Quantum speedup of Monte Carlo methods.

PubMed

Montanaro, Ashley

2015-09-08

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.

Quantum speedup of Monte Carlo methods

PubMed Central

Montanaro, Ashley

2015-01-01

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently. PMID:26528079

Deterministic realization of collective measurements via photonic quantum walks.

PubMed

Hou, Zhibo; Tang, Jun-Feng; Shang, Jiangwei; Zhu, Huangjun; Li, Jian; Yuan, Yuan; Wu, Kang-Da; Xiang, Guo-Yong; Li, Chuan-Feng; Guo, Guang-Can

2018-04-12

Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here, we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity 0.9946 without post selection. As an application, we achieve the highest tomographic efficiency in qubit state tomography to date. Our work offers an effective recipe for beating the precision limit of local measurements in quantum state tomography and metrology. In addition, our study opens an avenue for harvesting the power of collective measurements in quantum information-processing and for exploring the intriguing physics behind this power.

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.

δ-exceedance records and random adaptive walks

NASA Astrophysics Data System (ADS)

Park, Su-Chan; Krug, Joachim

2016-08-01

We study a modified record process where the kth record in a series of independent and identically distributed random variables is defined recursively through the condition {Y}k\\gt {Y}k-1-{δ }k-1 with a deterministic sequence {δ }k\\gt 0 called the handicap. For constant {δ }k\\equiv δ and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of δ between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records (Park et al 2015 Phys. Rev. E 91 042707). Here we explore the behavior for general probability distributions and decreasing and increasing sequences {δ }k, focusing in particular on the case when {δ }k matches the typical spacing between subsequent records in the underlying simple record process without handicap. We find that a continuous phase transition occurs only in the exponential case, but a novel kind of first order transition emerges when {δ }k is increasing. The problem is partly motivated by the dynamics of evolutionary adaptation in biological fitness landscapes, where {δ }k corresponds to the change of the deterministic fitness component after k mutational steps. The results for the record process are used to compute the mean number of steps that a population performs in such a landscape before being trapped at a local fitness maximum.

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations

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

Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C., E-mail: waymire@math.oregonstate.edu

2015-07-15

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturallymore » arise as a result of this investigation.« less

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations.

PubMed

Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C

2015-07-01

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.

Trade-off study and computer simulation for assessing spacecraft pointing accuracy and stability capabilities

NASA Astrophysics Data System (ADS)

Algrain, Marcelo C.; Powers, Richard M.

1997-05-01

A case study, written in a tutorial manner, is presented where a comprehensive computer simulation is developed to determine the driving factors contributing to spacecraft pointing accuracy and stability. Models for major system components are described. Among them are spacecraft bus, attitude controller, reaction wheel assembly, star-tracker unit, inertial reference unit, and gyro drift estimators (Kalman filter). The predicted spacecraft performance is analyzed for a variety of input commands and system disturbances. The primary deterministic inputs are the desired attitude angles and rate set points. The stochastic inputs include random torque disturbances acting on the spacecraft, random gyro bias noise, gyro random walk, and star-tracker noise. These inputs are varied over a wide range to determine their effects on pointing accuracy and stability. The results are presented in the form of trade- off curves designed to facilitate the proper selection of subsystems so that overall spacecraft pointing accuracy and stability requirements are met.

A deterministic Lagrangian particle separation-based method for advective-diffusion problems

NASA Astrophysics Data System (ADS)

Wong, Ken T. M.; Lee, Joseph H. W.; Choi, K. W.

2008-12-01

A simple and robust Lagrangian particle scheme is proposed to solve the advective-diffusion transport problem. The scheme is based on relative diffusion concepts and simulates diffusion by regulating particle separation. This new approach generates a deterministic result and requires far less number of particles than the random walk method. For the advection process, particles are simply moved according to their velocity. The general scheme is mass conservative and is free from numerical diffusion. It can be applied to a wide variety of advective-diffusion problems, but is particularly suited for ecological and water quality modelling when definition of particle attributes (e.g., cell status for modelling algal blooms or red tides) is a necessity. The basic derivation, numerical stability and practical implementation of the NEighborhood Separation Technique (NEST) are presented. The accuracy of the method is demonstrated through a series of test cases which embrace realistic features of coastal environmental transport problems. Two field application examples on the tidal flushing of a fish farm and the dynamics of vertically migrating marine algae are also presented.

The structure of evaporating and combusting sprays: Measurements and predictions

NASA Technical Reports Server (NTRS)

Shuen, J. S.; Solomon, A. S. P.; Faeth, F. M.

1983-01-01

The structure of particle-laden jets and nonevaporating and evaporating sprays was measured in order to evaluate models of these processes. Three models are being evaluated: (1) a locally homogeneous flow model, where slip between the phases is neglected and the flow is assumed to be in local thermodynamic equilibrium; (2) a deterministic separated flow model, where slip and finite interphase transport rates are considered but effects of particle/drop dispersion by turbulence and effects of turbulence on interphase transport rates are ignored; and (3) a stochastic separated flow model, where effects of interphase slip, turbulent dispersion and turbulent fluctuations are considered using random sampling for turbulence properties in conjunction with random-walk computations for particle motion. All three models use a k-e-g turbulence model. All testing and data reduction are completed for the particle laden jets. Mean and fluctuating velocities of the continuous phase and mean mixture fraction were measured in the evaporating sprays.

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.

Deterministic chaotic dynamics of Raba River flow (Polish Carpathian Mountains)

NASA Astrophysics Data System (ADS)

Kędra, Mariola

2014-02-01

Is the underlying dynamics of river flow random or deterministic? If it is deterministic, is it deterministic chaotic? This issue is still controversial. The application of several independent methods, techniques and tools for studying daily river flow data gives consistent, reliable and clear-cut results to the question. The outcomes point out that the investigated discharge dynamics is not random but deterministic. Moreover, the results completely confirm the nonlinear deterministic chaotic nature of the studied process. The research was conducted on daily discharge from two selected gauging stations of the mountain river in southern Poland, the Raba River.

The Combined Effect of Periodic Signals and Noise on the Dilution of Precision of GNSS Station Velocity Uncertainties

NASA Astrophysics Data System (ADS)

Klos, Anna; Olivares, German; Teferle, Felix Norman; Bogusz, Janusz

2016-04-01

Station velocity uncertainties determined from a series of Global Navigation Satellite System (GNSS) position estimates depend on both the deterministic and stochastic models applied to the time series. While the deterministic model generally includes parameters for a linear and several periodic terms the stochastic model is a representation of the noise character of the time series in form of a power-law process. For both of these models the optimal model may vary from one time series to another while the models also depend, to some degree, on each other. In the past various power-law processes have been shown to fit the time series and the sources for the apparent temporally-correlated noise were attributed to, for example, mismodelling of satellites orbits, antenna phase centre variations, troposphere, Earth Orientation Parameters, mass loading effects and monument instabilities. Blewitt and Lavallée (2002) demonstrated how improperly modelled seasonal signals affected the estimates of station velocity uncertainties. However, in their study they assumed that the time series followed a white noise process with no consideration of additional temporally-correlated noise. Bos et al. (2010) empirically showed for a small number of stations that the noise character was much more important for the reliable estimation of station velocity uncertainties than the seasonal signals. In this presentation we pick up from Blewitt and Lavallée (2002) and Bos et al. (2010), and have derived formulas for the computation of the General Dilution of Precision (GDP) under presence of periodic signals and temporally-correlated noise in the time series. We show, based on simulated and real time series from globally distributed IGS (International GNSS Service) stations processed by the Jet Propulsion Laboratory (JPL), that periodic signals dominate the effect on the velocity uncertainties at short time scales while for those beyond four years, the type of noise becomes much more important. In other words, for time series long enough, the assumed periodic signals do not affect the velocity uncertainties as much as the assumed noise model. We calculated the GDP to be the ratio between two errors of velocity: without and with inclusion of seasonal terms of periods equal to one year and its overtones till 3rd. To all these cases power-law processes of white, flicker and random-walk noise were added separately. Few oscillations in GDP can be noticed for integer years, which arise from periodic terms added. Their amplitudes in GDP increase along with the increasing spectral index. Strong peaks of oscillations in GDP are indicated for short time scales, especially for random-walk processes. This means that badly monumented stations are affected the most. Local minima and maxima in GDP are also enlarged as the noise approaches random walk. We noticed that the semi-annual signal increased the local GDP minimum for white noise. This suggests that adding power-law noise to a deterministic model with annual term or adding a semi-annual term to white noise causes an increased velocity uncertainty even at the points, where determined velocity is not biased.

Random walks and diffusion on networks

NASA Astrophysics Data System (ADS)

Masuda, Naoki; Porter, Mason A.; Lambiotte, Renaud

2017-11-01

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.

Statistics of Delta v magnitude for a trajectory correction maneuver containing deterministic and random components

NASA Technical Reports Server (NTRS)

Bollman, W. E.; Chadwick, C.

1982-01-01

A number of interplanetary missions now being planned involve placing deterministic maneuvers along the flight path to alter the trajectory. Lee and Boain (1973) examined the statistics of trajectory correction maneuver (TCM) magnitude with no deterministic ('bias') component. The Delta v vector magnitude statistics were generated for several values of random Delta v standard deviations using expansions in terms of infinite hypergeometric series. The present investigation uses a different technique (Monte Carlo simulation) to generate Delta v magnitude statistics for a wider selection of random Delta v standard deviations and also extends the analysis to the case of nonzero deterministic Delta v's. These Delta v magnitude statistics are plotted parametrically. The plots are useful in assisting the analyst in quickly answering questions about the statistics of Delta v magnitude for single TCM's consisting of both a deterministic and a random component. The plots provide quick insight into the nature of the Delta v magnitude distribution for the TCM.

Line-of-sight pointing accuracy/stability analysis and computer simulation for small spacecraft

NASA Astrophysics Data System (ADS)

Algrain, Marcelo C.; Powers, Richard M.

1996-06-01

This paper presents a case study where a comprehensive computer simulation is developed to determine the driving factors contributing to spacecraft pointing accuracy and stability. The simulation is implemented using XMATH/SystemBuild software from Integrated Systems, Inc. The paper is written in a tutorial manner and models for major system components are described. Among them are spacecraft bus, attitude controller, reaction wheel assembly, star-tracker unit, inertial reference unit, and gyro drift estimators (Kalman filter). THe predicted spacecraft performance is analyzed for a variety of input commands and system disturbances. The primary deterministic inputs are desired attitude angles and rate setpoints. The stochastic inputs include random torque disturbances acting on the spacecraft, random gyro bias noise, gyro random walk, and star-tracker noise. These inputs are varied over a wide range to determine their effects on pointing accuracy and stability. The results are presented in the form of trade-off curves designed to facilitate the proper selection of subsystems so that overall spacecraft pointing accuracy and stability requirements are met.

Diffusion tensor tractography of the arcuate fasciculus in patients with brain tumors: Comparison between deterministic and probabilistic models

PubMed Central

Li, Zhixi; Peck, Kyung K.; Brennan, Nicole P.; Jenabi, Mehrnaz; Hsu, Meier; Zhang, Zhigang; Holodny, Andrei I.; Young, Robert J.

2014-01-01

Purpose The purpose of this study was to compare the deterministic and probabilistic tracking methods of diffusion tensor white matter fiber tractography in patients with brain tumors. Materials and Methods We identified 29 patients with left brain tumors <2 cm from the arcuate fasciculus who underwent pre-operative language fMRI and DTI. The arcuate fasciculus was reconstructed using a deterministic Fiber Assignment by Continuous Tracking (FACT) algorithm and a probabilistic method based on an extended Monte Carlo Random Walk algorithm. Tracking was controlled using two ROIs corresponding to Broca’s and Wernicke’s areas. Tracts in tumoraffected hemispheres were examined for extension between Broca’s and Wernicke’s areas, anterior-posterior length and volume, and compared with the normal contralateral tracts. Results Probabilistic tracts displayed more complete anterior extension to Broca’s area than did FACT tracts on the tumor-affected and normal sides (p < 0.0001). The median length ratio for tumor: normal sides was greater for probabilistic tracts than FACT tracts (p < 0.0001). The median tract volume ratio for tumor: normal sides was also greater for probabilistic tracts than FACT tracts (p = 0.01). Conclusion Probabilistic tractography reconstructs the arcuate fasciculus more completely and performs better through areas of tumor and/or edema. The FACT algorithm tends to underestimate the anterior-most fibers of the arcuate fasciculus, which are crossed by primary motor fibers. PMID:25328583

Optimal trading from minimizing the period of bankruptcy risk

NASA Astrophysics Data System (ADS)

Liehr, S.; Pawelzik, K.

2001-04-01

Assuming that financial markets behave similar to random walk processes we derive a trading strategy with variable investment which is based on the equivalence of the period of bankruptcy risk and the risk to profit ratio. We define a state dependent predictability measure which can be attributed to the deterministic and stochastic components of the price dynamics. The influence of predictability variations and especially of short term inefficiency structures on the optimal amount of investment is analyzed in the given context and a method for adaptation of a trading system to the proposed objective function is presented. Finally we show the performance of our trading strategy on the DAX and S&P 500 as examples for real world data using different types of prediction models in comparison.

A random walk on water (Henry Darcy Medal Lecture)

NASA Astrophysics Data System (ADS)

Koutsoyiannis, D.

