention condition received a theory-based program for increasing physical activity behavior that was delivered via the Internet, and one-on-one video chat sessions with a behavior-change coach. Participants completed self-report measures of physical activity and disability status, and underwent the oral Symbol Digit Modalities Test (SDMT) and 6-minute walk (6MW) test before and after the 6-month period. Analysis using mixed-model ANOVA indicated a significant time × condition × disability group interaction on SDMT scores (p = 0.02, partial-η (2) = 0.08), such that persons with mild disability in the intervention condition demonstrated a clinically meaningful improvement in SDMT scores (~6 point change). There was a further significant time × condition interaction on 6MW distance (p = 0.02, partial-η (2) = 0.07), such that those in the intervention condition demonstrated an increase in 6MW distance relative to those in the control group. The current study supports physical activity as a promising tool for managing cognitive impairment and impaired walking performance in persons with MS, and suggests that physical activity might have specific effects on cognition and non-specific effects on walking performance in this population.

[Association between walking time and perception of built environment among urban adults in Hangzhou].

PubMed

Liu, Qingmin; Ren, Yanjun; Cao, Chengjian; Su, Meng; Lyu, Jun; Li, Liming

2015-10-01

To explore the association between walking time and the perception of built environment among local adults in Hangzhou. Through multistage stratified random sampling, a total of 1 440 urban residents aged 25-59 years were surveyed in Hangzhou by face-to face interview in 2012. The international physical activity questionnaire-long version (IPAQ-L) was used to assess the physical activity levels, including walking time in the past week. Neighborhood Environment Walkability Scale-Abbreviated (NEWS-A) was used to obtain information about their perception of built environment. Multiple logistic regression was applied to estimate the relationship between waking and the perception of built environment. Among the local adults in Hangzhou, the median of total physical activity was 2 766 met·min⁻¹·week⁻¹, the average walking time per week was 90 min for leisure and 100 min for transportation respectively. After controlling the age, marital status, BMI, educational level, employment, community type and the total PA scores, the leisure-time walking was negatively related to the accessibility to stores, facilities and other things for both man (OR=0.764, 95% CI: 0.588-0.992) and woman (OR=0.633, 95% CI: 0.481-0.833). In sex specific analysis, the leisure-time walking was negatively related with the residential density (OR=0.997, 95% CI: 0.996-0.999) while transportation related walking was positively related with walking/cycling way scores (OR=1.537, 95% CI: 1.138-2.075) in females. In contrast, there were no significant associations between perception of built environment and transportation related walking in males. Improving the built environment, such as the walking/cycling way, might be useful to increase the transportation related walking time for adults. The sex specific differences need to be considered in the environment intervention for walking promotion.

Leader behaviors, group cohesion, and participation in a walking group program

PubMed Central

Izumi, Betty T.; Schulz, Amy J.; Mentz, Graciela; Israel, Barbara A.; Sand, Sharon L.; Reyes, Angela G.; Hoston, Bernadine; Richardson, Dawn; Gamboa, Cindy; Rowe, Zachary; Diaz, Goya

2015-01-01

Background Fewer than half of all U.S. adults meet the 2008 Physical Activity Guidelines. Leader behaviors and group cohesion have been associated with increased participation or adherence in sports team and exercise class settings. Physical activity interventions in community settings that encompass these factors may enhance intervention adherence. Purpose To examine the impact of Community Health Promoter leader behaviors and group cohesion on participation in a walking group intervention among racially/ethnically diverse adults in low-to-moderate income communities in Detroit, Mich. Design Data for the current study were drawn from the Walk Your Heart to Health (WYHH) data set. WYHH was a multi-site cluster randomized controlled study with a lagged intervention and outcome measurements at baseline, four, eight, and 32 weeks. Pooled survey data from both intervention arms is used for the current study. Data were analyzed between August 2013 and October 2014. Setting/participants A total of 603 non-Hispanic Black, non-Hispanic White, and Hispanic adults across five cohorts that began the 32-week WYHH intervention between March 2009 and October 2011. Intervention A 32-week long walking group program hosted by community- and faith-based organizations and facilitated by Community Health Promoters. Walking groups met three times per week for 90-minutes per session. To promote participation in or adherence to WYHH, Community Health Promoters used evidence-based strategies to facilitate group cohesion. Group members assumed increasing leadership responsibility for facilitating sessions over time. Main outcome measures Participation in WYHH as measured by consistency of attendance. Results Community Health Promoter leader behaviors were positively associated with participation in WYHH. Social but not task cohesion was significantly associated with consistent participation. Social cohesion may mediate the relationship between leader behaviors and walking group participation. Conclusions Providing leaders with training to build socially cohesive groups may help motivate individuals to continue participation in community-based physical activity programs. PMID:26094226

Transport and Reactive Flow Modelling Using A Particle Tracking Method Based on Continuous Time Random Walks

NASA Astrophysics Data System (ADS)

Oliveira, R.; Bijeljic, B.; Blunt, M. J.; Colbourne, A.; Sederman, A. J.; Mantle, M. D.; Gladden, L. F.

2017-12-01

Mixing and reactive processes have a large impact on the viability of enhanced oil and gas recovery projects that involve acid stimulation and CO2 injection. To achieve a successful design of the injection schemes an accurate understanding of the interplay between pore structure, flow and reactive transport is necessary. Dependent on transport and reactive conditions, this complex coupling can also be dependent on initial rock heterogeneity across a variety of scales. To address these issues, we devise a new method to study transport and reactive flow in porous media at multiple scales. The transport model is based on an efficient Particle Tracking Method based on Continuous Time Random Walks (CTRW-PTM) on a lattice. Transport is modelled using an algorithm described in Rhodes and Blunt (2006) and Srinivasan et al. (2010); this model is expanded to enable for reactive flow predictions in subsurface rock undergoing a first-order fluid/solid chemical reaction. The reaction-induced alteration in fluid/solid interface is accommodated in the model through changes in porosity and flow field, leading to time dependent transport characteristics in the form of transit time distributions which account for rock heterogeneity change. This also enables the study of concentration profiles at the scale of interest. Firstly, we validate transport model by comparing the probability of molecular displacement (propagators) measured by Nuclear Magnetic Resonance (NMR) with our modelled predictions for concentration profiles. The experimental propagators for three different porous media of increasing complexity, a beadpack, a Bentheimer sandstone and a Portland carbonate, show a good agreement with the model. Next, we capture the time evolution of the propagators distribution in a reactive flow experiment, where hydrochloric acid is injected into a limestone rock. We analyse the time-evolving non-Fickian signatures for the transport during reactive flow and observe an increase in transport heterogeneity at latter times, representing the increase in rock heterogeneity. Evolution of transit time distribution is associated with the evolution of concentration profiles, thus highlighting the impact of initial rock structure on the reactive transport for a range of Pe and Da numbers.

Action observation training of community ambulation for improving walking ability of patients with post-stroke hemiparesis: a randomized controlled pilot trial.

PubMed

Park, Hyun-Ju; Oh, Duck-Won; Choi, Jong-Duk; Kim, Jong-Man; Kim, Suhn-Yeop; Cha, Yong-Jun; Jeon, Su-Jin

2017-08-01

To investigate the effects of action observation training involving community-based ambulation for improving walking ability after stroke. Randomized, controlled pilot study. Inpatient rehabilitation hospital. A total of 25 inpatients with post-stroke hemiparesis were randomly assigned to either the experimental group ( n = 12) or control group ( n = 13). Subjects of the experimental group watched video clips demonstrating four-staged ambulation training with a more complex environment factor for 30 minutes, three times a week for four weeks. Meanwhile, subjects of the control group watched video clips, which showed different landscape pictures. Walking function was evaluated before and after the four-week intervention using a 10-m walk test, community walk test, activities-specific balance confidence scale, and spatiotemporal gait measures. Changes in the values for the 10-m walk test (0.17 ±0.19 m/s vs. 0.05 ±0.08 m/s), community walk test (-151.42 ±123.82 seconds vs. 67.08 ±176.77 seconds), and activities-specific balance confidence (6.25 ±5.61 scores vs. 0.72 ±2.24 scores) and the spatiotemporal parameters (i.e. stride length (19.00 ±11.34 cm vs. 3.16 ±11.20 cm), single support (5.87 ±5.13% vs. 0.25 ±5.95%), and velocity (15.66 ±12.34 cm/s vs. 2.96 ±10.54 cm/s)) indicated a significant improvement in the experimental group compared with the control group. In the experimental group, walking function and ambulation confidence was significantly different between the pre- and post-intervention, whereas the control group showed a significant difference only in the 10-m walk test. Action observation training of community ambulation may be favorably used for improving walking function of patients with post-stroke hemiparesis.

Motor Learning Versus StandardWalking Exercise in Older Adults with Subclinical Gait Dysfunction: A Randomized Clinical Trial

PubMed Central

Brach, Jennifer S.; Van Swearingen, Jessie M.; Perera, Subashan; Wert, David M.; Studenski, Stephanie

2013-01-01

Background Current exercise recommendationsfocus on endurance and strength, but rarely incorporate principles of motor learning. Motor learning exerciseis designed to address neurological aspects of movement. Motor learning exercise has not been evaluated in older adults with subclinical gait dysfunction. Objectives Tocompare motor learning versus standard exercise on measures of mobility and perceived function and disability. Design Single-blind randomized trial. Setting University research center. Participants Olderadults (n=40), mean age 77.1±6.0 years), who had normal walking speed (≥1.0 m/s) and impaired motor skill (Figure of 8 walk time > 8 s). Interventions The motor learning program (ML) incorporated goal-oriented stepping and walking to promote timing and coordination within the phases of the gait cycle. The standard program (S) employed endurance training by treadmill walking.Both included strength training and were offered twice weekly for one hour for 12 weeks. Measurements Primary outcomes included mobility performance (gait efficiency, motor skill in walking, gait speed, and walking endurance)and secondary outcomes included perceived function and disability (Late Life Function and Disability Instrument). Results 38 of 40 participants completed the trial (ML, n=18; S, n=20). ML improved more than Sin gait speed (0.13 vs. 0.05 m/s, p=0.008) and motor skill (−2.2 vs. −0.89 s, p<0.0001). Both groups improved in walking endurance (28.3 and 22.9m, but did not differ significantly p=0.14). Changes in gait efficiency and perceived function and disability were not different between the groups (p>0.10). Conclusion In older adults with subclinical gait dysfunction, motor learning exercise improved some parameters of mobility performance more than standard exercise. PMID:24219189

When Human Walking is a Random Walk

NASA Astrophysics Data System (ADS)

Hausdorff, J. M.

1998-03-01

The complex, hierarchical locomotor system normally does a remarkable job of controlling an inherently unstable, multi-joint system. Nevertheless, the stride interval --- the duration of a gait cycle --- fluctuates from one stride to the next, even under stationary conditions. We used random walk analysis to study the dynamical properties of these fluctuations under normal conditions and how they change with disease and aging. Random walk analysis of the stride-to-stride fluctuations of healthy, young adult men surprisingly reveals a self-similar pattern: fluctuations at one time scale are statistically similar to those at multiple other time scales (Hausdorff et al, J Appl Phsyiol, 1995). To study the stability of this fractal property, we analyzed data obtained from healthy subjects who walked for 1 hour at their usual pace, as well as at slower and faster speeds. The stride interval fluctuations exhibited long-range correlations with power-law decay for up to a thousand strides at all three walking rates. In contrast, during metronomically-paced walking, these long-range correlations disappeared; variations in the stride interval were uncorrelated and non-fractal (Hausdorff et al, J Appl Phsyiol, 1996). To gain insight into the mechanism(s) responsible for this fractal property, we examined the effects of aging and neurological impairment. Using detrended fluctuation analysis (DFA), we computed α, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. α was significantly lower in healthy elderly subjects compared to young adults (p < .003) and in subjects with Huntington's disease, a neuro-degenerative disorder of the central nervous system, compared to disease-free controls (p < 0.005) (Hausdorff et al, J Appl Phsyiol, 1997). α was also significantly related to degree of functional impairment in subjects with Huntington's disease (r=0.78). Recently, we have observed that just as there are changes with α during aging, there also changes with development. Apparently, the fractal scaling of walking does not become mature until children are eleven years old. Conclusions: The fractal dynamics of spontaneous stride interval fluctuations are normally quite robust and are apparently intrinsic to the healthy adult locomotor system. However, alterations in this fractal scaling property are associated with impairment in central nervous system control, aging and neural development.

Treadmill exercise rehabilitation improves ambulatory function and cardiovascular fitness in patients with chronic stroke: a randomized, controlled trial.

PubMed

Macko, Richard F; Ivey, Frederick M; Forrester, Larry W; Hanley, Daniel; Sorkin, John D; Katzel, Leslie I; Silver, Kenneth H; Goldberg, Andrew P

2005-10-01

Physical inactivity propagates disability after stroke through physical deconditioning and learned nonuse. We investigated whether treadmill aerobic training (T-AEX) is more effective than conventional rehabilitation to improve ambulatory function and cardiovascular fitness in patients with chronic stroke. Sixty-one adults with chronic hemiparetic gait after ischemic stroke (>6 months) were randomized to 6 months (3x/week) progressive T-AEX or a reference rehabilitation program of stretching plus low-intensity walking (R-CONTROL). Peak exercise capacity (Vo2 peak), o2 consumption during submaximal effort walking (economy of gait), timed walks, Walking Impairment Questionnaire (WIQ), and Rivermead Mobility Index (RMI) were measured before and after 3 and 6 months of training. Twenty-five patients completed T-AEX and 20 completed R-CONTROL. Only T-AEX increased cardiovascular fitness (17% versus 3%, delta% T-AEX versus R-CONTROL, P<0.005). Group-by-time analyses revealed T-AEX improved ambulatory performance on 6-minute walks (30% versus 11%, P<0.02) and mobility function indexed by WIQ distance scores (56% versus 12%, P<0.05). In the T-AEX group, increasing training velocity predicted improved Vo2 peak (r=0.43, P<0.05), but not walking function. In contrast, increasing training session duration predicted improved 6-minute walk (r=0.41, P<0.05), but not fitness gains. T-AEX improves both functional mobility and cardiovascular fitness in patients with chronic stroke and is more effective than reference rehabilitation common to conventional care. Specific characteristics of training may determine the nature of exercise-mediated adaptations.

Walking-adaptability assessments with the Interactive Walkway: Between-systems agreement and sensitivity to task and subject variations.

PubMed

Geerse, Daphne J; Coolen, Bert H; Roerdink, Melvyn

2017-05-01

The ability to adapt walking to environmental circumstances is an important aspect of walking, yet difficult to assess. The Interactive Walkway was developed to assess walking adaptability by augmenting a multi-Kinect-v2 10-m walkway with gait-dependent visual context (stepping targets, obstacles) using real-time processed markerless full-body kinematics. In this study we determined Interactive Walkway's usability for walking-adaptability assessments in terms of between-systems agreement and sensitivity to task and subject variations. Under varying task constraints, 21 healthy subjects performed obstacle-avoidance, sudden-stops-and-starts and goal-directed-stepping tasks. Various continuous walking-adaptability outcome measures were concurrently determined with the Interactive Walkway and a gold-standard motion-registration system: available response time, obstacle-avoidance and sudden-stop margins, step length, stepping accuracy and walking speed. The same holds for dichotomous classifications of success and failure for obstacle-avoidance and sudden-stops tasks and performed short-stride versus long-stride obstacle-avoidance strategies. Continuous walking-adaptability outcome measures generally agreed well between systems (high intraclass correlation coefficients for absolute agreement, low biases and narrow limits of agreement) and were highly sensitive to task and subject variations. Success and failure ratings varied with available response times and obstacle types and agreed between systems for 85-96% of the trials while obstacle-avoidance strategies were always classified correctly. We conclude that Interactive Walkway walking-adaptability outcome measures are reliable and sensitive to task and subject variations, even in high-functioning subjects. We therefore deem Interactive Walkway walking-adaptability assessments usable for obtaining an objective and more task-specific examination of one's ability to walk, which may be feasible for both high-functioning and fragile populations since walking adaptability can be assessed at various levels of difficulty. Copyright © 2017 Elsevier B.V. All rights reserved.

Pilates and aerobic training improve levels of depression, anxiety and quality of life in overweight and obese individuals.

PubMed

Vancini, Rodrigo Luiz; Rayes, Angeles Bonal Rosell; Lira, Claudio Andre Barbosa de; Sarro, Karine Jacon; Andrade, Marilia Santos

2017-12-01

To compare the effects of Pilates and walking on quality of life, depression, and anxiety levels. Sixty-three overweight/obese participants were randomly divided into: control (n = 20), walking (n = 21), and Pilates (n = 22) groups. Pilates and walking groups attended eight weeks of 60-minute exercise sessions three times per week. Quality of life, depression, and state- and trait-anxiety levels were evaluated before and after eight weeks of training. Scores of quality of life, depression, and trait-anxiety improved in the Pilates and walking groups. State-anxiety levels improved only in the walking group. Pilates and walking positively impact quality of life, depression and anxiety. The Pilates method could be used as an alternative to improve mood disorders in overweight/obese individuals.

Community-based walking exercise for peripheral artery disease: An exploratory pilot study

PubMed Central

Mays, Ryan J; Hiatt, William R; Casserly, Ivan P; Rogers, R Kevin; Main, Deborah S; Kohrt, Wendy M; Ho, P Michael; Regensteiner, Judith G

2016-01-01

Supervised walking exercise is an effective treatment to improve walking ability of patients with peripheral artery disease (PAD), but few exercise programs in community settings have been effective. The aim of this study was to determine the efficacy of a community-based walking exercise program with training, monitoring, and coaching (TMC) components to improve exercise performance and patient-reported outcomes in PAD patients. This was a randomized, controlled trial including PAD patients who previously received peripheral endovascular therapy or presented with stable claudication. Patients randomized (n=25) to the intervention group received a comprehensive community-based walking exercise program with elements of TMC over 14 weeks. Patients in the control group did not receive treatment beyond standard advice to walk. The primary outcome in the intent-to-treat (ITT) analyses was peak walking time (PWT) on a graded treadmill. Secondary outcomes included claudication onset time (COT) and patient-reported outcomes assessed via the Walking Impairment Questionnaire (WIQ). Intervention group patients (n=10) did not significantly improve PWT when compared with the control group patients (n=10) (mean±standard error: +2.1±0.7 vs. 0.0±0.7 min, p=0.052). Changes in COT and WIQ scores were greater for intervention patients compared with control patients (COT: +1.6±0.8 vs. −0.6±0.7 min, p=0.045; WIQ: +18.3±4.2 vs. −4.6±4.2%, p=0.001). This pilot using a walking program with TMC and an ITT analyses did not improve the primary outcome in PAD patients. Other walking performance and patient self-reported outcomes were improved following exercise in community settings. Further study is needed to determine whether this intervention improves outcomes in a trial employing a larger sample size. PMID:25755148

Gradient-free MCMC methods for dynamic causal modelling.

PubMed

Sengupta, Biswa; Friston, Karl J; Penny, Will D

2015-05-15

In this technical note we compare the performance of four gradient-free MCMC samplers (random walk Metropolis sampling, slice-sampling, adaptive MCMC sampling and population-based MCMC sampling with tempering) in terms of the number of independent samples they can produce per unit computational time. For the Bayesian inversion of a single-node neural mass model, both adaptive and population-based samplers are more efficient compared with random walk Metropolis sampler or slice-sampling; yet adaptive MCMC sampling is more promising in terms of compute time. Slice-sampling yields the highest number of independent samples from the target density - albeit at almost 1000% increase in computational time, in comparison to the most efficient algorithm (i.e., the adaptive MCMC sampler). Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Can a motivational intervention overcome an unsupportive environment for walking--findings from the Step-by-Step Study.

PubMed

Merom, Dafna; Bauman, Adrian; Phongsavan, Philayrath; Cerin, Ester; Kassis, Mazen; Brown, Wendy; Smith, Ben J; Rissel, Chris

2009-10-01

Interventions to promote walking have rarely examined how their effects varied by the attributes of the physical environment. The purpose of this study is to examine whether perceptions of environmental walkability predicted change in walking behavior following an individual-based intervention to promote walking and whether the intervention buffered the effects of unsupportive environment for walking. Inactive adults (aged 30-65 years, 85% women) who completed a 3-month randomized control trial comparing the effect of a single mail-out of a theoretically based self-help walking program (WP, n = 102); the same program plus a pedometer (WPP, n = 105); and a "no-treatment" control group (C, n = 107). Measures included change in self-reported walking time for all purposes and in the proportion of people reporting regular walking (i.e., > or =150 min/week and > or =5 sessions/wk). Perceptions of environmental esthetics, safety from crime, proximity to destinations, access to walking facilities, traffic, streetlights, connectivity, and hilliness were assessed at baseline and dichotomized into "low" or "high" by the median score. Covariates were social support, self-efficacy, intention to change behavior, and sociodemographic characteristics. Adjusting for baseline walking, significant covariates, and study groups, walking time at follow-up was lower if streetlights or esthetics were perceived to be "low" (-24% and -22%, respectively) compared with "high" (p < 0.05). In "low" esthetic conditions, those in the WPP were significantly more likely than controls to increase total walking time (Exp (b) = 2.53, p < 0.01) and to undertake regular walking (OR = 5.85, 95% CI 2.60-12.2), whereas in esthetically pleasing environments, the between-group differences were nonsignificant. Walkability attributes can influence individual-based walking programs. Some environmental barriers for walking can be overcome by motivational aids.

Supervised and non-supervised Nordic walking in the treatment of chronic low back pain: a single blind randomized clinical trial

PubMed Central

2010-01-01

Background Active approaches including both specific and unspecific exercise are probably the most widely recommended treatment for patients with chronic low back pain but it is not known exactly which types of exercise provide the most benefit. Nordic Walking - power walking using ski poles - is a popular and fast growing type of exercise in Northern Europe that has been shown to improve cardiovascular metabolism. Until now, no studies have been performed to investigate whether Nordic Walking has beneficial effects in relation to back pain. Methods A total of 151 patients with low back and/or leg pain of greater than eight weeks duration were recruited from a hospital based outpatient back pain clinic. Patients continuing to have pain greater than three on the 11-point numeric rating scale after a multidisciplinary intervention were included. Fifteen patients were unable to complete the baseline evaluation and 136 patients were randomized to receive A) Nordic walking supervised by a specially trained instructor twice a week for eight weeks B) One-hour instruction in Nordic walking by a specially trained instructor followed by advice to perform Nordic walking at home as much as they liked for eight weeks or C) Individual oral information consisting of advice to remain active and about maintaining the daily function level that they had achieved during their stay at the backcenter. Primary outcome measures were pain and disability using the Low Back Pain Rating Scale, and functional limitation further assessed using the Patient Specific Function Scale. Furthermore, information on time off work, use of medication, and concurrent treatment for their low back pain was collected. Objective measurements of physical activity levels for the supervised and unsupervised Nordic walking groups were performed using accelerometers. Data were analyzed on an intention-to-treat basis. Results No mean differences were found between the three groups in relation to any of the outcomes at baseline. For pain, disability, and patient specific function the supervised Nordic walking group generally faired best however no statistically significant differences were found. Regarding the secondary outcome measures, patients in the supervised group tended to use less pain medication, to seek less concurrent care for their back pain, at the eight-week follow-up. There was no difference between physical activity levels for the supervised and unsupervised Nordic walking groups. No negative side effects were reported. Conclusion We did not find statistically significant differences between eight weeks of supervised or unsupervised Nordic walking and advice to remain active in a group of chronic low back pain patients. Nevertheless, the greatest average improvement tended to favor the supervised Nordic walking group and - taking into account other health related benefits of Nordic walking - this form of exercise may potentially be of benefit to selected groups of chronic back pain patients. Trial registration http://www.ClinicalTrials.gov # NCT00209820 PMID:20146793

The Not-so-Random Drunkard's Walk

ERIC Educational Resources Information Center

Ehrhardt, George

2013-01-01

This dataset contains the results of a quasi-experiment, testing Karl Pearson's "drunkard's walk" analogy for an abstract random walk. Inspired by the alternate hypothesis that drunkards stumble to the side of their dominant hand, it includes data on intoxicated test subjects walking a 10' line. Variables include: the…

The effects of Nordic and general walking on depression disorder patients’ depression, sleep, and body composition

PubMed Central

Park, Seong Doo; Yu, Seong Hun

2015-01-01

[Purpose] This study examined Nordic walking as an exercise intervention for the elderly with depression. [Subjects] Twenty-four patients who were diagnosed with depression were randomly selected and divided into two groups, an experimental group which performed Nordic walking, and a control group, which performed normal walking. [Methods] Both groups practiced their respective walking exercise for 50 minutes per day, three times a week for eight weeks. To compare the effects of the intervention, psychological factors using the Beck depression inventory and sleep quality was assessed using the Korean version Pittsburgh sleep quality index. Skeletal muscle mass, fat free mass, body mass index, body fat percentage, and basal metabolism were estimated three times by a body composition analyzer, before the intervention, four weeks after the intervention, and eight weeks after the intervention. [Results] There was a significant difference in depression with a main effect of time in both groups. There was also a significant difference in sleep in over time and interaction. The differences over time between the two groups were significant for depression, sleep, and skeletal muscle mass. [Conclusion] The results suggests that Nordic walking has a positive effect on depression and sleeping disorders of the elderly, suggesting that Nordic walking based exercise programs should be developed for the elderly who suffer from depression or a sleeping disorder. PMID:26357429

Antipersistent dynamics in kinetic models of wealth exchange

NASA Astrophysics Data System (ADS)

Goswami, Sanchari; Chatterjee, Arnab; Sen, Parongama

2011-11-01

We investigate the detailed dynamics of gains and losses made by agents in some kinetic models of wealth exchange. An earlier work suggested that a walk in an abstract gain-loss space can be conceived for the agents. For models in which agents do not save, or save with uniform saving propensity, the walk has diffusive behavior. For the case in which the saving propensity λ is distributed randomly (0≤λ<1), the resultant walk showed a ballistic nature (except at a particular value of λ*≈0.47). Here we consider several other features of the walk with random λ. While some macroscopic properties of this walk are comparable to a biased random walk, at microscopic level, there are gross differences. The difference turns out to be due to an antipersistent tendency toward making a gain (loss) immediately after making a loss (gain). This correlation is in fact present in kinetic models without saving or with uniform saving as well, such that the corresponding walks are not identical to ordinary random walks. In the distributed saving case, antipersistence occurs with a simultaneous overall bias.

Hydrogen diffusion in liquid aluminum from ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Jakse, N.; Pasturel, A.

2014-05-01

Ab initio molecular dynamics simulations are used to describe the diffusion of hydrogen in liquid aluminum at different temperatures. Quasi-instantaneous jumps separating periods of localized vibrations around a mean position are found to characterize the hydrogen motion at the microscopic scale. The hydrogen motion is furthermore analyzed using the van Hove function. We highlight a non-Fickian behavior for the hydrogen diffusion due to a large spatial distribution of hydrogen jumps. We show that a generalized continuous time random walk (CTRW) model describes the experimental diffusion coefficients in a satisfactory manner. Finally, the impact of impurities and alloying elements on hydrogen diffusion in aluminum is discussed.

Generalized fractional diffusion equations for subdiffusion in arbitrarily growing domains

NASA Astrophysics Data System (ADS)

Angstmann, C. N.; Henry, B. I.; McGann, A. V.

2017-10-01

The ubiquity of subdiffusive transport in physical and biological systems has led to intensive efforts to provide robust theoretical models for this phenomena. These models often involve fractional derivatives. The important physical extension of this work to processes occurring in growing materials has proven highly nontrivial. Here we derive evolution equations for modeling subdiffusive transport in a growing medium. The derivation is based on a continuous-time random walk. The concise formulation of these evolution equations requires the introduction of a new, comoving, fractional derivative. The implementation of the evolution equation is illustrated with a simple model of subdiffusing proteins in a growing membrane.

The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time

NASA Astrophysics Data System (ADS)

Hu, Xiaohu; Hong, Liang; Dean Smith, Micholas; Neusius, Thomas; Cheng, Xiaolin; Smith, Jeremy C.

2016-02-01

Internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behaviour with effective relaxation times existing over many decades in time, from ps up to ~102 s (refs ,,,). Here, using molecular dynamics simulations, we show that, on timescales from 10-12 to 10-5 s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance fluctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of the energy landscape explored. Diffusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behaviour persists up to timescales approaching the in vivo lifespan of individual protein molecules.

Temporal correlation functions of concentration fluctuations: an anomalous case.

PubMed

Lubelski, Ariel; Klafter, Joseph

2008-10-09

We calculate, within the framework of the continuous time random walk (CTRW) model, multiparticle temporal correlation functions of concentration fluctuations (CCF) in systems that display anomalous subdiffusion. The subdiffusion stems from the nonstationary nature of the CTRW waiting times, which also lead to aging and ergodicity breaking. Due to aging, a system of diffusing particles tends to slow down as time progresses, and therefore, the temporal correlation functions strongly depend on the initial time of measurement. As a consequence, time averages of the CCF differ from ensemble averages, displaying therefore ergodicity breaking. We provide a simple example that demonstrates the difference between these two averages, a difference that might be amenable to experimental tests. We focus on the case of ensemble averaging and assume that the preparation time of the system coincides with the starting time of the measurement. Our analytical calculations are supported by computer simulations based on the CTRW model.