2009-04-01

Randomness and uncertainty had been well appreciated in hydrology and water resources engineering in their initial steps as scientific disciplines. However, this changed through the years and, following other geosciences, hydrology adopted a naïve view of randomness in natural processes. Such a view separates natural phenomena into two mutually exclusive types, random or stochastic, and deterministic. When a classification of a specific process into one of these two types fails, then a separation of the process into two different, usually additive, parts is typically devised, each of which may be further subdivided into subparts (e.g., deterministic subparts such as periodic and aperiodic or trends). This dichotomous logic is typically combined with a manichean perception, in which the deterministic part supposedly represents cause-effect relationships and thus is physics and science (the "good"), whereas randomness has little relationship with science and no relationship with understanding (the "evil"). Probability theory and statistics, which traditionally provided the tools for dealing with randomness and uncertainty, have been regarded by some as the "necessary evil" but not as an essential part of hydrology and geophysics. Some took a step further to banish them from hydrology, replacing them with deterministic sensitivity analysis and fuzzy-logic representations. Others attempted to demonstrate that irregular fluctuations observed in natural processes are au fond manifestations of underlying chaotic deterministic dynamics with low dimensionality, thus attempting to render probabilistic descriptions unnecessary. Some of the above recent developments are simply flawed because they make erroneous use of probability and statistics (which, remarkably, provide the tools for such analyses), whereas the entire underlying logic is just a false dichotomy. To see this, it suffices to recall that Pierre Simon Laplace, perhaps the most famous proponent of determinism in the history of philosophy of science (cf. Laplace's demon), is, at the same time, one of the founders of probability theory, which he regarded as "nothing but common sense reduced to calculation". This harmonizes with James Clerk Maxwell's view that "the true logic for this world is the calculus of Probabilities" and was more recently and epigrammatically formulated in the title of Edwin Thompson Jaynes's book "Probability Theory: The Logic of Science" (2003). Abandoning dichotomous logic, either on ontological or epistemic grounds, we can identify randomness or stochasticity with unpredictability. Admitting that (a) uncertainty is an intrinsic property of nature; (b) causality implies dependence of natural processes in time and thus suggests predictability; but, (c) even the tiniest uncertainty (e.g., in initial conditions) may result in unpredictability after a certain time horizon, we may shape a stochastic representation of natural processes that is consistent with Karl Popper's indeterministic world view. In this representation, probability quantifies uncertainty according to the Kolmogorov system, in which probability is a normalized measure, i.e., a function that maps sets (areas where the initial conditions or the parameter values lie) to real numbers (in the interval [0, 1]). In such a representation, predictability (suggested by deterministic laws) and unpredictability (randomness) coexist, are not separable or additive components, and it is a matter of specifying the time horizon of prediction to decide which of the two dominates. An elementary numerical example has been devised to illustrate the above ideas and demonstrate that they offer a pragmatic and useful guide for practice, rather than just pertaining to philosophical discussions. A chaotic model, with fully and a priori known deterministic dynamics and deterministic inputs (without any random agent), is assumed to represent the hydrological balance in an area partly covered by vegetation. Experimentation with this toy model demonstrates, inter alia, that: (1) for short time horizons the deterministic dynamics is able to give good predictions; but (2) these predictions become extremely inaccurate and useless for long time horizons; (3) for such horizons a naïve statistical prediction (average of past data) which fully neglects the deterministic dynamics is more skilful; and (4) if this statistical prediction, in addition to past data, is combined with the probability theory (the principle of maximum entropy, in particular), it can provide a more informative prediction. Also, the toy model shows that the trajectories of the system state (and derivative properties thereof) do not resemble a regular (e.g., periodic) deterministic process nor a purely random process, but exhibit patterns indicating anti-persistence and persistence (where the latter statistically complies with a Hurst-Kolmogorov behaviour). If the process is averaged over long time scales, the anti-persistent behaviour improves predictability, whereas the persistent behaviour substantially deteriorates it. A stochastic representation of this deterministic system, which incorporates dynamics, is not only possible, but also powerful as it provides good predictions for both short and long horizons and helps to decide on when the deterministic dynamics should be considered or neglected. Obviously, a natural system is extremely more complex than this simple toy model and hence unpredictability is naturally even more prominent in the former. In addition, in a complex natural system, we can never know the exact dynamics and we must infer it from past data, which implies additional uncertainty and an additional role of stochastics in the process of formulating the system equations and estimating the involved parameters. Data also offer the only solid grounds to test any hypothesis about the dynamics, and failure of performing such testing against evidence from data renders the hypothesised dynamics worthless. If this perception of natural phenomena is adequately plausible, then it may help in studying interesting fundamental questions regarding the current state and the trends of hydrological and water resources research and their promising future paths. For instance: (i) Will it ever be possible to achieve a fully "physically based" modelling of hydrological systems that will not depend on data or stochastic representations? (ii) To what extent can hydrological uncertainty be reduced and what are the effective means for such reduction? (iii) Are current stochastic methods in hydrology consistent with observed natural behaviours? What paths should we explore for their advancement? (iv) Can deterministic methods provide solid scientific grounds for water resources engineering and management? In particular, can there be risk-free hydraulic engineering and water management? (v) Is the current (particularly important) interface between hydrology and climate satisfactory?. In particular, should hydrology rely on climate models that are not properly validated (i.e., for periods and scales not used in calibration)? In effect, is the evolution of climate and its impacts on water resources deterministically predictable?

Record statistics of a strongly correlated time series: random walks and Lévy flights

NASA Astrophysics Data System (ADS)

Godrèche, Claude; Majumdar, Satya N.; Schehr, Grégory

2017-08-01

We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few years, it was indeed realized that random walks are a very useful ‘laboratory’ to test the effects of correlations on the record statistics. We start with the simple one-dimensional random walk with symmetric jumps (both continuous and discrete) and discuss in detail the statistics of the number of records, as well as of the ages of the records, i.e. the lapses of time between two successive record breaking events. Then we review the results that were obtained for a wide variety of random walk models, including random walks with a linear drift, continuous time random walks, constrained random walks (like the random walk bridge) and the case of multiple independent random walkers. Finally, we discuss further observables related to records, like the record increments, as well as some questions raised by physical applications of record statistics, like the effects of measurement error and noise.

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.

Human brain detects short-time nonlinear predictability in the temporal fine structure of deterministic chaotic sounds

NASA Astrophysics Data System (ADS)

Itoh, Kosuke; Nakada, Tsutomu

2013-04-01

Deterministic nonlinear dynamical processes are ubiquitous in nature. Chaotic sounds generated by such processes may appear irregular and random in waveform, but these sounds are mathematically distinguished from random stochastic sounds in that they contain deterministic short-time predictability in their temporal fine structures. We show that the human brain distinguishes deterministic chaotic sounds from spectrally matched stochastic sounds in neural processing and perception. Deterministic chaotic sounds, even without being attended to, elicited greater cerebral cortical responses than the surrogate control sounds after about 150 ms in latency after sound onset. Listeners also clearly discriminated these sounds in perception. The results support the hypothesis that the human auditory system is sensitive to the subtle short-time predictability embedded in the temporal fine structure of sounds.

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

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.

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.

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.

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.

Deterministic multidimensional nonuniform gap sampling.

PubMed

Worley, Bradley; Powers, Robert

2015-12-01

Born from empirical observations in nonuniformly sampled multidimensional NMR data relating to gaps between sampled points, the Poisson-gap sampling method has enjoyed widespread use in biomolecular NMR. While the majority of nonuniform sampling schemes are fully randomly drawn from probability densities that vary over a Nyquist grid, the Poisson-gap scheme employs constrained random deviates to minimize the gaps between sampled grid points. We describe a deterministic gap sampling method, based on the average behavior of Poisson-gap sampling, which performs comparably to its random counterpart with the additional benefit of completely deterministic behavior. We also introduce a general algorithm for multidimensional nonuniform sampling based on a gap equation, and apply it to yield a deterministic sampling scheme that combines burst-mode sampling features with those of Poisson-gap schemes. Finally, we derive a relationship between stochastic gap equations and the expectation value of their sampling probability densities. Copyright © 2015 Elsevier Inc. All rights reserved.

Inverse kinematic problem for a random gradient medium in geometric optics approximation

NASA Astrophysics Data System (ADS)

Petersen, N. V.

1990-03-01

Scattering at random inhomogeneities in a gradient medium results in systematic deviations of the rays and travel times of refracted body waves from those corresponding to the deterministic velocity component. The character of the difference depends on the parameters of the deterministic and random velocity component. However, at great distances to the source, independently of the velocity parameters (weakly or strongly inhomogeneous medium), the most probable depth of the ray turning point is smaller than that corresponding to the deterministic velocity component, the most probable travel times also being lower. The relative uncertainty in the deterministic velocity component, derived from the mean travel times using methods developed for laterally homogeneous media (for instance, the Herglotz-Wiechert method), is systematic in character, but does not exceed the contrast of velocity inhomogeneities by magnitude. The gradient of the deterministic velocity component has a significant effect on the travel-time fluctuations. The variance at great distances to the source is mainly controlled by shallow inhomogeneities. The travel-time flucutations are studied only for weakly inhomogeneous media.

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.

Amputation effects on the underlying complexity within transtibial amputee ankle motion

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

Wurdeman, Shane R., E-mail: shanewurdeman@gmail.com; Advanced Prosthetics Center, Omaha, Nebraska 68134; Myers, Sara A.

2014-03-15

The presence of chaos in walking is considered to provide a stable, yet adaptable means for locomotion. This study examined whether lower limb amputation and subsequent prosthetic rehabilitation resulted in a loss of complexity in amputee gait. Twenty-eight individuals with transtibial amputation participated in a 6 week, randomized cross-over design study in which they underwent a 3 week adaptation period to two separate prostheses. One prosthesis was deemed “more appropriate” and the other “less appropriate” based on matching/mismatching activity levels of the person and the prosthesis. Subjects performed a treadmill walking trial at self-selected walking speed at multiple points ofmore » the adaptation period, while kinematics of the ankle were recorded. Bilateral sagittal plane ankle motion was analyzed for underlying complexity through the pseudoperiodic surrogation analysis technique. Results revealed the presence of underlying deterministic structure in both prostheses and both the prosthetic and sound leg ankle (discriminant measure largest Lyapunov exponent). Results also revealed that the prosthetic ankle may be more likely to suffer loss of complexity than the sound ankle, and a “more appropriate” prosthesis may be better suited to help restore a healthy complexity of movement within the prosthetic ankle motion compared to a “less appropriate” prosthesis (discriminant measure sample entropy). Results from sample entropy results are less likely to be affected by the intracycle periodic dynamics as compared to the largest Lyapunov exponent. Adaptation does not seem to influence complexity in the system for experienced prosthesis users.« less

Swimming path statistics of an active Brownian particle with time-dependent self-propulsion

NASA Astrophysics Data System (ADS)

Babel, S.; ten Hagen, B.; Löwen, H.

2014-02-01

Typically, in the description of active Brownian particles, a constant effective propulsion force is assumed, which is then subjected to fluctuations in orientation and translation, leading to a persistent random walk with an enlarged long-time diffusion coefficient. Here, we generalize previous results for the swimming path statistics to a time-dependent, and thus in many situations more realistic, propulsion which is a prescribed input. We analytically calculate both the noise-free and the noise-averaged trajectories for time-periodic propulsion under the action of an additional torque. In the deterministic case, such an oscillatory microswimmer moves on closed paths that can be much more complicated than the commonly observed straight lines and circles. When exposed to random fluctuations, the mean trajectories turn out to be self-similar curves which bear the characteristics of their noise-free counterparts. Furthermore, we consider a propulsion force which scales in time t as ∝tα (with α = 0,1,2, …) and analyze the resulting superdiffusive behavior. Our predictions are verifiable for diffusiophoretic artificial microswimmers with prescribed propulsion protocols.

Prediction of the structure of fuel sprays in gas turbine combustors

NASA Technical Reports Server (NTRS)

Shuen, J. S.

1985-01-01

The structure of fuel sprays in a combustion chamber is theoretically investigated using computer models of current interest. Three representative spray models are considered: (1) a locally homogeneous flow (LHF) model, which assumes infinitely fast interphase transport rates; (2) a deterministic separated flow (DSF) model, which considers finite rates of interphase transport but ignores effects of droplet/turbulence interactions; and (3) a stochastic separated flow (SSF) model, which considers droplet/turbulence interactions using random sampling for turbulence properties in conjunction with random-walk computations for droplet motion and transport. Two flow conditions are studied to investigate the influence of swirl on droplet life histories and the effects of droplet/turbulence interactions on flow properties. Comparison of computed results with the experimental data show that general features of the flow structure can be predicted with reasonable accuracy using the two separated flow models. In contrast, the LHF model overpredicts the rate of development of the flow. While the SSF model provides better agreement with measurements than the DSF model, definitive evaluation of the significance of droplet/turbulence interaction is not achieved due to uncertainties in the spray initial conditions.

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.

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.

Coupled continuous time-random walks in quenched random environment

NASA Astrophysics Data System (ADS)

Magdziarz, M.; Szczotka, W.

2018-02-01

We introduce a coupled continuous-time random walk with coupling which is characteristic for Lévy walks. Additionally we assume that the walker moves in a quenched random environment, i.e. the site disorder at each lattice point is fixed in time. We analyze the scaling limit of such a random walk. We show that for large times the behaviour of the analyzed process is exactly the same as in the case of uncoupled quenched trap model for Lévy flights.

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.

NMR diffusion simulation based on conditional random walk.

PubMed

Gudbjartsson, H; Patz, S

1995-01-01

The authors introduce here a new, very fast, simulation method for free diffusion in a linear magnetic field gradient, which is an extension of the conventional Monte Carlo (MC) method or the convolution method described by Wong et al. (in 12th SMRM, New York, 1993, p.10). In earlier NMR-diffusion simulation methods, such as the finite difference method (FD), the Monte Carlo method, and the deterministic convolution method, the outcome of the calculations depends on the simulation time step. In the authors' method, however, the results are independent of the time step, although, in the convolution method the step size has to be adequate for spins to diffuse to adjacent grid points. By always selecting the largest possible time step the computation time can therefore be reduced. Finally the authors point out that in simple geometric configurations their simulation algorithm can be used to reduce computation time in the simulation of restricted diffusion.

Theory of Stochastic Laplacian Growth

NASA Astrophysics Data System (ADS)

Alekseev, Oleg; Mineev-Weinstein, Mark

2017-07-01

We generalize the diffusion-limited aggregation by issuing many randomly-walking particles, which stick to a cluster at the discrete time unit providing its growth. Using simple combinatorial arguments we determine probabilities of different growth scenarios and prove that the most probable evolution is governed by the deterministic Laplacian growth equation. A potential-theoretical analysis of the growth probabilities reveals connections with the tau-function of the integrable dispersionless limit of the two-dimensional Toda hierarchy, normal matrix ensembles, and the two-dimensional Dyson gas confined in a non-uniform magnetic field. We introduce the time-dependent Hamiltonian, which generates transitions between different classes of equivalence of closed curves, and prove the Hamiltonian structure of the interface dynamics. Finally, we propose a relation between probabilities of growth scenarios and the semi-classical limit of certain correlation functions of "light" exponential operators in the Liouville conformal field theory on a pseudosphere.

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.

Continuous-time quantum random walks require discrete space

NASA Astrophysics Data System (ADS)

Manouchehri, K.; Wang, J. B.

2007-11-01

Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks.

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.

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

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.

Data-driven modelling of vertical dynamic excitation of bridges induced by people running

NASA Astrophysics Data System (ADS)

Racic, Vitomir; Morin, Jean Benoit

2014-02-01

With increasingly popular marathon events in urban environments, structural designers face a great deal of uncertainty when assessing dynamic performance of bridges occupied and dynamically excited by people running. While the dynamic loads induced by pedestrians walking have been intensively studied since the infamous lateral sway of the London Millennium Bridge in 2000, reliable and practical descriptions of running excitation are still very rare and limited. This interdisciplinary study has addressed the issue by bringing together a database of individual running force signals recorded by two state-of-the-art instrumented treadmills and two attempts to mathematically describe the measurements. The first modelling strategy is adopted from the available design guidelines for human walking excitation of structures, featuring perfectly periodic and deterministic characterisation of pedestrian forces presentable via Fourier series. This modelling approach proved to be inadequate for running loads due to the inherent near-periodic nature of the measured signals, a great inter-personal randomness of the dominant Fourier amplitudes and the lack of strong correlation between the amplitudes and running footfall rate. Hence, utilising the database established and motivated by the existing models of wind and earthquake loading, speech recognition techniques and a method of replicating electrocardiogram signals, this paper finally presents a numerical generator of random near-periodic running force signals which can reliably simulate the measurements. Such a model is an essential prerequisite for future quality models of dynamic loading induced by individuals, groups and crowds running under a wide range of conditions, such as perceptibly vibrating bridges and different combinations of visual, auditory and tactile cues.

From Random Walks to Brownian Motion, from Diffusion to Entropy: Statistical Principles in Introductory Physics

NASA Astrophysics Data System (ADS)

Reeves, Mark

2014-03-01

Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is dominant contribution of the entropy in driving important biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy) that enable students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce seemingly complex biological processes and structures to be described by tractable models that include deterministic processes and simple probabilistic inference. The students test these models in simulations and in laboratory experiments that are biologically relevant. The students are challenged to bridge the gap between statistical parameterization of their data (mean and standard deviation) and simple model-building by inference. This allows the students to quantitatively describe realistic cellular processes such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront ``random'' forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk will present a number of these exercises, with particular focus on the hands-on experiments done by the students, and will give examples of the tangible material that our students work with throughout the two-semester sequence of their course on introductory physics with a bio focus. Supported by NSF DUE.