Exercise in Patients on Dialysis: A Multicenter, Randomized Clinical Trial

PubMed Central

Manfredini, Fabio; Mallamaci, Francesca; D’Arrigo, Graziella; Baggetta, Rossella; Bolignano, Davide; Torino, Claudia; Lamberti, Nicola; Bertoli, Silvio; Ciurlino, Daniele; Rocca-Rey, Lisa; Barillà, Antonio; Battaglia, Yuri; Rapanà, Renato Mario; Zuccalà, Alessandro; Bonanno, Graziella; Fatuzzo, Pasquale; Rapisarda, Francesco; Rastelli, Stefania; Fabrizi, Fabrizio; Messa, Piergiorgio; De Paola, Luciano; Lombardi, Luigi; Cupisti, Adamasco; Fuiano, Giorgio; Lucisano, Gaetano; Summaria, Chiara; Felisatti, Michele; Pozzato, Enrico; Malagoni, Anna Maria; Castellino, Pietro; Aucella, Filippo; Abd ElHafeez, Samar; Provenzano, Pasquale Fabio; Tripepi, Giovanni; Catizone, Luigi

2017-01-01

Previous studies have suggested the benefits of physical exercise for patients on dialysis. We conducted the Exercise Introduction to Enhance Performance in Dialysis trial, a 6-month randomized, multicenter trial to test whether a simple, personalized walking exercise program at home, managed by dialysis staff, improves functional status in adult patients on dialysis. The main study outcomes included change in physical performance at 6 months, assessed by the 6-minute walking test and the five times sit-to-stand test, and in quality of life, assessed by the Kidney Disease Quality of Life Short Form (KDQOL-SF) questionnaire. We randomized 296 patients to normal physical activity (control; n=145) or walking exercise (n=151); 227 patients (exercise n=104; control n=123) repeated the 6-month evaluations. The distance covered during the 6-minute walking test improved in the exercise group (mean distance±SD: baseline, 328±96 m; 6 months, 367±113 m) but not in the control group (baseline, 321±107 m; 6 months, 324±116 m; P<0.001 between groups). Similarly, the five times sit-to-stand test time improved in the exercise group (mean time±SD: baseline, 20.5±6.0 seconds; 6 months, 18.2±5.7 seconds) but not in the control group (baseline, 20.9±5.8 seconds; 6 months, 20.2±6.4 seconds; P=0.001 between groups). The cognitive function score (P=0.04) and quality of social interaction score (P=0.01) in the kidney disease component of the KDQOL-SF improved significantly in the exercise arm compared with the control arm. Hence, a simple, personalized, home-based, low-intensity exercise program managed by dialysis staff may improve physical performance and quality of life in patients on dialysis. PMID:27909047

Normal and tumoral melanocytes exhibit q-Gaussian random search patterns.

PubMed

da Silva, Priscila C A; Rosembach, Tiago V; Santos, Anésia A; Rocha, Márcio S; Martins, Marcelo L

2014-01-01

In multicellular organisms, cell motility is central in all morphogenetic processes, tissue maintenance, wound healing and immune surveillance. Hence, failures in its regulation potentiates numerous diseases. Here, cell migration assays on plastic 2D surfaces were performed using normal (Melan A) and tumoral (B16F10) murine melanocytes in random motility conditions. The trajectories of the centroids of the cell perimeters were tracked through time-lapse microscopy. The statistics of these trajectories was analyzed by building velocity and turn angle distributions, as well as velocity autocorrelations and the scaling of mean-squared displacements. We find that these cells exhibit a crossover from a normal to a super-diffusive motion without angular persistence at long time scales. Moreover, these melanocytes move with non-Gaussian velocity distributions. This major finding indicates that amongst those animal cells supposedly migrating through Lévy walks, some of them can instead perform q-Gaussian walks. Furthermore, our results reveal that B16F10 cells infected by mycoplasmas exhibit essentially the same diffusivity than their healthy counterparts. Finally, a q-Gaussian random walk model was proposed to account for these melanocytic migratory traits. Simulations based on this model correctly describe the crossover to super-diffusivity in the cell migration tracks.

Impact of physical exercise on reaction time in patients with Parkinson's disease-data from the Berlin BIG Study.

PubMed

Ebersbach, Georg; Ebersbach, Almut; Gandor, Florin; Wegner, Brigitte; Wissel, Jörg; Kupsch, Andreas

2014-05-01

To determine whether physical activity may affect cognitive performance in patients with Parkinson's disease by measuring reaction times in patients participating in the Berlin BIG study. Randomized controlled trial, rater-blinded. Ambulatory care. Patients with mild to moderate Parkinson's disease (N=60) were randomly allocated to 3 treatment arms. Outcome was measured at the termination of training and at follow-up 16 weeks after baseline in 58 patients (completers). Patients received 16 hours of individual Lee Silverman Voice Treatment-BIG training (BIG; duration of treatment, 4wk), 16 hours of group training with Nordic Walking (WALK; duration of treatment, 8wk), or nonsupervised domestic exercise (HOME; duration of instruction, 1hr). Cued reaction time (cRT) and noncued reaction time (nRT). Differences between treatment groups in improvement in reaction times from baseline to intermediate and baseline to follow-up assessments were observed for cRT but not for nRT. Pairwise t test comparisons revealed differences in change in cRT at both measurements between BIG and HOME groups (intermediate: -52ms; 95% confidence interval [CI], -84/-20; P=.002; follow-up: 55ms; CI, -105/-6; P=.030) and between WALK and HOME groups (intermediate: -61ms; CI, -120/-2; P=.042; follow-up: -78ms; CI, -136/-20; P=.010). There was no difference between BIG and WALK groups (intermediate: 9ms; CI, -49/67; P=.742; follow-up: 23ms; CI, -27/72; P=.361). Supervised physical exercise with Lee Silverman Voice Treatment-BIG or Nordic Walking is associated with improvement in cognitive aspects of movement preparation. Copyright © 2014 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

Approximate Locality for Quantum Systems on Graphs

NASA Astrophysics Data System (ADS)

Osborne, Tobias J.

2008-10-01

In this Letter we make progress on a long-standing open problem of Aaronson and Ambainis [Theory Comput. 1, 47 (2005)1557-2862]: we show that if U is a sparse unitary operator with a gap Δ in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/Δ increases. This result can be interpreted as a way to convert between local continuous-time and local discrete-time quantum processes. As an example we show that the discrete-time coined quantum walk can be realized stroboscopically from an approximately local continuous-time quantum walk.

Modeling of waiting times and price changes in currency exchange data

NASA Astrophysics Data System (ADS)

Repetowicz, Przemysław; Richmond, Peter

2004-11-01

A theory which describes the share price evolution at financial markets as a continuous-time random walk (Physica A 287 (2000) 468, Physica A 314 (2002) 749, Eur. Phys. J. B 27 (2002) 273, Physica A 376 (2000) 284) has been generalized in order to take into account the dependence of waiting times t on price returns x. A joint probability density function (pdf) φ(x,t) which uses the concept of a Lévy stable distribution is worked out. The theory is fitted to high-frequency US $/Japanese Yen exchange rate and low-frequency 19th century Irish stock data. The theory has been fitted both to price return and to waiting time data and the adherence to data, in terms of the χ2 test statistic, has been improved when compared to the old theory.

When to be discrete: the importance of time formulation in understanding animal movement.

PubMed

McClintock, Brett T; Johnson, Devin S; Hooten, Mevin B; Ver Hoef, Jay M; Morales, Juan M

2014-01-01

Animal movement is essential to our understanding of population dynamics, animal behavior, and the impacts of global change. Coupled with high-resolution biotelemetry data, exciting new inferences about animal movement have been facilitated by various specifications of contemporary models. These approaches differ, but most share common themes. One key distinction is whether the underlying movement process is conceptualized in discrete or continuous time. This is perhaps the greatest source of confusion among practitioners, both in terms of implementation and biological interpretation. In general, animal movement occurs in continuous time but we observe it at fixed discrete-time intervals. Thus, continuous time is conceptually and theoretically appealing, but in practice it is perhaps more intuitive to interpret movement in discrete intervals. With an emphasis on state-space models, we explore the differences and similarities between continuous and discrete versions of mechanistic movement models, establish some common terminology, and indicate under which circumstances one form might be preferred over another. Counter to the overly simplistic view that discrete- and continuous-time conceptualizations are merely different means to the same end, we present novel mathematical results revealing hitherto unappreciated consequences of model formulation on inferences about animal movement. Notably, the speed and direction of movement are intrinsically linked in current continuous-time random walk formulations, and this can have important implications when interpreting animal behavior. We illustrate these concepts in the context of state-space models with multiple movement behavior states using northern fur seal (Callorhinus ursinus) biotelemetry data.

When to be discrete: The importance of time formulation in understanding animal movement

USGS Publications Warehouse

McClintock, Brett T.; Johnson, Devin S.; Hooten, Mevin B.; Ver Hoef, Jay M.; Morales, Juan M.

2014-01-01

Animal movement is essential to our understanding of population dynamics, animal behavior, and the impacts of global change. Coupled with high-resolution biotelemetry data, exciting new inferences about animal movement have been facilitated by various specifications of contemporary models. These approaches differ, but most share common themes. One key distinction is whether the underlying movement process is conceptualized in discrete or continuous time. This is perhaps the greatest source of confusion among practitioners, both in terms of implementation and biological interpretation. In general, animal movement occurs in continuous time but we observe it at fixed discrete-time intervals. Thus, continuous time is conceptually and theoretically appealing, but in practice it is perhaps more intuitive to interpret movement in discrete intervals. With an emphasis on state-space models, we explore the differences and similarities between continuous and discrete versions of mechanistic movement models, establish some common terminology, and indicate under which circumstances one form might be preferred over another. Counter to the overly simplistic view that discrete- and continuous-time conceptualizations are merely different means to the same end, we present novel mathematical results revealing hitherto unappreciated consequences of model formulation on inferences about animal movement. Notably, the speed and direction of movement are intrinsically linked in current continuous-time random walk formulations, and this can have important implications when interpreting animal behavior. We illustrate these concepts in the context of state-space models with multiple movement behavior states using northern fur seal (Callorhinus ursinus) biotelemetry data.

Universal behavior of the interoccurrence times between losses in financial markets: independence of the time resolution.

PubMed

Ludescher, Josef; Bunde, Armin

2014-12-01

We consider representative financial records (stocks and indices) on time scales between one minute and one day, as well as historical monthly data sets, and show that the distribution P(Q)(r) of the interoccurrence times r between losses below a negative threshold -Q, for fixed mean interoccurrence times R(Q) in multiples of the corresponding time resolutions, can be described on all time scales by the same q exponentials, P(Q)(r)∝1/{[1+(q-1)βr](1/(q-1))}. We propose that the asset- and time-scale-independent analytic form of P(Q)(r) can be regarded as an additional stylized fact of the financial markets and represents a nontrivial test for market models. We analyze the distribution P(Q)(r) as well as the autocorrelation C(Q)(s) of the interoccurrence times for three market models: (i) multiplicative random cascades, (ii) multifractal random walks, and (iii) the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. We find that only one of the considered models, the multifractal random walk model, approximately reproduces the q-exponential form of P(Q)(r) and the power-law decay of C(Q)(s).

Universal behavior of the interoccurrence times between losses in financial markets: Independence of the time resolution

NASA Astrophysics Data System (ADS)

Ludescher, Josef; Bunde, Armin

2014-12-01

We consider representative financial records (stocks and indices) on time scales between one minute and one day, as well as historical monthly data sets, and show that the distribution PQ(r ) of the interoccurrence times r between losses below a negative threshold -Q , for fixed mean interoccurrence times RQ in multiples of the corresponding time resolutions, can be described on all time scales by the same q exponentials, PQ(r ) ∝1 /{[1+(q -1 ) β r ] 1 /(q -1 )} . We propose that the asset- and time-scale-independent analytic form of PQ(r ) can be regarded as an additional stylized fact of the financial markets and represents a nontrivial test for market models. We analyze the distribution PQ(r ) as well as the autocorrelation CQ(s ) of the interoccurrence times for three market models: (i) multiplicative random cascades, (ii) multifractal random walks, and (iii) the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. We find that only one of the considered models, the multifractal random walk model, approximately reproduces the q -exponential form of PQ(r ) and the power-law decay of CQ(s ) .

Effective degrees of freedom of a random walk on a fractal.

PubMed

Balankin, Alexander S

2015-12-01

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν-dimensional space F(ν) equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in F(ν) is inferred. The Laplacian operator in F(ν) is constructed. This allows us to map physical problems on fractals into the corresponding problems in F(ν). In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

Random walk numerical simulation for hopping transport at finite carrier concentrations: diffusion coefficient and transport energy concept.

PubMed

Gonzalez-Vazquez, J P; Anta, Juan A; Bisquert, Juan

2009-11-28

The random walk numerical simulation (RWNS) method is used to compute diffusion coefficients for hopping transport in a fully disordered medium at finite carrier concentrations. We use Miller-Abrahams jumping rates and an exponential distribution of energies to compute the hopping times in the random walk simulation. The computed diffusion coefficient shows an exponential dependence with respect to Fermi-level and Arrhenius behavior with respect to temperature. This result indicates that there is a well-defined transport level implicit to the system dynamics. To establish the origin of this transport level we construct histograms to monitor the energies of the most visited sites. In addition, we construct "corrected" histograms where backward moves are removed. Since these moves do not contribute to transport, these histograms provide a better estimation of the effective transport level energy. The analysis of this concept in connection with the Fermi-level dependence of the diffusion coefficient and the regime of interest for the functioning of dye-sensitised solar cells is thoroughly discussed.

The effectiveness of body weight-supported gait training and floor walking in patients with chronic stroke.

PubMed

Peurala, Sinikka H; Tarkka, Ina M; Pitkänen, Kauko; Sivenius, Juhani

2005-08-01

To compare body weight-supported exercise on a gait trainer with walking exercise overground. Randomized controlled trial. Rehabilitation hospital. Forty-five ambulatory patients with chronic stroke. Patients were randomized to 3 groups: (1) gait trainer exercise with functional electric stimulation (GTstim), (2) gait trainer exercise without stimulation (GT), and (3) walking overground (WALK). All patients practiced gait for 15 sessions during 3 weeks (each session, 20 min), and they received additional physiotherapy 55 minutes daily. Ten-meter walk test (10MWT), six-minute walk test (6MWT), lower-limb spasticity and muscle force, postural sway tests, Modified Motor Assessment Scale (MMAS), and FIM instrument scores were recorded before, during, and after the rehabilitation and at 6 months follow-up. The mean walking distance using the gait trainer was 6900+/-1200 m in the GTstim group and 6500+/-1700 m in GT group. In the WALK group, the distance was 4800+/-2800 m, which was less than the walking distance obtained in the GTstim group (P=.027). The body-weight support was individually reduced from 30% to 9% of the body weight over the course of the program. In the pooled 45 patients, the 10MWT (P<.001), 6MWT (P<.001), MMAS (P<.001), dynamic balance test time (P<.001), and test trip (P=.005) scores improved; however, no differences were found between the groups. Both the body weight-supported training and walking exercise training programs resulted in faster gait after the intensive rehabilitation program. Patients' motor performance remained improved at the follow-up.

A Pearson Random Walk with Steps of Uniform Orientation and Dirichlet Distributed Lengths

NASA Astrophysics Data System (ADS)

Le Caër, Gérard

2010-08-01

A constrained diffusive random walk of n steps in ℝ d and a random flight in ℝ d , which are equivalent, were investigated independently in recent papers (J. Stat. Phys. 127:813, 2007; J. Theor. Probab. 20:769, 2007, and J. Stat. Phys. 131:1039, 2008). The n steps of the walk are independent and identically distributed random vectors of exponential length and uniform orientation. Conditioned on the sum of their lengths being equal to a given value l, closed-form expressions for the distribution of the endpoint of the walk were obtained altogether for any n for d=1,2,4. Uniform distributions of the endpoint inside a ball of radius l were evidenced for a walk of three steps in 2D and of two steps in 4D. The previous walk is generalized by considering step lengths which have independent and identical gamma distributions with a shape parameter q>0. Given the total walk length being equal to 1, the step lengths have a Dirichlet distribution whose parameters are all equal to q. The walk and the flight above correspond to q=1. Simple analytical expressions are obtained for any d≥2 and n≥2 for the endpoint distributions of two families of walks whose q are integers or half-integers which depend solely on d. These endpoint distributions have a simple geometrical interpretation. Expressed for a two-step planar walk whose q=1, it means that the distribution of the endpoint on a disc of radius 1 is identical to the distribution of the projection on the disc of a point M uniformly distributed over the surface of the 3D unit sphere. Five additional walks, with a uniform distribution of the endpoint in the inside of a ball, are found from known finite integrals of products of powers and Bessel functions of the first kind. They include four different walks in ℝ3, two of two steps and two of three steps, and one walk of two steps in ℝ4. Pearson-Liouville random walks, obtained by distributing the total lengths of the previous Pearson-Dirichlet walks according to some specified probability law are finally discussed. Examples of unconstrained random walks, whose step lengths are gamma distributed, are more particularly considered.

The influence of panic on the efficiency of escape

NASA Astrophysics Data System (ADS)

Shen, Jia-Quan; Wang, Xu-Wen; Jiang, Luo-Luo

2018-02-01

Whenever we (such as pedestrians) perceive a high density or imminent danger in a confined space, we tend to be panic, which can lead to severe injuries even in the absence of real dangers. Although it is difficult to measure panics in real conditions, we introduced a simple model to study the collective behaviors in condition of fire with dense smoke. Owing to blocking the sight with dense smoke, pedestrians in this condition have two strategies to escape: random-walking or walking along the wall. When the pedestrians are in moderate panic that mean the two types of behaviors are mixed(random-walking and walking along the wall). Our simulation results show that moderate panic, meaning that two escape strategies are mixed, reduces the escape time. In addition, the results indicate that moderate panic can improve the efficiency of escape, this theory also can be useful in a real escape situation. We hope that our research provides the theoretical understanding of underlying mechanisms of panic escape in the condition of poor sight.

Testing self-regulation interventions to increase walking using factorial randomized N-of-1 trials.

PubMed

Sniehotta, Falko F; Presseau, Justin; Hobbs, Nicola; Araújo-Soares, Vera

2012-11-01

To investigate the suitability of N-of-1 randomized controlled trials (RCTs) as a means of testing the effectiveness of behavior change techniques based on self-regulation theory (goal setting and self-monitoring) for promoting walking in healthy adult volunteers. A series of N-of-1 RCTs in 10 normal and overweight adults ages 19-67 (M = 36.9 years). We randomly allocated 60 days within each individual to text message-prompted daily goal-setting and/or self-monitoring interventions in accordance with a 2 (step-count goal prompt vs. alternative goal prompt) × 2 (self-monitoring: open vs. blinded Omron-HJ-113-E pedometer) factorial design. Aggregated data were analyzed using random intercept multilevel models. Single cases were analyzed individually. The primary outcome was daily pedometer step counts over 60 days. Single-case analyses showed that 4 participants significantly increased walking: 2 on self-monitoring days and 2 on goal-setting days, compared with control days. Six participants did not benefit from the interventions. In aggregated analyses, mean step counts were higher on goal-setting days (8,499.9 vs. 7,956.3) and on self-monitoring days (8,630.3 vs. 7,825.9). Multilevel analyses showed a significant effect of the self-monitoring condition (p = .01), the goal-setting condition approached significance (p = .08), and there was a small linear increase in walking over time (p = .03). N-of-1 randomized trials are a suitable means to test behavioral interventions in individual participants.

On the physical realizability of quantum stochastic walks

NASA Astrophysics Data System (ADS)

Taketani, Bruno; Govia, Luke; Schuhmacher, Peter; Wilhelm, Frank

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The recently developed quantum stochastic walk combines the concepts of a quantum walk and a classical random walk through open system evolution of a quantum system, and have been shown to have applications in as far reaching fields as artificial intelligence. However, nature puts significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution, and the physical assumptions underpinning them. We then introduce a way to circumvent some of these restrictions, and simulate a more general quantum stochastic walk on a quantum computer, using a technique we call quantum trajectories on a quantum computer. We finally describe a circuit QED approach to implement discrete time quantum stochastic walks.

Protocol for the Locomotor Experience Applied Post-stroke (LEAPS) trial: a randomized controlled trial

PubMed Central

Duncan, Pamela W; Sullivan, Katherine J; Behrman, Andrea L; Azen, Stanley P; Wu, Samuel S; Nadeau, Stephen E; Dobkin, Bruce H; Rose, Dorian K; Tilson, Julie K

2007-01-01

Background Locomotor training using body weight support and a treadmill as a therapeutic modality for rehabilitation of walking post-stroke is being rapidly adopted into clinical practice. There is an urgent need for a well-designed trial to determine the effectiveness of this intervention. The objective of the Locomotor Experience Applied Post-Stroke (LEAPS) trial is to determine if there is a difference in the proportion of participants who recover walking ability at one year post-stroke when randomized to a specialized locomotor training program (LTP), conducted at 2- or 6-months post-stroke, or those randomized to a home based non-specific, low intensity exercise intervention (HEP) provided 2 months post-stroke. We will determine if the timing of LTP delivery affects gait speed at 1 year and whether initial impairment severity interacts with the timing of LTP. The effect of number of treatment sessions will be determined by changes in gait speed taken pre-treatment and post-12, -24, and -36 sessions. Methods/Design We will recruit 400 adults with moderate or severe walking limitations within 30 days of stroke onset. At two months post stroke, participants are stratified by locomotor impairment severity as determined by overground walking speed and randomly assigned to one of three groups: (a) LTP-Early; (b) LTP-Late or (c) Home Exercise Program -Early. The LTP program includes body weight support on a treadmill and overground training. The LTP and HEP interventions are delivered for 36 sessions over 12 weeks. Primary outcome measure include successful walking recovery defined as the achievement of a 0.4 m/s gait speed or greater by persons with initial severe gait impairment or the achievement of a 0.8 m/s gait speed or greater by persons with initial moderate gait impairment. LEAPS is powered to detect a 20% difference in the proportion of participants achieving successful locomotor recovery between the LTP groups and the HEP group, and a 0.1 m/s mean difference in gait speed change between the two LTP groups. Discussion The goal of this single-blinded, phase III randomized clinical trial is to provide evidence to guide post-stroke walking recovery programs. Trial registration NCT00243919. PMID:17996052

Turbulent transport with intermittency: Expectation of a scalar concentration.

PubMed

Rast, Mark Peter; Pinton, Jean-François; Mininni, Pablo D

2016-04-01

Scalar transport by turbulent flows is best described in terms of Lagrangian parcel motions. Here we measure the Eulerian distance travel along Lagrangian trajectories in a simple point vortex flow to determine the probabilistic impulse response function for scalar transport in the absence of molecular diffusion. As expected, the mean squared Eulerian displacement scales ballistically at very short times and diffusively for very long times, with the displacement distribution at any given time approximating that of a random walk. However, significant deviations in the displacement distributions from Rayleigh are found. The probability of long distance transport is reduced over inertial range time scales due to spatial and temporal intermittency. This can be modeled as a series of trapping events with durations uniformly distributed below the Eulerian integral time scale. The probability of long distance transport is, on the other hand, enhanced beyond that of the random walk for both times shorter than the Lagrangian integral time and times longer than the Eulerian integral time. The very short-time enhancement reflects the underlying Lagrangian velocity distribution, while that at very long times results from the spatial and temporal variation of the flow at the largest scales. The probabilistic impulse response function, and with it the expectation value of the scalar concentration at any point in space and time, can be modeled using only the evolution of the lowest spatial wave number modes (the mean and the lowest harmonic) and an eddy based constrained random walk that captures the essential velocity phase relations associated with advection by vortex motions. Preliminary examination of Lagrangian tracers in three-dimensional homogeneous isotropic turbulence suggests that transport in that setting can be similarly modeled.

Monte Carlo Sampling in Fractal Landscapes

NASA Astrophysics Data System (ADS)

Leitão, Jorge C.; Lopes, J. M. Viana Parente; Altmann, Eduardo G.

2013-05-01

We design a random walk to explore fractal landscapes such as those describing chaotic transients in dynamical systems. We show that the random walk moves efficiently only when its step length depends on the height of the landscape via the largest Lyapunov exponent of the chaotic system. We propose a generalization of the Wang-Landau algorithm which constructs not only the density of states (transient time distribution) but also the correct step length. As a result, we obtain a flat-histogram Monte Carlo method which samples fractal landscapes in polynomial time, a dramatic improvement over the exponential scaling of traditional uniform-sampling methods. Our results are not limited by the dimensionality of the landscape and are confirmed numerically in chaotic systems with up to 30 dimensions.

Fluid-fluid interfacial mobility from random walks

NASA Astrophysics Data System (ADS)

Barclay, Paul L.; Lukes, Jennifer R.

2017-12-01

Dual control volume grand canonical molecular dynamics is used to perform the first calculation of fluid-fluid interfacial mobilities. The mobility is calculated from one-dimensional random walks of the interface by relating the diffusion coefficient to the interfacial mobility. Three different calculation methods are employed: one using the interfacial position variance as a function of time, one using the mean-squared interfacial displacement, and one using the time-autocorrelation of the interfacial velocity. The mobility is calculated for two liquid-liquid interfaces and one liquid-vapor interface to examine the robustness of the methods. Excellent agreement between the three calculation methods is shown for all the three interfaces, indicating that any of them could be used to calculate the interfacial mobility.

Why some walk and others don't: exploring interactions of perceived safety and social neighborhood factors with psychosocial cognitions.

PubMed

Beenackers, Mariëlle A; Kamphuis, Carlijn B M; Mackenbach, Johan P; Burdorf, Alex; van Lenthe, Frank J

2013-04-01

Although physical activity is often believed to be influenced by both environmental and individual factors, little is known about their interaction. This study explores interactions of perceived safety and social neighborhood factors with psychosocial cognitions for leisure-time walking. Cross-sectional data were obtained from residents (age 25-75 years) of 212 neighborhoods in the South-East of the Netherlands, who participated in the Dutch GLOBE study in 2004 (N = 4395, survey response 64.4%). Direct associations of, and interactions between perceived neighborhood safety, social neighborhood factors (social cohesion, social network and feeling at home) and psychosocial cognitions (attitude, self-efficacy, social influence and intention) on two outcomes of leisure-time walking [yes versus no (binary), and among walkers: minutes per week (continuous)] were analyzed in multilevel regression models. The association between attitude and participating in leisure-time walking was stronger in those who felt less at home in their neighborhood. Social influence and attitude were stronger associated with participation in leisure-time walking in those who sometimes felt unsafe in their neighborhood. A positive intention was associated with more minutes walked in those who perceived their neighborhood as unsafe among those who walked. Only limited support was found for interactions between neighborhood perceptions and psychosocial cognitions for leisure-time walking.

Musical motor feedback (MMF) in walking hemiparetic stroke patients: randomized trials of gait improvement.

PubMed

Schauer, Michael; Mauritz, Karl-Heinz

2003-11-01

To demonstrate the effect of rhythmical auditory stimulation in a musical context for gait therapy in hemiparetic stroke patients, when the stimulation is played back measure by measure initiated by the patient's heel-strikes (musical motor feedback). Does this type of musical feedback improve walking more than a less specific gait therapy? The randomized controlled trial considered 23 registered stroke patients. Two groups were created by randomization: the control group received 15 sessions of conventional gait therapy and the test group received 15 therapy sessions with musical motor feedback. Inpatient rehabilitation hospital. Median post-stroke interval was 44 days and the patients were able to walk without technical aids with a speed of approximately 0.71 m/s. Gait velocity, step duration, gait symmetry, stride length and foot rollover path length (heel-on-toe-off distance). The test group showed more mean improvement than the control group: stride length increased by 18% versus 0%, symmetry deviation decreased by 58% versus 20%, walking speed increased by 27% versus 4% and rollover path length increased by 28% versus 11%. Musical motor feedback improves the stroke patient's walk in selected parameters more than conventional gait therapy. A fixed memory in the patient's mind about the song and its timing may stimulate the improvement of gait even without the presence of an external pacemaker.

Continuous-time random-walk approach to supercooled liquids: Self-part of the van Hove function and related quantities.

PubMed

Helfferich, J; Brisch, J; Meyer, H; Benzerara, O; Ziebert, F; Farago, J; Baschnagel, J

2018-06-01

From equilibrium molecular dynamics (MD) simulations of a bead-spring model for short-chain glass-forming polymer melts we calculate several quantities characterizing the single-monomer dynamics near the (extrapolated) critical temperature [Formula: see text] of mode-coupling theory: the mean-square displacement g 0 (t), the non-Gaussian parameter [Formula: see text] and the self-part of the van Hove function [Formula: see text] which measures the distribution of monomer displacements r in time t. We also determine these quantities from a continuous-time random walk (CTRW) approach. The CTRW is defined in terms of various probability distributions which we know from previous analysis. Utilizing these distributions the CTRW can be solved numerically and compared to the MD data with no adjustable parameter. The MD results reveal the heterogeneous and non-Gaussian single-particle dynamics of the supercooled melt near [Formula: see text]. In the time window of the early [Formula: see text] relaxation [Formula: see text] is large and [Formula: see text] is broad, reflecting the coexistence of monomer displacements that are much smaller ("slow particles") and much larger ("fast particles") than the average at time t, i.e. than [Formula: see text]. For large r the tail of [Formula: see text] is compatible with an exponential decay, as found for many glassy systems. The CTRW can reproduce the spatiotemporal dependence of [Formula: see text] at a qualitative to semiquantitative level. However, it is not quantitatively accurate in the studied temperature regime, although the agreement with the MD data improves upon cooling. In the early [Formula: see text] regime we also analyze the MD results for [Formula: see text] via the space-time factorization theorem predicted by ideal mode-coupling theory. While we find the factorization to be well satisfied for small r, both above and below [Formula: see text] , deviations occur for larger r comprising the tail of [Formula: see text]. The CTRW analysis suggests that single-particle "hops" are a contributing factor for these deviations.

IS THE SUICIDE RATE A RANDOM WALK?

PubMed

Yang, Bijou; Lester, David; Lyke, Jennifer; Olsen, Robert

2015-06-01

The yearly suicide rates for the period 1933-2010 and the daily suicide numbers for 1990 and 1991 were examined for whether the distribution of difference scores (from year to year and from day to day) fitted a normal distribution, a characteristic of stochastic processes that follow a random walk. If the suicide rate were a random walk, then any disturbance to the suicide rate would have a permanent effect and national suicide prevention efforts would likely fail. The distribution of difference scores from day to day (but not the difference scores from year to year) fitted a normal distribution and, therefore, were consistent with a random walk.

Changes in balance, functional performance and fall risk following whole body vibration training and vitamin D supplementation in institutionalized elderly women. A 6 month randomized controlled trial.

PubMed

Bogaerts, An; Delecluse, Christophe; Boonen, Steven; Claessens, Albrecht L; Milisen, Koen; Verschueren, Sabine M P

2011-03-01

Falls in the elderly constitute a growing public health problem. This randomized controlled trial investigated the potential benefit of 6 months of whole body vibration (WBV) training and/or vitamin D supplementation on balance, functionality and estimated fall risk in institutionalized elderly women. A total of 113 women (mean age: 79.6) were randomly assigned to either a WBV or a no-training group, receiving either a conventional dose (880 IU/d) or a high dose (1600 IU/d) of vitamin D3. The WBV group performed exercises on a vibration platform 3×/week. Balance was evaluated by computerized posturography. Functionality was assessed by 10 m walk test, Timed up and Go (TUG) performance and endurance capacity (Shuttle Walk). Fall risk was determined with the Physiological Profile Assessment. Performance on the 10 m walk test and on TUG improved over time in all groups. For none of the parameters, high-dose vitamin D resulted in a better performance than conventional dosing. The improvements in the WBV group in endurance capacity, walking at preferred speed, and TUG were significantly larger than the changes with supplementation alone. No additional benefit of WBV training could be detected on fall risk and postural control, although sway velocity and maximal isometric knee extension strength improved only in the WBV group. This trial showed that a high-dose vitamin D supplementation is not more efficient than conventional dosing in improving functionality in institutionalized elderly. WBV training on top of vitamin D supplementation provided an added benefit with regard to walking, TUG performance, and endurance capacity. Copyright © 2010 Elsevier B.V. All rights reserved.