Sampled-Data Consensus of Linear Multi-agent Systems With Packet Losses.

PubMed

Zhang, Wenbing; Tang, Yang; Huang, Tingwen; Kurths, Jurgen

In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.

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.

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.

Randomized central limit theorems: A unified theory.

PubMed

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

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

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.

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.

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.

Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

DOE PAGES

Rudinger, Kenneth; Gamble, John King; Bach, Eric; ...

2013-07-01

Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erencesmore » in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.« less

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.

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.

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

Genetic drift and selection in many-allele range expansions.

PubMed

Weinstein, Bryan T; Lavrentovich, Maxim O; Möbius, Wolfram; Murray, Andrew W; Nelson, David R

2017-12-01

We experimentally and numerically investigate the evolutionary dynamics of four competing strains of E. coli with differing expansion velocities in radially expanding colonies. We compare experimental measurements of the average fraction, correlation functions between strains, and the relative rates of genetic domain wall annihilations and coalescences to simulations modeling the population as a one-dimensional ring of annihilating and coalescing random walkers with deterministic biases due to selection. The simulations reveal that the evolutionary dynamics can be collapsed onto master curves governed by three essential parameters: (1) an expansion length beyond which selection dominates over genetic drift; (2) a characteristic angular correlation describing the size of genetic domains; and (3) a dimensionless constant quantifying the interplay between a colony's curvature at the frontier and its selection length scale. We measure these parameters with a new technique that precisely measures small selective differences between spatially competing strains and show that our simulations accurately predict the dynamics without additional fitting. Our results suggest that the random walk model can act as a useful predictive tool for describing the evolutionary dynamics of range expansions composed of an arbitrary number of genotypes with different fitnesses.

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.

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.

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…

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.

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

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.

Complex scaling behavior in animal foraging patterns

NASA Astrophysics Data System (ADS)

Premachandra, Prabhavi Kaushalya

This dissertation attempts to answer questions from two different areas of biology, ecology and neuroscience, using physics-based techniques. In Section 2, suitability of three competing random walk models is tested to describe the emergent movement patterns of two species of primates. The truncated power law (power law with exponential cut off) is the most suitable random walk model that characterizes the emergent movement patterns of these primates. In Section 3, an agent-based model is used to simulate search behavior in different environments (landscapes) to investigate the impact of the resource landscape on the optimal foraging movement patterns of deterministic foragers. It should be noted that this model goes beyond previous work in that it includes parameters such as spatial memory and satiation, which have received little consideration to date in the field of movement ecology. When the food availability is scarce in a tropical forest-like environment with feeding trees distributed in a clumped fashion and the size of those trees are distributed according to a lognormal distribution, the optimal foraging pattern of a generalist who can consume various and abundant food types indeed reaches the Levy range, and hence, show evidence for Levy-flight-like (power law distribution with exponent between 1 and 3) behavior. Section 4 of the dissertation presents an investigation of phase transition behavior in a network of locally coupled self-sustained oscillators as the system passes through various bursting states. The results suggest that a phase transition does not occur for this locally coupled neuronal network. The data analysis in the dissertation adopts a model selection approach and relies on methods based on information theory and maximum likelihood.

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.

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 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.

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.

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.

The structure of dilute combusting sprays

NASA Technical Reports Server (NTRS)

Shuen, J. S.; Solomon, A. S. P.; Faeth, F. M.

1985-01-01

An experimental and theoretical study of drop processes in a turbulent flame is described. The experiments involved a monodisperse (105 and 180 micro m initial diameter) stream of methanol drops injected at the base of a turbulent methane-fueled diffusion flame burning in still air. The following measurements were made: mean and fluctuating phase velocities, mean drop number flux, drop-size distributions and mean gas-phase temperatures. Measurements were compared with predictions of two separated flow models: (1) deterministic separated flow, where drop-turbulence interactions are ignored; and (2) stochastic separated flow, where drop-turbulence interactions are considered using random-walk computations. The stochastic separated flow analysis yielded best agreement with measurements, since it provides for turbulent dispersion of drops which was important for present test conditions (and probably for most combusting sprays as well). Distinguishing the presence or absence of envelope flames around the drops, however, was relatively unimportant for present test conditions, since the drops spent most of their lifetime in fuel-rich regions of the flow where this distinction is irrelevant.

The structure of particle-laden jets and nonevaporating sprays

NASA Technical Reports Server (NTRS)

Shuen, J. S.; Solomon, A. S. P.; Zhang, Q. F.; Faeth, G. M.

1983-01-01

Mean and fluctuating gas velocities, liquid mass fluxes and drop sizes were in nonevaporating sprays. These results, as well as existing measurements in solid particle-laden jets, were used to evaluate models of these processes. The following models were considered: (1) a locally homogeneous flow (LHF) model, where slip between the phases was neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of particle dispersion by turbulence were ignored; and (3) a stochastic separated flow (SSF) model, where effects of interphase slip and turbulent dispersion were considered using random-walk computations for particle motion. The LHF and DSF models did not provide very satisfactory predictions over the present data base. In contrast, the SSF model performed reasonably well - including conditions in nonevaporating sprays where enhanced dispersion of particles by turbulence caused the spray to spread more rapidly than single-phase jets for comparable conditions. While these results are encouraging, uncertainties in initial conditions limit the reliability of the evaluation. Current work is seeking to eliminate this deficiency.

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.

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.

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.

Mesoscopic description of random walks on combs

NASA Astrophysics Data System (ADS)

Méndez, Vicenç; Iomin, Alexander; Campos, Daniel; Horsthemke, Werner

2015-12-01

Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic method to obtain their transport properties. The random walk along the branches may be biased, and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone. We analyze the overall diffusion properties along the backbone and find normal diffusion, anomalous diffusion, and stochastic localization (diffusion failure), respectively, depending on the characteristics of the continuous time random walk along the branches, and compare our analytical results with stochastic simulations.

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.

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.

Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices

PubMed Central

Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan; Gross, Sam; Hills, Gage; Hornstein, Michael; Lakkam, Milinda; Lee, Jason; Li, Jian; Liu, Linxi; Sing-Long, Carlos; Marx, Mike; Mittal, Akshay; Monajemi, Hatef; No, Albert; Omrani, Reza; Pekelis, Leonid; Qin, Junjie; Raines, Kevin; Ryu, Ernest; Saxe, Andrew; Shi, Dai; Siilats, Keith; Strauss, David; Tang, Gary; Wang, Chaojun; Zhou, Zoey; Zhu, Zhen

2013-01-01

In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to for four different sets , and the results establish our finding for each of the four associated phase transitions. PMID:23277588

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.

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.

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.

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).

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.

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 }.

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.

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.

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.

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.

Origins and applications of the Montroll-Weiss continuous time random walk

NASA Astrophysics Data System (ADS)

Shlesinger, Michael F.

2017-05-01

The Continuous Time Random Walk (CTRW) was introduced by Montroll and Weiss in 1965 in a purely mathematical paper. Its antecedents and later applications beginning in 1973 are discussed, especially for the case of fractal time where the mean waiting time between jumps is infinite. 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.

Integrability and Chaos: The Classical Uncertainty

ERIC Educational Resources Information Center

Masoliver, Jaume; Ros, Ana

2011-01-01

In recent years there has been a considerable increase in the publishing of textbooks and monographs covering what was formerly known as random or irregular deterministic motion, now referred to as deterministic chaos. There is still substantial interest in a matter that is included in many graduate and even undergraduate courses on classical…

The development of the deterministic nonlinear PDEs in particle physics to stochastic case

NASA Astrophysics Data System (ADS)

Abdelrahman, Mahmoud A. E.; Sohaly, M. A.

2018-06-01

In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution.

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.

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.

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.

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.

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.

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.

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.

Quantitative analysis of random ameboid motion

NASA Astrophysics Data System (ADS)

Bödeker, H. U.; Beta, C.; Frank, T. D.; Bodenschatz, E.

2010-04-01

We quantify random migration of the social ameba Dictyostelium discoideum. We demonstrate that the statistics of cell motion can be described by an underlying Langevin-type stochastic differential equation. An analytic expression for the velocity distribution function is derived. The separation into deterministic and stochastic parts of the movement shows that the cells undergo a damped motion with multiplicative noise. Both contributions to the dynamics display a distinct response to external physiological stimuli. The deterministic component depends on the developmental state and ambient levels of signaling substances, while the stochastic part does not.

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.

Stochastic assembly in a subtropical forest chronosequence: evidence from contrasting changes of species, phylogenetic and functional dissimilarity over succession.

PubMed

Mi, Xiangcheng; Swenson, Nathan G; Jia, Qi; Rao, Mide; Feng, Gang; Ren, Haibao; Bebber, Daniel P; Ma, Keping

2016-09-07

Deterministic and stochastic processes jointly determine the community dynamics of forest succession. However, it has been widely held in previous studies that deterministic processes dominate forest succession. Furthermore, inference of mechanisms for community assembly may be misleading if based on a single axis of diversity alone. In this study, we evaluated the relative roles of deterministic and stochastic processes along a disturbance gradient by integrating species, functional, and phylogenetic beta diversity in a subtropical forest chronosequence in Southeastern China. We found a general pattern of increasing species turnover, but little-to-no change in phylogenetic and functional turnover over succession at two spatial scales. Meanwhile, the phylogenetic and functional beta diversity were not significantly different from random expectation. This result suggested a dominance of stochastic assembly, contrary to the general expectation that deterministic processes dominate forest succession. On the other hand, we found significant interactions of environment and disturbance and limited evidence for significant deviations of phylogenetic or functional turnover from random expectations for different size classes. This result provided weak evidence of deterministic processes over succession. Stochastic assembly of forest succession suggests that post-disturbance restoration may be largely unpredictable and difficult to control in subtropical forests.

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

Random Walks in a One-Dimensional Lévy Random Environment

NASA Astrophysics Data System (ADS)

Bianchi, Alessandra; Cristadoro, Giampaolo; Lenci, Marco; Ligabò, Marilena

2016-04-01

We consider a generalization of a one-dimensional stochastic process known in the physical literature as Lévy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random walk on the point process, proving the CLT and the convergence of all the accordingly rescaled moments. Then we derive the quenched and annealed CLTs for the continuous-time process.

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.

Learning automata-based solutions to the nonlinear fractional knapsack problem with applications to optimal resource allocation.

PubMed

Granmo, Ole-Christoffer; Oommen, B John; Myrer, Svein Arild; Olsen, Morten Goodwin

2007-02-01

This paper considers the nonlinear fractional knapsack problem and demonstrates how its solution can be effectively applied to two resource allocation problems dealing with the World Wide Web. The novel solution involves a "team" of deterministic learning automata (LA). The first real-life problem relates to resource allocation in web monitoring so as to "optimize" information discovery when the polling capacity is constrained. The disadvantages of the currently reported solutions are explained in this paper. The second problem concerns allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. This is the scenario encountered when the user has to evaluate multiple web sites by accessing a limited number of web pages, and the proportions of interest are the fraction of each web site that is successfully validated by an HTML validator. Using the general LA paradigm to tackle both of the real-life problems, the proposed scheme improves a current solution in an online manner through a series of informed guesses that move toward the optimal solution. At the heart of the scheme, a team of deterministic LA performs a controlled random walk on a discretized solution space. Comprehensive experimental results demonstrate that the discretization resolution determines the precision of the scheme, and that for a given precision, the current solution (to both problems) is consistently improved until a nearly optimal solution is found--even for switching environments. Thus, the scheme, while being novel to the entire field of LA, also efficiently handles a class of resource allocation problems previously not addressed in the literature.

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.

Deterministic and probabilistic analysis of damping device resistance under impact loads from nuclear fuel container drop

NASA Astrophysics Data System (ADS)

Kala, J.; Bajer, M.; Barnat, J.; Smutný, J.

2010-12-01

Pedestrian-induced vibrations are a criterion for serviceability. This loading is significant for light-weight footbridge structures, but was established as a basic loading for the ceilings of various ordinary buildings. Wide variations of this action exist. To verify the different conclusions of various authors, vertical pressure measurements invoked during walking were performed. In the article the approaches of different design codes are also shown.

Counterfactual Quantum Deterministic Key Distribution

NASA Astrophysics Data System (ADS)

Zhang, Sheng; Wang, Jian; Tang, Chao-Jing

2013-01-01

We propose a new counterfactual quantum cryptography protocol concerning about distributing a deterministic key. By adding a controlled blocking operation module to the original protocol [T.G. Noh, Phys. Rev. Lett. 103 (2009) 230501], the correlation between the polarizations of the two parties, Alice and Bob, is extended, therefore, one can distribute both deterministic keys and random ones using our protocol. We have also given a simple proof of the security of our protocol using the technique we ever applied to the original protocol. Most importantly, our analysis produces a bound tighter than the existing ones.

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.

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.

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

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.

Aspen succession in the Intermountain West: A deterministic model

Treesearch

Dale L. Bartos; Frederick R. Ward; George S. Innis

1983-01-01

A deterministic model of succession in aspen forests was developed using existing data and intuition. The degree of uncertainty, which was determined by allowing the parameter values to vary at random within limits, was larger than desired. This report presents results of an analysis of model sensitivity to changes in parameter values. These results have indicated...

Taking Control: Stealth Assessment of Deterministic Behaviors within a Game-Based System

ERIC Educational Resources Information Center

Snow, Erica L.; Likens, Aaron D.; Allen, Laura K.; McNamara, Danielle S.

2016-01-01

Game-based environments frequently afford students the opportunity to exert agency over their learning paths by making various choices within the environment. The combination of log data from these systems and dynamic methodologies may serve as a stealth means to assess how students behave (i.e., deterministic or random) within these learning…

Taking Control: Stealth Assessment of Deterministic Behaviors within a Game-Based System

ERIC Educational Resources Information Center

Snow, Erica L.; Likens, Aaron D.; Allen, Laura K.; McNamara, Danielle S.

2015-01-01

Game-based environments frequently afford students the opportunity to exert agency over their learning paths by making various choices within the environment. The combination of log data from these systems and dynamic methodologies may serve as a stealth means to assess how students behave (i.e., deterministic or random) within these learning…

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...