Gait Pattern Alterations during Walking, Texting and Walking and Texting during Cognitively Distractive Tasks while Negotiating Common Pedestrian Obstacles

PubMed Central

Licence, Sammy; Smith, Robynne; McGuigan, Miranda P.; Earnest, Conrad P.

2015-01-01

Objectives Mobile phone texting is a common daily occurrence with a paucity of research examining corresponding gait characteristics. To date, most studies have participants walk in a straight line vs. overcoming barriers and obstacles that occur during regular walking. The aim of our study is to examine the effect of mobile phone texting during periods of cognitive distraction while walking and negotiating barriers synonymous with pedestrian traffic. Methods Thirty participants (18-50y) completed three randomized, counter-balanced walking tasks over a course during: (1) normal walking (control), (2) texting and walking, and (3) texting and walking whilst being cognitively distraction via a standard mathematical test performed while negotiating the obstacle course. We analyzed gait characteristics during course negotiation using a 3-dimensional motion analysis system and a general linear model and Dunnet-Hsu post-hoc procedure the normal walking condition to assess gait characteristic differences. Primary outcomes included the overall time to complete the course time and barrier contact. Secondary outcomes included obstacle clearance height, step frequency, step time, double support phase and lateral deviation. Results Participants took significantly longer (mean ± SD) to complete the course while texting (24.96±4.20 sec) and during cognitive distraction COG (24.09±3.36 sec) vs. normal walking (19.32±2.28 sec; all, P<0.001). No significant differences were noted for barrier contacts (P = 0.28). Step frequency, step time, double support phase and lateral deviation all increased in duration during the texting and cognitive distraction trial. Texting and being cognitively distracted also increased obstacle clearance versus the walking condition (all, P<0.02). Conclusions Texting while walking and/or being cognitively distracted significantly affect gait characteristics concordant to mobile phone usage resulting in a more cautious gate pattern. Future research should also examine a similar study in older participants who may be at a greater risk of tripping with such walking deviations. PMID:26222430

A New Family of Solvable Pearson-Dirichlet Random Walks

NASA Astrophysics Data System (ADS)

Le Caër, Gérard

2011-07-01

An n-step Pearson-Gamma random walk in ℝ d starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations. The gamma distribution of each step length has a shape parameter q>0. Constrained random walks of n steps in ℝ d are obtained from the latter walks by imposing that the sum of the step lengths is equal to a fixed value. Simple closed-form expressions were obtained in particular for the distribution of the endpoint of such constrained walks for any d≥ d 0 and any n≥2 when q is either q = d/2 - 1 ( d 0=3) or q= d-1 ( d 0=2) (Le Caër in J. Stat. Phys. 140:728-751, 2010). When the total walk length is chosen, without loss of generality, to be equal to 1, then the constrained step lengths have a Dirichlet distribution whose parameters are all equal to q and the associated walk is thus named a Pearson-Dirichlet random walk. The density of the endpoint position of a n-step planar walk of this type ( n≥2), with q= d=2, was shown recently to be a weighted mixture of 1+ floor( n/2) endpoint densities of planar Pearson-Dirichlet walks with q=1 (Beghin and Orsingher in Stochastics 82:201-229, 2010). The previous result is generalized to any walk space dimension and any number of steps n≥2 when the parameter of the Pearson-Dirichlet random walk is q= d>1. We rely on the connection between an unconstrained random walk and a constrained one, which have both the same n and the same q= d, to obtain a closed-form expression of the endpoint density. The latter is a weighted mixture of 1+ floor( n/2) densities with simple forms, equivalently expressed as a product of a power and a Gauss hypergeometric function. The weights are products of factors which depends both on d and n and Bessel numbers independent of d.

Noise in two-color electronic distance meter measurements revisited

USGS Publications Warehouse

Langbein, J.

2004-01-01

Frequent, high-precision geodetic data have temporally correlated errors. Temporal correlations directly affect both the estimate of rate and its standard error; the rate of deformation is a key product from geodetic measurements made in tectonically active areas. Various models of temporally correlated errors are developed and these provide relations between the power spectral density and the data covariance matrix. These relations are applied to two-color electronic distance meter (EDM) measurements made frequently in California over the past 15-20 years. Previous analysis indicated that these data have significant random walk error. Analysis using the noise models developed here indicates that the random walk model is valid for about 30% of the data. A second 30% of the data can be better modeled with power law noise with a spectral index between 1 and 2, while another 30% of the data can be modeled with a combination of band-pass-filtered plus random walk noise. The remaining 10% of the data can be best modeled as a combination of band-pass-filtered plus power law noise. This band-pass-filtered noise is a product of an annual cycle that leaks into adjacent frequency bands. For time spans of more than 1 year these more complex noise models indicate that the precision in rate estimates is better than that inferred by just the simpler, random walk model of noise.

Stochastic modeling of a serial killer

PubMed Central

Simkin, M.V.; Roychowdhury, V.P.

2014-01-01

We analyze the time pattern of the activity of a serial killer, who during twelve years had murdered 53 people. The plot of the cumulative number of murders as a function of time is of “Devil’s staircase” type. The distribution of the intervals between murders (step length) follows a power law with the exponent of 1.4. We propose a model according to which the serial killer commits murders when neuronal excitation in his brain exceeds certain threshold. We model this neural activity as a branching process, which in turn is approximated by a random walk. As the distribution of the random walk return times is a power law with the exponent 1.5, the distribution of the inter-murder intervals is thus explained. We illustrate analytical results by numerical simulation. Time pattern activity data from two other serial killers further substantiate our analysis. PMID:24721476

Stochastic modeling of a serial killer.

PubMed

Simkin, M V; Roychowdhury, V P

2014-08-21

We analyze the time pattern of the activity of a serial killer, who during 12 years had murdered 53 people. The plot of the cumulative number of murders as a function of time is of "Devil's staircase" type. The distribution of the intervals between murders (step length) follows a power law with the exponent of 1.4. We propose a model according to which the serial killer commits murders when neuronal excitation in his brain exceeds certain threshold. We model this neural activity as a branching process, which in turn is approximated by a random walk. As the distribution of the random walk return times is a power law with the exponent 1.5, the distribution of the inter-murder intervals is thus explained. We illustrate analytical results by numerical simulation. Time pattern activity data from two other serial killers further substantiate our analysis. Copyright © 2014 Elsevier Ltd. All rights reserved.

Generalized ruin problems and asynchronous random walks

NASA Astrophysics Data System (ADS)

Abad, E.

2005-07-01

We consider a gambling game with two different kinds of trials and compute the duration of the game (averaged over all possible initial capitals of the players) by a mapping of the problem to a 1D lattice walk of two particles reacting upon encounter. The relative frequency of the trials is governed by the synchronicity parameter p of the random walk. The duration of the game is given by the mean time to reaction, which turns out to display a different behavior for even and odd lattices, i.e. this quantity is monotonic in p for odd lattices and non-monotonic for even lattices. In the game picture, this implies that the players minimize the duration of the game by restricting themselves to one type of trial if their joint capital is odd, otherwise a non-symmetric mixture of both trials is needed.

Self-Attractive Random Walks: The Case of Critical Drifts

NASA Astrophysics Data System (ADS)

Ioffe, Dmitry; Velenik, Yvan

2012-07-01

Self-attractive random walks (polymers) undergo a phase transition in terms of the applied drift (force): If the drift is strong enough, then the walk is ballistic, whereas in the case of small drifts self-attraction wins and the walk is sub-ballistic. We show that, in any dimension d ≥ 2, this transition is of first order. In fact, we prove that the walk is already ballistic at critical drifts, and establish the corresponding LLN and CLT.

Effects of Buddhism walking meditation on depression, functional fitness, and endothelium-dependent vasodilation in depressed elderly.

PubMed

Prakhinkit, Susaree; Suppapitiporn, Siriluck; Tanaka, Hirofumi; Suksom, Daroonwan

2014-05-01

The objectives of this study were to determine the effects of the novel Buddhism-based walking meditation (BWM) and the traditional walking exercise (TWE) on depression, functional fitness, and vascular reactivity. This was a randomized exercise intervention study. The study was conducted in a university hospital setting. Forty-five elderly participants aged 60-90 years with mild-to-moderate depressive symptoms were randomly allocated to the sedentary control, TWE, and BWM groups. The BWM program was based on aerobic walking exercise incorporating the Buddhist meditations performed 3 times/week for 12 weeks. Depression score, functional fitness, and endothelium-dependent vasodilation as measured by the flow-mediated dilation (FMD) were the outcome measures used. Muscle strength, flexibility, agility, dynamic balance, and cardiorespiratory endurance increased in both exercise groups (p<0.05). Depression score decreased (p<0.05) only in the BWM group. FMD improved (p<0.05) in both exercise groups. Significant reduction in plasma cholesterol, triglyceride, high-density lipoprotein cholesterol, and C-reactive protein were found in both exercise groups, whereas low-density lipoprotein cholesterol, cortisol, and interleukin-6 concentrations decreased only in the BWM group. Buddhist walking meditation was effective in reducing depression, improving functional fitness and vascular reactivity, and appears to confer greater overall improvements than the traditional walking program.

Continuous-time random-walk model for anomalous diffusion in expanding media

NASA Astrophysics Data System (ADS)

Le Vot, F.; Abad, E.; Yuste, S. B.

2017-09-01

Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium. From this hierarchy, the full time evolution of the second-order moment is obtained for some specific types of expansion. In the case of an exponential expansion, exact recurrence relations for the Laplace-transformed moments are obtained, whence the long-time behavior of moments of arbitrary order is subsequently inferred. Our analytical and numerical results for both Lévy flights and subdiffusive CTRWs confirm the intuitive expectation that the medium expansion hinders the mixing of diffusive particles occupying separate regions. In the case of Lévy flights, we quantify this effect by means of the so-called "Lévy horizon."

Continuous-time random-walk model for anomalous diffusion in expanding media.

PubMed

Le Vot, F; Abad, E; Yuste, S B

2017-09-01

Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium. From this hierarchy, the full time evolution of the second-order moment is obtained for some specific types of expansion. In the case of an exponential expansion, exact recurrence relations for the Laplace-transformed moments are obtained, whence the long-time behavior of moments of arbitrary order is subsequently inferred. Our analytical and numerical results for both Lévy flights and subdiffusive CTRWs confirm the intuitive expectation that the medium expansion hinders the mixing of diffusive particles occupying separate regions. In the case of Lévy flights, we quantify this effect by means of the so-called "Lévy horizon."

Intra-fraction motion of the prostate is a random walk

NASA Astrophysics Data System (ADS)

Ballhausen, H.; Li, M.; Hegemann, N.-S.; Ganswindt, U.; Belka, C.

2015-01-01

A random walk model for intra-fraction motion has been proposed, where at each step the prostate moves a small amount from its current position in a random direction. Online tracking data from perineal ultrasound is used to validate or reject this model against alternatives. Intra-fraction motion of a prostate was recorded by 4D ultrasound (Elekta Clarity system) during 84 fractions of external beam radiotherapy of six patients. In total, the center of the prostate was tracked for 8 h in intervals of 4 s. Maximum likelihood model parameters were fitted to the data. The null hypothesis of a random walk was tested with the Dickey-Fuller test. The null hypothesis of stationarity was tested by the Kwiatkowski-Phillips-Schmidt-Shin test. The increase of variance in prostate position over time and the variability in motility between fractions were analyzed. Intra-fraction motion of the prostate was best described as a stochastic process with an auto-correlation coefficient of ρ = 0.92  ±  0.13. The random walk hypothesis (ρ = 1) could not be rejected (p = 0.27). The static noise hypothesis (ρ = 0) was rejected (p < 0.001). The Dickey-Fuller test rejected the null hypothesis ρ = 1 in 25% to 32% of cases. On average, the Kwiatkowski-Phillips-Schmidt-Shin test rejected the null hypothesis ρ = 0 with a probability of 93% to 96%. The variance in prostate position increased linearly over time (r2 = 0.9  ±  0.1). Variance kept increasing and did not settle at a maximum as would be expected from a stationary process. There was substantial variability in motility between fractions and patients with maximum aberrations from isocenter ranging from 0.5 mm to over 10 mm in one patient alone. In conclusion, evidence strongly suggests that intra-fraction motion of the prostate is a random walk and neither static (like inter-fraction setup errors) nor stationary (like a cyclic motion such as breathing, for example). The prostate tends to drift away from the isocenter during a fraction, and this variance increases with time, such that shorter fractions are beneficial to the problem of intra-fraction motion. As a consequence, fixed safety margins (which would over-compensate at the beginning and under-compensate at the end of a fraction) cannot optimally account for intra-fraction motion. Instead, online tracking and position correction on-the-fly should be considered as the preferred approach to counter intra-fraction motion.

A Challenge-Based Approach to Body Weight-Supported Treadmill Training Poststroke: Protocol for a Randomized Controlled Trial.

PubMed

Naidu, Avantika; Brown, David; Roth, Elliot

2018-05-03

Body weight support treadmill training protocols in conjunction with other modalities are commonly used to improve poststroke balance and walking function. However, typical body weight support paradigms tend to use consistently stable balance conditions, often with handrail support and or manual assistance. In this paper, we describe our study protocol, which involved 2 unique body weight support treadmill training paradigms of similar training intensity that integrated dynamic balance challenges to help improve ambulatory function post stroke. The first paradigm emphasized walking without any handrails or manual assistance, that is, hands-free walking, and served as the control group, whereas the second paradigm incorporated practicing 9 essential challenging mobility skills, akin to environmental barriers encountered during community ambulation along with hands-free walking (ie hands-free + challenge walking). We recruited individuals with chronic poststroke hemiparesis and randomized them to either group. Participants trained for 6 weeks on a self-driven, robotic treadmill interface that provided body weight support and a safe gait-training environment. We assessed participants at pre-, mid- and post 6 weeks of intervention-training, with a 6-month follow-up. We hypothesized greater walking improvements in the hands-free + challenge walking group following training because of increased practice opportunity of essential mobility skills along with hands-free walking. We assessed 77 individuals with chronic hemiparesis, and enrolled and randomized 30 individuals poststroke for our study (hands-free group=19 and hands-free + challenge walking group=20) from June 2012 to January 2015. Data collection along with 6-month follow-up continued until January 2016. Our primary outcome measure is change in comfortable walking speed from pre to post intervention for each group. We will also assess feasibility, adherence, postintervention efficacy, and changes in various exploratory secondary outcome measures. Additionally, we will also assess participant responses to a study survey, conducted at the end of training week, to gauge each group's training experiences. Our treadmill training paradigms, and study protocol represent advances in standardized approaches to selecting body weight support levels without the necessity for using handrails or manual assistance, while progressively providing dynamic challenges for improving poststroke ambulatory function during rehabilitation. ClinicalTrials.gov NCT02787759; https://clinicaltrials.gov/ct2/show/NCT02787759 (Archived by Webcite at http://www.webcitation.org/6yJZCrIea). ©Avantika Naidu, David Brown, Elliot Roth. Originally published in JMIR Research Protocols (http://www.researchprotocols.org), 03.05.2018.

Model for interevent times with long tails and multifractality in human communications: An application to financial trading

NASA Astrophysics Data System (ADS)

Perelló, Josep; Masoliver, Jaume; Kasprzak, Andrzej; Kutner, Ryszard

2008-09-01

Social, technological, and economic time series are divided by events which are usually assumed to be random, albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics has therefore become a central issue. The approach we present is taken from the continuous-time random-walk formalism and represents an analytical alternative to models of nontrivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the intertransaction time intervals of several financial markets. We observe that empirical data describe a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. A stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region.

Cellular telephone use during free-living walking significantly reduces average walking speed.

PubMed

Barkley, Jacob E; Lepp, Andrew

2016-03-31

Cellular telephone (cell phone) use decreases walking speed in controlled laboratory experiments and there is an inverse relationship between free-living walking speed and heart failure risk. The purpose of this study was to examine the impact of cell phone use on walking speed in a free-living environment. Subjects (n = 1142) were randomly observed walking on a 50 m University campus walkway. The time it took each subject to walk 50 m was recorded and subjects were coded into categories: cell phone held to the ear (talking, n = 95), holding and looking at the cell phone (texting, n = 118), not visibly using the cell phone (no use, n = 929). Subjects took significantly (p < 0.001) longer traversing the walkway when talking (39.3 s) and texting (37.9 s) versus no use (35.3 s). As was the case with the previous laboratory experiments, cell phone use significantly reduces average speed during free-living walking.

Time series analysis of collective motions in proteins

NASA Astrophysics Data System (ADS)

Alakent, Burak; Doruker, Pemra; ćamurdan, Mehmet C.

2004-01-01

The dynamics of α-amylase inhibitor tendamistat around its native state is investigated using time series analysis of the principal components of the Cα atomic displacements obtained from molecular dynamics trajectories. Collective motion along a principal component is modeled as a homogeneous nonstationary process, which is the result of the damped oscillations in local minima superimposed on a random walk. The motion in local minima is described by a stationary autoregressive moving average model, consisting of the frequency, damping factor, moving average parameters and random shock terms. Frequencies for the first 50 principal components are found to be in the 3-25 cm-1 range, which are well correlated with the principal component indices and also with atomistic normal mode analysis results. Damping factors, though their correlation is less pronounced, decrease as principal component indices increase, indicating that low frequency motions are less affected by friction. The existence of a positive moving average parameter indicates that the stochastic force term is likely to disturb the mode in opposite directions for two successive sampling times, showing the modes tendency to stay close to minimum. All these four parameters affect the mean square fluctuations of a principal mode within a single minimum. The inter-minima transitions are described by a random walk model, which is driven by a random shock term considerably smaller than that for the intra-minimum motion. The principal modes are classified into three subspaces based on their dynamics: essential, semiconstrained, and constrained, at least in partial consistency with previous studies. The Gaussian-type distributions of the intermediate modes, called "semiconstrained" modes, are explained by asserting that this random walk behavior is not completely free but between energy barriers.

Simple Example of Backtest Overfitting (SEBO)

DOE Office of Scientific and Technical Information (OSTI.GOV)

In the field of mathematical finance, a "backtest" is the usage of historical market data to assess the performance of a proposed trading strategy. It is a relatively simple matter for a present-day computer system to explore thousands, millions or even billions of variations of a proposed strategy, and pick the best performing variant as the "optimal" strategy "in sample" (i.e., on the input dataset). Unfortunately, such an "optimal" strategy often performs very poorly "out of sample" (i.e. on another dataset), because the parameters of the invest strategy have been oversit to the in-sample data, a situation known as "backtestmore » overfitting". While the mathematics of backtest overfitting has been examined in several recent theoretical studies, here we pursue a more tangible analysis of this problem, in the form of an online simulator tool. Given a input random walk time series, the tool develops an "optimal" variant of a simple strategy by exhaustively exploring all integer parameter values among a handful of parameters. That "optimal" strategy is overfit, since by definition a random walk is unpredictable. Then the tool tests the resulting "optimal" strategy on a second random walk time series. In most runs using our online tool, the "optimal" strategy derived from the first time series performs poorly on the second time series, demonstrating how hard it is not to overfit a backtest. We offer this online tool, "Simple Example of Backtest Overfitting (SEBO)", to facilitate further research in this area.« less

The effects of smartphone multitasking on gait and dynamic balance.

PubMed

Lee, Jeon Hyeong; Lee, Myoung Hee

2018-02-01

[Purpose] This study was performed to analyze the influence of smartphone multitasking on gait and dynamic balance. [Subjects and Methods] The subjects were 19 male and 20 female university students. There were 4 types of gait tasks: General Gait (walking without a task), Task Gait 1 (walking while writing a message), Task Gait 2 (walking while writing a message and listening to music), Task Gait 3 (walking while writing a message and having a conversation). To exclude the learning effect, the order of tasks was randomized. The Zebris FDM-T treadmill system (Zebris Medical GmbH, Germany) was used to measure left and right step length and width, and a 10 m walking test (10MWT) was conducted for gait velocity. In addition, a Timed Up and Go test (TUG) was used to measure dynamic balance. All the tasks were performed 3 times, and the mean of the measured values was analyzed. [Results] There were no statistically significant differences in step length and width. There were statistically significant differences in the 10MWT and TUG tests. [Conclusion] Using a smartphone while walking decreases a person's dynamic balance and walking ability. It is considered that accident rates are higher when using a smartphone.

Short-burst interval treadmill training walking capacity and performance in cerebral palsy: a pilot study.

PubMed

Bjornson, Kristie F; Moreau, Noelle; Bodkin, Amy Winter

2018-04-16

To examine the effect of short-burst interval locomotor treadmill training (SBLTT) on walking capacity and performance in cerebral palsy (CP). Twelve children with spastic diplegic CP (average 8.6 years) across Gross Motor Function Classification System levels II (8) and III (4) were randomized to 20 SBLTT sessions over 4 or 10 weeks. SBLTT consisted of alternating 30 seconds of slow and fast walking for 30 minutes/session. Outcomes included the 10 m walk test, one-minute walk test (1MWT), and timed-up-and go (TUG) (capacity) and StepWatch (performance) collected at baseline, post, and 6 weeks post. Fast speed (+.11, p = .04; +.11 m/s, p = .006), 1MWT (+11.2; +11.7 m, p = .006) and TUG (-1.7; -1.9 seconds, p = .006) improved post SBLTT and 6 weeks, respectively. Walking performance increased: average strides/day (+948; +1712, p < .001) and percent time in high strides rates (+0.4, p = 0.07; +0.2, p = .008). Pilot study suggests SBLTT may improve short-term walking capacity and performance.

The Impact of Weight and Fat Mass Loss and Increased Physical Activity on Physical Function in Overweight, Postmenopausal Women: Results from the WOMAN Study

PubMed Central

Gabriel, Kelley Pettee; Conroy, Molly B.; Schmid, Kendra K.; Storti, Kristi L.; High, Robin R.; Underwood, Darcy A.; Kriska, Andrea M.; Kuller, Lewis H.

2011-01-01

Objective To determine whether changes in leisure time physical activity (LTPA) and body composition reflect concomitant changes in 400 m walk time. Methods Data were collected at the baseline and 48 month visits in Women on the Move through Activity and Nutrition Study. At baseline, participants (n=508) were randomized to the Lifestyle Intervention (LC) or Health Education (HE) group. The LC intervention focused on weight (7–10%) and waist circumference reduction through healthy lifestyle behavior change. Change in walk time over 48 months was the primary outcome. Secondary measures included change in LTPA and body composition measures including, body weight, BMI, waist circumference (WC), and dual energy x-ray absorptiometry-derived fat and lean mass. Results Increased LTPA and reductions in body weight, BMI, WC, and fat mass were associated with decreased walk time from baseline to 48 months (p<0.01). After stratification by group, LTPA was no longer significantly related to walk time in the HE group. Conclusions Increased LTPA and weight loss resulted in improved physical function, as measured by the 400 m walk, in a group of overweight, post-menopausal women. These findings support the utility of the 400 m walk to evaluate progress in physical activity or weight loss programs. PMID:21705864

The impact of weight and fat mass loss and increased physical activity on physical function in overweight, postmenopausal women: results from the Women on the Move Through Activity and Nutrition study.

PubMed

Gabriel, Kelley K Pettee; Conroy, Molly B; Schmid, Kendra K; Storti, Kristi L; High, Robin R; Underwood, Darcy A; Kriska, Andrea M; Kuller, Lewis H

2011-07-01

The aim of this study was to determine whether changes in leisure time physical activity (LTPA) and body composition reflect concomitant changes in 400-meter walk time. Data were collected at the baseline and 48-month visits in the Women on the Move Through Activity and Nutrition study. At baseline, participants (n = 508) were randomized to the lifestyle intervention or health education group. The lifestyle intervention focused on weight (7%-10%) and waist circumference reduction through healthy lifestyle behavior change. Change in walk time over 48 months was the primary outcome. Secondary measures included change in LTPA and body composition measures including, body weight, body mass index, waist circumference, and dual-energy x-ray absorptiometry--derived fat and lean mass. Increased LTPA and reductions in body weight, body mass index, waist circumference, and fat mass were associated with decreased walk time from baseline to 48 months (P < 0.01). After stratification by group, LTPA was no longer significantly related to walk time in the health education group. Increased LTPA and weight loss resulted in improved physical function, as measured by the 400-meter walk, in a group of overweight, postmenopausal women. These findings support the use of the 400-meter walk to evaluate progress in physical activity or weight loss programs.

Effects of curved-walking training on curved-walking performance and freezing of gait in individuals with Parkinson's disease: A randomized controlled trial.

PubMed

Cheng, Fang-Yu; Yang, Yea-Ru; Wu, Yih-Ru; Cheng, Shih-Jung; Wang, Ray-Yau

2017-10-01

The purpose of this study was to investigate the effects of curved-walking training (CWT) on curved-walking performance and freezing of gait (FOG) in people with Parkinson's disease (PD). Twenty-four PD subjects were recruited and randomly assigned to the CWT group or control exercise (CE) group and received 12 sessions of either CWT with a turning-based treadmill or general exercise training for 30 min followed by 10 min of over-ground walking in each session for 4-6 weeks. The primary outcomes included curved-walking performance and FOG. All measurements were assessed at baseline, after training, and at 1-month follow-up. Our results showed significant improvements in curved-walking performance (speed, p = 0.007; cadence, p = 0.003; step length, p < 0.001) and FOG, measured by a FOG questionnaire (p = 0.004). The secondary outcomes including straight-walking performance (speed, cadence and step length, p < 0.001), timed up and go test (p = 0.014), functional gait assessment (p < 0.001), Unified Parkinson's disease Rating Scale III (p = 0.001), and quality of life (p < 0.001) were also improved in the experimental group. We further noted that the improvements were maintained for at least one month after training (p < 0.05). A 12-session CWT program can improve curved-walking ability, FOG, and other measures of functional walking performance in individuals with PD. Most of the improvements were sustained for at least one month after training. Copyright © 2017 Elsevier Ltd. All rights reserved.

An invariance property of generalized Pearson random walks in bounded geometries

NASA Astrophysics Data System (ADS)

Mazzolo, Alain

2009-03-01

Invariance properties of random walks in bounded domains are a topic of growing interest since they contribute to improving our understanding of diffusion in confined geometries. Recently, limited to Pearson random walks with exponentially distributed straight paths, it has been shown that under isotropic uniform incidence, the average length of the trajectories through the domain is independent of the random walk characteristic and depends only on the ratio of the volume's domain over its surface. In this paper, thanks to arguments of integral geometry, we generalize this property to any isotropic bounded stochastic process and we give the conditions of its validity for isotropic unbounded stochastic processes. The analytical form for the traveled distance from the boundary to the first scattering event that ensures the validity of the Cauchy formula is also derived. The generalization of the Cauchy formula is an analytical constraint that thus concerns a very wide range of stochastic processes, from the original Pearson random walk to a Rayleigh distribution of the displacements, covering many situations of physical importance.

Impact of continuous positive airway pressure (CPAP) on the respiratory capacity of chronic kidney disease patients under hemodialysis treatment.

PubMed

Xavier, Vivian Bertoni; Roxo, Renata Spósito; Miorin, Luiz Antônio; Dos Santos Alves, Vera Lúcia; Dos Santos Sens, Yvoty Alves

2015-06-01

Chronic kidney disease (CKD) patients on long-term dialysis present changes in pulmonary function and respiratory muscle strength, negatively influencing physical capacity. To analyze the impact of a continuous positive airway pressure (CPAP) protocol on the respiratory capacity of CKD patients under hemodialysis. A randomized clinical trial was conducted involving 40 CKD patients 19-83 years old divided into two groups: control (n = 20) and CPAP (n = 20). Subjects were assessed on the respiratory muscle function test, maximal respiratory pressures, peak flow and 6-min walk test, at baseline and again at the 2-month follow-up. CPAP group patients were submitted to CPAP protocol (PEEP: 5 cm H2O, flow: 15 L/min, FiO2: 33 %) three times per week during hemodialysis sessions. The CPAP group showed higher forced vital capacity, forced expiratory volume in one second, peak expiratory flow, maximal inspiratory pressure, peak flow, as well as lower systolic blood pressure, heart rate, respiratory rate and Borg scale, in addition to a longer distance travelled on the 6-min walk test, compared with the control group. The introduction of a CPAP protocol during hemodialysis sessions had a positive impact on pulmonary function and physical capacity in CKD patients.

Random Walk of Single Gold Nanoparticles in Zebrafish Embryos Leading to Stochastic Toxic Effects on Embryonic Developments

PubMed Central

Browning, Lauren M.; Lee, Kerry J.; Huang, Tao; Nallathamby, Prakash D.; Lowman, Jill E.; Xu, Xiao-Hong Nancy

2010-01-01

We have synthesized and characterized stable (non-aggregation, non-photobleaching and non-blinking), nearly monodisperse and highly-purified Au nanoparticles, and used them to probe transport of cleavage-stage zebrafish embryos and to study their effects on embryonic development in real time. We found that single Au nanoparticles (11.6 ± 0.9 nm in diameter) passively diffused into chorionic space of the embryos via their chorionic-pore-canals and continued their random-walk through chorionic space and into inner mass of embryos. Diffusion coefficients of single nanoparticles vary dramatically (2.8×10-11 to 1.3×10-8 cm2/s) as nanoparticles diffuse through various parts of embryos, suggesting highly diverse transport barriers and viscosity gradients of embryos. The amount of Au nanoparticles accumulated in embryos increase with its concentration. Interestingly, their effects on embryonic development are not proportionally related to the concentration. Majority of embryos (74% on average) incubated chronically with 0.025-1.2 nM Au nanoparticles for 120 h developed to normal zebrafish, with some (24%) being dead and few (2%) deformed. We developed a new approach to image and characterize individual Au nanoparticles embedded in tissues using histology sample preparation methods and LSRP spectra of single nanoparticles. We found that Au nanoparticles in various parts of normally developed and deformed zebrafish, suggesting that random-walk of nanoparticles in embryos during their development might have led to stochastic effects on embryonic development. These results show that Au nanoparticles are much more biocompatible (less toxic) to the embryos than Ag nanoparticles that we reported previously, suggesting that they are better suited as biocompatible probes for imaging embryos in vivo. The results provide powerful evidences that biocompatibility and toxicity of nanoparticles highly depend on their chemical properties, and the embryos can serve as effective in-vivo assays to screen their biocompatibility. PMID:20644873

Existence of the Harmonic Measure for Random Walks on Graphs and in Random Environments

NASA Astrophysics Data System (ADS)

Boivin, Daniel; Rau, Clément

2013-01-01

We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on ℤ d , d≥3, when the conductances are i.i.d. and the bonds with positive conductance percolate. The harmonic measure from infinity also exists for random walks on supercritical clusters of ℤ2. This is proved using results of Barlow (Ann. Probab. 32:3024-3084, 2004) and Barlow and Hambly (Electron. J. Probab. 14(1):1-27, 2009).

Gait rehabilitation machines based on programmable footplates.

PubMed

Schmidt, Henning; Werner, Cordula; Bernhardt, Rolf; Hesse, Stefan; Krüger, Jörg

2007-02-09

Gait restoration is an integral part of rehabilitation of brain lesioned patients. Modern concepts favour a task-specific repetitive approach, i.e. who wants to regain walking has to walk, while tone-inhibiting and gait preparatory manoeuvres had dominated therapy before. Following the first mobilization out of the bed, the wheelchair-bound patient should have the possibility to practise complex gait cycles as soon as possible. Steps in this direction were treadmill training with partial body weight support and most recently gait machines enabling the repetitive training of even surface gait and even of stair climbing. With treadmill training harness-secured and partially relieved wheelchair-mobilised patients could practise up to 1000 steps per session for the first time. Controlled trials in stroke and SCI patients, however, failed to show a superior result when compared to walking exercise on the floor. Most likely explanation was the effort for the therapists, e.g. manually setting the paretic limbs during the swing phase resulting in a too little gait intensity. The next steps were gait machines, either consisting of a powered exoskeleton and a treadmill (Lokomat, AutoAmbulator) or an electromechanical solution with the harness secured patient placed on movable foot plates (Gait Trainer GT I). For the latter, a large multi-centre trial with 155 non-ambulatory stroke patients (DEGAS) revealed a superior gait ability and competence in basic activities of living in the experimental group. The HapticWalker continued the end effector concept of movable foot plates, now fully programmable and equipped with 6 DOF force sensors. This device for the first time enables training of arbitrary walking situations, hence not only the simulation of floor walking but also for example of stair climbing and perturbations. Locomotor therapy is a fascinating new tool in rehabilitation, which is in line with modern principles of motor relearning promoting a task-specific repetitive approach. Sophisticated technical developments and positive randomized controlled trials form the basis of a growing acceptance worldwide to the benefits or our patients.

Random Walk Quantum Clustering Algorithm Based on Space

NASA Astrophysics Data System (ADS)

Xiao, Shufen; Dong, Yumin; Ma, Hongyang

2018-01-01

In the random quantum walk, which is a quantum simulation of the classical walk, data points interacted when selecting the appropriate walk strategy by taking advantage of quantum-entanglement features; thus, the results obtained when the quantum walk is used are different from those when the classical walk is adopted. A new quantum walk clustering algorithm based on space is proposed by applying the quantum walk to clustering analysis. In this algorithm, data points are viewed as walking participants, and similar data points are clustered using the walk function in the pay-off matrix according to a certain rule. The walk process is simplified by implementing a space-combining rule. The proposed algorithm is validated by a simulation test and is proved superior to existing clustering algorithms, namely, Kmeans, PCA + Kmeans, and LDA-Km. The effects of some of the parameters in the proposed algorithm on its performance are also analyzed and discussed. Specific suggestions are provided.

Anomalous transport in cellular flows: The role of initial conditions and aging

NASA Astrophysics Data System (ADS)

Pöschke, Patrick; Sokolov, Igor M.; Nepomnyashchy, Alexander A.; Zaks, Michael A.

2016-09-01

We consider the diffusion-advection problem in two simple cellular flow models (often invoked as examples of subdiffusive tracer motion) and concentrate on the intermediate time range, in which the tracer motion indeed may show subdiffusion. We perform extensive numerical simulations of the systems under different initial conditions and show that the pure intermediate-time subdiffusion regime is only evident when the particles start at the border between different cells, i.e., at the separatrix, and is less pronounced or absent for other initial conditions. The motion moreover shows quite peculiar aging properties, which are also mirrored in the behavior of the time-averaged mean squared displacement for single trajectories. This kind of behavior is due to the complex motion of tracers trapped inside the cell and is absent in classical models based on continuous-time random walks with no dynamics in the trapped state.

Inertial Effects on Flow and Transport in Heterogeneous Porous Media.

PubMed

Nissan, Alon; Berkowitz, Brian

2018-02-02

We investigate the effects of high fluid velocities on flow and tracer transport in heterogeneous porous media. We simulate fluid flow and advective transport through two-dimensional pore-scale matrices with varying structural complexity. As the Reynolds number increases, the flow regime transitions from linear to nonlinear; this behavior is controlled by the medium structure, where higher complexity amplifies inertial effects. The result is, nonintuitively, increased homogenization of the flow field, which leads in the context of conservative chemical transport to less anomalous behavior. We quantify the transport patterns via a continuous time random walk, using the spatial distribution of the kinetic energy within the fluid as a characteristic measure.

The effects of exercise-based rehabilitation on balance and gait for stroke patients: a systematic review.

PubMed

An, Minjeong; Shaughnessy, Marianne

2011-12-01

This review evaluated the effects of balance and/or gait exercise interventions for stroke survivors and summarized the available evidence on these exercise interventions. A search for studies published between January 2001 and January 2010 was performed using the keywords stroke, walking or balance, and physical activity or exercise. Seventeen randomized clinical trials were identified. The findings suggest that initiating early rehabilitation during acute to subacute stroke recovery can improve balance and walking capacity. The findings also demonstrate that at least 1 hour, three to five times per week, of balance training and 30 minutes, three to five times per week, of gait-oriented exercise are effective to improve balance and walking. This review confirms that balance and walking capacity are improved with specific exercise modalities. A combination of balance, gait, and aerobic exercises would be ideal.

Overground walking training with the i-Walker, a robotic servo-assistive device, enhances balance in patients with subacute stroke: a randomized controlled trial.

PubMed

Morone, Giovanni; Annicchiarico, Roberta; Iosa, Marco; Federici, Alessia; Paolucci, Stefano; Cortés, Ulises; Caltagirone, Carlo

2016-05-26

Patients affected by mild stroke benefit more from physiological overground walking training than walking-like training performed in place using specific devices. The aim of the study was to evaluate the effects of overground robotic walking training performed with the servo-assistive robotic rollator (i-Walker) on walking, balance, gait stability and falls in a community setting in patients with mild subacute stroke. Forty-four patients were randomly assigned to two different groups that received the same therapy in two daily 40-min sessions 5 days a week for 4 weeks. Twenty sessions of standard therapy were performed by both groups. In the other 20 sessions the subjects enrolled in the i-Walker-Group (iWG) performed with the i-Walker and the Control-Group patients (CG) performed the same amount of conventional walking oriented therapy. Clinical and instrumented gait assessments were made pre- and post-treatment. The follow-up observation consisted of recording the number of fallers in the community setting after 6 months. Treatment effectiveness was higher in the iWG group in terms of balance improvement (Tinetti: 68.4 ± 27.6 % vs. 48.1 ± 33.9 %, p = 0.033) and 10-m and 6-min timed walking tests (significant interaction between group and time: F(1,40) = 14.252, p = 0.001; and F(1,40) = 7.883, p = 0.008, respectively). When measured, latero-lateral upper body accelerations were reduced in iWG (F = 4.727, p = 0.036), suggesting increased gait stability, which was supported by a reduced number of falls at home. A robotic servo-assisted i-Walker improved walking performance and balance in patients affected by mild/moderate stroke, leading to increased gait stability and reduced falls in the community. This study was registered on anzctr.org.au (July 1, 2015; ACTRN12615000681550 ).

Social aggregation in pea aphids: experiment and random walk modeling.

PubMed

Nilsen, Christa; Paige, John; Warner, Olivia; Mayhew, Benjamin; Sutley, Ryan; Lam, Matthew; Bernoff, Andrew J; Topaz, Chad M

2013-01-01

From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid's nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control.

Predictability of monthly temperature and precipitation using automatic time series forecasting methods

NASA Astrophysics Data System (ADS)

Papacharalampous, Georgia; Tyralis, Hristos; Koutsoyiannis, Demetris

2018-02-01

We investigate the predictability of monthly temperature and precipitation by applying automatic univariate time series forecasting methods to a sample of 985 40-year-long monthly temperature and 1552 40-year-long monthly precipitation time series. The methods include a naïve one based on the monthly values of the last year, as well as the random walk (with drift), AutoRegressive Fractionally Integrated Moving Average (ARFIMA), exponential smoothing state-space model with Box-Cox transformation, ARMA errors, Trend and Seasonal components (BATS), simple exponential smoothing, Theta and Prophet methods. Prophet is a recently introduced model inspired by the nature of time series forecasted at Facebook and has not been applied to hydrometeorological time series before, while the use of random walk, BATS, simple exponential smoothing and Theta is rare in hydrology. The methods are tested in performing multi-step ahead forecasts for the last 48 months of the data. We further investigate how different choices of handling the seasonality and non-normality affect the performance of the models. The results indicate that: (a) all the examined methods apart from the naïve and random walk ones are accurate enough to be used in long-term applications; (b) monthly temperature and precipitation can be forecasted to a level of accuracy which can barely be improved using other methods; (c) the externally applied classical seasonal decomposition results mostly in better forecasts compared to the automatic seasonal decomposition used by the BATS and Prophet methods; and (d) Prophet is competitive, especially when it is combined with externally applied classical seasonal decomposition.

Effects of Participation in Sports Programs on Walking Ability and Endurance Over Time in Children With Cerebral Palsy.

PubMed

Ross, Sandy A; Yount, Morgan; Ankarstad, Sara; Bock, Samantha; Orso, Britta; Perry, Kimberly; Miros, Jennifer; Brunstrom-Hernandez, Janice E

2017-12-01

Children with cerebral palsy may benefit from maintaining a high level of physical fitness similar to typically developing children especially in terms of long-term physical performance, although in practice this is often difficult. The purpose of this study was to determine the effect of participation in sports programs on walking ability and endurance over time. A retrospective cohort study included participants with cerebral palsy, aged 6 to 20 yrs, who attended a summer sports program from 2004 to 2012. There were 256 participant sessions with pre/post data recorded. The participants consisted of a total of 97 children (mean age [SD] = 11.4 [3.1] yrs), many of whom attended multiple programs throughout the years. Programs were held 6 hrs/d, 5 d/wk for up to 4 wks. Outcome measures included the Timed Up and Go, modified 6-min walk, and 25-ft walk/run. The results showed significant improvements in the Timed Up and Go, modified 6-min walk distance and 25-ft walk/run over time. Children in Gross Motor Classification System level III made the largest gains. Walking ability and endurance seem to improve after participation in an intensive summer sports programs. Higher frequency of program attendance resulted in significant improvements in the Timed Up and Go. Complete the self-assessment activity and evaluation online at http://www.physiatry.org/JournalCME CME OBJECTIVES: Upon completion of this article, the reader should be able to: (1) Discuss the importance of physical activity at the participation level (sports programs) for children with cerebral palsy; (2) Contrast the changes in walking ability and endurance for children in Gross Motor Function Classification System level I, II, and III after sports programs; and (3) Identify the impact of higher frequency of sports program attendance over time on walking ability. Advanced ACCREDITATION: The Association of Academic Physiatrists is accredited by the Accreditation Council for Continuing Medical Education to provide continuing medical education for physicians.The Association of Academic Physiatrists designates this Journal-based CME activity for a maximum of 0.75 AMA PRA Category 1 Credit(s)™. Physicians should only claim credit commensurate with the extent of their participation in the activity.

Memoryless self-reinforcing directionality in endosomal active transport within living cells

NASA Astrophysics Data System (ADS)

Chen, Kejia; Wang, Bo; Granick, Steve

2015-06-01

In contrast to Brownian transport, the active motility of microbes, cells, animals and even humans often follows another random process known as truncated Lévy walk. These stochastic motions are characterized by clustered small steps and intermittent longer jumps that often extend towards the size of the entire system. As there are repeated suggestions, although disagreement, that Lévy walks have functional advantages over Brownian motion in random searching and transport kinetics, their intentional engineering into active materials could be useful. Here, we show experimentally in the classic active matter system of intracellular trafficking that Brownian-like steps self-organize into truncated Lévy walks through an apparent time-independent positive feedback such that directional persistence increases with the distance travelled persistently. A molecular model that allows the maximum output of the active propelling forces to fluctuate slowly fits the experiments quantitatively. Our findings offer design principles for programming efficient transport in active materials.

Test-retest reliability and sensitivity of the 20-meter walk test among patients with knee osteoarthritis.

PubMed

Motyl, Jillian M; Driban, Jeffrey B; McAdams, Erica; Price, Lori Lyn; McAlindon, Timothy E

2013-05-10

The 20-meter walk test is a physical function measure commonly used in clinical research studies and rehabilitation clinics to measure gait speed and monitor changes in patients' physical function over time. Unfortunately, the reliability and sensitivity of this walk test are not well defined and, therefore, limit our ability to evaluate real changes in gait speed not attributable to normal variability. The aim of this study was to assess the test-restest reliability and sensitivity of the 20-meter walk test, at a self-selected pace, among patients with mild to moderate knee osteoarthritis (OA) and to suggest a standardized protocol for future test administration. This was a measurement reliability study. Fifteen consecutive people enrolled in a randomized-controlled trial of intra-articular corticosteroid injections for knee OA participated in this study. All participants completed 4 trials on 2 separate days, 7 to 21 days apart (8 trials total). Each day was divided into 2 sessions, which each involved 2 walking trials. We compared walk times between trials with Wilcoxon signed-rank tests. Similar analyses compared average walk times between sessions. To confirm these analyses, we also calculated Spearman correlation coefficients to assess the relationship between sessions. Finally, smallest detectable differences (SDD) were calculated to estimate the sensitivity of the 20-meter walk test. Wilcoxon signed-rank tests between trials within the same session demonstrated that trials in session 1 were significantly different and in the subsequent 3 sessions, the median differences between trials were not significantly different. Therefore, the first session of each day was considered a practice session, and the SDD between the second session of each day were calculated. SDD was -1.59 seconds (walking slower) and 0.15 seconds (walking faster). Practice trials and a standardized protocol should be used in administration of the 20-meter walk test. Changes in walk time between -1.59 seconds (walking slower) and 0.15 seconds (walking faster) should be considered within the range of normal variability of 20-meter walking speed. The primary limitation of our study was a small sample size, which may influence the generalizability of our findings.

A random walk model to evaluate autism

NASA Astrophysics Data System (ADS)

Moura, T. R. S.; Fulco, U. L.; Albuquerque, E. L.

2018-02-01

A common test administered during neurological examination in children is the analysis of their social communication and interaction across multiple contexts, including repetitive patterns of behavior. Poor performance may be associated with neurological conditions characterized by impairments in executive function, such as the so-called pervasive developmental disorders (PDDs), a particular condition of the autism spectrum disorders (ASDs). Inspired in these diagnosis tools, mainly those related to repetitive movements and behaviors, we studied here how the diffusion regimes of two discrete-time random walkers, mimicking the lack of social interaction and restricted interests developed for children with PDDs, are affected. Our model, which is based on the so-called elephant random walk (ERW) approach, consider that one of the random walker can learn and imitate the microscopic behavior of the other with probability f (1 - f otherwise). The diffusion regimes, measured by the Hurst exponent (H), is then obtained, whose changes may indicate a different degree of autism.

Random walks on activity-driven networks with attractiveness

NASA Astrophysics Data System (ADS)

Alessandretti, Laura; Sun, Kaiyuan; Baronchelli, Andrea; Perra, Nicola

2017-05-01

Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously distributed. Here, we present a time-varying network model where each node and the dynamical formation of ties are characterized by these two features. We study how these properties affect random-walk processes unfolding on the network when the time scales describing the process and the network evolution are comparable. We derive analytical solutions for the stationary state and the mean first-passage time of the process, and we study cases informed by empirical observations of social networks. Our work shows that previously disregarded properties of real social systems, such as heterogeneous distributions of activity and attractiveness as well as the correlations between them, substantially affect the dynamical process unfolding on the network.

Self-avoiding walks on scale-free networks

NASA Astrophysics Data System (ADS)

Herrero, Carlos P.

2005-01-01

Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAW’s) are expected to be more suitable than unrestricted random walks to explore various kinds of real-life networks. Here we study long-range properties of random SAW’s on scale-free networks, characterized by a degree distribution P (k) ˜ k-γ . In the limit of large networks (system size N→∞ ), the average number sn of SAW’s starting from a generic site increases as μn , with μ= < k2 > / -1 . For finite N , sn is reduced due to the presence of loops in the network, which causes the emergence of attrition of the paths. For kinetic growth walks, the average maximum length increases as a power of the system size: ˜ Nα , with an exponent α increasing as the parameter γ is raised. We discuss the dependence of α on the minimum allowed degree in the network. A similar power-law dependence is found for the mean self-intersection length of nonreversal random walks. Simulation results support our approximate analytical calculations.

Two-Dimensional Anisotropic Random Walks: Fixed Versus Random Column Configurations for Transport Phenomena

NASA Astrophysics Data System (ADS)

Csáki, Endre; Csörgő, Miklós; Földes, Antónia; Révész, Pál

2018-04-01

We consider random walks on the square lattice of the plane along the lines of Heyde (J Stat Phys 27:721-730, 1982, Stochastic processes, Springer, New York, 1993) and den Hollander (J Stat Phys 75:891-918, 1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics. Two-dimensional anisotropic random walks with anisotropic density conditions á la Heyde (J Stat Phys 27:721-730, 1982, Stochastic processes, Springer, New York, 1993) yield fixed column configurations and nearest-neighbour random walks in a random environment on the square lattice of the plane as in den Hollander (J Stat Phys 75:891-918, 1994) result in random column configurations. In both cases we conclude simultaneous weak Donsker and strong Strassen type invariance principles in terms of appropriately constructed anisotropic Brownian motions on the plane, with self-contained proofs in both cases. The style of presentation throughout will be that of a semi-expository survey of related results in a historical context.

Two-Dimensional Anisotropic Random Walks: Fixed Versus Random Column Configurations for Transport Phenomena

NASA Astrophysics Data System (ADS)

Csáki, Endre; Csörgő, Miklós; Földes, Antónia; Révész, Pál

2018-06-01

We consider random walks on the square lattice of the plane along the lines of Heyde (J Stat Phys 27:721-730, 1982, Stochastic processes, Springer, New York, 1993) and den Hollander (J Stat Phys 75:891-918, 1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics. Two-dimensional anisotropic random walks with anisotropic density conditions á la Heyde (J Stat Phys 27:721-730, 1982, Stochastic processes, Springer, New York, 1993) yield fixed column configurations and nearest-neighbour random walks in a random environment on the square lattice of the plane as in den Hollander (J Stat Phys 75:891-918, 1994) result in random column configurations. In both cases we conclude simultaneous weak Donsker and strong Strassen type invariance principles in terms of appropriately constructed anisotropic Brownian motions on the plane, with self-contained proofs in both cases. The style of presentation throughout will be that of a semi-expository survey of related results in a historical context.

One Hundred Ways to be Non-Fickian - A Rigorous Multi-Variate Statistical Analysis of Pore-Scale Transport

NASA Astrophysics Data System (ADS)

Most, Sebastian; Nowak, Wolfgang; Bijeljic, Branko

2015-04-01

Fickian transport in groundwater flow is the exception rather than the rule. Transport in porous media is frequently simulated via particle methods (i.e. particle tracking random walk (PTRW) or continuous time random walk (CTRW)). These methods formulate transport as a stochastic process of particle position increments. At the pore scale, geometry and micro-heterogeneities prohibit the commonly made assumption of independent and normally distributed increments to represent dispersion. Many recent particle methods seek to loosen this assumption. Hence, it is important to get a better understanding of the processes at pore scale. For our analysis we track the positions of 10.000 particles migrating through the pore space over time. The data we use come from micro CT scans of a homogeneous sandstone and encompass about 10 grain sizes. Based on those images we discretize the pore structure and simulate flow at the pore scale based on the Navier-Stokes equation. This flow field realistically describes flow inside the pore space and we do not need to add artificial dispersion during the transport simulation. Next, we use particle tracking random walk and simulate pore-scale transport. Finally, we use the obtained particle trajectories to do a multivariate statistical analysis of the particle motion at the pore scale. Our analysis is based on copulas. Every multivariate joint distribution is a combination of its univariate marginal distributions. The copula represents the dependence structure of those univariate marginals and is therefore useful to observe correlation and non-Gaussian interactions (i.e. non-Fickian transport). The first goal of this analysis is to better understand the validity regions of commonly made assumptions. We are investigating three different transport distances: 1) The distance where the statistical dependence between particle increments can be modelled as an order-one Markov process. This would be the Markovian distance for the process, where the validity of yet-unexplored non-Gaussian-but-Markovian random walks start. 2) The distance where bivariate statistical dependence simplifies to a multi-Gaussian dependence based on simple linear correlation (validity of correlated PTRW/CTRW). 3) The distance of complete statistical independence (validity of classical PTRW/CTRW). The second objective is to reveal characteristic dependencies influencing transport the most. Those dependencies can be very complex. Copulas are highly capable of representing linear dependence as well as non-linear dependence. With that tool we are able to detect persistent characteristics dominating transport even across different scales. The results derived from our experimental data set suggest that there are many more non-Fickian aspects of pore-scale transport than the univariate statistics of longitudinal displacements. Non-Fickianity can also be found in transverse displacements, and in the relations between increments at different time steps. Also, the found dependence is non-linear (i.e. beyond simple correlation) and persists over long distances. Thus, our results strongly support the further refinement of techniques like correlated PTRW or correlated CTRW towards non-linear statistical relations.

Migration of lymphocytes on fibronectin-coated surfaces: temporal evolution of migratory parameters

NASA Technical Reports Server (NTRS)

Bergman, A. J.; Zygourakis, K.; McIntire, L. V. (Principal Investigator)

1999-01-01

Lymphocytes typically interact with implanted biomaterials through adsorbed exogenous proteins. To provide a more complete characterization of these interactions, analysis of lymphocyte migration on adsorbed extracellular matrix proteins must accompany the commonly performed adhesion studies. We report here a comparison of the migratory and adhesion behavior of Jurkat cells (a T lymphoblastoid cell line) on tissue culture treated and untreated polystyrene surfaces coated with various concentrations of fibronectin. The average speed of cell locomotion showed a biphasic response to substrate adhesiveness for cells migrating on untreated polystyrene and a monotonic decrease for cells migrating on tissue culture-treated polystyrene. A modified approach to the persistent random walk model was implemented to determine the time dependence of cell migration parameters. The random motility coefficient showed significant increases with time when cells migrated on tissue culture-treated polystyrene surfaces, while it remained relatively constant for experiments with untreated polystyrene plates. Finally, a cell migration computer model was developed to verify our modified persistent random walk analysis. Simulation results suggest that our experimental data were consistent with temporally increasing random motility coefficients.

Hierarchical random walks in trace fossils and the origin of optimal search behavior

PubMed Central

Sims, David W.; Reynolds, Andrew M.; Humphries, Nicolas E.; Southall, Emily J.; Wearmouth, Victoria J.; Metcalfe, Brett; Twitchett, Richard J.

2014-01-01

Efficient searching is crucial for timely location of food and other resources. Recent studies show that diverse living animals use a theoretically optimal scale-free random search for sparse resources known as a Lévy walk, but little is known of the origins and evolution of foraging behavior and the search strategies of extinct organisms. Here, using simulations of self-avoiding trace fossil trails, we show that randomly introduced strophotaxis (U-turns)—initiated by obstructions such as self-trail avoidance or innate cueing—leads to random looping patterns with clustering across increasing scales that is consistent with the presence of Lévy walks. This predicts that optimal Lévy searches may emerge from simple behaviors observed in fossil trails. We then analyzed fossilized trails of benthic marine organisms by using a novel path analysis technique and find the first evidence, to our knowledge, of Lévy-like search strategies in extinct animals. Our results show that simple search behaviors of extinct animals in heterogeneous environments give rise to hierarchically nested Brownian walk clusters that converge to optimal Lévy patterns. Primary productivity collapse and large-scale food scarcity characterizing mass extinctions evident in the fossil record may have triggered adaptation of optimal Lévy-like searches. The findings suggest that Lévy-like behavior has been used by foragers since at least the Eocene but may have a more ancient origin, which might explain recent widespread observations of such patterns among modern taxa. PMID:25024221

Uphill and Downhill Walking in Multiple Sclerosis

PubMed Central

Samaei, Afshin; Hajihasani, Abdolhamid; Fatemi, Elham; Motaharinezhad, Fatemeh

2016-01-01

Background: Various exercise protocols have been recommended for patients with multiple sclerosis (MS). We investigated the effects of uphill and downhill walking exercise on mobility, functional activities, and muscle strength in MS patients. Methods: Thirty-four MS patients were randomly allocated to either the downhill or uphill treadmill walking group for 12 sessions (3 times/wk) of 30 minutes' walking on a 10% negative slope (n = 17) or a 10% positive slope (n = 17), respectively. Measurements were taken before and after the intervention and after 4-week follow-up and included fatigue by Modified Fatigue Impact Scale; mobility by Modified Rivermead Mobility Index; disability by Guy's Neurological Disability Scale; functional activities by 2-Minute Walk Test, Timed 25-Foot Walk test, and Timed Up and Go test; balance indices by Biodex Balance System; and quadriceps and hamstring isometric muscles by torque of left and right knee joints. Analysis of variance with repeated measures was used to investigate the intervention effects on the measurements. Results: After the intervention, significant improvement was found in the downhill group versus the uphill group in terms of fatigue, mobility, and disability indices; functional activities; balance indices; and quadriceps isometric torque (P < .05). The results were stable at 4-week follow-up. Conclusions: Downhill walking on a treadmill may improve muscle performance, functional activity, and balance control in MS patients. These findings support the idea of using eccentric exercise training in MS rehabilitation protocols. PMID:26917996

Scanning method as an unbiased simulation technique and its application to the study of self-attracting random walks

NASA Astrophysics Data System (ADS)

Meirovitch, Hagai

1985-12-01

The scanning method proposed by us [J. Phys. A 15, L735 (1982); Macromolecules 18, 563 (1985)] for simulation of polymer chains is further developed and applied, for the first time, to a model with finite interactions. In addition to ``importance sampling,'' we remove the bias introduced by the scanning method with a procedure suggested recently by Schmidt [Phys. Rev. Lett. 51, 2175 (1983)]; this procedure has the advantage of enabling one to estimate the statistical error. We find these two procedures to be equally efficient. The model studied is an N-step random walk on a lattice, in which a random walk i has a statistical weight &, where p<1 is an attractive energy parameter and Mi is the number of distinct sites visited by walk i. This model, which corresponds to a model of random walks moving in a medium with randomly distributed static traps, has been solved analytically for N-->∞ for any dimension d by Donsker and Varadhan (DV) and by others. and lnφ, where φ is the survival probability in the trapping problem, diverge like Nα with α=d/(d+2). Most numerical studies, however, have failed to reach the DV regime in which d/(d+2) becomes a good approximation for α. On the other hand, our results for α (obtained for N<=150) are close to the DV values for p<=0.7 and p<=0.6 for d=2 and 3, respectively. This suggests that the scanning method is more efficient than both the commonly used direct Monte Carlo technique, and the Rosenbluth and Rosenbluth method [J. Chem. Phys. 23, 356 (1954)]. Our results support the conclusion of Havlin et al. [Phys. Rev. Lett. 53, 407 (1984)] that the DV regime exists already for φ<=10-13 for both d=2 and 3. We also find that at the percolation threshold pc the exponents for the end-to-end distance are small, but larger than zero, and that the probability of a walk returning to the origin behaves approximately as N-1/3 for both d=2 and 3.

Coined quantum walks on weighted graphs

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2017-11-01

We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy’s quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has l integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight l. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover’s algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when l < 3 + 2\\sqrt{2} ≈ 5.828 .

Stochastic nature of series of waiting times.

PubMed

Anvari, Mehrnaz; Aghamohammadi, Cina; Dashti-Naserabadi, H; Salehi, E; Behjat, E; Qorbani, M; Nezhad, M Khazaei; Zirak, M; Hadjihosseini, Ali; Peinke, Joachim; Tabar, M Reza Rahimi

2013-06-01

Although fluctuations in the waiting time series have been studied for a long time, some important issues such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied. Here we find that the "waiting times" series for a given increment level have long-range correlations with Hurst exponents belonging to the interval 1/2

Effects of Single Bouts of Walking Exercise and Yoga on Acute Mood Symptoms in People with Multiple Sclerosis

PubMed Central

Ensari, Ipek; Sandroff, Brian M.

2016-01-01

Background: Little is known about the acute or immediate effects of walking exercise and yoga on mood in people with multiple sclerosis (MS). Such an examination is important for identifying an exercise modality for inclusion in exercise-training interventions that yields mood benefits in MS. We examined the effects of single bouts of treadmill walking and yoga compared with a quiet, seated-rest control condition on acute mood symptoms in MS. Methods: Twenty-four participants with MS completed 20 minutes of treadmill walking, yoga, or quiet rest in a randomized, counterbalanced order with 1 week between sessions. Participants completed the Profile of Mood States questionnaire before and immediately after each condition. Total mood disturbance (TMD) and the six subscales of the Profile of Mood States were analyzed using repeated-measures analysis of variance and paired-samples t tests. Results: There was a significant condition × time interaction on TMD scores (ηp2 = 0.13). Walking and yoga conditions yielded comparable reductions in TMD scores. There was a significant condition × time interaction on vigor (ηp2 = 0.23) whereby walking but not yoga yielded an improvement in vigor. There was a significant main effect of time on anger, confusion, depression, and tension (P < .05) but not on fatigue. Conclusions: Walking and yoga yielded similar improvements in overall acute mood symptoms, and walking improved feelings of vigor. These effects should be further investigated in long-term exercise-training studies. PMID:26917992

3D Tracking via Shoe Sensing.