Rare Event Simulation in Radiation Transport

NASA Astrophysics Data System (ADS)

Kollman, Craig

This dissertation studies methods for estimating extremely small probabilities by Monte Carlo simulation. Problems in radiation transport typically involve estimating very rare events or the expected value of a random variable which is with overwhelming probability equal to zero. These problems often have high dimensional state spaces and irregular geometries so that analytic solutions are not possible. Monte Carlo simulation must be used to estimate the radiation dosage being transported to a particular location. If the area is well shielded the probability of any one particular particle getting through is very small. Because of the large number of particles involved, even a tiny fraction penetrating the shield may represent an unacceptable level of radiation. It therefore becomes critical to be able to accurately estimate this extremely small probability. Importance sampling is a well known technique for improving the efficiency of rare event calculations. Here, a new set of probabilities is used in the simulation runs. The results are multiplied by the likelihood ratio between the true and simulated probabilities so as to keep our estimator unbiased. The variance of the resulting estimator is very sensitive to which new set of transition probabilities are chosen. It is shown that a zero variance estimator does exist, but that its computation requires exact knowledge of the solution. A simple random walk with an associated killing model for the scatter of neutrons is introduced. Large deviation results for optimal importance sampling in random walks are extended to the case where killing is present. An adaptive "learning" algorithm for implementing importance sampling is given for more general Markov chain models of neutron scatter. For finite state spaces this algorithm is shown to give, with probability one, a sequence of estimates converging exponentially fast to the true solution. In the final chapter, an attempt to generalize this algorithm to a continuous state space is made. This involves partitioning the space into a finite number of cells. There is a tradeoff between additional computation per iteration and variance reduction per iteration that arises in determining the optimal grid size. All versions of this algorithm can be thought of as a compromise between deterministic and Monte Carlo methods, capturing advantages of both techniques.

Algorithm refinement for stochastic partial differential equations: II. Correlated systems

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

Alexander, Francis J.; Garcia, Alejandro L.; Tartakovsky, Daniel M.

2005-08-10

We analyze a hybrid particle/continuum algorithm for a hydrodynamic system with long ranged correlations. Specifically, we consider the so-called train model for viscous transport in gases, which is based on a generalization of the random walk process for the diffusion of momentum. This discrete model is coupled with its continuous counterpart, given by a pair of stochastic partial differential equations. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass and momentum conservation. This methodology is an extension of our stochastic Algorithm Refinement (AR) hybrid for simple diffusion [F. Alexander, A. Garcia,more » D. Tartakovsky, Algorithm refinement for stochastic partial differential equations: I. Linear diffusion, J. Comput. Phys. 182 (2002) 47-66]. Results from a variety of numerical experiments are presented for steady-state scenarios. In all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the long-range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude.« less

Particle-laden swirling free jets: Measurements and predictions

NASA Technical Reports Server (NTRS)

Bulzan, D. L.; Shuen, J.-S.; Faeth, G. M.

1987-01-01

A theoretical and experimental investigation of single-phase and particle-laden weakly swirling jets was conducted. The jets were injected vertically downward from a 19 mm diameter tube with swirl numbers ranging from 0 to 0.33. The particle-laden jets had a single loading ratio (0.2) with particles having a SMD of 39 microns. Mean and fluctuating properties of both phases were measured using nonintrusive laser based methods while particle mass flux was measured using an isokinetic sampling probe. The continuous phase was analyzed using both a baseline kappa-epsilon turbulence model and an extended version with modifications based on the flux Richardson number to account for effects of streamline curvature. To highlight effects of interphase transport rates and particle/turbulence interactions, effects of the particles were analyzed as follows: (1) locally homogeneous flow (LHF) analysis, where interphase transport rates are assumed to be infinitely fast; (2) deterministic separated flow (DSF) analysis, where finite interphase transport rates are considered but particle/turbulence interactions are ignored; and (3) stochastic separated flow (SSF) analysis, where both effects are considered using random-walk computations.

Probabilistic track coverage in cooperative sensor networks.

PubMed

Ferrari, Silvia; Zhang, Guoxian; Wettergren, Thomas A

2010-12-01

The quality of service of a network performing cooperative track detection is represented by the probability of obtaining multiple elementary detections over time along a target track. Recently, two different lines of research, namely, distributed-search theory and geometric transversals, have been used in the literature for deriving the probability of track detection as a function of random and deterministic sensors' positions, respectively. In this paper, we prove that these two approaches are equivalent under the same problem formulation. Also, we present a new performance function that is derived by extending the geometric-transversal approach to the case of random sensors' positions using Poisson flats. As a result, a unified approach for addressing track detection in both deterministic and probabilistic sensor networks is obtained. The new performance function is validated through numerical simulations and is shown to bring about considerable computational savings for both deterministic and probabilistic sensor networks.

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.

Anomalous Diffusion of Single Particles in Cytoplasm

PubMed Central

Regner, Benjamin M.; Vučinić, Dejan; Domnisoru, Cristina; Bartol, Thomas M.; Hetzer, Martin W.; Tartakovsky, Daniel M.; Sejnowski, Terrence J.

2013-01-01

The crowded intracellular environment poses a formidable challenge to experimental and theoretical analyses of intracellular transport mechanisms. Our measurements of single-particle trajectories in cytoplasm and their random-walk interpretations elucidate two of these mechanisms: molecular diffusion in crowded environments and cytoskeletal transport along microtubules. We employed acousto-optic deflector microscopy to map out the three-dimensional trajectories of microspheres migrating in the cytosolic fraction of a cellular extract. Classical Brownian motion (BM), continuous time random walk, and fractional BM were alternatively used to represent these trajectories. The comparison of the experimental and numerical data demonstrates that cytoskeletal transport along microtubules and diffusion in the cytosolic fraction exhibit anomalous (nonFickian) behavior and posses statistically distinct signatures. Among the three random-walk models used, continuous time random walk provides the best representation of diffusion, whereas microtubular transport is accurately modeled with fractional BM. PMID:23601312

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 logic using correlated one-dimensional quantum walks

NASA Astrophysics Data System (ADS)

Lahini, Yoav; Steinbrecher, Gregory R.; Bookatz, Adam D.; Englund, Dirk

2018-01-01

Quantum Walks are unitary processes describing the evolution of an initially localized wavefunction on a lattice potential. The complexity of the dynamics increases significantly when several indistinguishable quantum walkers propagate on the same lattice simultaneously, as these develop non-trivial spatial correlations that depend on the particle's quantum statistics, mutual interactions, initial positions, and the lattice potential. We show that even in the simplest case of a quantum walk on a one dimensional graph, these correlations can be shaped to yield a complete set of compact quantum logic operations. We provide detailed recipes for implementing quantum logic on one-dimensional quantum walks in two general cases. For non-interacting bosons—such as photons in waveguide lattices—we find high-fidelity probabilistic quantum gates that could be integrated into linear optics quantum computation schemes. For interacting quantum-walkers on a one-dimensional lattice—a situation that has recently been demonstrated using ultra-cold atoms—we find deterministic logic operations that are universal for quantum information processing. The suggested implementation requires minimal resources and a level of control that is within reach using recently demonstrated techniques. Further work is required to address error-correction.

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.

Estimating the epidemic threshold on networks by deterministic connections

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

Li, Kezan, E-mail: lkzzr@sohu.com; Zhu, Guanghu; Fu, Xinchu

2014-12-15

For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect thanmore » those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.« less

Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties

NASA Astrophysics Data System (ADS)

Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing; Walker, Paul D.

2017-02-01

This paper proposes an uncertain modelling and computational method to analyze dynamic responses of rigid-flexible multibody systems (or mechanisms) with random geometry and material properties. Firstly, the deterministic model for the rigid-flexible multibody system is built with the absolute node coordinate formula (ANCF), in which the flexible parts are modeled by using ANCF elements, while the rigid parts are described by ANCF reference nodes (ANCF-RNs). Secondly, uncertainty for the geometry of rigid parts is expressed as uniform random variables, while the uncertainty for the material properties of flexible parts is modeled as a continuous random field, which is further discretized to Gaussian random variables using a series expansion method. Finally, a non-intrusive numerical method is developed to solve the dynamic equations of systems involving both types of random variables, which systematically integrates the deterministic generalized-α solver with Latin Hypercube sampling (LHS) and Polynomial Chaos (PC) expansion. The benchmark slider-crank mechanism is used as a numerical example to demonstrate the characteristics of the proposed method.

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.

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.

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.

Random-Walk Type Model with Fat Tails for Financial Markets

NASA Astrophysics Data System (ADS)

Matuttis, Hans-Geors

Starting from the random-walk model, practices of financial markets are included into the random-walk so that fat tail distributions like those in the high frequency data of the SP500 index are reproduced, though the individual mechanisms are modeled by normally distributed data. The incorporation of local correlation narrows the distribution for "frequent" events, whereas global correlations due to technical analysis leads to fat tails. Delay of market transactions in the trading process shifts the fat tail probabilities downwards. Such an inclusion of reactions to market fluctuations leads to mini-trends which are distributed with unit variance.

Optoenergy storage and random walks assisted broadband amplification in Er3+-doped (Pb,La)(Zr,Ti)O3 disordered ceramics.

PubMed

Xu, Long; Zhao, Hua; Xu, Caixia; Zhang, Siqi; Zou, Yingyin K; Zhang, Jingwen

2014-02-01

A broadband optical amplification was observed and investigated in Er3+-doped electrostrictive ceramics of lanthanum-modified lead zirconate titanate under a corona atmosphere. The ceramic structure change caused by UV light, electric field, and random walks originated from the diffusive process in intrinsically disordered materials may all contribute to the optical amplification and the associated energy storage. Discussion based on optical energy storage and diffusive equations was given to explain the findings. Those experiments performed made it possible to study random walks and optical amplification in transparent ceramics materials.

A complexity theory model in science education problem solving: random walks for working memory and mental capacity.

PubMed

Stamovlasis, Dimitrios; Tsaparlis, Georgios

2003-07-01

The present study examines the role of limited human channel capacity from a science education perspective. A model of science problem solving has been previously validated by applying concepts and tools of complexity theory (the working memory, random walk method). The method correlated the subjects' rank-order achievement scores in organic-synthesis chemistry problems with the subjects' working memory capacity. In this work, we apply the same nonlinear approach to a different data set, taken from chemical-equilibrium problem solving. In contrast to the organic-synthesis problems, these problems are algorithmic, require numerical calculations, and have a complex logical structure. As a result, these problems cause deviations from the model, and affect the pattern observed with the nonlinear method. In addition to Baddeley's working memory capacity, the Pascual-Leone's mental (M-) capacity is examined by the same random-walk method. As the complexity of the problem increases, the fractal dimension of the working memory random walk demonstrates a sudden drop, while the fractal dimension of the M-capacity random walk decreases in a linear fashion. A review of the basic features of the two capacities and their relation is included. The method and findings have consequences for problem solving not only in chemistry and science education, but also in other disciplines.

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

NASA Astrophysics Data System (ADS)

Salimi, S.; Jafarizadeh, M. A.

2009-06-01

In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product Cayley graphs (complete cycle, complete Kn, charter and n-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as t → ∞ but for quantum state is not always satisfied.

Dynamic speckle - Interferometry of micro-displacements

NASA Astrophysics Data System (ADS)

Vladimirov, A. P.

2012-06-01

The problem of the dynamics of speckles in the image plane of the object, caused by random movements of scattering centers is solved. We consider three cases: 1) during the observation the points move at random, but constant speeds, and 2) the relative displacement of any pair of points is a continuous random process, and 3) the motion of the centers is the sum of a deterministic movement and random displacement. For the cases 1) and 2) the characteristics of temporal and spectral autocorrelation function of the radiation intensity can be used for determining of individually and the average relative displacement of the centers, their dispersion and the relaxation time. For the case 3) is showed that under certain conditions, the optical signal contains a periodic component, the number of periods is proportional to the derivations of the deterministic displacements. The results of experiments conducted to test and application of theory are given.

Modeling 2D and 3D diffusion.

PubMed

Saxton, Michael J

2007-01-01

Modeling obstructed diffusion is essential to the understanding of diffusion-mediated processes in the crowded cellular environment. Simple Monte Carlo techniques for modeling obstructed random walks are explained and related to Brownian dynamics and more complicated Monte Carlo methods. Random number generation is reviewed in the context of random walk simulations. Programming techniques and event-driven algorithms are discussed as ways to speed simulations.

Walking Aids Moderate Exercise Effects on Gait Speed in People With Dementia: A Randomized Controlled Trial.

PubMed

Toots, Annika; Littbrand, Håkan; Holmberg, Henrik; Nordström, Peter; Lundin-Olsson, Lillemor; Gustafson, Yngve; Rosendahl, Erik

2017-03-01

To investigate the effects of exercise on gait speed, when tested using walking aids and without, and whether effects differed according to amount of support in the test. A cluster-randomized controlled trial. The Umeå Dementia and Exercise (UMDEX) study was set in 16 nursing homes in Umeå, Sweden. One hundred forty-one women and 45 men (mean age 85 years) with dementia, of whom 145 (78%) habitually used walking aids. Participants were randomized to the high-intensity functional exercise program or a seated attention control activity. Blinded assessors measured 4-m usual gait speed with walking aids if any gait speed (GS), and without walking aids and with minimum amount of support, at baseline, 4 months (on intervention completion), and 7 months. Linear mixed models showed no between-group effect in either gait speed test at 4 or 7 months. In interaction analyses exercise effects differed significantly between participants who walked unsupported compared with when walking aids or minimum support was used. Positive between-group exercise effects on gait speed (m/s) were found in subgroups that walked unsupported at 4 and 7 months (GS: 0.07, P = .009 and 0.13, P < .001; and GS test without walking aids: 0.05, P = .011 and 0.07, P = .029, respectively). In people with dementia living in nursing homes exercise had positive effects on gait when tested unsupported compared with when walking aids or minimum support was used. The study suggests that the use of walking aids in gait speed tests may conceal exercise effects. Copyright © 2016 AMDA – The Society for Post-Acute and Long-Term Care Medicine. Published by Elsevier Inc. All rights reserved.

Screening effects in flow through rough channels.

PubMed

Andrade, J S; Araújo, A D; Filoche, M; Sapoval, B

2007-05-11

A surprising similarity is found between the distribution of hydrodynamic stress on the wall of an irregular channel and the distribution of flux from a purely Laplacian field on the same geometry. This finding is a direct outcome of numerical simulations of the Navier-Stokes equations for flow at low Reynolds numbers in two-dimensional channels with rough walls presenting either deterministic or random self-similar geometries. For high Reynolds numbers, the distribution of wall stresses on deterministic and random fractal rough channels becomes substantially dependent on the microscopic details of the walls geometry. Finally, the effects on the flow behavior of the channel symmetry and aspect ratio are also investigated.

On problems of analyzing aerodynamic properties of blunted rotary bodies with small random surface distortions under supersonic and hypersonic flows

NASA Astrophysics Data System (ADS)

Degtyar, V. G.; Kalashnikov, S. T.; Mokin, Yu. A.

2017-10-01

The paper considers problems of analyzing aerodynamic properties (ADP) of reenetry vehicles (RV) as blunted rotary bodies with small random surface distortions. The interactions of math simulation of surface distortions, selection of tools for predicting ADPs of shaped bodies, evaluation of different-type ADP variations and their adaptation for dynamic problems are analyzed. The possibilities of deterministic and probabilistic approaches to evaluation of ADP variations are considered. The practical value of the probabilistic approach is demonstrated. The examples of extremal deterministic evaluations of ADP variations for a sphere and a sharp cone are given.

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.

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.

Random walk to a nonergodic equilibrium concept

NASA Astrophysics Data System (ADS)

Bel, G.; Barkai, E.

2006-01-01

Random walk models, such as the trap model, continuous time random walks, and comb models, exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this paper a nonergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. We show that when conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics. In the ergodic phase the distribution function of the occupation times approaches a δ function centered on the value predicted based on standard Boltzmann-Gibbs statistics. The relation of our work to single-molecule experiments is briefly discussed.

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.