PubMed

Li, Fangmin; Liu, Guo; Liu, Jian; Chen, Xiaochuang; Ma, Xiaolin

2016-10-28

Most location-based services are based on a global positioning system (GPS), which only works well in outdoor environments. Compared to outdoor environments, indoor localization has created more buzz in recent years as people spent most of their time indoors working at offices and shopping at malls, etc. Existing solutions mainly rely on inertial sensors (i.e., accelerometer and gyroscope) embedded in mobile devices, which are usually not accurate enough to be useful due to the mobile devices' random movements while people are walking. In this paper, we propose the use of shoe sensing (i.e., sensors attached to shoes) to achieve 3D indoor positioning. Specifically, a short-time energy-based approach is used to extract the gait pattern. Moreover, in order to improve the accuracy of vertical distance estimation while the person is climbing upstairs, a state classification is designed to distinguish the walking status including plane motion (i.e., normal walking and jogging horizontally), walking upstairs, and walking downstairs. Furthermore, we also provide a mechanism to reduce the vertical distance accumulation error. Experimental results show that we can achieve nearly 100% accuracy when extracting gait patterns from walking/jogging with a low-cost shoe sensor, and can also achieve 3D indoor real-time positioning with high accuracy.

Effect of adding one 15-minute-walk on the day of surgery to fast-track rehabilitation after total knee arthroplasty: a randomized, single-blind study.

PubMed

Zietek, P; Zietek, J; Szczypior, K; Safranow, K

2015-06-01

Earlier and more intensive physiotherapy exercise after total knee arthroplasty (TKA) enhance recovery, but the best combination of intensity and duration has not been determined. To determine whether adding a single, 15-minute walk on the day of surgery to a fast-track rehabilitation protocol would reduce knee pain and improve knee function after TKA. A randomized single-blind study. Inpatient. Patients with primary osteoarthrosis after TKA. Patients undergoing TKA were randomly assigned to a standard, fast-track rehabilitation protocol consisting of a single, 15-minute walk with a high-rolling walker 4 to 6 hours after recovery from spinal anesthesia or to an intensive protocol, in which patients took a second 15-minute walk at least 3 hours after the first, only on the day of surgery. Outcomes were pain measured on a visual analog scale, Knee Society's (KSS) clinical and functional scores, Oxford knee scores, and Spielberger State-Trait Anxiety Inventory scores. Patients were blinded to group assignment. Since most data were non-normally distributed non-parametric tests were used. Groups were compared with Mann-Whitney U test (for continuous variables). Association between continuous variables was evaluated with Spearman`s rank correlation coefficient. Chi-square or Fisher's exact test was used to assess differences in categorical variables. Of 86 patients assessed for eligibility, 66 were randomly assigned. The 31 evaluable patients on the intensive protocol (mean age, 68 years; 18 women) did not differ significantly from the 31 (mean age, 70 years; 20 women) on the standard protocol on any baseline characteristic or on any outcome measure on any day. On the second postoperative day, pain while walking dropped from a mean of 6.1 to a mean of 4.9 in the intensive group and from 6.4 to 5.4 in the standard group. Results for pain at rest were 3.3 to 2.2, respectively, for the intensive group and 4.0 to 3.0 for the standard group. At 2 weeks, pain at rest was 2.8 in both groups, and pain while walking was 3.0, respectively, for the intensive group and 3.4 for the standard group. At 2 weeks, mean (SD) KSS clinical and KSS function scores were, respectively, 74.9 (12.5) and 51.6 (16.2) in the intensive group and 71.2 (14.3) and 46.3 (16.1) in the standard group. Older age correlated with decreasing knee function (rS=-0.43, P<0.001), and less knee flexion correlated with preoperatively higher state anxiety (rS=-0.37, P=0.005) and trait anxiety (rS=-0.29, P=0.027). The study is limited by its small sample. The fast-track program was not in line with the best available evidence following knee arthroplasty, because patients did not undergo such treatment as NMES. Finally, the intervention itself was modest. Adding an additional 15-minute walk to a fast-track rehabilitation protocol did not increase pain, but neither did it improve functional recovery. A 15-minute walk immediately after recovery from spinal anesthesia did not increase pain in patients with TKA. More intense exercise during this period might improve functional recovery without increasing pain.

How do ants make sense of gravity? A Boltzmann Walker analysis of Lasius niger trajectories on various inclines.

PubMed

Khuong, Anaïs; Lecheval, Valentin; Fournier, Richard; Blanco, Stéphane; Weitz, Sébastian; Bezian, Jean-Jacques; Gautrais, Jacques

2013-01-01

The goal of this study is to describe accurately how the directional information given by support inclinations affects the ant Lasius niger motion in terms of a behavioral decision. To this end, we have tracked the spontaneous motion of 345 ants walking on a 0.5×0.5 m plane canvas, which was tilted with 5 various inclinations by [Formula: see text] rad ([Formula: see text] data points). At the population scale, support inclination favors dispersal along uphill and downhill directions. An ant's decision making process is modeled using a version of the Boltzmann Walker model, which describes an ant's random walk as a series of straight segments separated by reorientation events, and was extended to take directional influence into account. From the data segmented accordingly ([Formula: see text] segments), this extension allows us to test separately how average speed, segments lengths and reorientation decisions are affected by support inclination and current walking direction of the ant. We found that support inclination had a major effect on average speed, which appeared approximately three times slower on the [Formula: see text] incline. However, we found no effect of the walking direction on speed. Contrastingly, we found that ants tend to walk longer in the same direction when they move uphill or downhill, and also that they preferentially adopt new uphill or downhill headings at turning points. We conclude that ants continuously adapt their decision making about where to go, and how long to persist in the same direction, depending on how they are aligned with the line of maximum declivity gradient. Hence, their behavioral decision process appears to combine klinokinesis with geomenotaxis. The extended Boltzmann Walker model parameterized by these effects gives a fair account of the directional dispersal of ants on inclines.

How Do Ants Make Sense of Gravity? A Boltzmann Walker Analysis of Lasius niger Trajectories on Various Inclines

PubMed Central

Khuong, Anaïs; Lecheval, Valentin; Fournier, Richard; Blanco, Stéphane; Weitz, Sébastian; Bezian, Jean-Jacques; Gautrais, Jacques

2013-01-01

The goal of this study is to describe accurately how the directional information given by support inclinations affects the ant Lasius niger motion in terms of a behavioral decision. To this end, we have tracked the spontaneous motion of 345 ants walking on a 0.5×0.5 m plane canvas, which was tilted with 5 various inclinations by rad ( data points). At the population scale, support inclination favors dispersal along uphill and downhill directions. An ant's decision making process is modeled using a version of the Boltzmann Walker model, which describes an ant's random walk as a series of straight segments separated by reorientation events, and was extended to take directional influence into account. From the data segmented accordingly ( segments), this extension allows us to test separately how average speed, segments lengths and reorientation decisions are affected by support inclination and current walking direction of the ant. We found that support inclination had a major effect on average speed, which appeared approximately three times slower on the incline. However, we found no effect of the walking direction on speed. Contrastingly, we found that ants tend to walk longer in the same direction when they move uphill or downhill, and also that they preferentially adopt new uphill or downhill headings at turning points. We conclude that ants continuously adapt their decision making about where to go, and how long to persist in the same direction, depending on how they are aligned with the line of maximum declivity gradient. Hence, their behavioral decision process appears to combine klinokinesis with geomenotaxis. The extended Boltzmann Walker model parameterized by these effects gives a fair account of the directional dispersal of ants on inclines. PMID:24204636

Robotic Resistance Treadmill Training Improves Locomotor Function in Children With Cerebral Palsy: A Randomized Controlled Pilot Study.

PubMed

Wu, Ming; Kim, Janis; Gaebler-Spira, Deborah J; Schmit, Brian D; Arora, Pooja

2017-11-01

To determine whether applying controlled resistance forces to the legs during the swing phase of gait may improve the efficacy of treadmill training as compared with applying controlled assistance forces in children with cerebral palsy (CP). Randomized controlled study. Research unit of a rehabilitation hospital. Children with spastic CP (N=23; mean age, 10.6y; range, 6-14y; Gross Motor Function Classification System levels, I-IV). Participants were randomly assigned to receive controlled assistance (n=11) or resistance (n=12) loads applied to the legs at the ankle. Participants underwent robotic treadmill training 3 times a week for 6 weeks (18 sessions). A controlled swing assistance/resistance load was applied to both legs starting from the toe-off to mid-swing phase of gait during training. Outcome measures consisted of overground walking speed, 6-minute walk distance, and Gross Motor Function Measure scores and were assessed pre and post 6 weeks of training and 8 weeks after the end of training. After 6 weeks of treadmill training in participants from the resistance training group, fast walking speed and 6-minute walk distance significantly improved (18% and 30% increases, respectively), and 6-minute walk distance was still significantly greater than that at baseline (35% increase) 8 weeks after the end of training. In contrast, overground gait speed and 6-minute walk distance had no significant changes after robotic assistance training. The results of the present study indicated that robotic resistance treadmill training is more effective than assistance training in improving locomotor function in children with CP. Copyright © 2017 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

Movement analyses of wood cricket ( Nemobius sylvestris) (Orthoptera: Gryllidae).

PubMed

Brouwers, N C; Newton, A C

2010-12-01

Information on the dispersal ability of invertebrate species associated with woodland habitats is severely lacking. Therefore, a study was conducted examining the movement patterns of wood cricket (Nemobius sylvestris) (Orthoptera: Gryllidae) on the Isle of Wight, UK. Juvenile (i.e. nymphs) and adult wood crickets were released and observed over time within different ground surface substrates. Their movement paths were recorded and subsequently analysed using random walk models. Nymphs were found to move more slowly than adults did; and, when given a choice, both nymphs and adults showed a preference for moving through or over leaf litter compared to bare soil or grass. A correlated random walk (CRW) model accurately described the movement pattern of adult wood crickets through leaf litter, indicating a level of directional persistence in their movements. The estimated population spread through leaf litter for adults was 17.9 cm min-1. Movements of nymphs through leaf litter could not accurately be described by a random walk model, showing a change in their movement pattern over time from directed to more random movements. The estimated population spread through leaf litter for nymphs was 10.1 cm min-1. The results indicate that wood cricket adults can be considered as more powerful dispersers than nymphs; however, further analysis of how the insects move through natural heterogeneous environments at a range of spatio-temporal scales needs to be performed to provide a complete understanding of the dispersal ability of the species.

The influence of continuous versus interval walking exercise on knee joint loading and pain in patients with knee osteoarthritis.

PubMed

Farrokhi, Shawn; Jayabalan, Prakash; Gustafson, Jonathan A; Klatt, Brian A; Sowa, Gwendolyn A; Piva, Sara R

2017-07-01

To evaluate whether knee contact force and knee pain are different between continuous and interval walking exercise in patients with knee osteoarthritis (OA). Twenty seven patients with unilateral symptomatic knee OA completed two separate walking exercise sessions on a treadmill at 1.3m/s on two different days: 1) a continuous 45min walking exercise session, and 2) three 15min bouts of walking exercise separated by 1h rest periods for a total of 45min of exercise in an interval format. Estimated knee contact forces using the OpenSim software and knee pain were evaluated at baseline (1st minute of walking) and after every 15min between the continuous and interval walking conditions. A significant increase from baseline was observed in peak knee contact force during the weight-acceptance phase of gait after 30 and 45min of walking, irrespective of the walking exercise condition. Additionally, whereas continuous walking resulted in an increase in knee pain, interval walking did not lead to increased knee pain. Walking exercise durations of 30min or greater may lead to undesirable knee joint loading in patients with knee OA, while performing the same volume of exercise in multiple bouts as opposed to one continuous bout may be beneficial for limiting knee pain. Copyright © 2017. Published by Elsevier B.V.

Cardiovascular Health Effects of Internet-Based Encouragements to Do Daily Workplace Stair-Walks: Randomized Controlled Trial

PubMed Central

Sundstrup, Emil; Boysen, Marianne; Jakobsen, Markus Due; Mortensen, Ole Steen; Persson, Roger

2013-01-01

Background Although the hazardous health effects of a sedentary lifestyle are well known, many adults struggle with regular physical activity. Simple and efficient encouragements for increased physical activity are needed. Objective To determine the effect on cardiovascular health of email-based encouragements to do daily stair-walks at work together with colleagues among adults in sedentary occupations. Methods A single-blind randomized controlled trial was performed at a large administrative company in Copenhagen, Denmark. Participants were 160 office workers (125 women, 35 men; mean age 42 years, SD 10; sitting 89.5% of work time). At baseline, aerobic fitness was 37 mL/min/kg (SD 9), mean blood pressure was 118/79 mmHg (SD 14/9), and mean body mass index (BMI) was 23 kg/m2 (SD 4). Participants were randomly assigned (2:1 ratio) to an email group receiving weekly email-based encouragements to walk the stairs for 10 minutes a day or to a control group receiving weekly reminders to continue their usual physical activities. The primary outcome was the change from baseline to 10-week follow-up in aerobic fitness determined from a maximal cycle test. The examiner was blinded to group allocation. Results Adherence to the email encouragements was fairly high with 82.7% of the participants performing at least 3 sessions of 10-minute stair-walks per week (mean 3.3, SD 1.3). Mean heart rate reached 167 beats/min (SD 10) during stair-walks. In the intention-to-treat analysis, aerobic fitness increased 1.45 mL/min/kg (95% CI 0.64-2.27) at 10-week follow-up in the email group compared with the control group. In participants with low aerobic fitness at baseline (n=56), aerobic fitness increased 1.89 mL/min/kg (95% CI 0.53-3.24), and systolic and diastolic blood pressure decreased 4.81 mmHg (95% CI 0.47-9.16) and 2.67 mmHg (95% CI 0.01-5.32), respectively, in the email group compared with the control group. Body weight decreased in the email group of those with low aerobic fitness compared with the control group, but this was not statistically significant. Conclusions Simple and inexpensive email-based encouragements to do daily stair-walks together with colleagues at work improves cardiovascular health among adults in sedentary occupations. There exists an enormous potential to prevent the hazardous health effects of a sedentary lifestyle through the use of email-based encouragements to do short bouts of physical activity at the workplace. Trial Registration Clinicaltrials.gov NCT01293253; http://clinicaltrials.gov/ct2/show/NCT01293253 (Archived by WebCite at http://www.webcitation.org/6HWG2jw68). PMID:23793032

Cardiovascular health effects of internet-based encouragements to do daily workplace stair-walks: randomized controlled trial.

PubMed

Andersen, Lars Louis; Sundstrup, Emil; Boysen, Marianne; Jakobsen, Markus Due; Mortensen, Ole Steen; Persson, Roger

2013-06-21

Although the hazardous health effects of a sedentary lifestyle are well known, many adults struggle with regular physical activity. Simple and efficient encouragements for increased physical activity are needed. To determine the effect on cardiovascular health of email-based encouragements to do daily stair-walks at work together with colleagues among adults in sedentary occupations. A single-blind randomized controlled trial was performed at a large administrative company in Copenhagen, Denmark. Participants were 160 office workers (125 women, 35 men; mean age 42 years, SD 10; sitting 89.5% of work time). At baseline, aerobic fitness was 37 mL/min/kg (SD 9), mean blood pressure was 118/79 mmHg (SD 14/9), and mean body mass index (BMI) was 23 kg/m(2) (SD 4). Participants were randomly assigned (2:1 ratio) to an email group receiving weekly email-based encouragements to walk the stairs for 10 minutes a day or to a control group receiving weekly reminders to continue their usual physical activities. The primary outcome was the change from baseline to 10-week follow-up in aerobic fitness determined from a maximal cycle test. The examiner was blinded to group allocation. Adherence to the email encouragements was fairly high with 82.7% of the participants performing at least 3 sessions of 10-minute stair-walks per week (mean 3.3, SD 1.3). Mean heart rate reached 167 beats/min (SD 10) during stair-walks. In the intention-to-treat analysis, aerobic fitness increased 1.45 mL/min/kg (95% CI 0.64-2.27) at 10-week follow-up in the email group compared with the control group. In participants with low aerobic fitness at baseline (n=56), aerobic fitness increased 1.89 mL/min/kg (95% CI 0.53-3.24), and systolic and diastolic blood pressure decreased 4.81 mmHg (95% CI 0.47-9.16) and 2.67 mmHg (95% CI 0.01-5.32), respectively, in the email group compared with the control group. Body weight decreased in the email group of those with low aerobic fitness compared with the control group, but this was not statistically significant. Simple and inexpensive email-based encouragements to do daily stair-walks together with colleagues at work improves cardiovascular health among adults in sedentary occupations. There exists an enormous potential to prevent the hazardous health effects of a sedentary lifestyle through the use of email-based encouragements to do short bouts of physical activity at the workplace. Clinicaltrials.gov NCT01293253; http://clinicaltrials.gov/ct2/show/NCT01293253 (Archived by WebCite at http://www.webcitation.org/6HWG2jw68).

Random walks with shape prior for cochlea segmentation in ex vivo μCT.

PubMed

Ruiz Pujadas, Esmeralda; Kjer, Hans Martin; Piella, Gemma; Ceresa, Mario; González Ballester, Miguel Angel

2016-09-01

Cochlear implantation is a safe and effective surgical procedure to restore hearing in deaf patients. However, the level of restoration achieved may vary due to differences in anatomy, implant type and surgical access. In order to reduce the variability of the surgical outcomes, we previously proposed the use of a high-resolution model built from [Formula: see text] images and then adapted to patient-specific clinical CT scans. As the accuracy of the model is dependent on the precision of the original segmentation, it is extremely important to have accurate [Formula: see text] segmentation algorithms. We propose a new framework for cochlea segmentation in ex vivo [Formula: see text] images using random walks where a distance-based shape prior is combined with a region term estimated by a Gaussian mixture model. The prior is also weighted by a confidence map to adjust its influence according to the strength of the image contour. Random walks is performed iteratively, and the prior mask is aligned in every iteration. We tested the proposed approach in ten [Formula: see text] data sets and compared it with other random walks-based segmentation techniques such as guided random walks (Eslami et al. in Med Image Anal 17(2):236-253, 2013) and constrained random walks (Li et al. in Advances in image and video technology. Springer, Berlin, pp 215-226, 2012). Our approach demonstrated higher accuracy results due to the probability density model constituted by the region term and shape prior information weighed by a confidence map. The weighted combination of the distance-based shape prior with a region term into random walks provides accurate segmentations of the cochlea. The experiments suggest that the proposed approach is robust for cochlea segmentation.

Stochastic nature of series of waiting times

NASA Astrophysics Data System (ADS)

Anvari, Mehrnaz; Aghamohammadi, Cina; Dashti-Naserabadi, H.; Salehi, E.; Behjat, E.; Qorbani, M.; Khazaei Nezhad, M.; Zirak, M.; Hadjihosseini, Ali; Peinke, Joachim; Tabar, M. Reza Rahimi

2013-06-01

Although fluctuations in the waiting time series have been studied for a long time, some important issues such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied. Here we find that the “waiting times” series for a given increment level have long-range correlations with Hurst exponents belonging to the interval 1/2

Random walks with long-range steps generated by functions of Laplacian matrices

NASA Astrophysics Data System (ADS)

Riascos, A. P.; Michelitsch, T. M.; Collet, B. A.; Nowakowski, A. F.; Nicolleau, F. C. G. A.

2018-04-01

In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information in the Laplacian matrix, that describes the connections of a network, to a dynamic determined by functions of this matrix. The resulting processes are non-local allowing transitions of the random walker from one node to nodes beyond its nearest neighbors. We find that only two types of Laplacian functions are admissible with distinct behaviors for long-range steps in the infinite network limit: type (i) functions generate Brownian motions, type (ii) functions Lévy flights. For this asymptotic long-range step behavior only the lowest non-vanishing order of the Laplacian function is relevant, namely first order for type (i), and fractional order for type (ii) functions. In the first part, we discuss spectral properties of the Laplacian matrix and a series of relations that are maintained by a particular type of functions that allow to define random walks on any type of undirected connected networks. Once described general properties, we explore characteristics of random walk strategies that emerge from particular cases with functions defined in terms of exponentials, logarithms and powers of the Laplacian as well as relations of these dynamics with non-local strategies like Lévy flights and fractional transport. Finally, we analyze the global capacity of these random walk strategies to explore networks like lattices and trees and different types of random and complex networks.

Limit theorems for Lévy walks in d dimensions: rare and bulk fluctuations

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak; Denisov, Sergey; Zaburdaev, Vasily; Barkai, Eli

2017-04-01

We consider super-diffusive Lévy walks in d≥slant 2 dimensions when the duration of a single step, i.e. a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean. We demonstrate that the probability density function (PDF) of the coordinate of the random walker has two different scaling limits at large times. One limit describes the bulk of the PDF. It is the d-dimensional generalization of the one-dimensional Lévy distribution and is the counterpart of the central limit theorem (CLT) for random walks with finite dispersion. In contrast with the one-dimensional Lévy distribution and the CLT this distribution does not have a universal shape. The PDF reflects anisotropy of the single-step statistics however large the time is. The other scaling limit, the so-called ‘infinite density’, describes the tail of the PDF which determines second (dispersion) and higher moments of the PDF. This limit repeats the angular structure of the PDF of velocity in one step. A typical realization of the walk consists of anomalous diffusive motion (described by anisotropic d-dimensional Lévy distribution) interspersed with long ballistic flights (described by infinite density). The long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion. We illustrate the concept by considering two types of Lévy walks, with isotropic and anisotropic distributions of velocities. Furthermore, we show that for isotropic but otherwise arbitrary velocity distributions the d-dimensional process can be reduced to a one-dimensional Lévy walk. We briefly discuss the consequences of non-universality for the d  >  1 dimensional fractional diffusion equation, in particular the non-uniqueness of the fractional Laplacian.

Exercise in Patients on Dialysis: A Multicenter, Randomized Clinical Trial.

PubMed

Manfredini, Fabio; Mallamaci, Francesca; D'Arrigo, Graziella; Baggetta, Rossella; Bolignano, Davide; Torino, Claudia; Lamberti, Nicola; Bertoli, Silvio; Ciurlino, Daniele; Rocca-Rey, Lisa; Barillà, Antonio; Battaglia, Yuri; Rapanà, Renato Mario; Zuccalà, Alessandro; Bonanno, Graziella; Fatuzzo, Pasquale; Rapisarda, Francesco; Rastelli, Stefania; Fabrizi, Fabrizio; Messa, Piergiorgio; De Paola, Luciano; Lombardi, Luigi; Cupisti, Adamasco; Fuiano, Giorgio; Lucisano, Gaetano; Summaria, Chiara; Felisatti, Michele; Pozzato, Enrico; Malagoni, Anna Maria; Castellino, Pietro; Aucella, Filippo; Abd ElHafeez, Samar; Provenzano, Pasquale Fabio; Tripepi, Giovanni; Catizone, Luigi; Zoccali, Carmine

2017-04-01

Previous studies have suggested the benefits of physical exercise for patients on dialysis. We conducted the Exercise Introduction to Enhance Performance in Dialysis trial, a 6-month randomized, multicenter trial to test whether a simple, personalized walking exercise program at home, managed by dialysis staff, improves functional status in adult patients on dialysis. The main study outcomes included change in physical performance at 6 months, assessed by the 6-minute walking test and the five times sit-to-stand test, and in quality of life, assessed by the Kidney Disease Quality of Life Short Form (KDQOL-SF) questionnaire. We randomized 296 patients to normal physical activity (control; n =145) or walking exercise ( n =151); 227 patients (exercise n =104; control n =123) repeated the 6-month evaluations. The distance covered during the 6-minute walking test improved in the exercise group (mean distance±SD: baseline, 328±96 m; 6 months, 367±113 m) but not in the control group (baseline, 321±107 m; 6 months, 324±116 m; P <0.001 between groups). Similarly, the five times sit-to-stand test time improved in the exercise group (mean time±SD: baseline, 20.5±6.0 seconds; 6 months, 18.2±5.7 seconds) but not in the control group (baseline, 20.9±5.8 seconds; 6 months, 20.2±6.4 seconds; P =0.001 between groups). The cognitive function score ( P =0.04) and quality of social interaction score ( P =0.01) in the kidney disease component of the KDQOL-SF improved significantly in the exercise arm compared with the control arm. Hence, a simple, personalized, home-based, low-intensity exercise program managed by dialysis staff may improve physical performance and quality of life in patients on dialysis. Copyright © 2017 by the American Society of Nephrology.

Sunspot random walk and 22-year variation

USGS Publications Warehouse

Love, Jeffrey J.; Rigler, E. Joshua

2012-01-01

We examine two stochastic models for consistency with observed long-term secular trends in sunspot number and a faint, but semi-persistent, 22-yr signal: (1) a null hypothesis, a simple one-parameter random-walk model of sunspot-number cycle-to-cycle change, and, (2) an alternative hypothesis, a two-parameter random-walk model with an imposed 22-yr alternating amplitude. The observed secular trend in sunspots, seen from solar cycle 5 to 23, would not be an unlikely result of the accumulation of multiple random-walk steps. Statistical tests show that a 22-yr signal can be resolved in historical sunspot data; that is, the probability is low that it would be realized from random data. On the other hand, the 22-yr signal has a small amplitude compared to random variation, and so it has a relatively small effect on sunspot predictions. Many published predictions for cycle 24 sunspots fall within the dispersion of previous cycle-to-cycle sunspot differences. The probability is low that the Sun will, with the accumulation of random steps over the next few cycles, walk down to a Dalton-like minimum. Our models support published interpretations of sunspot secular variation and 22-yr variation resulting from cycle-to-cycle accumulation of dynamo-generated magnetic energy.

A randomized controlled trial to evaluate the feasibility of the Wii Fit for improving walking in older adults with lower limb amputation.

PubMed

Imam, Bita; Miller, William C; Finlayson, Heather; Eng, Janice J; Jarus, Tal

2017-01-01

To assess the feasibility of Wii.n.Walk for improving walking capacity in older adults with lower limb amputation. A parallel, evaluator-blind randomized controlled feasibility trial. Community-living. Individuals who were ⩾50 years old with a unilateral lower limb amputation. Wii.n.Walk consisted of Wii Fit training, 3x/week (40 minute sessions), for 4 weeks. Training started in the clinic in groups of 3 and graduated to unsupervised home training. Control group were trained using cognitive games. Feasibility indicators: trial process (recruitment, retention, participants' perceived benefit from the Wii.n.Walk intervention measured by exit questionnaire), resources (adherence), management (participant processing, blinding), and treatment (adverse event, and Cohen's d effect size and variance). Primary clinical outcome: walking capacity measured using the 2 Minute Walk Test at baseline, end of treatment, and 3-week retention. Of 28 randomized participants, 24 completed the trial (12/arm). Median (range) age was 62.0 (50-78) years. Mean (SD) score for perceived benefit from the Wii.n.Walk intervention was 38.9/45 (6.8). Adherence was 83.4%. The effect sizes for the 2 Minute Walk Test were 0.5 (end of treatment) and 0.6 (3-week retention) based on intention to treat with imputed data; and 0.9 (end of treatment) and 1.2 (3-week retention) based on per protocol analysis. The required sample size for a future larger RCT was deemed to be 72 (36 per arm). The results suggested the feasibility of the Wii.n.Walk with a medium effect size for improving walking capacity. Future larger randomized controlled trials investigating efficacy are warranted.

Effect of Resveratrol on Walking Performance in Older People With Peripheral Artery Disease

PubMed Central

Leeuwenburgh, Christiaan; Guralnik, Jack M.; Tian, Lu; Sufit, Robert; Zhao, Lihui; Criqui, Michael H.; Kibbe, Melina R.; Stein, James H.; Lloyd-Jones, Donald; Anton, Stephen D.; Polonsky, Tamar S.; Gao, Ying; de Cabo, Rafael; Ferrucci, Luigi

2017-01-01

Importance Research shows that resveratrol, a sirtuin activator in red wine, improves exercise endurance and skeletal-muscle oxidative metabolism in animals and may enhance vascular function in humans. Resveratrol supplement sales exceed $30 million annually in the United States, but few data are available regarding its efficacy in humans. Objective To determine whether resveratrol, 125 mg/d or 500 mg/d, improves the 6-minute walk performance in patients with peripheral artery disease (PAD). Design, Setting, and Participants This parallel-design, double-blind, randomized clinical trial, called Resveratrol to Improve Outcomes in Older People With PAD (RESTORE), was conducted at Northwestern University. Sixty-six participants 65 years or older with PAD were randomized to receive a daily capsule of resveratrol, 125 mg or 500 mg, or placebo for 6 months. Participants were randomized using a randomly permuted block method stratified by baseline 6-minute walk test performance. This trial was conducted between January 1, 2015, and August 5, 2016, and data analyses were performed according to the intention-to-treat concept. Interventions Administration of resveratrol, 125 or 500 mg/d, or placebo once daily. Main Outcomes and Measures The primary outcome measure was the change in 6-minute walk distance at the 6-month follow-up. One of the secondary outcomes was change in maximal treadmill walking time. Because of the preliminary nature of the trial, the a priori power calculation used a 1-sided test with a significance level of P < .10. Results The 66 participants were predominantly men (45 [68%]), had a mean (SD) age of 74.4 (6.6) years, and had a mean (SD) ankle brachial index of 0.67 (0.18). Sixty-four (97%) completed follow-up. Six-month mean (SE) changes in 6-minute walk distance were 4.6 (8.1) m for the 125-mg resveratrol group, −12.8 (7.5) m for the 500-mg resveratrol group, and −12.3 (7.9) m for the placebo group (P = .07 for the 125-mg resveratrol group vs placebo; P = .96 for the 500-mg resveratrol group vs placebo). Six-month mean (SE) changes in maximal treadmill walking time were 0.5 (2.3) minutes for the 125-mg resveratrol group, −0.6 (2.1) minutes for the 500-mg resveratrol group, and 0.4 (2.1) minutes for the placebo group (P = .18 for the 125-mg resveratrol group vs placebo; P = .12 for the 500-mg resveratrol group vs placebo). Conclusions and Relevance The RESTORE trial found no consistent evidence that resveratrol improves walking performance in patients 65 years or older with PAD. Trial Registration clinicaltrials.gov Identifier: NCT02246660 PMID:28403379

The effects of interval- vs. continuous exercise on excess post-exercise oxygen consumption and substrate oxidation rates in subjects with type 2 diabetes.