Methods for a Randomized Trial of Weight-Supported Treadmill Training versus Conventional Training for Walking during Inpatient Rehabilitation after Incomplete Traumatic Spinal Cord Injury

PubMed Central

Dobkin, Bruce H.; Apple, David; Barbeau, Hugues; Basso, Michele; Behrman, Andrea; Deforge, Dan; Ditunno, John; Dudley, Gary; Elashoff, Robert; Fugate, Lisa; Harkema, Susan; Saulino, Michael; Scott, Michael

2014-01-01

The authors describe the rationale and methodology for the first prospective, multicenter, randomized clinical trial (RCT) of a task-oriented walking intervention for subjects during early rehabilitation for an acute traumatic spinal cord injury (SCI). The experimental strategy, body weight–supported treadmill training (BWSTT), allows physical therapists to systematically train patients to walk on a treadmill at increasing speeds typical of community ambulation with increasing weight bearing. The therapists provide verbal and tactile cues to facilitate the kinematic, kinetic, and temporal features of walking. Subjects were randomly assigned to a conventional therapy program for mobility versus the same intensity and duration of a combination of BWSTT and over-ground locomotor retraining. Subjects had an incomplete SCI (American Spinal Injury Association grades B, C, and D) from C-4 to T-10 (upper motoneuron group) or from T-11 to L-3 (lower motoneuron group). Within 8 weeks of a SCI, 146 subjects were entered for 12 weeks of intervention. The 2 single-blinded primary outcome measures are the level of independence for ambulation and, for those who are able to walk, the maximal speed for walking 50 feet, tested 6 and 12 months after randomization. The trial’s methodology offers a model for the feasibility of translating neuroscientific experiments into a RCT to develop evidence-based rehabilitation practices. PMID:14503436

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.

Chemical Distances for Percolation of Planar Gaussian Free Fields and Critical Random Walk Loop Soups

NASA Astrophysics Data System (ADS)

Ding, Jian; Li, Li

2018-05-01

We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.

Chemical Distances for Percolation of Planar Gaussian Free Fields and Critical Random Walk Loop Soups

NASA Astrophysics Data System (ADS)

Ding, Jian; Li, Li

2018-06-01

We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.

Treadmill training improves overground walking economy in Parkinson's disease: a randomized, controlled pilot study.

PubMed

Fernández-Del-Olmo, Miguel Angel; Sanchez, Jose Andres; Bello, Olalla; Lopez-Alonso, Virginia; Márquez, Gonzalo; Morenilla, Luis; Castro, Xabier; Giraldez, Manolo; Santos-García, Diego

2014-01-01

Gait disturbances are one of the principal and most incapacitating symptoms of Parkinson's disease (PD). In addition, walking economy is impaired in PD patients and could contribute to excess fatigue in this population. An important number of studies have shown that treadmill training can improve kinematic parameters in PD patients. However, the effects of treadmill and overground walking on the walking economy remain unknown. The goal of this study was to explore the walking economy changes in response to a treadmill and an overground training program, as well as the differences in the walking economy during treadmill and overground walking. Twenty-two mild PD patients were randomly assigned to a treadmill or overground training group. The training program consisted of 5 weeks (3 sessions/week). We evaluated the energy expenditure of overground walking, before and after each of the training programs. The energy expenditure of treadmill walking (before the program) was also evaluated. The treadmill, but not the overground training program, lead to an improvement in the walking economy (the rate of oxygen consumed per distance during overground walking at a preferred speed) in PD patients. In addition, walking on a treadmill required more energy expenditure compared with overground walking at the same speed. This study provides evidence that in mild PD patients, treadmill training is more beneficial compared with that of walking overground, leading to a greater improvement in the walking economy. This finding is of clinical importance for the therapeutic administration of exercise in PD.

Combinatorial vector fields and the valley structure of fitness landscapes.

PubMed

Stadler, Bärbel M R; Stadler, Peter F

2010-12-01

Adaptive (downhill) walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. Here we develop a framework that interprets adaptive walks as deterministic trajectories in combinatorial vector fields and in return associate these combinatorial vector fields with weights that measure their steepness across the landscape. We show that the combinatorial vector fields and their weights have a product structure that is governed by the neutrality of the landscape. This product structure makes practical computations feasible. The framework presented here also provides an alternative, and mathematically more convenient, way of defining notions of valleys, saddle points, and barriers in landscape. As an application, we propose a refined approximation for transition rates between macrostates that are associated with the valleys of the landscape.

Convex hulls of random walks in higher dimensions: A large-deviation study

NASA Astrophysics Data System (ADS)

Schawe, Hendrik; Hartmann, Alexander K.; Majumdar, Satya N.

2017-12-01

The distribution of the hypervolume V and surface ∂ V of convex hulls of (multiple) random walks in higher dimensions are determined numerically, especially containing probabilities far smaller than P =10-1000 to estimate large deviation properties. For arbitrary dimensions and large walk lengths T , we suggest a scaling behavior of the distribution with the length of the walk T similar to the two-dimensional case and behavior of the distributions in the tails. We underpin both with numerical data in d =3 and d =4 dimensions. Further, we confirm the analytically known means of those distributions and calculate their variances for large T .

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.

How the growth rate of host cells affects cancer risk in a deterministic way

NASA Astrophysics Data System (ADS)

Draghi, Clément; Viger, Louise; Denis, Fabrice; Letellier, Christophe

2017-09-01

It is well known that cancers are significantly more often encountered in some tissues than in other ones. In this paper, by using a deterministic model describing the interactions between host, effector immune and tumor cells at the tissue level, we show that this can be explained by the dependency of tumor growth on parameter values characterizing the type as well as the state of the tissue considered due to the "way of life" (environmental factors, food consumption, drinking or smoking habits, etc.). Our approach is purely deterministic and, consequently, the strong correlation (r = 0.99) between the number of detectable growing tumors and the growth rate of cells from the nesting tissue can be explained without evoking random mutation arising during DNA replications in nonmalignant cells or "bad luck". Strategies to limit the mortality induced by cancer could therefore be well based on improving the way of life, that is, by better preserving the tissue where mutant cells randomly arise.

Random walks with random velocities.

PubMed

Zaburdaev, Vasily; Schmiedeberg, Michael; Stark, Holger

2008-07-01

We consider a random walk model that takes into account the velocity distribution of random walkers. Random motion with alternating velocities is inherent to various physical and biological systems. Moreover, the velocity distribution is often the first characteristic that is experimentally accessible. Here, we derive transport equations describing the dispersal process in the model and solve them analytically. The asymptotic properties of solutions are presented in the form of a phase diagram that shows all possible scaling regimes, including superdiffusive, ballistic, and superballistic motion. The theoretical results of this work are in excellent agreement with accompanying numerical simulations.

Random attractor of non-autonomous stochastic Boussinesq lattice system

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

Zhao, Min, E-mail: zhaomin1223@126.com; Zhou, Shengfan, E-mail: zhoushengfan@yahoo.com

2015-09-15

In this paper, we first consider the existence of tempered random attractor for second-order non-autonomous stochastic lattice dynamical system of nonlinear Boussinesq equations effected by time-dependent coupled coefficients and deterministic forces and multiplicative white noise. Then, we establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

Randomized central limit theorems: A unified theory

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

Exploring activity-driven network with biased walks

NASA Astrophysics Data System (ADS)

Wang, Yan; Wu, Ding Juan; Lv, Fang; Su, Meng Long

We investigate the concurrent dynamics of biased random walks and the activity-driven network, where the preferential transition probability is in terms of the edge-weighting parameter. We also obtain the analytical expressions for stationary distribution and the coverage function in directed and undirected networks, all of which depend on the weight parameter. Appropriately adjusting this parameter, more effective search strategy can be obtained when compared with the unbiased random walk, whether in directed or undirected networks. Since network weights play a significant role in the diffusion process.

Finding paths in tree graphs with a quantum walk

NASA Astrophysics Data System (ADS)

Koch, Daniel; Hillery, Mark

2018-01-01

We analyze the potential for different types of searches using the formalism of scattering random walks on quantum computers. Given a particular type of graph consisting of nodes and connections, a "tree maze," we would like to find a selected final node as quickly as possible, faster than any classical search algorithm. We show that this can be done using a quantum random walk, both through numerical calculations as well as by using the eigenvectors and eigenvalues of the quantum system.

Quantum walk computation

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

Kendon, Viv

2014-12-04

Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. Recent results showing quantum walks are “universal for quantum computation” relate to algorithms, to be run on quantum computers. We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer.

Characterization of normality of chaotic systems including prediction and detection of anomalies

NASA Astrophysics Data System (ADS)

Engler, Joseph John

Accurate prediction and control pervades domains such as engineering, physics, chemistry, and biology. Often, it is discovered that the systems under consideration cannot be well represented by linear, periodic nor random data. It has been shown that these systems exhibit deterministic chaos behavior. Deterministic chaos describes systems which are governed by deterministic rules but whose data appear to be random or quasi-periodic distributions. Deterministically chaotic systems characteristically exhibit sensitive dependence upon initial conditions manifested through rapid divergence of states initially close to one another. Due to this characterization, it has been deemed impossible to accurately predict future states of these systems for longer time scales. Fortunately, the deterministic nature of these systems allows for accurate short term predictions, given the dynamics of the system are well understood. This fact has been exploited in the research community and has resulted in various algorithms for short term predictions. Detection of normality in deterministically chaotic systems is critical in understanding the system sufficiently to able to predict future states. Due to the sensitivity to initial conditions, the detection of normal operational states for a deterministically chaotic system can be challenging. The addition of small perturbations to the system, which may result in bifurcation of the normal states, further complicates the problem. The detection of anomalies and prediction of future states of the chaotic system allows for greater understanding of these systems. The goal of this research is to produce methodologies for determining states of normality for deterministically chaotic systems, detection of anomalous behavior, and the more accurate prediction of future states of the system. Additionally, the ability to detect subtle system state changes is discussed. The dissertation addresses these goals by proposing new representational techniques and novel prediction methodologies. The value and efficiency of these methods are explored in various case studies. Presented is an overview of chaotic systems with examples taken from the real world. A representation schema for rapid understanding of the various states of deterministically chaotic systems is presented. This schema is then used to detect anomalies and system state changes. Additionally, a novel prediction methodology which utilizes Lyapunov exponents to facilitate longer term prediction accuracy is presented and compared with other nonlinear prediction methodologies. These novel methodologies are then demonstrated on applications such as wind energy, cyber security and classification of social networks.

Random walk in generalized quantum theory

NASA Astrophysics Data System (ADS)

Martin, Xavier; O'Connor, Denjoe; Sorkin, Rafael D.

2005-01-01

One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we “quantize” the classical random walk by finding, subject to a certain condition of “strong positivity”, the most general Markovian, translationally invariant “decoherence functional” with nearest neighbor transitions.

Financial Data Analysis by means of Coupled Continuous-Time Random Walk in Rachev-Rűschendorf Model

NASA Astrophysics Data System (ADS)

Jurlewicz, A.; Wyłomańska, A.; Żebrowski, P.

2008-09-01

We adapt the continuous-time random walk formalism to describe asset price evolution. We expand the idea proposed by Rachev and Rűschendorf who analyzed the binomial pricing model in the discrete time with randomization of the number of price changes. As a result, in the framework of the proposed model we obtain a mixture of the Gaussian and a generalized arcsine laws as the limiting distribution of log-returns. Moreover, we derive an European-call-option price that is an extension of the Black-Scholes formula. We apply the obtained theoretical results to model actual financial data and try to show that the continuous-time random walk offers alternative tools to deal with several complex issues of financial markets.

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.

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.

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

Stochasticity and determinism in models of hematopoiesis.

PubMed

Kimmel, Marek

2014-01-01

This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.

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.

A Stochastic Simulation Framework for the Prediction of Strategic Noise Mapping and Occupational Noise Exposure Using the Random Walk Approach

PubMed Central

Haron, Zaiton; Bakar, Suhaimi Abu; Dimon, Mohamad Ngasri

2015-01-01

Strategic noise mapping provides important information for noise impact assessment and noise abatement. However, producing reliable strategic noise mapping in a dynamic, complex working environment is difficult. This study proposes the implementation of the random walk approach as a new stochastic technique to simulate noise mapping and to predict the noise exposure level in a workplace. A stochastic simulation framework and software, namely RW-eNMS, were developed to facilitate the random walk approach in noise mapping prediction. This framework considers the randomness and complexity of machinery operation and noise emission levels. Also, it assesses the impact of noise on the workers and the surrounding environment. For data validation, three case studies were conducted to check the accuracy of the prediction data and to determine the efficiency and effectiveness of this approach. The results showed high accuracy of prediction results together with a majority of absolute differences of less than 2 dBA; also, the predicted noise doses were mostly in the range of measurement. Therefore, the random walk approach was effective in dealing with environmental noises. It could predict strategic noise mapping to facilitate noise monitoring and noise control in the workplaces. PMID:25875019

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 generalized model via random walks for information filtering

NASA Astrophysics Data System (ADS)

Ren, Zhuo-Ming; Kong, Yixiu; Shang, Ming-Sheng; Zhang, Yi-Cheng

2016-08-01

There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation.

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.

Metastability of Reversible Random Walks in Potential Fields

NASA Astrophysics Data System (ADS)

Landim, C.; Misturini, R.; Tsunoda, K.

2015-09-01

Let be an open and bounded subset of , and let be a twice continuously differentiable function. Denote by the discretization of , , and denote by the continuous-time, nearest-neighbor, random walk on which jumps from to at rate . We examine in this article the metastable behavior of among the wells of the potential F.

Electrical Resistance of the Low Dimensional Critical Branching Random Walk

NASA Astrophysics Data System (ADS)

Járai, Antal A.; Nachmias, Asaf

2014-10-01

We show that the electrical resistance between the origin and generation n of the incipient infinite oriented branching random walk in dimensions d < 6 is O( n 1- α ) for some universal constant α > 0. This answers a question of Barlow et al. (Commun Math Phys 278:385-431, 2008).

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

Accumulator and random-walk models of psychophysical discrimination: a counter-evaluation.

PubMed

Vickers, D; Smith, P

1985-01-01

In a recent assessment of models of psychophysical discrimination, Heath criticises the accumulator model for its reliance on computer simulation and qualitative evidence, and contrasts it unfavourably with a modified random-walk model, which yields exact predictions, is susceptible to critical test, and is provided with simple parameter-estimation techniques. A counter-evaluation is presented, in which the approximations employed in the modified random-walk analysis are demonstrated to be seriously inaccurate, the resulting parameter estimates to be artefactually determined, and the proposed test not critical. It is pointed out that Heath's specific application of the model is not legitimate, his data treatment inappropriate, and his hypothesis concerning confidence inconsistent with experimental results. Evidence from adaptive performance changes is presented which shows that the necessary assumptions for quantitative analysis in terms of the modified random-walk model are not satisfied, and that the model can be reconciled with data at the qualitative level only by making it virtually indistinguishable from an accumulator process. A procedure for deriving exact predictions for an accumulator process is outlined.