PubMed

Karstoft, Kristian; Wallis, Gareth A; Pedersen, Bente K; Solomon, Thomas P J

2016-09-01

For unknown reasons, interval training often reduces body weight more than energy-expenditure matched continuous training. We compared the acute effects of time-duration and oxygen-consumption matched interval- vs. continuous exercise on excess post-exercise oxygen consumption (EPOC), substrate oxidation rates and lipid metabolism in the hours following exercise in subjects with type 2 diabetes (T2D). Following an overnight fast, ten T2D subjects (M/F: 7/3; age=60.3±2.3years; body mass index (BMI)=28.3±1.1kg/m(2)) completed three 60-min interventions in a counterbalanced, randomized order: 1) control (CON), 2) continuous walking (CW), 3) interval-walking (IW - repeated cycles of 3min of fast and 3min of slow walking). Indirect calorimetry was applied during each intervention and repeatedly for 30min per hour during the following 5h. A liquid mixed meal tolerance test (MMTT, 450kcal) was consumed by the subjects 45min after completion of the intervention with blood samples taken regularly. Exercise interventions were successfully matched for total oxygen consumption (CW=1641±133mL/min; IW=1634±126mL/min, P>0.05). EPOC was higher after IW (8.4±1.3l) compared to CW (3.7±1.4l, P<0.05). Lipid oxidation rates were increased during the MMTT in IW (1.03±0.12mg/kg per min) and CW (0.87±0.04mg/kg per min) compared with CON (0.73±0.04mg/kg per min, P<0.01 and P<0.05, respectively), with no difference between IW and CW. Moreover, free fatty acids and glycerol concentrations, and glycerol kinetics were increased comparably during and after IW and CW compared to CON. Interval exercise results in greater EPOC than oxygen-consumption matched continuous exercise during a post-exercise MMTT in subjects with T2D, whereas effects on substrate oxidation and lipid metabolism are comparable. Copyright © 2016 Elsevier Inc. All rights reserved.

Single- versus dual-process models of lexical decision performance: insights from response time distributional analysis.

PubMed

Yap, Melvin J; Balota, David A; Cortese, Michael J; Watson, Jason M

2006-12-01

This article evaluates 2 competing models that address the decision-making processes mediating word recognition and lexical decision performance: a hybrid 2-stage model of lexical decision performance and a random-walk model. In 2 experiments, nonword type and word frequency were manipulated across 2 contrasts (pseudohomophone-legal nonword and legal-illegal nonword). When nonwords became more wordlike (i.e., BRNTA vs. BRANT vs. BRANE), response latencies to nonwords were slowed and the word frequency effect increased. More important, distributional analyses revealed that the Nonword Type = Word Frequency interaction was modulated by different components of the response time distribution, depending on the specific nonword contrast. A single-process random-walk model was able to account for this particular set of findings more successfully than the hybrid 2-stage model. (c) 2006 APA, all rights reserved.

Study protocol: the effectiveness and cost effectiveness of an employer-led intervention to increase walking during the daily commute: the Travel to Work randomised controlled trial.

PubMed

Audrey, Suzanne; Cooper, Ashley R; Hollingworth, William; Metcalfe, Chris; Procter, Sunita; Davis, Adrian; Campbell, Rona; Gillison, Fiona; Rodgers, Sarah E

2015-02-18

Physical inactivity increases the risk of many chronic diseases including coronary heart disease, type 2 diabetes and some cancers. It is recommended that adults should undertake at least 150 minutes of moderate intensity physical activity throughout the week but many adults do not achieve this. An opportunity for working adults to accumulate the recommended activity levels is through the daily commute. Employees will be recruited from workplaces in south-west England and south Wales. In the intervention arm, workplace Walk-to-Work promoters will be recruited and trained. Participating employees will receive Walk-to-Work materials and support will be provided through four contacts from the promoters over 10 weeks. Workplaces in the control arm will continue with their usual practice. The intervention will be evaluated by a cluster randomized controlled trial including economic and process evaluations. The primary outcome is daily minutes of moderate to vigorous physical activity (MVPA). Secondary outcomes are: overall physical activity; sedentary time; modal shift away from private car use during the commute; and physical activity/MVPA during the commute. Accelerometers, GPS receivers and travel diaries will be used at baseline and one year follow-up. Questionnaires will be used at baseline, immediately post intervention, and one year follow-up. The process evaluation will examine the context, delivery and response to the intervention from the perspectives of employers, Walk-to-Work promoters and employees using questionnaires, descriptive statistics, fieldnotes and interviews. A cost-consequence study will include employer, employee and health service costs and outcomes. Time and consumables used in implementing the intervention will be measured. Journey time, household commuting costs and expenses will be recorded using travel diaries to estimate costs to employees. Presenteeism, absenteeism, employee wellbeing and health service use will be recorded. Compared with other forms of physical activity, walking is a popular, familiar and convenient, and the main option for increasing physical activity in sedentary populations. To our knowledge, this is the first full-scale randomised controlled trial to objectively measure (using accelerometers and GPS receivers) the effectiveness of a workplace intervention to promote walking during the commute to and from work. ISRCTN15009100 (10 December 2014).

Optimization and universality of Brownian search in a basic model of quenched heterogeneous media

NASA Astrophysics Data System (ADS)

Godec, Aljaž; Metzler, Ralf

2015-05-01

The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time (MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.

The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time

DOE PAGES

Hu, Xiaohu; Hong, Liang; Smith, Micholas Dean; ...

2015-11-23

Here, internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behavior with effective relaxation times existing over many decades in time, from ps up to ~10 2s (refs 1-4). Here, using molecular dynamics simulations, we show that, on timescales from 10 –12 to 10 –5s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance fluctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of themore » energy landscape explored. Diffusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behavior persists up to timescales approaching the in vivo lifespan of individual protein molecules.« less

Time-delayed feedback control of diffusion in random walkers.

PubMed

Ando, Hiroyasu; Takehara, Kohta; Kobayashi, Miki U

2017-07-01

Time delay in general leads to instability in some systems, while specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a stochastic process, i.e., a random walk, and observe its diffusion phenomenon with time-delayed feedback. As a result, the diffusion coefficient decreases with increasing delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying time-delayed feedback to a molecular dynamics model.

Active video-gaming effects on balance and mobility in individuals with chronic stroke: a randomized controlled trial.

PubMed

Fritz, Stacy L; Peters, Denise M; Merlo, Angela M; Donley, Jonathan

2013-01-01

Treatments that provide feedback, increase practice with multiple repetitions, and motivate patients are essential to rehabilitation post stroke. To determine whether playing active video games results in improved balance and mobility post stroke. Thirty participants with chronic (time since stroke = 3.0 [2.9] years) hemiparesis post stroke were randomly assigned to a gaming group or normal activity control group. Gaming systems provided participants with an interactive interface of real-time movement of either themselves or an avatar on the screen. Participants played games 50-60 minutes/day, 4 days/week, for 5 weeks. The intervention was strictly game-play, in standing position, without physical therapy. The control group received no special intervention and continued with normal activity. Both groups were tested prior to, following the 5 weeks (post test), and 3 months following the completion of the study. Outcome measures included the Fugl-Meyer Assessment, Berg Balance Scale, Dynamic Gait Index, Timed Up & Go, 6-minute walk test, 3-meter walk (self-selected and fast), and perception of recovery. No statistically significant differences between or within groups were found through analysis of covariance (covaried for side of hemiparesis) at post test or follow-up. Although the within-group effect sizes were primarily indexed as "small" (< .36), the gaming group exhibited higher within-group effect sizes before and after testing than did the control group on all 7 dependent variables analyzed. Even though the only intervention was game-play, there were small positive effects. Therapist assistance in making more optimum movement choices may be needed before significant improvements are seen with commercially available, general purpose games.

The effects of smartphone multitasking on gait and dynamic balance

PubMed Central

Lee, Jeon Hyeong; Lee, Myoung Hee

2018-01-01

[Purpose] This study was performed to analyze the influence of smartphone multitasking on gait and dynamic balance. [Subjects and Methods] The subjects were 19 male and 20 female university students. There were 4 types of gait tasks: General Gait (walking without a task), Task Gait 1 (walking while writing a message), Task Gait 2 (walking while writing a message and listening to music), Task Gait 3 (walking while writing a message and having a conversation). To exclude the learning effect, the order of tasks was randomized. The Zebris FDM-T treadmill system (Zebris Medical GmbH, Germany) was used to measure left and right step length and width, and a 10 m walking test (10MWT) was conducted for gait velocity. In addition, a Timed Up and Go test (TUG) was used to measure dynamic balance. All the tasks were performed 3 times, and the mean of the measured values was analyzed. [Results] There were no statistically significant differences in step length and width. There were statistically significant differences in the 10MWT and TUG tests. [Conclusion] Using a smartphone while walking decreases a person’s dynamic balance and walking ability. It is considered that accident rates are higher when using a smartphone. PMID:29545698

Weak Ergodicity Breaking of Receptor Motion in Living Cells Stemming from Random Diffusivity

NASA Astrophysics Data System (ADS)

Manzo, Carlo; Torreno-Pina, Juan A.; Massignan, Pietro; Lapeyre, Gerald J.; Lewenstein, Maciej; Garcia Parajo, Maria F.

2015-01-01

Molecular transport in living systems regulates numerous processes underlying biological function. Although many cellular components exhibit anomalous diffusion, only recently has the subdiffusive motion been associated with nonergodic behavior. These findings have stimulated new questions for their implications in statistical mechanics and cell biology. Is nonergodicity a common strategy shared by living systems? Which physical mechanisms generate it? What are its implications for biological function? Here, we use single-particle tracking to demonstrate that the motion of dendritic cell-specific intercellular adhesion molecule 3-grabbing nonintegrin (DC-SIGN), a receptor with unique pathogen-recognition capabilities, reveals nonergodic subdiffusion on living-cell membranes In contrast to previous studies, this behavior is incompatible with transient immobilization, and, therefore, it cannot be interpreted according to continuous-time random-walk theory. We show that the receptor undergoes changes of diffusivity, consistent with the current view of the cell membrane as a highly dynamic and diverse environment. Simulations based on a model of an ordinary random walk in complex media quantitatively reproduce all our observations, pointing toward diffusion heterogeneity as the cause of DC-SIGN behavior. By studying different receptor mutants, we further correlate receptor motion to its molecular structure, thus establishing a strong link between nonergodicity and biological function. These results underscore the role of disorder in cell membranes and its connection with function regulation. Because of its generality, our approach offers a framework to interpret anomalous transport in other complex media where dynamic heterogeneity might play a major role, such as those found, e.g., in soft condensed matter, geology, and ecology.

Schramm-Loewner evolution of the accessible perimeter of isoheight lines of correlated landscapes

NASA Astrophysics Data System (ADS)

Posé, N.; Schrenk, K. J.; Araújo, N. A. M.; Herrmann, H. J.

Real landscapes exhibit long-range height-height correlations, which are quantified by the Hurst exponent H. We give evidence that for negative H, in spite of the long-range nature of correlations, the statistics of the accessible perimeter of isoheight lines is compatible with Schramm-Loewner evolution curves and therefore can be mapped to random walks, their fractal dimension determining the diffusion constant. Analytic results are recovered for H=-1 and H=0 and a conjecture is proposed for the values in between. By contrast, for positive H, we find that the random walk is not Markovian but strongly correlated in time. Theoretical and practical implications are discussed.

The Social Relations of a Health Walk Group: An Ethnographic Study.

PubMed

Grant, Gordon; Pollard, Nick; Allmark, Peter; Machaczek, Kasia; Ramcharan, Paul

2017-09-01

It is already well established that regular walks are conducive to health and well-being. This article considers the production of social relations of regular, organized weekly group walks for older people. It is based on an ethnographic study of a Walking for Health group in a rural area of the United Kingdom. Different types of social relations are identified arising from the walk experience. The social relations generated are seen to be shaped by organizational factors that are constitutive of the walks; the resulting culture having implications for the sustainability of the experience. As there appears to be no single uniting theory linking group walk experiences to the production of social relations at this time, the findings are considered against therapeutic landscape, therapeutic mobility, and social capital theorizing. Finally, implications for the continuance of walking schemes for older people and for further research are considered.

Continuous-time quantum walks on multilayer dendrimer networks

NASA Astrophysics Data System (ADS)

Galiceanu, Mircea; Strunz, Walter T.

2016-08-01

We consider continuous-time quantum walks (CTQWs) on multilayer dendrimer networks (MDs) and their application to quantum transport. A detailed study of properties of CTQWs is presented and transport efficiency is determined in terms of the exact and average return probabilities. The latter depends only on the eigenvalues of the connectivity matrix, which even for very large structures allows a complete analytical solution for this particular choice of network. In the case of MDs we observe an interplay between strong localization effects, due to the dendrimer topology, and good efficiency from the linear segments. We show that quantum transport is enhanced by interconnecting more layers of dendrimers.

An evaluation of the impact of flooring types on exposures to fine and coarse particles within the residential micro-environment using CONTAM.

PubMed

Bramwell, Lisa; Qian, Jing; Howard-Reed, Cynthia; Mondal, Sumona; Ferro, Andrea R

2016-01-01

Typical resuspension activities within the home, such as walking, have been estimated to contribute up to 25% of personal exposures to PM10. Chamber studies have shown that for moderate walking intensities, flooring type can impact the rate at which particles are re-entrained into the air. For this study, the impact of residential flooring type on incremental average daily (24 h) time-averaged exposure was investigated. Distributions of incremental time-averaged daily exposures to fine and coarse PM while walking within the residential micro-environment were predicted using CONTAM, the multizone airflow and contaminant transport program of the National Institute of Standards and Technology. Knowledge of when and where a person was walking was determined by randomly selecting 490 daily diaries from the EPA's consolidated human activity database (CHAD). On the basis of the results of this study, residential flooring type can significantly impact incremental time-averaged daily exposures to coarse and fine particles (α=0.05, P<0.05, N=490, Kruskal-Wallis test) with high-density cut pile carpeting resulting in the highest exposures. From this study, resuspension from walking within the residential micro-environment contributed 6-72% of time-averaged daily exposures to PM10.

Exact Asymptotics of the Freezing Transition of a Logarithmically Correlated Random Energy Model

NASA Astrophysics Data System (ADS)

Webb, Christian

2011-12-01

We consider a logarithmically correlated random energy model, namely a model for directed polymers on a Cayley tree, which was introduced by Derrida and Spohn. We prove asymptotic properties of a generating function of the partition function of the model by studying a discrete time analogy of the KPP-equation—thus translating Bramson's work on the KPP-equation into a discrete time case. We also discuss connections to extreme value statistics of a branching random walk and a rescaled multiplicative cascade measure beyond the critical point.

Superdiffusive Dispersals Impart the Geometry of Underlying Random Walks

NASA Astrophysics Data System (ADS)

Zaburdaev, V.; Fouxon, I.; Denisov, S.; Barkai, E.

2016-12-01

It is recognized now that a variety of real-life phenomena ranging from diffusion of cold atoms to the motion of humans exhibit dispersal faster than normal diffusion. Lévy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive Lévy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

Sensorimotor-Conceptual Integration in Free Walking Enhances Divergent Thinking for Young and Older Adults

PubMed Central

Kuo, Chun-Yu; Yeh, Yei-Yu

2016-01-01

Prior research has shown that free walking can enhance creative thinking. Nevertheless, it remains unclear whether bidirectional body-mind links are essential for the positive effect of free walking on creative thinking. Moreover, it is unknown whether the positive effect can be generalized to older adults. In Experiment 1, we replicated previous findings with two additional groups of young participants. Participants in the rectangular-walking condition walked along a rectangular path while generating unusual uses for chopsticks. Participants in the free-walking group walked freely as they wished, and participants in the free-generation condition generated unconstrained free paths while the participants in the random-experienced condition walked those paths. Only the free-walking group showed better performance in fluency, flexibility, and originality. In Experiment 2, two groups of older adults were randomly assigned to the free-walking and rectangular-walking conditions. The free-walking group showed better performance than the rectangular-walking group. Moreover, older adults in the free-walking group outperformed young adults in the rectangular-walking group in originality and performed comparably in fluency and flexibility. Bidirectional links between proprioceptive-motor kinematics and metaphorical abstract concepts can enhance divergent thinking for both young and older adults. PMID:27790178

Dynamic model of time-dependent complex networks.

PubMed

Hill, Scott A; Braha, Dan

2010-10-01

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness against failures, vulnerability to deliberate attacks, and diffusion properties. However, recent empirical research of large dynamic networks (characterized by irregular connections that evolve rapidly) has demonstrated that there is little continuity in degree centrality of nodes over time, even when their degree distributions follow a power law. This unexpected dynamic centrality suggests that the connections in these systems are not driven by preferential attachment or other known mechanisms. We present an approach to explain real-world dynamic networks and qualitatively reproduce these dynamic centrality phenomena. This approach is based on a dynamic preferential attachment mechanism, which exhibits a sharp transition from a base pure random walk scheme.

Correlated errors in geodetic time series: Implications for time-dependent deformation

USGS Publications Warehouse

Langbein, J.; Johnson, H.

1997-01-01

Analysis of frequent trilateration observations from the two-color electronic distance measuring networks in California demonstrate that the noise power spectra are dominated by white noise at higher frequencies and power law behavior at lower frequencies. In contrast, Earth scientists typically have assumed that only white noise is present in a geodetic time series, since a combination of infrequent measurements and low precision usually preclude identifying the time-correlated signature in such data. After removing a linear trend from the two-color data, it becomes evident that there are primarily two recognizable types of time-correlated noise present in the residuals. The first type is a seasonal variation in displacement which is probably a result of measuring to shallow surface monuments installed in clayey soil which responds to seasonally occurring rainfall; this noise is significant only for a small fraction of the sites analyzed. The second type of correlated noise becomes evident only after spectral analysis of line length changes and shows a functional relation at long periods between power and frequency of and where f is frequency and ?? ??? 2. With ?? = 2, this type of correlated noise is termed random-walk noise, and its source is mainly thought to be small random motions of geodetic monuments with respect to the Earth's crust, though other sources are possible. Because the line length changes in the two-color networks are measured at irregular intervals, power spectral techniques cannot reliably estimate the level of I//" noise. Rather, we also use here a maximum likelihood estimation technique which assumes that there are only two sources of noise in the residual time series (white noise and randomwalk noise) and estimates the amount of each. From this analysis we find that the random-walk noise level averages about 1.3 mm/Vyr and that our estimates of the white noise component confirm theoretical limitations of the measurement technique. In addition, the seasonal noise can be as large as 3 mm in amplitude but typically is less than 0.5 mm. Because of the presence of random-walk noise in these time series, modeling and interpretation of the geodetic data must account for this source of error. By way of example we show that estimating the time-varying strain tensor (a form of spatial averaging) from geodetic data having both random-walk and white noise error components results in seemingly significant variations in the rate of strain accumulation; spatial averaging does reduce the size of both noise components but not their relative influence on the resulting strain accumulation model. Copyright 1997 by the American Geophysical Union.

A comparison of the health benefits of reduced-exertion high-intensity interval training (REHIT) and moderate-intensity walking in type 2 diabetes patients.

PubMed

Ruffino, José S; Songsorn, Preeyaphorn; Haggett, Malindi; Edmonds, Daniel; Robinson, Anthony M; Thompson, Dylan; Vollaard, Niels B J

2017-02-01

Reduced-exertion high-intensity interval training (REHIT) is a genuinely time-efficient intervention that can improve aerobic capacity and insulin sensitivity in sedentary individuals. The present study compared the effects of REHIT and moderate-intensity walking on health markers in patients with type 2 diabetes (T2D) in a counter-balanced crossover study. Sixteen men with T2D (mean ± SD age: 55 ± 5 years, body mass index: 30.6 ± 2.8 kg·m -2 , maximal aerobic capacity: 27 ± 4 mL·kg -1 ·min -1 ) completed 8 weeks of REHIT (three 10-min low-intensity cycling sessions/week with two "all-out" 10-20-s sprints) and 8 weeks of moderate-intensity walking (five 30-min sessions/week at an intensity corresponding to 40%-55% of heart-rate reserve), with a 2-month wash-out period between interventions. Before and after each intervention, participants underwent an incremental fitness test, an oral glucose tolerance test (OGTT), a whole-body dual-energy X-ray absorptiometry scan, and continuous glucose monitoring. REHIT was associated with a significantly larger increase in maximal aerobic capacity compared with walking (7% vs. 1%; time × intervention interaction effect: p < 0.05). Both REHIT and walking decreased resting mean arterial pressure (-4%; main effect of time: p < 0.05) and plasma fructosamine (-5%; main effect of time: p < 0.05). Neither intervention significantly improved OGTT-derived measures of insulin sensitivity, glycaemic control measured using continuous glucose monitors, blood lipid profile, or body composition. We conclude that REHIT is superior to a 5-fold larger volume of moderate-intensity walking in improving aerobic fitness, but similar to walking REHIT is not an effective intervention for improving insulin sensitivity or glycaemic control in T2D patients in the short term.

Effect of aquatic versus land based exercise programs on physical performance in severely burned patients: a randomized controlled trial.

PubMed

Zoheiry, Ibrahim M; Ashem, Haidy N; Ahmed, Hamada Ahmed Hamada; Abbas, Rami

2017-12-01

[Purpose] To compare the effect of an aquatic-based versus a land-based exercise regimen on the physical performance of severely burned patients. [Subjects and Methods] Forty patients suffering from severe burn (total body surface area more than 30%) were recruited from several outpatient clinics in Greater Cairo. Their ages ranged between 20 to 40 years and were randomly assigned into two equal groups: group (A), which received an aquatic based exercise program, and group (B), which received a land-based exercise program. The exercise program, which took place in 12 consecutive weeks, consisted of flexibility, endurance, and lower and upper body training. Physical performance was assessed using 30 seconds chair stand test, stair climb test, 30 meter fast paced walk test, time up and go test, 6-minute walk test and a VO2max evaluation. [Results] Significantly increase in the 30 second chair stand, 6-minute walk, 30 meter fast paced walk, stair climb, and VO2 max tests and significantly decrease in the time up and go test in group A (aquatic based exercise) compared with group B (a land-based exercise) at the post treatment. [Conclusion] Twelve-week program of an aquatic program yields improvement in both physical performance and VO2 max in patients with severe burns.

Effect of aquatic versus land based exercise programs on physical performance in severely burned patients: a randomized controlled trial

PubMed Central

Zoheiry, Ibrahim M.; Ashem, Haidy N.; Ahmed, Hamada Ahmed Hamada; Abbas, Rami

2017-01-01

[Purpose] To compare the effect of an aquatic-based versus a land-based exercise regimen on the physical performance of severely burned patients. [Subjects and Methods] Forty patients suffering from severe burn (total body surface area more than 30%) were recruited from several outpatient clinics in Greater Cairo. Their ages ranged between 20 to 40 years and were randomly assigned into two equal groups: group (A), which received an aquatic based exercise program, and group (B), which received a land-based exercise program. The exercise program, which took place in 12 consecutive weeks, consisted of flexibility, endurance, and lower and upper body training. Physical performance was assessed using 30 seconds chair stand test, stair climb test, 30 meter fast paced walk test, time up and go test, 6-minute walk test and a VO2max evaluation. [Results] Significantly increase in the 30 second chair stand, 6-minute walk, 30 meter fast paced walk, stair climb, and VO2 max tests and significantly decrease in the time up and go test in group A (aquatic based exercise) compared with group B (a land-based exercise) at the post treatment. [Conclusion] Twelve-week program of an aquatic program yields improvement in both physical performance and VO2 max in patients with severe burns. PMID:29643605

Quantum transport with long-range steps on Watts-Strogatz networks

NASA Astrophysics Data System (ADS)

Wang, Yan; Xu, Xin-Jian

2016-07-01

We study transport dynamics of quantum systems with long-range steps on the Watts-Strogatz network (WSN) which is generated by rewiring links of the regular ring. First, we probe physical systems modeled by the discrete nonlinear schrödinger (DNLS) equation. Using the localized initial condition, we compute the time-averaged occupation probability of the initial site, which is related to the nonlinearity, the long-range steps and rewiring links. Self-trapping transitions occur at large (small) nonlinear parameters for coupling ɛ=-1 (1), as long-range interactions are intensified. The structure disorder induced by random rewiring, however, has dual effects for ɛ=-1 and inhibits the self-trapping behavior for ɛ=1. Second, we investigate continuous-time quantum walks (CTQW) on the regular ring ruled by the discrete linear schrödinger (DLS) equation. It is found that only the presence of the long-range steps does not affect the efficiency of the coherent exciton transport, while only the allowance of random rewiring enhances the partial localization. If both factors are considered simultaneously, localization is greatly strengthened, and the transport becomes worse.

Repelling, binding, and oscillating of two-particle discrete-time quantum walks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Qinghao; Li, Zhi-Jian, E-mail: zjli@sxu.edu.cn

In this paper, we investigate the effects of particle–particle interaction and static force on the propagation of probability distribution in two-particle discrete-time quantum walk, where the interaction and static force are expressed as a collision phase and a linear position-dependent phase, respectively. It is found that the interaction can lead to boson repelling and fermion binding. The static force also induces Bloch oscillation and results in a continuous transition from boson bunching to fermion anti-bunching. The interplays of particle–particle interaction, quantum interference, and Bloch oscillation provide a versatile framework to study and simulate many-particle physics via quantum walks.

A Mixed-Methods Randomized Controlled Trial of Financial Incentives and Peer Networks to Promote Walking among Older Adults

ERIC Educational Resources Information Center

Kullgren, Jeffrey T.; Harkins, Kristin A.; Bellamy, Scarlett L.; Gonzales, Amy; Tao, Yuanyuan; Zhu, Jingsan; Volpp, Kevin G.; Asch, David A.; Heisler, Michele; Karlawish, Jason

2014-01-01

Background: Financial incentives and peer networks could be delivered through eHealth technologies to encourage older adults to walk more. Methods: We conducted a 24-week randomized trial in which 92 older adults with a computer and Internet access received a pedometer, daily walking goals, and weekly feedback on goal achievement. Participants…

Random Walks on Cartesian Products of Certain Nonamenable Groups and Integer Lattices

NASA Astrophysics Data System (ADS)

Vishnepolsky, Rachel

A random walk on a discrete group satisfies a local limit theorem with power law exponent \\alpha if the return probabilities follow the asymptotic law. P{ return to starting point after n steps } ˜ Crhonn-alpha.. A group has a universal local limit theorem if all random walks on the group with finitely supported step distributions obey a local limit theorem with the same power law exponent. Given two groups that obey universal local limit theorems, it is not known whether their cartesian product also has a universal local limit theorem. We settle the question affirmatively in one case, by considering a random walk on the cartesian product of a nonamenable group whose Cayley graph is a tree, and the integer lattice. As corollaries, we derive large deviations estimates and a central limit theorem.

An exact formulation of the time-ordered exponential using path-sums

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giscard, P.-L., E-mail: p.giscard1@physics.ox.ac.uk; Lui, K.; Thwaite, S. J.

2015-05-15

We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitudemore » of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.« less

Exact Results for the Nonergodicity of d -Dimensional Generalized Lévy Walks

NASA Astrophysics Data System (ADS)

Albers, Tony; Radons, Günter

2018-03-01

We provide analytical results for the ensemble-averaged and time-averaged squared displacement, and the randomness of the latter, in the full two-dimensional parameter space of the d -dimensional generalized Lévy walk introduced by Shlesinger et al. [Phys. Rev. Lett. 58, 1100 (1987), 10.1103/PhysRevLett.58.1100]. In certain regions of the parameter plane, we obtain surprising results such as the divergence of the mean-squared displacements, the divergence of the ergodicity breaking parameter despite a finite mean-squared displacement, and subdiffusion which appears superdiffusive when one only considers time averages.

Combining motivational and volitional strategies to promote unsupervised walking in patients with fibromyalgia: study protocol for a randomized controlled trial.

PubMed

Pastor, María-Ángeles; López-Roig, Sofía; Lledó, Ana; Peñacoba, Cecilia; Velasco, Lilian; Schweiger-Gallo, Inge; Cigarán, Margarita; Ecija, Carmen; Limón, Ramón; Sanz, Yolanda

2014-04-11

Fibromyalgia patients are often advised to engage in regular low- to moderate-intensity physical exercise. The need of fibromyalgia patients to walk has been stressed in previous research. Behavioral self-regulation theories suggest that a combination of motivational aspects (to develop or strengthen a behavioral intention: Theory of Planned Behavior) and volitional aspects (engagement of intention in behavior: implementation intentions) is more effective than a single intervention. In this paper, we describe a protocol for identifying the motivational processes (using the Theory of Planned Behavior) involved in the practice of walking (phase I) and for studying the efficacy of an intervention that combines motivational and volitional contents to enhance the acquisition and continuation of this exercise behavior (phase II). The paper also shows the characteristics of eligible individuals (women who do not walk) and ineligible populations (women who walk or do not walk because of comorbidity without medical recommendation to walk). Both groups consist of members of any of four patients' associations in Spain who are between 18 and 70 years of age and meet the London Fibromyalgia Epidemiology Study Screening Questionnaire criteria for fibromyalgia. Furthermore, using this study protocol, we will explore the characteristics of participants (eligible women who agreed to participate in the study) and nonparticipants (eligible women who refused to participate). Two studies will be conducted: Phase I will be a cross-sectional study, and phase II will be a triple-blind, randomized longitudinal study with two treatment groups and one active control group. The questionnaires were sent to a total of 2,227 members of four patients' associations in Spain. A total of 920 participants with fibromyalgia returned the questionnaires, and 582 were ultimately selected to participate. The first data gathered have allowed us to identify the characteristics of the study population and they support the appropriateness of the inclusion criteria.. When the study is complete, the results will enable us to establish whether this kind of intervention can be used as a self-regulation tool for increasing and maintaining walking as unsupervised physical exercise of low to moderate intensity in fibromyalgia patients. ISRCTN68584893.

Dancing for Parkinson Disease: A Randomized Trial of Irish Set Dancing Compared With Usual Care.

PubMed

Shanahan, Joanne; Morris, Meg E; Bhriain, Orfhlaith Ni; Volpe, Daniele; Lynch, Tim; Clifford, Amanda M

2017-09-01

To examine the feasibility of a randomized controlled study design and to explore the benefits of a set dancing intervention compared with usual care. Randomized controlled design, with participants randomized to Irish set dance classes or a usual care group. Community based. Individuals with idiopathic Parkinson disease (PD) (N=90). The dance group attended a 1.5-hour dancing class each week for 10 weeks and undertook a home dance program for 20 minutes, 3 times per week. The usual care group continued with their usual care and daily activities. The primary outcome was feasibility, determined by recruitment rates, success of randomization and allocation procedures, attrition, adherence, safety, willingness of participants to be randomized, resource availability, and cost. Secondary outcomes were motor function (motor section of the Unified Parkinson's Disease Rating Scale), quality of life (Parkinson's Disease Questionnaire-39), functional endurance (6-min walk test), and balance (mini-BESTest). Ninety participants were randomized (45 per group). There were no adverse effects or resource constraints. Although adherence to the dancing program was 93.5%, there was >40% attrition in each group. Postintervention, the dance group had greater nonsignificant gains in quality of life than the usual care group. There was a meaningful deterioration in endurance in the usual care group. There were no meaningful changes in other outcomes. The exit questionnaire showed participants enjoyed the classes and would like to continue participation. For people with mild to moderately severe PD, set dancing is feasible and enjoyable and may improve quality of life. Copyright © 2016 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

A randomized study of reinforcing ambulatory exercise in older adults

PubMed Central

Petry, Nancy M.; Andrade, Leonardo F.; Barry, Danielle; Byrne, Shannon

2014-01-01

Many older adults do not meet physical activity recommendations and suffer from health-related complications. Reinforcement interventions can have pronounced effects on promoting behavior change; this study evaluated the efficacy of a reinforcement intervention to enhance walking in older adults. Forty-five sedentary adults with mild to moderate hypertension were randomized to 12-week interventions consisting of pedometers and guidelines to walk 10,000 steps/day or that same intervention with chances to win $1-$100 prizes for meeting recommendations. Patients walked an average of about 4,000 steps/day at baseline. Throughout the intervention, participants in the reinforcement intervention met walking goals on 82.5% ± 25.8% of days versus 55.3% ± 37.1% of days in the control condition, p < .01. Even though steps walked increased significantly in both groups relative to baseline, participants in the reinforcement condition walked an average of about 2,000 more steps/day than participants in the control condition, p < .02. Beneficial effects of the reinforcement condition relative to the control condition persisted at a 24-week follow-up evaluation, p < .02, although steps/day were lower than during the intervention period in both groups. Participants in the reinforcement intervention also evidenced greater reductions in blood pressure and weight over time and improvements in fitness indices, ps < .05. This reinforcement-based intervention substantially increased walking and improved clinical parameters, suggesting that larger-scale evaluations of reinforcement-based interventions for enhancing active lifestyles in older adults are warranted. Ultimately, economic analyses may reveal reinforcement interventions to be cost-effective, especially in high-risk populations of older adults. PMID:24128075

Refining Time-Activity Classification of Human Subjects Using the Global Positioning System.

PubMed

Hu, Maogui; Li, Wei; Li, Lianfa; Houston, Douglas; Wu, Jun

2016-01-01

Detailed spatial location information is important in accurately estimating personal exposure to air pollution. Global Position System (GPS) has been widely used in tracking personal paths and activities. Previous researchers have developed time-activity classification models based on GPS data, most of them were developed for specific regions. An adaptive model for time-location classification can be widely applied to air pollution studies that use GPS to track individual level time-activity patterns. Time-activity data were collected for seven days using GPS loggers and accelerometers from thirteen adult participants from Southern California under free living conditions. We developed an automated model based on random forests to classify major time-activity patterns (i.e. indoor, outdoor-static, outdoor-walking, and in-vehicle travel). Sensitivity analysis was conducted to examine the contribution of the accelerometer data and the supplemental spatial data (i.e. roadway and tax parcel data) to the accuracy of time-activity classification. Our model was evaluated using both leave-one-fold-out and leave-one-subject-out methods. Maximum speeds in averaging time intervals of 7 and 5 minutes, and distance to primary highways with limited access were found to be the three most important variables in the classification model. Leave-one-fold-out cross-validation showed an overall accuracy of 99.71%. Sensitivities varied from 84.62% (outdoor walking) to 99.90% (indoor). Specificities varied from 96.33% (indoor) to 99.98% (outdoor static). The exclusion of accelerometer and ambient light sensor variables caused a slight loss in sensitivity for outdoor walking, but little loss in overall accuracy. However, leave-one-subject-out cross-validation showed considerable loss in sensitivity for outdoor static and outdoor walking conditions. The random forests classification model can achieve high accuracy for the four major time-activity categories. The model also performed well with just GPS, road and tax parcel data. However, caution is warranted when generalizing the model developed from a small number of subjects to other populations.

Walking and Hiking as a Way of Life

ERIC Educational Resources Information Center

Roberson, Donald N., Jr.; Babic, Vesna

2008-01-01

Exercise usually takes place in leisure time. The benefits, mental and physical, of exercise are well documented, yet, many choose to remain inactive. There is a need for more research concerning those who continue to exercise. The purpose of this study was to understand more about the experience of those who are hiking and walking on Medvednica…

Effect of Granulocyte-Macrophage Colony-Stimulating Factor With or Without Supervised Exercise on Walking Performance in Patients With Peripheral Artery Disease

PubMed Central

Ferrucci, Luigi; Tian, Lu; Guralnik, Jack M.; Lloyd-Jones, Donald; Kibbe, Melina R.; Polonsky, Tamar S.; Domanchuk, Kathryn; Stein, James H.; Zhao, Lihui; Taylor, Doris; Skelly, Christopher; Pearce, William; Perlman, Harris; McCarthy, Walter; Li, Lingyu; Gao, Ying; Sufit, Robert; Bloomfield, Christina L.; Criqui, Michael H.

2017-01-01

Importance Benefits of granulocyte-macrophage colony-stimulating factor (GM-CSF) for improving walking ability in people with lower extremity peripheral artery disease (PAD) are unclear. Walking exercise may augment the effects of GM-CSF in PAD, since exercise-induced ischemia enhances progenitor cell release and may promote progenitor cell homing to ischemic calf muscle. Objectives To determine whether GM-CSF combined with supervised treadmill exercise improves 6-minute walk distance, compared with exercise alone and compared with GM-CSF alone; to determine whether GM-CSF alone improves 6-minute walk more than placebo and whether exercise improves 6-minute walk more than an attention control intervention. Design, Setting, and Participants Randomized clinical trial with 2 × 2 factorial design. Participants were identified from the Chicago metropolitan area and randomized between January 6, 2012, and December 22, 2016, to 1 of 4 groups: supervised exercise + GM-CSF (exercise + GM-CSF) (n = 53), supervised exercise + placebo (exercise alone) (n = 53), attention control  + GM-CSF (GM-CSF alone) (n = 53), attention control + placebo (n = 51). The final follow-up visit was on August 15, 2017. Interventions Supervised exercise consisted of treadmill exercise 3 times weekly for 6 months. The attention control consisted of weekly educational lectures by clinicians for 6 months. GM-CSF (250 μg/m2/d) or placebo were administered subcutaneously (double-blinded) 3 times/wk for the first 2 weeks of the intervention. Main Outcomes and Measures The primary outcome was change in 6-minute walk distance at 12-week follow-up (minimum clinically important difference, 20 m). P values were adjusted based on the Hochberg step-up method. Results Of 827 persons evaluated, 210 participants with PAD were randomized (mean age, 67.0 [SD, 8.6] years; 141 [67%] black, 82 [39%] women). One hundred ninety-five (93%) completed 12-week follow-up. At 12-week follow-up, exercise + GM-CSF did not significantly improve 6-minute walk distance more than exercise alone (mean difference, −6.3 m [95% CI, −30.2 to +17.6]; P = .61) or more than GM-CSF alone (mean difference, +28.7 m [95% CI, +5.1 to +52.3]; Hochberg-adjusted P = .052). GM-CSF alone did not improve 6-minute walk more than attention control + placebo (mean difference, −1.4 m [95% CI, −25.2 to +22.4]; P = .91). Exercise alone improved 6-minute walk compared with attention control + placebo (mean difference, +33.6 m [95% CI, +9.4 to +57.7]; Hochberg-adjusted P = .02). Conclusions and Relevance Among patients with PAD, supervised treadmill exercise significantly improved 6-minute walk distance compared with attention control + placebo, whereas GM-CSF did not significantly improve walking performance, either when used alone or when combined with supervised treadmill exercise. These results confirm the benefits of exercise but do not support using GM-CSF to treat walking impairment in patients with PAD. Trial Registration clinicaltrials.gov Identifier: NCT01408901 PMID:29141087

Ergodicity convergence test suggests telomere motion obeys fractional dynamics

NASA Astrophysics Data System (ADS)

Kepten, E.; Bronshtein, I.; Garini, Y.

2011-04-01

Anomalous diffusion, observed in many biological processes, is a generalized description of a wide variety of processes, all obeying the same law of mean-square displacement. Identifying the basic mechanisms of these observations is important for deducing the nature of the biophysical systems measured. We implement a previously suggested method for distinguishing between fractional Langevin dynamics, fractional Brownian motion, and continuous time random walk based on the ergodic nature of the data. We apply the method together with the recently suggested P-variation test and the displacement correlation to the lately measured dynamics of telomeres in the nucleus of mammalian cells and find strong evidence that the telomeres motion obeys fractional dynamics. The ergodic dynamics are observed experimentally to fit fractional Brownian or Langevin dynamics.

A comparative analysis of pedometry in measuring physical activity of children.

PubMed

Scruggs, Philip W

2007-10-01

The purpose of this study was to examine the step and physical activity time output features of the Walk4Life LS2505 pedometer under field physical activity conditions. Data were collected on 288 (12.62 +/- 1.23 yr) participants during a school-based structured physical activity program. Participants' physical activity levels were concurrently measured via the Yamax SW701 (Yamax Corp., Japan) and Walk4Life LS2505 (Walk4Life Inc., Plainfield, IL) pedometers, and System for Observing Fitness Instruction Time (SOFIT) physical activity coding mechanism. Relative and absolute agreement between SW701 (criterion) and LS2505 steps per minute, and SOFIT (criterion) and LS2505 physical activity time (min) were analyzed overall, and across physical activity content themes and physical activity quartiles. Physical activity measure correlations were moderately strong to strong (r = 0.85-0.98, P < 0.05); however, the LS2505 significantly underestimated steps per minute (M(diff) = 6.37 +/- 5.79, P < 0.05) and overestimated physical activity time (M(diff) = -7.73 +/- 3.13, P < 0.05). When LS2505 steps per minute were examined across physical activity themes and quartiles, clinically acceptable absolute error scores (

Total Knee Arthroplasty for Knee Osteoarthritis: Support for a Foregone Conclusion?

PubMed

Steinhaus, Michael E; Christ, Alexander B; Cross, Michael B

2017-07-01

Total knee arthroplasty (TKA) is generally accepted as the definitive treatment for advanced knee arthritis after patients fail nonoperative treatments; however, the safety and efficacy of TKA compared to continued nonoperative treatment has never been proven in high-quality, randomized controlled trials. Recently, a 2015 Danish study published a 12-month follow-up on a cohort of patients randomized to either a TKA or continued nonsurgical management for advanced knee osteoarthritis (OA). The authors reported significantly greater improvement in the TKA group in functional outcome scores such as the overall Knee Injury and Osteoarthritis Outcome Score (KOOS 4 score), the KOOS subscales, EQ-5D descriptive index, and timed get up-and-go and 20-m walk tests; however, patients in the TKA did suffer significantly more serious adverse events (SAE). The authors concluded that TKA combined with additional nonoperative care postoperatively is more efficacious than nonsurgical treatment alone in terms of improving pain, function, and quality of life at 12 months but is associated with more SAE. The purpose of this review is to identify the strengths and weaknesses of this trial, interpret its outcomes within the context of prior literature, and evaluate the validity of its conclusions.

Stochastic models for atomic clocks

NASA Technical Reports Server (NTRS)

Barnes, J. A.; Jones, R. H.; Tryon, P. V.; Allan, D. W.

1983-01-01

For the atomic clocks used in the National Bureau of Standards Time Scales, an adequate model is the superposition of white FM, random walk FM, and linear frequency drift for times longer than about one minute. The model was tested on several clocks using maximum likelihood techniques for parameter estimation and the residuals were acceptably random. Conventional diagnostics indicate that additional model elements contribute no significant improvement to the model even at the expense of the added model complexity.

A Rout to Protect Quantum Gates constructed via quantum walks from Noises.

PubMed

Du, Yi-Mu; Lu, Li-Hua; Li, You-Quan

2018-05-08

The continuous-time quantum walk on a one-dimensional graph of odd number of sites with an on-site potential at the center is studied. We show that such a quantum-walk system can construct an X-gate of a single qubit as well as a control gate for two qubits, when the potential is much larger than the hopping strength. We investigate the decoherence effect and find that the coherence time can be enhanced by either increasing the number of sites on the graph or the ratio of the potential to the hopping strength, which is expected to motivate the design of the quantum gate with long coherence time. We also suggest several experimental proposals to realize such a system.

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2018-03-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2}). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3}) and the level sets of the Gaussian free field ({d≥ 3}). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2017-12-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2} ). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3} ) and the level sets of the Gaussian free field ({d≥ 3} ). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

Impact of degree heterogeneity on the behavior of trapping in Koch networks

NASA Astrophysics Data System (ADS)

Zhang, Zhongzhi; Gao, Shuyang; Xie, Wenlei

2010-12-01

Previous work shows that the mean first-passage time (MFPT) for random walks to a given hub node (node with maximum degree) in uncorrelated random scale-free networks is closely related to the exponent γ of power-law degree distribution P(k )˜k-γ, which describes the extent of heterogeneity of scale-free network structure. However, extensive empirical research indicates that real networked systems also display ubiquitous degree correlations. In this paper, we address the trapping issue on the Koch networks, which is a special random walk with one trap fixed at a hub node. The Koch networks are power-law with the characteristic exponent γ in the range between 2 and 3, they are either assortative or disassortative. We calculate exactly the MFPT that is the average of first-passage time from all other nodes to the trap. The obtained explicit solution shows that in large networks the MFPT varies lineally with node number N, which is obviously independent of γ and is sharp contrast to the scaling behavior of MFPT observed for uncorrelated random scale-free networks, where γ influences qualitatively the MFPT of trapping problem.

A random-walk/giant-loop model for interphase chromosomes.

PubMed Central

Sachs, R K; van den Engh, G; Trask, B; Yokota, H; Hearst, J E

1995-01-01

Fluorescence in situ hybridization data on distances between defined genomic sequences are used to construct a quantitative model for the overall geometric structure of a human chromosome. We suggest that the large-scale geometry during the G0/G1 part of the cell cycle may consist of flexible chromatin loops, averaging approximately 3 million bp, with a random-walk backbone. A fully explicit, three-parametric polymer model of this random-walk/giant-loop structure can account well for the data. More general models consistent with the data are briefly discussed. PMID:7708711

Response-Time Tests of Logical-Rule Models of Categorization

ERIC Educational Resources Information Center

Little, Daniel R.; Nosofsky, Robert M.; Denton, Stephen E.

2011-01-01

A recent resurgence in logical-rule theories of categorization has motivated the development of a class of models that predict not only choice probabilities but also categorization response times (RTs; Fific, Little, & Nosofsky, 2010). The new models combine mental-architecture and random-walk approaches within an integrated framework and…

Optimal switching between geocentric and egocentric strategies in navigation

PubMed Central

Mahadevan, L.

2016-01-01

Animals use a combination of egocentric navigation driven by the internal integration of environmental cues, interspersed with geocentric course correction and reorientation. These processes are accompanied by uncertainty in sensory acquisition of information, planning and execution. Inspired by observations of dung beetle navigational strategies that show switching between geocentric and egocentric strategies, we consider the question of optimal reorientation rates for the navigation of an agent moving along a preferred direction in the presence of multiple sources of noise. We address this using a model that takes the form of a correlated random walk at short time scales that is punctuated by reorientation events leading to a biased random walks at long time scales. This allows us to identify optimal alternation schemes and characterize their robustness in the context of noisy sensory acquisition as well as performance errors linked with variations in environmental conditions and agent–environment interactions. PMID:27493769

On the simple random-walk models of ion-channel gate dynamics reflecting long-term memory.

PubMed

Wawrzkiewicz, Agata; Pawelek, Krzysztof; Borys, Przemyslaw; Dworakowska, Beata; Grzywna, Zbigniew J

2012-06-01

Several approaches to ion-channel gating modelling have been proposed. Although many models describe the dwell-time distributions correctly, they are incapable of predicting and explaining the long-term correlations between the lengths of adjacent openings and closings of a channel. In this paper we propose two simple random-walk models of the gating dynamics of voltage and Ca(2+)-activated potassium channels which qualitatively reproduce the dwell-time distributions, and describe the experimentally observed long-term memory quite well. Biological interpretation of both models is presented. In particular, the origin of the correlations is associated with fluctuations of channel mass density. The long-term memory effect, as measured by Hurst R/S analysis of experimental single-channel patch-clamp recordings, is close to the behaviour predicted by our models. The flexibility of the models enables their use as templates for other types of ion channel.

Calf Muscle Oxygen Saturation During Six-Minute Walk Test And Its Relationship With Walking Impairment In Symptomatic Peripheral Artery Disease.

PubMed

Andrade-Lima, Aluísio; Cucato, Gabriel G; Domingues, Wagner J R; Germano-Soares, Antônio H; Cavalcante, Bruno R; Correia, Marilia A; Saes, Glauco F; Wolosker, Nelson; Gardner, Andrew W; Zerati, Antônio E; Ritti-Dias, Raphael M

2018-05-21

Impaired microcirculation is associated with poor walking capacity in symptomatic peripheral artery disease (PAD) patients during treadmill test, however, this test does not simulate the efforts of daily walking of these patients. Thus, the aim of the study was to describe the microcirculation responses during six-minute walk test (6MWT) and to analyze the relationship between microcirculation indicators and walking impairment in symptomatic PAD patients. Thirty-four patients were included (mean age = 67.6 ± 11.2). The clinical characteristics were collected and they performed a 6MWT in which initial claudication distance (ICD) and total walking distance (TWD) were recorded. During and after the 6MWT, calf muscle oxygen saturation (StO 2 ) parameters were monitored continuously to measure microcirculation behavior. The association between calf muscle StO 2 parameters and walking impairment was analyzed by Pearson or Spearman correlations. Walking impairment was not associated with any StO 2 parameters during exercise. In contrast, after 6MWT, recovery time of StO 2 (r = -0.472, P = .008) and recovery time to maximal StO 2 (r= -0.402, P = .019) were negatively correlated with ICD. Furthermore, the distance walked under claudication symptoms (ΔTWD - ICD) was positively correlated with recovery time to maximal StO 2 (r = 0.347, P = .048). In symptomatic PAD patients, shorter ICD values during a 6MWT are associated with a delayed recovery in calf muscle StO 2 after exercise. Calf muscle StO 2 parameters decrease subtly during 6MWT, suggesting that the degree of ischemia in the calf muscle during ground walking, simulating efforts of the daily walking, is relatively low. Copyright © 2018 Elsevier Inc. All rights reserved.

Combining Fast-Walking Training and a Step Activity Monitoring Program to Improve Daily Walking Activity After Stroke: A Preliminary Study.

PubMed

Danks, Kelly A; Pohlig, Ryan; Reisman, Darcy S

2016-09-01

To determine preliminary efficacy and to identify baseline characteristics predicting who would benefit most from fast walking training plus a step activity monitoring program (FAST+SAM) compared with fast walking training (FAST) alone in persons with chronic stroke. Randomized controlled trial with blinded assessors. Outpatient clinical research laboratory. Individuals (N=37) >6 months poststroke. Subjects were assigned to either FAST, which was walking training at their fastest possible speed on the treadmill (30min) and overground 3 times per week for 12 weeks, or FAST+SAM. The step activity monitoring program consisted of daily step monitoring with an activity monitor, goal setting, and identification of barriers to activity and strategies to overcome barriers. Daily step activity metrics (steps/day [SPD], time walking per day), walking speed, and 6-minute walk test (6MWT) distance. There was a significant effect of time for both groups, with all outcomes improving from pre- to posttraining (all P values <.05). The FAST+SAM was superior to FAST for 6MWT (P=.018), with a larger increase in the FAST+SAM group. The interventions had differential effectiveness based on baseline step activity. Sequential moderated regression models demonstrated that for subjects with baseline levels of step activity and 6MWT distances that were below the mean, the FAST+SAM intervention was more effective than FAST (1715±1584 vs 254±933 SPD; P<.05 for overall model and ΔR(2) for SPD and 6MWT). The addition of a step activity monitoring program to a fast walking training intervention may be most effective in persons with chronic stroke who have initial low levels of walking endurance and activity. Regardless of baseline performance, the FAST+SAM intervention was more effective for improving walking endurance. Copyright © 2016 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

Combining fast walking training and a step activity monitoring program to improve daily walking activity after stroke: a preliminary study

PubMed Central

Danks, Kelly A.; Pohlig, Ryan; Reisman, Darcy S.

2016-01-01

Objective To determine preliminary efficacy and to identify baseline characteristics predicting who would benefit most from fast walking training plus a step activity monitoring program (FAST+SAM) compared to fast walking training alone (FAST) in persons with chronic stroke. Design Randomized controlled trial with blinded assessors Setting Outpatient clinical research laboratory Participants 37 individuals greater than 6 months post-stroke. Interventions Subjects were assigned to either FAST which was walking training at their fastest possible speed on the treadmill (30 minutes) and over ground 3 times/week for 12 weeks or FAST plus a step activity monitoring program (FAST+SAM). The step activity monitoring program consisted of daily step monitoring with a StepWatch Activity monitor, goal setting, and identification of barriers to activity and strategies to overcome barriers. Main Outcome Measures Daily step activity metrics (steps/day, time walking/day), walking speed and six minute walk test distance (6MWT). Results There was a significant effect of time for both groups with all outcomes improving from pre to post-training, (all p<0.05). The FAST+SAM was superior to FAST for 6MWT (p=0.018), with a larger increase in the FAST+SAM group. The interventions had differential effectiveness based on baseline step activity. Sequential moderated regression models demonstrated that for subjects with baseline levels of step activity and 6MWT distances that were below the mean, the FAST+SAM intervention was more effective than FAST (1715±1584 vs. 254±933 steps/day, respectively; p<0.05 for overall model and ΔR2 for steps/day and 6MWT). Conclusions The addition of a step activity monitoring program to a fast walking training intervention may be most effective in persons with chronic stroke that have initial low levels of walking endurance and activity. Regardless of baseline performance, the FAST + SAM intervention was more effective for improving walking endurance. PMID:27240430

Effects of an 8-Week Outdoor Brisk Walking Program on Fatigue in Hi-Tech Industry Employees: A Randomized Control Trial.

PubMed

Wu, Li-Ling; Wang, Kuo-Ming; Liao, Po-I; Kao, Yu-Hsiu; Huang, Yi-Ching

2015-10-01

Over 73% of hi-tech industry employees in Taiwan lack regular exercise. They are exposed to a highly variable and stressful work environment for extended periods of time, and may subsequently experience depression, detrimental to workers' physiological and mental health. In this cross-sectional survey, the authors explored the effect of an 8-week brisk walking program on the fatigue of employees in the hi-tech industry. The participants, from a hi-tech company in northern Taiwan, were randomly assigned to an experimental group (EG; 41 subjects, Mage = 33.34 ± 6.40) or control group (CG; 45 subjects, Mage = 29.40 ± 3.60). Following the 8-week brisk walking program, the EG showed significantly lower scores for subjective fatigue, working motivation, attention, and overall fatigue. The authors confirmed that the 8-week outdoor brisk walking program significantly improved the level of fatigue among employees of the hi-tech industry. The finding serves as an important reference for health authorities in Taiwan and provides awareness of workplace health promotion in the hi-tech industry. © 2015 The Author(s).

The Walking School Bus and children's physical activity: A pilot cluster randomized controlled trial

USDA-ARS?s Scientific Manuscript database

To evaluate the impact of a "walking school bus" program on children's rates of active commuting to school and physical activity. We conducted a pilot cluster randomized controlled trial among 4th-graders from 8 schools in Houston, Texas (N = 149). Random allocation to treatment or control condition...

A stochastic approach for quantifying immigrant integration: the Spanish test case

NASA Astrophysics Data System (ADS)

Agliari, Elena; Barra, Adriano; Contucci, Pierluigi; Sandell, Richard; Vernia, Cecilia

2014-10-01

We apply stochastic process theory to the analysis of immigrant integration. Using a unique and detailed data set from Spain, we study the relationship between local immigrant density and two social and two economic immigration quantifiers for the period 1999-2010. As opposed to the classic time-series approach, by letting immigrant density play the role of ‘time’ and the quantifier the role of ‘space,’ it becomes possible to analyse the behavior of the quantifiers by means of continuous time random walks. Two classes of results are then obtained. First, we show that social integration quantifiers evolve following diffusion law, while the evolution of economic quantifiers exhibits ballistic dynamics. Second, we make predictions of best- and worst-case scenarios taking into account large local fluctuations. Our stochastic process approach to integration lends itself to interesting forecasting scenarios which, in the hands of policy makers, have the potential to improve political responses to integration problems. For instance, estimating the standard first-passage time and maximum-span walk reveals local differences in integration performance for different immigration scenarios. Thus, by recognizing the importance of local fluctuations around national means, this research constitutes an important tool to assess the impact of immigration phenomena on municipal budgets and to set up solid multi-ethnic plans at the municipal level as immigration pressures build.

Branching random walk with step size coming from a power law

NASA Astrophysics Data System (ADS)

Bhattacharya, Ayan; Subhra Hazra, Rajat; Roy, Parthanil

2015-09-01

In their seminal work, Brunet and Derrida made predictions on the random point configurations associated with branching random walks. We shall discuss the limiting behavior of such point configurations when the displacement random variables come from a power law. In particular, we establish that two prediction of remains valid in this setup and investigate various other issues mentioned in their paper.

Random Interchange of Magnetic Connectivity

NASA Astrophysics Data System (ADS)

Matthaeus, W. H.; Ruffolo, D. J.; Servidio, S.; Wan, M.; Rappazzo, A. F.

2015-12-01

Magnetic connectivity, the connection between two points along a magnetic field line, has a stochastic character associated with field lines random walking in space due to magnetic fluctuations, but connectivity can also change in time due to dynamical activity [1]. For fluctuations transverse to a strong mean field, this connectivity change be caused by stochastic interchange due to component reconnection. The process may be understood approximately by formulating a diffusion-like Fokker-Planck coefficient [2] that is asymptotically related to standard field line random walk. Quantitative estimates are provided, for transverse magnetic field models and anisotropic models such as reduced magnetohydrodynamics. In heliospheric applications, these estimates may be useful for understanding mixing between open and close field line regions near coronal hole boundaries, and large latitude excursions of connectivity associated with turbulence. [1] A. F. Rappazzo, W. H. Matthaeus, D. Ruffolo, S. Servidio & M. Velli, ApJL, 758, L14 (2012) [2] D. Ruffolo & W. Matthaeus, ApJ, 806, 233 (2015)

Directional Bias and Pheromone for Discovery and Coverage on Networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fink, Glenn A.; Berenhaut, Kenneth S.; Oehmen, Christopher S.

2012-09-11

Natural multi-agent systems often rely on “correlated random walks” (random walks that are biased toward a current heading) to distribute their agents over a space (e.g., for foraging, search, etc.). Our contribution involves creation of a new movement and pheromone model that applies the concept of heading bias in random walks to a multi-agent, digital-ants system designed for cyber-security monitoring. We examine the relative performance effects of both pheromone and heading bias on speed of discovery of a target and search-area coverage in a two-dimensional network layout. We found that heading bias was unexpectedly helpful in reducing search time andmore » that it was more influential than pheromone for improving coverage. We conclude that while pheromone is very important for rapid discovery, heading bias can also greatly improve both performance metrics.« less

Random walk in nonhomogeneous environments: A possible approach to human and animal mobility

NASA Astrophysics Data System (ADS)

Srokowski, Tomasz

2017-03-01

The random walk process in a nonhomogeneous medium, characterized by a Lévy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is affected by the variable width and the variance may be finite; then all kinds of the anomalous diffusion are predicted. In the former case, only the time characteristics are sensitive to the variable width. The corresponding Langevin equation with different interpretations of the multiplicative noise is discussed. The dependence of the distribution width on position after jump is interpreted in terms of cognitive abilities and related to such problems as migration in a human population and foraging habits of animals.

Quantum Walks on the Line with Phase Parameters

NASA Astrophysics Data System (ADS)

Villagra, Marcos; Nakanishi, Masaki; Yamashita, Shigeru; Nakashima, Yasuhiko

In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step toward this objective, the following question is being addressed: Given a graph, what is the probability that a quantum walk arrives at a given vertex after some number of steps? This is a very natural question, and for random walks it can be answered by several different combinatorial arguments. For quantum walks this is a highly non-trivial task. Furthermore, this was only achieved before for one specific coin operator (Hadamard operator) for walks on the line. Even considering only walks on lines, generalizing these computations to a general SU(2) coin operator is a complex task. The main contribution is a closed-form formula for the amplitudes of the state of the walk (which includes the question above) for a general symmetric SU(2) operator for walks on the line. To this end, a coin operator with parameters that alters the phase of the state of the walk is defined. Then, closed-form solutions are computed by means of Fourier analysis and asymptotic approximation methods. We also present some basic properties of the walk which can be deducted using weak convergence theorems for quantum walks. In particular, the support of the induced probability distribution of the walk is calculated. Then, it is shown how changing the parameters in the coin operator affects the resulting probability distribution.

Spatial Variability of Organic Carbon in a Fractured Mudstone and Its Effect on the Retention and Release of Trichloroethene (TCE)

NASA Astrophysics Data System (ADS)

Sole-Mari, G.; Fernandez-Garcia, D.

2016-12-01

Random Walk Particle Tracking (RWPT) coupled with Kernel Density Estimation (KDE) has been recently proposed to simulate reactive transport in porous media. KDE provides an optimal estimation of the area of influence of particles which is a key element to simulate nonlinear chemical reactions. However, several important drawbacks can be identified: (1) the optimal KDE method is computationally intensive and thereby cannot be used at each time step of the simulation; (2) it does not take advantage of the prior information about the physical system and the previous history of the solute plume; (3) even if the kernel is optimal, the relative error in RWPT simulations typically increases over time as the particle density diminishes by dilution. To overcome these problems, we propose an adaptive branching random walk methodology that incorporates the physics, the particle history and maintains accuracy with time. The method allows particles to efficiently split and merge when necessary as well as to optimally adapt their local kernel shape without having to recalculate the kernel size. We illustrate the advantage of the method by simulating complex reactive transport problems in randomly heterogeneous porous media.

Energy distributions and radiation transport in uranium plasmas

NASA Technical Reports Server (NTRS)

Miley, G. H.; Bathke, C.; Maceda, E.; Choi, C.

1976-01-01

An approximate analytic model, based on continuous electron slowing, has been used for survey calculations. Where more accuracy is required, a Monte Carlo technique is used which combines an analytic representation of Coulombic collisions with a random walk treatment of inelastic collisions. The calculated electron distributions have been incorporated into another code that evaluates both the excited atomic state densities within the plasma and the radiative flux emitted from the plasma.

Acute effects of walking with Nordic poles in persons with mild to moderate low-back pain.