Saddlepoint approximation to the distribution of the total distance of the continuous time random walk

NASA Astrophysics Data System (ADS)

Gatto, Riccardo

2017-12-01

This article considers the random walk over Rp, with p ≥ 2, where a given particle starts at the origin and moves stepwise with uniformly distributed step directions and step lengths following a common distribution. Step directions and step lengths are independent. The case where the number of steps of the particle is fixed and the more general case where it follows an independent continuous time inhomogeneous counting process are considered. Saddlepoint approximations to the distribution of the distance from the position of the particle to the origin are provided. Despite the p-dimensional nature of the random walk, the computations of the saddlepoint approximations are one-dimensional and thus simple. Explicit formulae are derived with dimension p = 3: for uniformly and exponentially distributed step lengths, for fixed and for Poisson distributed number of steps. In these situations, the high accuracy of the saddlepoint approximations is illustrated by numerical comparisons with Monte Carlo simulation. 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.

Varied overground walking training versus body-weight-supported treadmill training in adults within 1 year of stroke: a randomized controlled trial.

PubMed

DePaul, Vincent G; Wishart, Laurie R; Richardson, Julie; Thabane, Lehana; Ma, Jinhui; Lee, Timothy D

2015-05-01

Although task-related walking training has been recommended after stroke, the theoretical basis, content, and impact of interventions vary across the literature. There is a need for a comparison of different approaches to task-related walking training after stroke. To compare the impact of a motor-learning-science-based overground walking training program with body-weight-supported treadmill training (BWSTT) in ambulatory, community-dwelling adults within 1 year of stroke onset. In this rater-blinded, 1:1 parallel, randomized controlled trial, participants were stratified by baseline gait speed. Participants assigned to the Motor Learning Walking Program (MLWP) practiced various overground walking tasks under the supervision of 1 physiotherapist. Cognitive effort was encouraged through random practice and limited provision of feedback and guidance. The BWSTT program emphasized repetition of the normal gait cycle while supported on a treadmill and assisted by 1 to 3 therapy staff. The primary outcome was comfortable gait speed at postintervention assessment (T2). In total, 71 individuals (mean age = 67.3; standard deviation = 11.6 years) with stroke (mean onset = 20.9 [14.1] weeks) were randomized (MLWP, n = 35; BWSTT, n = 36). There was no significant between-group difference in gait speed at T2 (0.002 m/s; 95% confidence interval [CI] = -0.11, 0.12; P > .05). The MLWP group improved by 0.14 m/s (95% CI = 0.09, 0.19), and the BWSTT group improved by 0.14 m/s (95% CI = 0.08, 0.20). In this sample of community-dwelling adults within 1 year of stroke, a 15-session program of varied overground walking-focused training was not superior to a BWSTT program of equal frequency, duration, and in-session step activity. © The Author(s) 2014.

On the genealogy of branching random walks and of directed polymers

NASA Astrophysics Data System (ADS)

Derrida, Bernard; Mottishaw, Peter

2016-08-01

It is well known that the mean-field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite-size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks.

Nonergodic property of the space-time coupled CTRW: Dependence on the long-tailed property and correlation

NASA Astrophysics Data System (ADS)

Liu, Jian; Li, Baohe; Chen, Xiaosong

2018-02-01

The space-time coupled continuous time random walk model is a stochastic framework of anomalous diffusion with many applications in physics, geology and biology. In this manuscript the time averaged mean squared displacement and nonergodic property of a space-time coupled continuous time random walk model is studied, which is a prototype of the coupled continuous time random walk presented and researched intensively with various methods. The results in the present manuscript show that the time averaged mean squared displacements increase linearly with lag time which means ergodicity breaking occurs, besides, we find that the diffusion coefficient is intrinsically random which shows both aging and enhancement, the analysis indicates that the either aging or enhancement phenomena are determined by the competition between the correlation exponent γ and the waiting time's long-tailed index α.

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.

Ordinal optimization and its application to complex deterministic problems

NASA Astrophysics Data System (ADS)

Yang, Mike Shang-Yu

1998-10-01

We present in this thesis a new perspective to approach a general class of optimization problems characterized by large deterministic complexities. Many problems of real-world concerns today lack analyzable structures and almost always involve high level of difficulties and complexities in the evaluation process. Advances in computer technology allow us to build computer models to simulate the evaluation process through numerical means, but the burden of high complexities remains to tax the simulation with an exorbitant computing cost for each evaluation. Such a resource requirement makes local fine-tuning of a known design difficult under most circumstances, let alone global optimization. Kolmogorov equivalence of complexity and randomness in computation theory is introduced to resolve this difficulty by converting the complex deterministic model to a stochastic pseudo-model composed of a simple deterministic component and a white-noise like stochastic term. The resulting randomness is then dealt with by a noise-robust approach called Ordinal Optimization. Ordinal Optimization utilizes Goal Softening and Ordinal Comparison to achieve an efficient and quantifiable selection of designs in the initial search process. The approach is substantiated by a case study in the turbine blade manufacturing process. The problem involves the optimization of the manufacturing process of the integrally bladed rotor in the turbine engines of U.S. Air Force fighter jets. The intertwining interactions among the material, thermomechanical, and geometrical changes makes the current FEM approach prohibitively uneconomical in the optimization process. The generalized OO approach to complex deterministic problems is applied here with great success. Empirical results indicate a saving of nearly 95% in the computing cost.

Analysis of correlations and search for evidence of deterministic chaos in rhythmic motor control by the human brain

NASA Astrophysics Data System (ADS)

Roberts, Sean; Eykholt, R.; Thaut, Michael H.

2000-08-01

We investigate rhythmic finger tapping in both the presence and the absence of a metronome. We examine both the time intervals between taps and the time lags between the stimulus tones from the metronome and the response taps by the subject. We analyze the correlations in these data sets, and we search for evidence of deterministic chaos, as opposed to randomness, in the fluctuations.

Population density equations for stochastic processes with memory kernels

NASA Astrophysics Data System (ADS)

Lai, Yi Ming; de Kamps, Marc

2017-06-01

We present a method for solving population density equations (PDEs)-a mean-field technique describing homogeneous populations of uncoupled neurons—where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation—a recent result from random network theory—describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.

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.

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.

Travelling Wave Solutions in Multigroup Age-Structured Epidemic Models

NASA Astrophysics Data System (ADS)

Ducrot, Arnaut; Magal, Pierre; Ruan, Shigui

2010-01-01

Age-structured epidemic models have been used to describe either the age of individuals or the age of infection of certain diseases and to determine how these characteristics affect the outcomes and consequences of epidemiological processes. Most results on age-structured epidemic models focus on the existence, uniqueness, and convergence to disease equilibria of solutions. In this paper we investigate the existence of travelling wave solutions in a deterministic age-structured model describing the circulation of a disease within a population of multigroups. Individuals of each group are able to move with a random walk which is modelled by the classical Fickian diffusion and are classified into two subclasses, susceptible and infective. A susceptible individual in a given group can be crisscross infected by direct contact with infective individuals of possibly any group. This process of transmission can depend upon the age of the disease of infected individuals. The goal of this paper is to provide sufficient conditions that ensure the existence of travelling wave solutions for the age-structured epidemic model. The case of two population groups is numerically investigated which applies to the crisscross transmission of feline immunodeficiency virus (FIV) and some sexual transmission diseases.

A theoretical and experimental study of turbulent nonevaporating sprays

NASA Technical Reports Server (NTRS)

Solomon, A. S. P.; Shuen, J. S.; Zhang, Q. F.; Faeth, G. M.

1984-01-01

Measurements and analysis limited to the dilute portions of turbulent nonevaporating sprays injected into a still air environment were completed. Mean and fluctuating velocities and Reynolds stress were measured in the continuous phase. Liquid phase measurements included liquid mass fluxes, drop sizes and drop size and velocity correlation. Initial conditions needed for model evaluation were measured at a location as close to the injector exit as possible. The test sprays showed significant effects of slip and turbulent dispersion of the discrete phase. The measurements were used to evaluate three typical models of these processes: (1) a locally homogenous flow (LHF) model, where slip between the phases were neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of drop dispersion by turbulence were ignored; and (3) a stochastic separated flow (SSF) model, where effects of interphase slip and turbulent dispersion were considered using random-walk computations for drop motion. The LHF and DSF models did not provide very satisfactory predictions for the present measurements. In contrast, the SSF model performed reasonably well with no modifications in the prescription of eddy properties from its original calibration. Some effects of drops on turbulence properties were observed near the dense regions of the sprays.

Scaling of average weighted shortest path and average receiving time on weighted expanded Koch networks

NASA Astrophysics Data System (ADS)

Wu, Zikai; Hou, Baoyu; Zhang, Hongjuan; Jin, Feng

2014-04-01

Deterministic network models have been attractive media for discussing dynamical processes' dependence on network structural features. On the other hand, the heterogeneity of weights affect dynamical processes taking place on networks. In this paper, we present a family of weighted expanded Koch networks based on Koch networks. They originate from a r-polygon, and each node of current generation produces m r-polygons including the node and whose weighted edges are scaled by factor w in subsequent evolutionary step. We derive closed-form expressions for average weighted shortest path length (AWSP). In large network, AWSP stays bounded with network order growing (0 < w < 1). Then, we focus on a special random walks and trapping issue on the networks. In more detail, we calculate exactly the average receiving time (ART). ART exhibits a sub-linear dependence on network order (0 < w < 1), which implies that nontrivial weighted expanded Koch networks are more efficient than un-weighted expanded Koch networks in receiving information. Besides, efficiency of receiving information at hub nodes is also dependent on parameters m and r. These findings may pave the way for controlling information transportation on general weighted networks.

Fishing Quotas, Induced Allee Effect, and Fluctuation-Driven Extinction.

PubMed

Hastings, Harold M; Radin, Michael; Wiandt, Tamas

2017-01-01

We explore the potential of modifications to standard fishery models (for example Gordon-Schafer-Munro) to help understand events such as the collapse of the North Atlantic cod fishery. In particular we find that quota-driven and similar harvesting strategies induce an effective strong Allee effect (collapse if the population falls below a critical level). In the presence of environmental noise, fish population dynamics is similar to a random walk with (non-linear) drift. The expected survival time (first passage time to collapse) is shown to depend sensitively upon the amount of environmental noise and size of the 'safe zone' between the deterministic steady state population and the critical population level at which the system collapses; more precisely it is exponential in the cube of the size of the safe zone divided by the variance of the noise process. Similar scaling can be expected for more survival in more general systems with multiple steady states. Our calculations imply an amplification effect under which small increases in harvest yield large decreases in expected survival time, and one should be cautious in changes in harvesting, especially in fisheries with poor or limited data and fisheries affected by climate change.

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.

Early application of tail nerve electrical stimulation-induced walking training promotes locomotor recovery in rats with spinal cord injury.

PubMed

Zhang, S-X; Huang, F; Gates, M; Shen, X; Holmberg, E G

2016-11-01

This is a randomized controlled prospective trial with two parallel groups. The objective of this study was to determine whether early application of tail nerve electrical stimulation (TANES)-induced walking training can improve the locomotor function. This study was conducted in SCS Research Center in Colorado, USA. A contusion injury to spinal cord T10 was produced using the New York University impactor device with a 25 -mm height setting in female, adult Long-Evans rats. Injured rats were randomly divided into two groups (n=12 per group). One group was subjected to TANES-induced walking training 2 weeks post injury, and the other group, as control, received no TANES-induced walking training. Restorations of behavior and conduction were assessed using the Basso, Beattie and Bresnahan open-field rating scale, horizontal ladder rung walking test and electrophysiological test (Hoffmann reflex). Early application of TANES-induced walking training significantly improved the recovery of locomotor function and benefited the restoration of Hoffmann reflex. TANES-induced walking training is a useful method to promote locomotor recovery in rats with spinal cord injury.

Nordic walking versus walking without poles for rehabilitation with cardiovascular disease: Randomized controlled trial.

PubMed

Girold, Sébastien; Rousseau, Jérome; Le Gal, Magalie; Coudeyre, Emmanuel; Le Henaff, Jacqueline

2017-07-01

With Nordic walking, or walking with poles, one can travel a greater distance and at a higher rate than with walking without poles, but whether the activity is beneficial for patients with cardiovascular disease is unknown. This randomized controlled trial was undertaken to determine whether Nordic walking was more effective than walking without poles on walk distance to support rehabilitation training for patients with acute coronary syndrome (ACS) and peripheral arterial occlusive disease (PAOD). Patients were recruited in a private specialized rehabilitation centre for cardiovascular diseases. The entire protocol, including patient recruitment, took place over 2 months, from September to October 2013. We divided patients into 2 groups: Nordic Walking Group (NWG, n=21) and Walking Group without poles (WG, n=21). All patients followed the same program over 4 weeks, except for the walk performed with or without poles. The main outcome was walk distance on the 6-min walk test. Secondary outcomes were maximum heart rate during exercise and walk distance and power output on a treadmill stress test. We included 42 patients (35 men; mean age 57.2±11 years and BMI 26.5±4.5kg/m 2 ). At the end of the training period, both groups showed improved walk distance on the 6-min walk test and treatment stress test as well as power on the treadmill stress test (P<0.05). The NWG showed significantly greater walk distance than the WG (P<0.05). Both ACS and PAOD groups showed improvement, but improvement was significant for only PAOD patients. After a 4-week training period, Nordic walking training appeared more efficient than training without poles for increasing walk distance on the 6-min walk test for patients with ACS and PAOD. Copyright © 2017. Published by Elsevier Masson SAS.

An Extended Deterministic Dendritic Cell Algorithm for Dynamic Job Shop Scheduling

NASA Astrophysics Data System (ADS)

Qiu, X. N.; Lau, H. Y. K.

The problem of job shop scheduling in a dynamic environment where random perturbation exists in the system is studied. In this paper, an extended deterministic Dendritic Cell Algorithm (dDCA) is proposed to solve such a dynamic Job Shop Scheduling Problem (JSSP) where unexpected events occurred randomly. This algorithm is designed based on dDCA and makes improvements by considering all types of signals and the magnitude of the output values. To evaluate this algorithm, ten benchmark problems are chosen and different kinds of disturbances are injected randomly. The results show that the algorithm performs competitively as it is capable of triggering the rescheduling process optimally with much less run time for deciding the rescheduling action. As such, the proposed algorithm is able to minimize the rescheduling times under the defined objective and to keep the scheduling process stable and efficient.

Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography.

PubMed

Kanter, Ido; Butkovski, Maria; Peleg, Yitzhak; Zigzag, Meital; Aviad, Yaara; Reidler, Igor; Rosenbluh, Michael; Kinzel, Wolfgang

2010-08-16

Random bit generators (RBGs) constitute an important tool in cryptography, stochastic simulations and secure communications. The later in particular has some difficult requirements: high generation rate of unpredictable bit strings and secure key-exchange protocols over public channels. Deterministic algorithms generate pseudo-random number sequences at high rates, however, their unpredictability is limited by the very nature of their deterministic origin. Recently, physical RBGs based on chaotic semiconductor lasers were shown to exceed Gbit/s rates. Whether secure synchronization of two high rate physical RBGs is possible remains an open question. Here we propose a method, whereby two fast RBGs based on mutually coupled chaotic lasers, are synchronized. Using information theoretic analysis we demonstrate security against a powerful computational eavesdropper, capable of noiseless amplification, where all parameters are publicly known. The method is also extended to secure synchronization of a small network of three RBGs.

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…

Random Walk Method for Potential Problems

NASA Technical Reports Server (NTRS)

Krishnamurthy, T.; Raju, I. S.

2002-01-01

A local Random Walk Method (RWM) for potential problems governed by Lapalace's and Paragon's equations is developed for two- and three-dimensional problems. The RWM is implemented and demonstrated in a multiprocessor parallel environment on a Beowulf cluster of computers. A speed gain of 16 is achieved as the number of processors is increased from 1 to 23.

Effects of Practice on Task Architecture: Combined Evidence from Interference Experiments and Random-Walk Models of Decision Making

ERIC Educational Resources Information Center

Kamienkowski, Juan E.; Pashler, Harold; Dehaene, Stanislas; Sigman, Mariano

2011-01-01

Does extensive practice reduce or eliminate central interference in dual-task processing? We explored the reorganization of task architecture with practice by combining interference analysis (delays in dual-task experiment) and random-walk models of decision making (measuring the decision and non-decision contributions to RT). The main delay…

Averaging in SU(2) open quantum random walk

NASA Astrophysics Data System (ADS)

Clement, Ampadu

2014-03-01

We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.

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

Exercise training for intermittent claudication.

PubMed

McDermott, Mary M

2017-11-01

The objective of this study was to provide an overview of evidence regarding exercise therapies for patients with lower extremity peripheral artery disease (PAD). This manuscript summarizes the content of a lecture delivered as part of the 2016 Crawford Critical Issues Symposium. Multiple randomized clinical trials demonstrate that supervised treadmill exercise significantly improves treadmill walking performance in people with PAD and intermittent claudication symptoms. A meta-analysis of 25 randomized trials demonstrated a 180-meter increase in treadmill walking distance in response to supervised exercise interventions compared with a nonexercising control group. Supervised treadmill exercise has been inaccessible to many patients with PAD because of lack of medical insurance coverage. However, in 2017, the Centers for Medicare and Medicaid Services issued a decision memorandum to support health insurance coverage of 12 weeks of supervised treadmill exercise for patients with walking impairment due to PAD. Recent evidence also supports home-based walking exercise to improve walking performance in people with PAD. Effective home-exercise programs incorporate behavioral change interventions such as a remote coach, goal setting, and self-monitoring. Supervised treadmill exercise programs preferentially improve treadmill walking performance, whereas home-based walking exercise programs preferentially improve corridor walking, such as the 6-minute walk test. Clinical trial evidence also supports arm or leg ergometry exercise to improve walking endurance in people with PAD. Treadmill walking exercise appears superior to resistance training alone for improving walking endurance. Supervised treadmill exercise significantly improves treadmill walking performance in people with PAD by approximately 180 meters compared with no exercise. Recent evidence suggests that home-based exercise is also effective and preferentially improves over-ground walking performance, such as the 6-minute walk test. Copyright © 2017 Society for Vascular Surgery. Published by Elsevier Inc. All rights reserved.

Using wireless technology in clinical practice: does feedback of daily walking activity improve walking outcomes of individuals receiving rehabilitation post-stroke? Study protocol for a randomized controlled trial

PubMed Central

2013-01-01

Background Regaining independent ambulation is the top priority for individuals recovering from stroke. Thus, physical rehabilitation post-stroke should focus on improving walking function and endurance. However, the amount of walking completed by individuals with stroke attending rehabilitation is far below that required for independent community ambulation. There has been increased interest in accelerometer-based monitoring of walking post-stroke. Walking monitoring could be integrated within the goal-setting process for those with ambulation goals in rehabilitation. The feedback from these devices can be downloaded to a computer to produce reports. The purpose of this study is to determine the effect of accelerometer-based feedback of daily walking activity during rehabilitation on the frequency and duration of walking post-stroke. Methods Participants will be randomly assigned to one of two groups: feedback or no feedback. Participants will wear accelerometers daily during in- and out-patient rehabilitation and, for participants in the feedback group, the participants’ treating physiotherapist will receive regular reports of walking activity. The primary outcome measures are the amount of daily walking completed, as measured using the accelerometers, and spatio-temporal characteristics of walking (e.g. walking speed). We will also examine goal attainment, satisfaction with progress towards goals, stroke self-efficacy, and community-integration. Discussion Increased walking activity during rehabilitation is expected to improve walking function and community re-integration following discharge. In addition, a focus on altering walking behaviour within the rehabilitation setting may lead to altered behaviour and increased activity patterns after discharge. Trial registration ClinicalTrials.gov NCT01521234 PMID:23865593

Analysis of Individual Social-ecological Mediators and Moderators and Their Ability to Explain Effect of a Randomized Neighborhood Walking Intervention.

PubMed

Michael, Yvonne L; Carlson, Nichole E

2009-07-30

Using data from the SHAPE trial, a randomized 6-month neighborhood-based intervention designed to increase walking activity among older adults, this study identified and analyzed social-ecological factors mediating and moderating changes in walking activity. Three potential mediators (social cohesion, walking efficacy, and perception of neighborhood problems) and minutes of brisk walking were assessed at baseline, 3-months, and 6-months. One moderator, neighborhood walkability, was assessed using an administrative GIS database. The mediating effect of change in process variables on change in brisk walking was tested using a product-of-coefficients test, and we evaluated the moderating effect of neighborhood walkability on change in brisk walking by testing the significance of the interaction between walkability and intervention status. Only one of the hypothesized mediators, walking efficacy, explained the intervention effect (product of the coefficients (95% CI) = 8.72 (2.53, 15.56). Contrary to hypotheses, perceived neighborhood problems appeared to suppress the intervention effects (product of the coefficients (95% CI = -2.48, -5.6, -0.22). Neighborhood walkability did not moderate the intervention effect. Walking efficacy may be an important mediator of lay-lead walking interventions for sedentary older adults. Social-ecologic theory-based analyses can support clinical interventions to elucidate the mediators and moderators responsible for producing intervention effects.

Controllability of Deterministic Networks with the Identical Degree Sequence

PubMed Central

Ma, Xiujuan; Zhao, Haixing; Wang, Binghong

2015-01-01

Controlling complex network is an essential problem in network science and engineering. Recent advances indicate that the controllability of complex network is dependent on the network's topology. Liu and Barabási, et.al speculated that the degree distribution was one of the most important factors affecting controllability for arbitrary complex directed network with random link weights. In this paper, we analysed the effect of degree distribution to the controllability for the deterministic networks with unweighted and undirected. We introduce a class of deterministic networks with identical degree sequence, called (x,y)-flower. We analysed controllability of the two deterministic networks ((1, 3)-flower and (2, 2)-flower) by exact controllability theory in detail and give accurate results of the minimum number of driver nodes for the two networks. In simulation, we compare the controllability of (x,y)-flower networks. Our results show that the family of (x,y)-flower networks have the same degree sequence, but their controllability is totally different. So the degree distribution itself is not sufficient to characterize the controllability of deterministic networks with unweighted and undirected. PMID:26020920

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

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.

Fermionic entanglement via quantum walks in quantum dots

NASA Astrophysics Data System (ADS)

Melnikov, Alexey A.; Fedichkin, Leonid E.

2018-02-01

Quantum walks are fundamentally different from random walks due to the quantum superposition property of quantum objects. Quantum walk process was found to be very useful for quantum information and quantum computation applications. In this paper we demonstrate how to use quantum walks as a tool to generate high-dimensional two-particle fermionic entanglement. The generated entanglement can survive longer in the presence of depolorazing noise due to the periodicity of quantum walk dynamics. The possibility to create two distinguishable qudits in a system of tunnel-coupled semiconductor quantum dots is discussed.

Continuous-Time Random Walk with multi-step memory: an application to market dynamics

NASA Astrophysics Data System (ADS)

Gubiec, Tomasz; Kutner, Ryszard

2017-11-01

An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary number of successive jumps of the process while waiting times between jumps are considered as i.i.d. random variables. This dependence was established analyzing empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale. Then, it was justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model appeared exactly analytically solvable. Therefore, it enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus, the present research significantly extends capabilities of the CTRW formalism. 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.

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.

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.

Analysis of stochastic model for non-linear volcanic dynamics

NASA Astrophysics Data System (ADS)

Alexandrov, D.; Bashkirtseva, I.; Ryashko, L.

2014-12-01

Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al. (2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random trajectories are scattered on both sides of the deterministic cycle or grouped on its internal side only. It is shown that dispersions are highly inhomogeneous along cycles in the presence of noises. The effects of noise-induced shifts, pressure stabilization and localization of random trajectories have been revealed with increasing the noise intensity. The plug velocity, pressure and displacement are highly dependent of noise intensity as well. These new stochastic phenomena are related with the nonlinear peculiarities of the deterministic phase portrait. It is demonstrated that the repetitive stick-slip motions of the magma-plug system in the case of stochastic forcing can be connected with drumbeat earthquakes.

Rotational diffusion of a molecular cat

NASA Astrophysics Data System (ADS)

Katz-Saporta, Ori; Efrati, Efi

We show that a simple isolated system can perform rotational random walk on account of internal excitations alone. We consider the classical dynamics of a ''molecular cat'': a triatomic molecule connected by three harmonic springs with non-zero rest lengths, suspended in free space. In this system, much like for falling cats, the angular momentum constraint is non-holonomic allowing for rotations with zero overall angular momentum. The geometric nonlinearities arising from the non-zero rest lengths of the springs suffice to break integrability and lead to chaotic dynamics. The coupling of the non-integrability of the system and its non-holonomic nature results in an angular random walk of the molecule. We study the properties and dynamics of this angular motion analytically and numerically. For low energy excitations the system displays normal-mode-like motion, while for high enough excitation energy we observe regular random-walk. In between, at intermediate energies we observe an angular Lévy-walk type motion associated with a fractional diffusion coefficient interpolating between the two regimes.

Chaotic sources of noise in machine acoustics

NASA Astrophysics Data System (ADS)

Moon, F. C., Prof.; Broschart, Dipl.-Ing. T.

1994-05-01

In this paper a model is posited for deterministic, random-like noise in machines with sliding rigid parts impacting linear continuous machine structures. Such problems occur in gear transmission systems. A mathematical model is proposed to explain the random-like structure-borne and air-borne noise from such systems when the input is a periodic deterministic excitation of the quasi-rigid impacting parts. An experimental study is presented which supports the model. A thin circular plate is impacted by a chaotically vibrating mass excited by a sinusoidal moving base. The results suggest that the plate vibrations might be predicted by replacing the chaotic vibrating mass with a probabilistic forcing function. Prechaotic vibrations of the impacting mass show classical period doubling phenomena.

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.

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

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.

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…

Random-walk diffusion and drying of porous materials

NASA Astrophysics Data System (ADS)

Mehrafarin, M.; Faghihi, M.

2001-12-01

Based on random-walk diffusion, a microscopic model for drying is proposed to explain the characteristic features of the drying-rate curve of porous materials. The constant drying-rate period is considered as a normal diffusion process. The transition to the falling-rate regime is attributed to the fractal nature of porous materials which results in crossover to anomalous diffusion.

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.

Essential energy space random walk via energy space metadynamics method to accelerate molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Li, Hongzhi; Min, Donghong; Liu, Yusong; Yang, Wei

2007-09-01

To overcome the possible pseudoergodicity problem, molecular dynamic simulation can be accelerated via the realization of an energy space random walk. To achieve this, a biased free energy function (BFEF) needs to be priori obtained. Although the quality of BFEF is essential for sampling efficiency, its generation is usually tedious and nontrivial. In this work, we present an energy space metadynamics algorithm to efficiently and robustly obtain BFEFs. Moreover, in order to deal with the associated diffusion sampling problem caused by the random walk in the total energy space, the idea in the original umbrella sampling method is generalized to be the random walk in the essential energy space, which only includes the energy terms determining the conformation of a region of interest. This essential energy space generalization allows the realization of efficient localized enhanced sampling and also offers the possibility of further sampling efficiency improvement when high frequency energy terms irrelevant to the target events are free of activation. The energy space metadynamics method and its generalization in the essential energy space for the molecular dynamics acceleration are demonstrated in the simulation of a pentanelike system, the blocked alanine dipeptide model, and the leucine model.

Do low step count goals inhibit walking behavior: a randomized controlled study.

PubMed

Anson, Denis; Madras, Diane

2016-07-01

Confirmation and quantification of observed differences in goal-directed walking behavior. Single-blind, split-half randomized trial. Small rural university, Pennsylvania, United States. A total of 94 able-bodied subjects (self-selected volunteer students, faculty and staff of a small university) were randomly assigned walking goals, and 53 completed the study. Incentivized pedometer-monitored program requiring recording the step-count for 56-days into a custom-made website providing daily feedback. Steps logged per day. During the first half of the study, the 5000 and 10,000 step group logged significantly different steps 7500 and 9000, respectively (P > 0.05). During the second half of the study, the 5000 and 10,000 step groups logged 7000 and 8600 steps, respectively (significance P > 0.05). The group switched from 5000 to →10,000 steps logged, 7900 steps for the first half and 9500 steps for the second half (significance P > 0.05). The group switched from 10,000 to 5000 steps logged 9700 steps for the first half and 9000 steps for the second half, which was significant (p > 0.05). Levels of walking behavior are influenced by the goals assigned. Subjects with high goals walk more than those with low goals, even if they do not meet the assigned goal. Reducing goals from a high to low level can reduce walking behavior. © The Author(s) 2015.

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.

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.

Do rational numbers play a role in selection for stochasticity?

PubMed

Sinclair, Robert

2014-01-01

When a given tissue must, to be able to perform its various functions, consist of different cell types, each fairly evenly distributed and with specific probabilities, then there are at least two quite different developmental mechanisms which might achieve the desired result. Let us begin with the case of two cell types, and first imagine that the proportion of numbers of cells of these types should be 1:3. Clearly, a regular structure composed of repeating units of four cells, three of which are of the dominant type, will easily satisfy the requirements, and a deterministic mechanism may lend itself to the task. What if, however, the proportion should be 10:33? The same simple, deterministic approach would now require a structure of repeating units of 43 cells, and this certainly seems to require a far more complex and potentially prohibitive deterministic developmental program. Stochastic development, replacing regular units with random distributions of given densities, might not be evolutionarily competitive in comparison with the deterministic program when the proportions should be 1:3, but it has the property that, whatever developmental mechanism underlies it, its complexity does not need to depend very much upon target cell densities at all. We are immediately led to speculate that proportions which correspond to fractions with large denominators (such as the 33 of 10/33) may be more easily achieved by stochastic developmental programs than by deterministic ones, and this is the core of our thesis: that stochastic development may tend to occur more often in cases involving rational numbers with large denominators. To be imprecise: that simple rationality and determinism belong together, as do irrationality and randomness.

Body weight supported treadmill training versus traditional training in patients dependent on walking assistance after stroke: a randomized controlled trial.

PubMed

Høyer, Ellen; Jahnsen, Reidun; Stanghelle, Johan Kvalvik; Strand, Liv Inger

2012-01-01

Treadmill training with body weight support (TTBWS) for relearning walking ability after brain damage is an approach under current investigation. Efficiency of this method beyond traditional training is lacking evidence, especially in patients needing walking assistance after stroke. The objective of this study was to investigate change in walking and transfer abilities, comparing TTBWS with traditional walking training. A single-blinded, randomized controlled trial was conducted. Sixty patients referred for multi-disciplinary primary rehabilitation were assigned into one of two intervention groups, one received 30 sessions of TTBWS plus traditional training, the other traditional training alone. Daily training was 1 hr. Outcome measures were Functional Ambulation Categories (FAC), Walking, Functional Independence Measure (FIM); shorter transfer and stairs, 10 m and 6-min walk tests. Substantial improvements in walking and transfer were shown within both groups after 5 and 11 weeks of intervention. Overall no statistical significant differences were found between the groups, but 12 of 17 physical measures tended to show improvements in favour of the treadmill approach. Both training strategies provided significant improvements in the tested activities, suggesting that similar outcomes can be obtained in the two modalities by systematic, intensive and goal directed training.