PubMed

Revord, Landon P; Lomond, Karen V; Loubert, Peter V; Hammer, Roger L

2016-01-01

Regular walking with or without Nordic poles is effective over time at reducing discomfort in individuals with chronic low back pain (LBP). Nordic pole use increases balance and stability, distributes weight through the arms and torso, and decreases loading of the spine and lower limbs. The purpose of this study was to determine if Nordic poles would reduce perceived acute discomfort while self-paced walking in individuals with LBP. We also examined whether walking with or without poles increased heart rate (HR) and ratings of perceived exertion (RPE) or speed of movement. Subjects included 20 adults (12 males, 8 females; mean age of 45.1±16.3) who were experiencing LBP of at least six months' duration (Oswestry Disability Index (ODI): mean 17 ± 8%, range 6-36% indicating minimal to moderate disability) with no current active flare-up. Participants walked a predetermined dirt-path course (805 m or 0.5 mi) with and without poles in randomized order. Data were analyzed using a 2 X 2 repeated measures ANOVA (Condition X Time), where Condition was poles vs no poles and Time was pre- and post-walk. HR and RPE increased significantly from walking the course, whereas pain did not change. There were also no differences between walking with or without poles for pain (ODI Sec #1: 0.2 points, p=0.324), HR (4 bpm, p=0.522) and RPE (0 points, p=0.759). The mean course time (sec) was slower with poles: 617±87 vs 566±65 (p<0.001). Unexpectedly, there was a noticeable drop in pain following the warm up which was done using poles (0.9 points, p<0.001). Nordic pole use is well tolerated in those with current back pain and can be encouraged, however it cannot be recommended as a superior method of addressing acute symptoms when walking.

Swimming Improves Pain and Functional Capacity of Patients With Fibromyalgia: A Randomized Controlled Trial.

PubMed

Fernandes, Giovana; Jennings, Fabio; Nery Cabral, Michele Vieira; Pirozzi Buosi, Ana Letícia; Natour, Jamil

2016-08-01

To evaluate the effect of swimming on pain, functional capacity, aerobic capacity, and quality of life in patients with fibromyalgia (FM). Randomized controlled trial. Rheumatology outpatient clinics of a university hospital. Women with FM (N=75; age range, 18-60y) randomly assigned to a swimming group (SG) (n=39) or a walking group (WG) (n=36). The SG performed 50 minutes of swimming 3 times a week for 12 weeks, with a heart rate at 11 beats under the anaerobic threshold. The WG performed walking with a heart rate at the anaerobic threshold, with the same duration and frequency as the SG. Participants were evaluated before the exercise protocols (t0), at 6 weeks (t6), and at 12 weeks (t12) after the onset of the protocols. The primary outcome measure was the visual analog scale for pain. The secondary measurements were the Fibromyalgia Impact Questionnaire and the Medical Outcomes Study 36-Item Short-Form Health Survey for quality of life; a spiroergometric test for cardiorespiratory variables; and the timed Up & Go test for functional performance. Patients in both groups experienced improvement in pain after the 12-week program, with no difference between groups (P=.658). The same results were found regarding functional capacity and quality of life. Moreover, no statistical difference between groups was found regarding aerobic capacity over time. Swimming, like walking, is an effective method for reducing pain and improving both functional capacity and quality of life in patients with FM. Copyright © 2016 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

Efficiency analysis of diffusion on T-fractals in the sense of random walks.

PubMed

Peng, Junhao; Xu, Guoai

2014-04-07

Efficiently controlling the diffusion process is crucial in the study of diffusion problem in complex systems. In the sense of random walks with a single trap, mean trapping time (MTT) and mean diffusing time (MDT) are good measures of trapping efficiency and diffusion efficiency, respectively. They both vary with the location of the node. In this paper, we analyze the effects of node's location on trapping efficiency and diffusion efficiency of T-fractals measured by MTT and MDT. First, we provide methods to calculate the MTT for any target node and the MDT for any source node of T-fractals. The methods can also be used to calculate the mean first-passage time between any pair of nodes. Then, using the MTT and the MDT as the measure of trapping efficiency and diffusion efficiency, respectively, we compare the trapping efficiency and diffusion efficiency among all nodes of T-fractal and find the best (or worst) trapping sites and the best (or worst) diffusing sites. Our results show that the hub node of T-fractal is the best trapping site, but it is also the worst diffusing site; and that the three boundary nodes are the worst trapping sites, but they are also the best diffusing sites. Comparing the maximum of MTT and MDT with their minimums, we find that the maximum of MTT is almost 6 times of the minimum of MTT and the maximum of MDT is almost equal to the minimum for MDT. Thus, the location of target node has large effect on the trapping efficiency, but the location of source node almost has no effect on diffusion efficiency. We also simulate random walks on T-fractals, whose results are consistent with the derived results.

Extreme events as foundation of Lévy walks with varying velocity

NASA Astrophysics Data System (ADS)

Kutner, Ryszard

2002-11-01

In this work we study the role of extreme events [E.W. Montroll, B.J. West, in: J.L. Lebowitz, E.W. Montrell (Eds.), Fluctuation Phenomena, SSM, vol. VII, North-Holland, Amsterdam, 1979, p. 63; J.-P. Bouchaud, M. Potters, Theory of Financial Risks from Statistical Physics to Risk Management, Cambridge University Press, Cambridge, 2001; D. Sornette, Critical Phenomena in Natural Sciences. Chaos, Fractals, Selforganization and Disorder: Concepts and Tools, Springer, Berlin, 2000] in determining the scaling properties of Lévy walks with varying velocity. This model is an extension of the well-known Lévy walks one [J. Klafter, G. Zumofen, M.F. Shlesinger, in M.F. Shlesinger, G.M. Zaslavsky, U. Frisch (Eds.), Lévy Flights and Related Topics ion Physics, Lecture Notes in Physics, vol. 450, Springer, Berlin, 1995, p. 196; G. Zumofen, J. Klafter, M.F. Shlesinger, in: R. Kutner, A. Pȩkalski, K. Sznajd-Weron (Eds.), Anomalous Diffusion. From Basics to Applications, Lecture Note in Physics, vol. 519, Springer, Berlin, 1999, p. 15] introduced in the context of chaotic dynamics where a fixed value of the walker velocity is assumed for simplicity. Such an extension seems to be necessary when the open and/or complex system is studied. The model of Lévy walks with varying velocity is spanned on two coupled velocity-temporal hierarchies: the first one consisting of velocities and the second of corresponding time intervals which the walker spends between the successive turning points. Both these hierarchical structures are characterized by their own self-similar dimensions. The extreme event, which can appear within a given time interval, is defined as a single random step of the walker having largest length. By finding power-laws which describe the time-dependence of this displacement and its statistics we obtained two independent diffusion exponents, which are related to the above-mentioned dimensions and which characterize the extreme event kinetics. In this work we show the principal influence of extreme events on the basic quantities (one-step distributions and moments as well as two-step correlation functions) of the continuous-time random walk formalism. Besides, we construct both the waiting-time distribution and sojourn probability density directly in a real space and time in the scaling form by proper component analysis which takes into account all possible fluctuations of the walker steps in contrast to the extreme event analysis. In this work we pay our attention to the basic quantities, since the summarized multi-step ones were already discussed earlier [Physica A 264 (1999) 107; Comp. Phys. Commun. 147 (2002) 565]. Moreover, we study not only the scaling phenomena but also, assuming a finite number of hierarchy levels, the breaking of scaling and its dependence on control parameters. This seems to be important for studying empirical systems the more so as there are still no closed formulae describing this phenomenon except the one for truncated Lévy flights [Phys. Rev. Lett. 73 (1994) 2946]. Our formulation of the model made possible to develop an efficient Monte Carlo algorithm [Physica A 264 (1999) 107; Comp. Phys. Commun. 147 (2002) 565] where no MC step is lost.

The Effect of Chinese Yuanji-Dance on Dynamic Balance and the Associated Attentional Demands in Elderly Adults

PubMed Central

Wu, Wen-Lan; Wei, Ta-Sen; Chen, Shen-Kai; Chang, Jyh-Jong; Guo, Lan-Yuen; Lin, Hwai-Ting

2010-01-01

Walking performance changes with age. This has implications for the problem of falls in older adults. The aim of this study was to investigate the effects of Yuanji-Dance practice on walking balance and the associated attention demand in healthy elderly. Fifteen community-dwelling elderly (comparison group, no regular exercise habit) and fifteen Yuanji- Dance elderly (exercise group, dancing experience: 5.40 ± 1.95 years), aged 60-70 years, were included in this study. The subjects in exercise group participated in a 90-minute Yuanji-Dance practice at least three times per week and the comparison group continued their normal daily physical activity. Walking balance measures (including walking velocity, step length, step width, and percentage of time spent in double limb support, COM velocity and COM-COP inclination angles) and attentional demand tests (button reaction time and accuracy) were conducted under different conditions. Our results showed that stride lengths, walking velocities, peak A/P velocities (AP V) of the COM, medial COM-COP inclination (M angle) angles, reaction time, and accuracy decrease significantly as the dual-task (walking plus hand button pressing tasks) applied for either the comparison or exercise groups. These results demonstrated that walking performance is attenuated in our elderly participants as the cognitive tasks applied. Analysis also identified a significantly faster RT for our exercise group both in standing and walking conditions. This may indicate that physical exercise (Yuanji-Dance) may have facilitating effects on general cognitive and perceptual- motor functions. This implies that Chinese Yuanji-Dance practice for elderly adults may improve their personal safety when walking especially under the condition of multiple task demand. Key points The purpose of this study was to investigate the training effects of a Chinese traditional exercise, Yuanji-Dance, on walking balance and the associated attention demand in the healthy elderly. Walking performance is attenuated in elderly participants as the cognitive tasks applied. A significantly faster reaction time for our exercise group both in standing and walking conditions. Yuanji-Dance exercise training can improve the information processing speed of elderly people and has no influence of the dynamic walking balance. PMID:24149395

The efficacy of treadmill training with and without projected visual context for improving walking ability and reducing fall incidence and fear of falling in older adults with fall-related hip fracture: a randomized controlled trial.

PubMed

van Ooijen, Mariëlle W; Roerdink, Melvyn; Trekop, Marga; Janssen, Thomas W J; Beek, Peter J

2016-12-28

The ability to adjust walking to environmental context is often reduced in older adults and, partly as result of this, falls are common in this population. A treadmill with visual context projected on its belt (e.g., obstacles and targets) allows for practicing step adjustments relative to that context, while concurrently exploiting the great amount of walking practice associated with conventional treadmill training. The present study was conducted to compare the efficacy of adaptability treadmill training, conventional treadmill training and usual physical therapy in improving walking ability and reducing fear of falling and fall incidence in older adults during rehabilitation from a fall-related hip fracture. In this parallel-group, open randomized controlled trial, seventy older adults with a recent fall-related hip fracture (83.3 ± 6.7 years, mean ± standard deviation) were recruited from inpatient rehabilitation care and block randomized to six weeks inpatient adaptability treadmill training (n = 24), conventional treadmill training (n = 23) or usual physical therapy (n = 23). Group allocation was only blind for assessors. Measures related to walking ability were assessed as the primary outcome before and after the intervention and at 4-week and 12-month follow-up. Secondary outcomes included general health, fear of falling, fall rate and proportion of fallers. Measures of general walking ability, general health and fear of falling improved significantly over time. Significant differences among the three intervention groups were only found for the Functional Ambulation Category and the dual-task effect on walking speed, which were in favor of respectively conventional treadmill training and adaptability treadmill training. Overall, adaptability treadmill training, conventional treadmill training and usual physical therapy resulted in similar effects on walking ability, fear of falling and fall incidence in older adults rehabilitating from a fall-related hip fracture. Additional post hoc subgroup analyses, with stratification for pre-fracture tolerated walking distance and executive function, revealed several intervention effects in favor of adaptability and conventional treadmill training, indicating superiority over usual physical therapy for certain subgroups. Future well-powered studies are necessary to univocally identify the characteristics of individuals who will benefit most from a particular intervention. The Netherlands Trial Register ( NTR3222 , 3 January 2012).

"On" freezing in Parkinson's disease: resistance to visual cue walking devices.

PubMed

Kompoliti, K; Goetz, C G; Leurgans, S; Morrissey, M; Siegel, I M

2000-03-01

To measure "on" freezing during unassisted walking (UW) and test if two devices, a modified inverted stick (MIS) and a visual laser beam stick (LBS) improved walking speed and number of "on" freezing episodes in patients with Parkinson's disease (PD). Multiple visual cues can overcome "off' freezing episodes and can be useful in improving gait function in parkinsonian patients. These devices have not been specifically tested in "on" freezing, which is unresponsive to pharmacologic manipulations. Patients with PD, motor fluctuations and freezing while "on," attempted walking on a 60-ft track with each of three walking conditions in a randomized order: UW, MIS, and LBS. Total time to complete a trial, number of freezes, and the ratio of walking time to the number of freezes were compared using Friedman's test. Twenty-eight patients with PD, mean age 67.81 years (standard deviation [SD] 7.54), mean disease duration 13.04 years (SD 7.49), and mean motor Unified Parkinson's Disease Rating Scale score "on" 32.59 (SD 10.93), participated in the study. There was a statistically significant correlation of time needed to complete a trial and number of freezes for all three conditions (Spearman correlations: UW 0.973, LBS 0.0.930, and MIS 0.842). The median number of freezes, median time to walk in each condition, and median walking time per freeze were not significantly different in pairwise comparisons of the three conditions (Friedman's test). Of the 28 subjects, six showed improvement with the MIS and six with the LBS in at least one outcome measure. Assisting devices, specifically based on visual cues, are not consistently beneficial in overcoming "on" freezing in most patients with PD. Because this is an otherwise untreatable clinical problem and because occasional subjects do respond, cautious trials of such devices under the supervision of a health professional should be conducted to identify those patients who might benefit from their long-term use.

Home-based walking improves cardiopulmonary function and health-related QOL in community-dwelling adults.

PubMed

Okamoto, N; Nakatani, T; Morita, N; Saeki, K; Kurumatani, N

2007-12-01

The objective of our study was to investigate the effects of a home-based walking program on physical fitness and QOL among community residents. Subjects (n = 200, mean age: 64.2 years, range: 42 - 75 years) who participated in the 32-week trial were randomly allocated to one of two groups: an exercise (E) group and a control (C) group. The E group was instructed to increase the number of steps a day that they walked and to perform aerobic walking at a target heart rate for 20 minutes or more daily, 2 or more days a week. The C group was told to continue their normal level of activity. Outcome measures were the 3-minute shuttle stamina walk test (SSWT), 30-second chair-stand test (CS-30), and SF-36. Increases in SSWT values were significantly greater in the E group than in the C group (men 24.1 m vs. 6.3 m; women 8.8 m vs. 2.4 m), as were increases in CS-30 values (men 5.9 vs. 2.6; women 4.5 vs. - 0.1). On the SF-36, the scores in the E group for vitality and mental health increased significantly. Home-based walking is considered to be an effective and feasible method to improve physical fitness and QOL among community residents.

Probability distributions for Markov chain based quantum walks

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.

2018-01-01

We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.

Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models

NASA Astrophysics Data System (ADS)

Kimura, Kenji; Higuchi, Saburo

2017-11-01

We introduce a novel random walk model that emerges in the event-chain Monte Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the spin to be updated changes its value to one of its interacting neighbor spins. This movement can be regarded as a random walk in a random environment with a feedback. We investigate this random walk numerically in the case of the classical XY model in 1, 2, and 3 dimensions to find that it is superdiffusive near the critical point of the underlying spin system. It is suggested that the performance improvement of the ECMC is related to this anomalous behavior.

Monte Carlo investigation of anomalous transport in presence of a discontinuity and of an advection field

NASA Astrophysics Data System (ADS)

Marseguerra, M.; Zoia, A.

2007-04-01

Anomalous diffusion has recently turned out to be almost ubiquitous in transport problems. When the physical properties of the medium where the transport process takes place are stationary and constant at each spatial location, anomalous transport has been successfully analysed within the Continuous Time Random Walk (CTRW) model. In this paper, within a Monte Carlo approach to CTRW, we focus on the particle transport through two regions characterized by different physical properties, in presence of an external driving action constituted by an additional advective field, modelled within both the Galilei invariant and Galilei variant schemes. Particular attention is paid to the interplay between the distributions of space and time across the discontinuity. The resident concentration and the flux of the particles are finally evaluated and it is shown that at the interface between the two regions the flux is continuous as required by mass conservation, while the concentration may reveal a neat discontinuity. This result could open the route to the Monte Carlo investigation of the effectiveness of a physical discontinuity acting as a filter on particle concentration.

An improved label propagation algorithm based on node importance and random walk for community detection

NASA Astrophysics Data System (ADS)

Ma, Tianren; Xia, Zhengyou

2017-05-01

Currently, with the rapid development of information technology, the electronic media for social communication is becoming more and more popular. Discovery of communities is a very effective way to understand the properties of complex networks. However, traditional community detection algorithms consider the structural characteristics of a social organization only, with more information about nodes and edges wasted. In the meanwhile, these algorithms do not consider each node on its merits. Label propagation algorithm (LPA) is a near linear time algorithm which aims to find the community in the network. It attracts many scholars owing to its high efficiency. In recent years, there are more improved algorithms that were put forward based on LPA. In this paper, an improved LPA based on random walk and node importance (NILPA) is proposed. Firstly, a list of node importance is obtained through calculation. The nodes in the network are sorted in descending order of importance. On the basis of random walk, a matrix is constructed to measure the similarity of nodes and it avoids the random choice in the LPA. Secondly, a new metric IAS (importance and similarity) is calculated by node importance and similarity matrix, which we can use to avoid the random selection in the original LPA and improve the algorithm stability. Finally, a test in real-world and synthetic networks is given. The result shows that this algorithm has better performance than existing methods in finding community structure.

Effects of intervention using a community-based walking program for prevention of mental decline: a randomized controlled trial.

PubMed

Maki, Yohko; Ura, Chiaki; Yamaguchi, Tomoharu; Murai, Tatsuhiko; Isahai, Mikie; Kaiho, Ayumi; Yamagami, Tetsuya; Tanaka, Satoshi; Miyamae, Fumiko; Sugiyama, Mika; Awata, Shuichi; Takahashi, Ryutaro; Yamaguchi, Haruyasu

2012-03-01

To evaluate the efficacy of a municipality-led walking program under the Japanese public Long-Term Care Insurance Act to prevent mental decline. Randomized controlled trial. The city of Takasaki. One hundred fifty community members aged 72.0 ± 4.0 were randomly divided into intervention (n = 75) and control (n = 75) groups. A walking program was conducted once a week for 90 minutes for 3 months. The program encouraged participants to walk on a regular basis and to increase their steps per day gradually. The intervention was conducted in small groups of approximately six, so combined benefits of exercise and social interaction were expected. Cognitive function was evaluated focusing on nine tests in five domains: memory, executive function, word fluency, visuospatial abilities, and sustained attention. Quality of life (QOL), depressive state, functional capacity, range of activities, and social network were assessed using questionnaires, and motor function was evaluated. Significant differences between the intervention and control groups were shown in word fluency related to frontal lobe function (F(1, 128) = 6.833, P = .01), QOL (F(1,128) = 9.751, P = .002), functional capacity including social interaction (F(1,128) = 13.055, P < .001), and motor function (Timed Up and Go Test: F(1,127) = 10.117, P = .002). No significant differences were observed in other cognitive tests. Walking programs may provide benefits in some aspects of cognition, QOL, and functional capacity including social interaction in elderly community members. This study could serve as the basis for implementation of a community-based intervention to prevent mental decline. © 2012, Copyright the Authors Journal compilation © 2012, The American Geriatrics Society.

Effects of Standing and Light-Intensity Activity on Ambulatory Blood Pressure.

PubMed

Zeigler, Zachary S; Mullane, Sarah L; Crespo, Noe C; Buman, Matthew P; Gaesser, Glenn A

2016-02-01

This study aimed to compare ambulatory blood pressure (ABP) response to accumulated standing (STAND), cycling (CYCLE), and walking (WALK) to a sitting-only (SIT) day in adults. Nine overweight or obese (body mass index, 28.7 ± 2.7 kg · m(-2)) adults (30 ± 15 yr) participated in this randomized crossover full-factorial study. Four conditions (WALK, STAND, CYCLE, and SIT) were randomly performed 1 wk apart. WALK, STAND, and CYCLE conditions consisted of progressively increasing activity time to accumulate 2.5 h during an 8-h simulated workday. WALK (1.0 mph) and STAND (0.0 mph) were completed on a treadmill placed underneath a standing-height desk. During CYCLE, participants pedaled on a Monark cycle ergometer at a cadence and energy expenditure equivalent to WALK. Participants remained seated during the SIT condition. Participants wore an ABP cuff from 0800 h until 2200 h on all conditions. Linear mixed models were used to test condition differences in systolic (SBP) and diastolic (DBP) blood pressure. Chi-square was used to detect frequency difference of BP load. There was a whole-day (during and after work hours) SBP and DBP treatment effect (P < 0.01). Systolic blood pressure during STAND (132 ± 17 mm Hg), WALK (133 ± 17 mm Hg), and CYCLE (130 ± 16 mm Hg) were lower compared with that during SIT (137 ± 17 mm Hg) (all P < 0.01). CYCLE was lower than STAND (P = 0.04) and WALK (P < 0.01). For DBP, only CYCLE (69 ± 12 mm Hg) was lower than SIT (71 ± 13 mm Hg; P < 0.01). Compared with SIT, WALK, STAND, and CYCLE reduced SBP load by 4%, 4%, and 13%, respectively (all P < 0.01). Compared with sitting, accumulating 2.5 h of light-intensity physical activity or standing during an 8-h workday may reduce ABP during and after work hours.

A kinetic model of the formation of organic monolayers on hydrogen-terminated silicon by hydrosilation of alkenes.

PubMed

Woods, M; Carlsson, S; Hong, Q; Patole, S N; Lie, L H; Houlton, A; Horrocks, B R

2005-12-22

We have analyzed a kinetic model for the formation of organic monolayers based on a previously suggested free radical chain mechanism for the reaction of unsaturated molecules with hydrogen-terminated silicon surfaces (Linford, M. R.; Fenter, P. M.; Chidsey, C. E. D. J. Am. Chem. Soc 1995, 117, 3145). A direct consequence of this mechanism is the nonexponential growth of the monolayer, and this has been observed spectroscopically. In the model, the initiation of silyl radicals on the surface is pseudo first order with rate constant, ki, and the rate of propagation is determined by the concentration of radicals and unreacted Si-H nearest neighbor sites with a rate constant, kp. This propagation step determines the rate at which the monolayer forms by addition of alkene molecules to form a track of molecules that constitute a self-avoiding random walk on the surface. The initiation step describes how frequently new random walks commence. A termination step by which the radicals are destroyed is also included. The solution of the kinetic equations yields the fraction of alkylated surface sites and the mean length of the random walks as a function of time. In mean-field approximation we show that (1) the average length of the random walk is proportional to (kp/ki)1/2, (2) the monolayer surface coverage grows exponentially only after an induction period, (3) the effective first-order rate constant describing the growth of the monolayer and the induction period (kt) is k = (2ki kp)1/2, (4) at long times the effective first-order rate constant drops to ki, and (5) the overall activation energy for the growth kinetics is the mean of the activation energies for the initiation and propagation steps. Monte Carlo simulations of the mechanism produce qualitatively similar kinetic plots, but the mean random walk length (and effective rate constant) is overestimated by the mean field approximation and when kp > ki, we find k approximately ki0.7kp0.3 and Ea = (0.7Ei+ 0.3Ep). However the most striking prediction of the Monte Carlo simulations is that at long times, t > 1/k, the effective first-order rate constant decreases to ki even in the absence of a chemical termination step. Experimental kinetic data for the reaction of undec-1-ene with hydrogen-terminated porous silicon under thermal reflux in toluene and ethylbenzene gave a value of k = 0.06 min(-1) and an activation energy of 107 kJ mol(-1). The activation energy is in reasonable agreement with density functional calculations of the transition state energies for the initiation and propagation steps.

Analysis of coined quantum walks with renormalization

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Li, Shanshan

2018-01-01

We introduce a framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights into the analytic structure as well as generic results about the long-time behavior can be extracted. The RG flow for such a walk on a dual Sierpinski gasket and a Migdal-Kadanoff hierarchical network is obtained explicitly from elementary algebraic manipulations, after transforming the unitary evolution equation into Laplace space. Unlike for classical random walks, we find that the long-time asymptotics for the quantum walk requires consideration of a diverging number of Laplace poles, which we demonstrate exactly for the closed-form solution available for the walk on a one-dimensional loop. In particular, we calculate the probability of the walk to overlap with its starting position, which oscillates with a period that scales as NdwQ/df with system size N . While the largest Jacobian eigenvalue λ1 of the RG flow merely reproduces the fractal dimension, df=log2λ1 , the asymptotic analysis shows that the second Jacobian eigenvalue λ2 becomes essential to determine the dimension of the quantum walk via dwQ=log2√{λ1λ2 } . We trace this fact to delicate cancellations caused by unitarity. We obtain identical relations for other networks, although the details of the RG analysis may exhibit surprisingly distinct features. Thus, our conclusions—which trivially reproduce those for regular lattices with translational invariance with df=d and dwQ=1 —appear to be quite general and likely apply to networks beyond those studied here.

Phase walk analysis of leptokurtic time series.

PubMed

Schreiber, Korbinian; Modest, Heike I; Räth, Christoph

2018-06-01

The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases. The method, being called phase walk analysis, is based on well established measures from random walk analysis, which are now applied to the unwrapped Fourier phases of time series. We provide an analytical description of its functionality and demonstrate its capabilities on systematically controlled leptokurtic noise. Hereby, we investigate the properties of leptokurtic time series and their influence on the Fourier phases of time series. The phase walk analysis is applied to measured and simulated intermittent time series, whose probability density distribution is approximated by power laws. We use the day-to-day returns of the Dow-Jones industrial average, a synthetic time series with tailored nonlinearities mimicing the power law behavior of the Dow-Jones and the acceleration of the wind at an Atlantic offshore site. Testing for nonlinearities by means of surrogates shows that the new method yields strong significances for nonlinear behavior. Due to the drastically decreased computing time as compared to embedding space methods, the number of surrogate realizations can be increased by orders of magnitude. Thereby, the probability distribution of the test statistics can very accurately be derived and parameterized, which allows for much more precise tests on nonlinearities.

Promoting healthy eating and physical activity short-term effects of a mass media campaign.

PubMed

Beaudoin, Christopher E; Fernandez, Carolyn; Wall, Jerry L; Farley, Thomas A

2007-03-01

Soaring obesity levels present a severe health risk in the United States, especially in low-income minority populations. High-frequency paid television and radio advertising, as well as bus and streetcar signage. A mass media campaign in New Orleans to promote walking and fruit and vegetable consumption in a low-income, predominantly African-American urban population. Messages tailored with consideration of the African-American majority. Random-digit-dial telephone surveys using cross-sectional representative samples at baseline in 2004 and following the onset of the campaign in 2005. Survey items on campaign message recall; attitudes toward walking, snack food avoidance, and fruit and vegetable consumption; and behaviors related to fruit and vegetable consumption, snack food consumption, and utilitarian and leisure walking. From baseline, there were significant increases in message recall measures, positive attitudes toward fruit and vegetable consumption, and positive attitudes toward walking. Behaviors did not change significantly. In 2005, message recall measures were associated with positive levels of each of the outcome variables. Over 5 months, the media campaign appeared to have stimulated improvements in attitudes toward healthy diet and walking behaviors addressed by the campaign. These findings encourage the continuation of the media campaign, with future evaluation to consider whether the behavioral measures change.

An investigation of the association between socio-demographic factors, dog-exercise requirements, and the amount of walking dogs receive.

PubMed

Degeling, Chris; Burton, Lindsay; McCormack, Gavin R

2012-07-01

Risk factors associated with canine obesity include the amount of walking a dog receives. The aim of this study was to investigate the relationships between canine exercise requirements, socio-demographic factors, and dog-walking behaviors in winter in Calgary. Dog owners, from a cross-sectional study which included a random sample of adults, were asked their household income, domicile type, gender, age, education level, number and breed(s) of dog(s) owned, and frequency and time spent dog-walking in a usual week. Canine exercise requirements were found to be significantly (P < 0.05) positively associated with the minutes pet dogs were walked, as was the owner being a female. Moreover, dog walking frequency, but not minutes of dog walking, was significantly associated with residing in attached housing (i.e., apartments). Different types of dogs have different exercise requirements to maintain optimal health. Understanding the role of socio-demographic factors and dog-related characteristics such as exercise requirements on dog-walking behaviors is essential for helping veterinarians and owners develop effective strategies to prevent and manage canine obesity. Furthermore, encouraging regular dog-walking has the potential to improve the health of pet dogs, and that of their owners.

Gait rehabilitation machines based on programmable footplates

PubMed Central

Schmidt, Henning; Werner, Cordula; Bernhardt, Rolf; Hesse, Stefan; Krüger, Jörg

2007-01-01

Background Gait restoration is an integral part of rehabilitation of brain lesioned patients. Modern concepts favour a task-specific repetitive approach, i.e. who wants to regain walking has to walk, while tone-inhibiting and gait preparatory manoeuvres had dominated therapy before. Following the first mobilization out of the bed, the wheelchair-bound patient should have the possibility to practise complex gait cycles as soon as possible. Steps in this direction were treadmill training with partial body weight support and most recently gait machines enabling the repetitive training of even surface gait and even of stair climbing. Results With treadmill training harness-secured and partially relieved wheelchair-mobilised patients could practise up to 1000 steps per session for the first time. Controlled trials in stroke and SCI patients, however, failed to show a superior result when compared to walking exercise on the floor. Most likely explanation was the effort for the therapists, e.g. manually setting the paretic limbs during the swing phase resulting in a too little gait intensity. The next steps were gait machines, either consisting of a powered exoskeleton and a treadmill (Lokomat, AutoAmbulator) or an electromechanical solution with the harness secured patient placed on movable foot plates (Gait Trainer GT I). For the latter, a large multi-centre trial with 155 non-ambulatory stroke patients (DEGAS) revealed a superior gait ability and competence in basic activities of living in the experimental group. The HapticWalker continued the end effector concept of movable foot plates, now fully programmable and equipped with 6 DOF force sensors. This device for the first time enables training of arbitrary walking situations, hence not only the simulation of floor walking but also for example of stair climbing and perturbations. Conclusion Locomotor therapy is a fascinating new tool in rehabilitation, which is in line with modern principles of motor relearning promoting a task-specific repetitive approach. Sophisticated technical developments and positive randomized controlled trials form the basis of a growing acceptance worldwide to the benefits or our patients. PMID:17291335