Dual-Task Does Not Increase Slip and Fall Risk in Healthy Young and Older Adults during Walking

PubMed Central

Soangra, Rahul

2017-01-01

Dual-task tests can identify gait characteristics peculiar to fallers and nonfallers. Understanding the relationship between gait performance and dual-task related cognitive-motor interference is important for fall prevention. Dual-task adapted changes in gait instability/variability can adversely affect fall risks. Although implicated, it is unclear if healthy participants' fall risks are modified by dual-task walking conditions. Seven healthy young and seven healthy older adults were randomly assigned to normal walking and dual-task walking sessions with a slip perturbation. In the dual-task session, the participants walked and simultaneously counted backwards from a randomly provided number. The results indicate that the gait changes in dual-task walking have no destabilizing effect on gait and slip responses in healthy individuals. We also found that, during dual-tasking, healthy individuals adopted cautious gait mode (CGM) strategy that is characterized by reduced walking speed, shorter step length, increased step width, and reduced heel contact velocity and is likely to be an adaptation to minimize attentional demand and decrease slip and fall risk during limited available attentional resources. Exploring interactions between gait variability and cognitive functions while walking may lead to designing appropriate fall interventions among healthy and patient population with fall risk. PMID:28255224

Neighborhood walkability, fear and risk of falling and response to walking promotion: The Easy Steps to Health 12-month randomized controlled trial.

PubMed

Merom, D; Gebel, K; Fahey, P; Astell-Burt, T; Voukelatos, A; Rissel, C; Sherrington, C

2015-01-01

In older adults the relationships between health, fall-related risk factors, perceived neighborhood walkability, walking behavior and intervention impacts are poorly understood. To determine whether: i) health and fall-related risk factors were associated with perceptions of neighborhood walkability; ii) perceived environmental attributes, and fall-related risk factors predicted change in walking behavior at 12 months; and iii) perceived environmental attributes and fall-related risk factors moderated the effect of a self-paced walking program on walking behavior. Randomized trial on walking and falls conducted between 2009 and 2012 involving 315 community-dwelling inactive adults ≥ 65 years living in Sydney, Australia. Measures were: mobility status, fall history, injurious fall and fear of falling (i.e., fall-related risk factors), health status, walking self-efficacy and 11 items from the neighborhood walkability scale and planned walking ≥ 150 min/week at 12 months. Participants with poorer mobility, fear of falling, and poor health perceived their surroundings as less walkable. Walking at 12 months was significantly greater in "less greenery" (AOR = 3.3, 95% CI: 1.11-9.98) and "high traffic" (AOR = 1.98, 95% CI: 1.00-3.91) neighborhoods. The intervention had greater effects in neighborhoods perceived to have poorer pedestrian infrastructure (p for interaction = 0.036). Low perceived walkability was shaped by health status and did not appear to be a barrier to walking behavior. There appears to be a greater impact of, and thus, need for, interventions to encourage walking in environments perceived not to have supportive walking infrastructure. Future studies on built environments and walking should gather information on fall-related risk factors to better understand how these characteristics interact.

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.

Biased and greedy random walks on two-dimensional lattices with quenched randomness: The greedy ant within a disordered environment

NASA Astrophysics Data System (ADS)

Mitran, T. L.; Melchert, O.; Hartmann, A. K.

2013-12-01

The main characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here the disorder allows for negative edge weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter ρ that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. The random walks are “greedy” in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight (associated with a net gain of “energy” for the walker). Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of ρ for different bias strengths B is put under scrutiny. Upon tuning ρ, the probability to find such a feasible lattice walk increases from zero to 1. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point ρc, resulting from numerically exact and “static” simulations in terms of the NWP model, can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems.

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.

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

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.

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.

An overview of the "Positive Action for Today's Health" (PATH) trial for increasing walking in low income, ethnic minority communities.

PubMed

Wilson, Dawn K; Trumpeter, Nevelyn N; St George, Sara M; Coulon, Sandra M; Griffin, Sarah; Lee Van Horn, M; Lawman, Hannah G; Wandersman, Abe; Egan, Brent; Forthofer, Melinda; Goodlett, Benjamin D; Kitzman-Ulrich, Heather; Gadson, Barney

2010-11-01

Ethnic minorities and lower-income adults have among the highest rates of obesity and lowest levels of regular physical activity (PA). The Positive Action for Today's Health (PATH) trial compares three communities that are randomly assigned to different levels of an environmental intervention to improve safety and access for walking in low income communities. Three communities matched on census tract information (crime, PA, ethnic minorities, and income) were randomized to receive either: an intervention that combines a police-patrolled-walking program with social marketing strategies to promote PA, a police-patrolled-walking only intervention, or no-walking intervention (general health education only). Measures include PA (7-day accelerometer estimates), body composition, blood pressure, psychosocial measures, and perceptions of safety and access for PA at baseline, 6, 12, 18, and 24 months. The police-patrolled walking plus social marketing intervention targets increasing safety (training community leaders as walking captains, hiring off-duty police officers to patrol the walking trail, and containing stray dogs), increasing access for PA (marking a walking route), and utilizes a social marketing campaign that targets psychosocial and environmental mediators for increasing PA. MAIN HYPOTHESES/OUTCOMES: It is hypothesized that the police-patrolled walking plus social marketing intervention will result in greater increases in moderate-to-vigorous PA as compared to the police-patrolled-walking only or the general health intervention after 12 months and that this effect will be maintained at 18 and 24 months. Implications of this community-based trial are discussed. Copyright © 2010. Published by Elsevier Inc.

An overview of the “Positive Action for Today's Health” (PATH) trial for increasing walking in low income, ethnic minority communities

PubMed Central

Wilson, Dawn K.; Trumpeter, Nevelyn N.; St. George, Sara M.; Coulon, Sandra M.; Griffin, Sarah; Van Horn, M. Lee; Lawman, Hannah G.; Wandersman, Abe; Egan, Brent; Forthofer, Melinda; Goodlett, Benjamin D.; Kitzman-Ulrich, Heather; Gadson, Barney

2012-01-01

Background Ethnic minorities and lower-income adults have among the highest rates of obesity and lowest levels of regular physical activity (PA). The Positive Action for Today's Health (PATH) trial compares three communities that are randomly assigned to different levels of an environmental intervention to improve safety and access for walking in low income communities. Design and setting Three communities matched on census tract information (crime, PA, ethnic minorities, and income) were randomized to receive either: an intervention that combines a police-patrolled-walking program with social marketing strategies to promote PA, a police-patrolled-walking only intervention, or no-walking intervention (general health education only). Measures include PA (7-day accelerometer estimates), body composition, blood pressure, psychosocial measures, and perceptions of safety and access for PA at baseline, 6, 12, 18, and 24 months. Intervention The police-patrolled walking plus social marketing intervention targets increasing safety (training community leaders as walking captains, hiring off-duty police officers to patrol the walking trail, and containing stray dogs), increasing access for PA (marking a walking route), and utilizes a social marketing campaign that targets psychosocial and environmental mediators for increasing PA. Main hypotheses/outcomes It is hypothesized that the police-patrolled walking plus social marketing intervention will result in greater increases in moderate-to-vigorous PA as compared to the police-patrolled-walking only or the general health intervention after 12 months and that this effect will be maintained at 18 and 24 months. Conclusions Implications of this community-based trial are discussed. PMID:20801233

Extreme events and event size fluctuations in biased random walks on networks.

PubMed

Kishore, Vimal; Santhanam, M S; Amritkar, R E

2012-05-01

Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the context of complex networks. This was motivated by the occurrence of rare events such as traffic jams, floods, and power blackouts which take place on networks. In this work, we study extreme events in a generalized random walk model in which the walk is preferentially biased by the network topology. The walkers preferentially choose to hop toward the hubs or small degree nodes. In this setting, we show that extremely large fluctuations in event sizes are possible on small degree nodes when the walkers are biased toward the hubs. In particular, we obtain the distribution of event sizes on the network. Further, the probability for the occurrence of extreme events on any node in the network depends on its "generalized strength," a measure of the ability of a node to attract walkers. The generalized strength is a function of the degree of the node and that of its nearest neighbors. We obtain analytical and simulation results for the probability of occurrence of extreme events on the nodes of a network using a generalized random walk model. The result reveals that the nodes with a larger value of generalized strength, on average, display lower probability for the occurrence of extreme events compared to the nodes with lower values of generalized strength.

Chaotic behavior in the locomotion of Amoeba proteus.

PubMed

Miyoshi, H; Kagawa, Y; Tsuchiya, Y

2001-01-01

The locomotion of Amoeba proteus has been investigated by algorithms evaluating correlation dimension and Lyapunov spectrum developed in the field of nonlinear science. It is presumed by these parameters whether the random behavior of the system is stochastic or deterministic. For the analysis of the nonlinear parameters, n-dimensional time-delayed vectors have been reconstructed from a time series of periphery and area of A. proteus images captured with a charge-coupled-device camera, which characterize its random motion. The correlation dimension analyzed has shown the random motion of A. proteus is subjected only to 3-4 macrovariables, though the system is a complex system composed of many degrees of freedom. Furthermore, the analysis of the Lyapunov spectrum has shown its largest exponent takes positive values. These results indicate the random behavior of A. proteus is chaotic and deterministic motion on an attractor with low dimension. It may be important for the elucidation of the cell locomotion to take account of nonlinear interactions among a small number of dynamics such as the sol-gel transformation, the cytoplasmic streaming, and the relating chemical reaction occurring in the cell.

Validation of a Deterministic Vibroacoustic Response Prediction Model

NASA Technical Reports Server (NTRS)

Caimi, Raoul E.; Margasahayam, Ravi

1997-01-01

This report documents the recently completed effort involving validation of a deterministic theory for the random vibration problem of predicting the response of launch pad structures in the low-frequency range (0 to 50 hertz). Use of the Statistical Energy Analysis (SEA) methods is not suitable in this range. Measurements of launch-induced acoustic loads and subsequent structural response were made on a cantilever beam structure placed in close proximity (200 feet) to the launch pad. Innovative ways of characterizing random, nonstationary, non-Gaussian acoustics are used for the development of a structure's excitation model. Extremely good correlation was obtained between analytically computed responses and those measured on the cantilever beam. Additional tests are recommended to bound the problem to account for variations in launch trajectory and inclination.

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.

Deterministic Mean-Field Ensemble Kalman Filtering

DOE PAGES

Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

2016-05-03

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d

Deterministic Mean-Field Ensemble Kalman Filtering

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

Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d

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.

Random and Directed Walk-Based Top-k Queries in Wireless Sensor Networks

PubMed Central

Fu, Jun-Song; Liu, Yun

2015-01-01

In wireless sensor networks, filter-based top-k query approaches are the state-of-the-art solutions and have been extensively researched in the literature, however, they are very sensitive to the network parameters, including the size of the network, dynamics of the sensors’ readings and declines in the overall range of all the readings. In this work, a random walk-based top-k query approach called RWTQ and a directed walk-based top-k query approach called DWTQ are proposed. At the beginning of a top-k query, one or several tokens are sent to the specific node(s) in the network by the base station. Then, each token walks in the network independently to record and process the readings in a random or directed way. A strategy of choosing the “right” way in DWTQ is carefully designed for the token(s) to arrive at the high-value regions as soon as possible. When designing the walking strategy for DWTQ, the spatial correlations of the readings are also considered. Theoretical analysis and simulation results indicate that RWTQ and DWTQ both are very robust against these parameters discussed previously. In addition, DWTQ outperforms TAG, FILA and EXTOK in transmission cost, energy consumption and network lifetime. PMID:26016914

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.

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.

A Random Variable Approach to Nuclear Targeting and Survivability

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

Undem, Halvor A.

We demonstrate a common mathematical formalism for analyzing problems in nuclear survivability and targeting. This formalism, beginning with a random variable approach, can be used to interpret past efforts in nuclear-effects analysis, including targeting analysis. It can also be used to analyze new problems brought about by the post Cold War Era, such as the potential effects of yield degradation in a permanently untested nuclear stockpile. In particular, we illustrate the formalism through four natural case studies or illustrative problems, linking these to actual past data, modeling, and simulation, and suggesting future uses. In the first problem, we illustrate themore » case of a deterministically modeled weapon used against a deterministically responding target. Classic "Cookie Cutter" damage functions result. In the second problem, we illustrate, with actual target test data, the case of a deterministically modeled weapon used against a statistically responding target. This case matches many of the results of current nuclear targeting modeling and simulation tools, including the result of distance damage functions as complementary cumulative lognormal functions in the range variable. In the third problem, we illustrate the case of a statistically behaving weapon used against a deterministically responding target. In particular, we show the dependence of target damage on weapon yield for an untested nuclear stockpile experiencing yield degradation. Finally, and using actual unclassified weapon test data, we illustrate in the fourth problem the case of a statistically behaving weapon used against a statistically responding target.« less

Understanding agent-based models of financial markets: A bottom-up approach based on order parameters and phase diagrams

NASA Astrophysics Data System (ADS)

Lye, Ribin; Tan, James Peng Lung; Cheong, Siew Ann

2012-11-01

We describe a bottom-up framework, based on the identification of appropriate order parameters and determination of phase diagrams, for understanding progressively refined agent-based models and simulations of financial markets. We illustrate this framework by starting with a deterministic toy model, whereby N independent traders buy and sell M stocks through an order book that acts as a clearing house. The price of a stock increases whenever it is bought and decreases whenever it is sold. Price changes are updated by the order book before the next transaction takes place. In this deterministic model, all traders based their buy decisions on a call utility function, and all their sell decisions on a put utility function. We then make the agent-based model more realistic, by either having a fraction fb of traders buy a random stock on offer, or a fraction fs of traders sell a random stock in their portfolio. Based on our simulations, we find that it is possible to identify useful order parameters from the steady-state price distributions of all three models. Using these order parameters as a guide, we find three phases: (i) the dead market; (ii) the boom market; and (iii) the jammed market in the phase diagram of the deterministic model. Comparing the phase diagrams of the stochastic models against that of the deterministic model, we realize that the primary effect of stochasticity is to eliminate the dead market phase.

A randomized controlled trial of movement strategies compared with exercise for people with Parkinson's disease.

PubMed

Morris, Meg E; Iansek, Robert; Kirkwood, Beth

2009-01-15

This randomized controlled clinical trial was conducted to compare the effects of movement rehabilitation strategies and exercise therapy in hospitalized patients with idiopathic Parkinson's disease. Participants were randomly assigned to a group that received movement strategy training or musculoskeletal exercises during 2 consecutive weeks of hospitalization. The primary outcome was disability as measured by the Unified Parkinson's Disease Rating Scale, UPDRS (motor and ADL components). Secondary outcomes were balance, walking speed, endurance, and quality of life. Assessments were carried out by blinded testers at baseline, after the 2 weeks of treatment and 3 months after discharge. The movement strategy group showed improvements on several outcome measures from admission to discharge, including the UPDRS, 10 m walk, 2 minute walk, balance, and PDQ39. However, from discharge to follow up there was significant regression in performance on the 2 minute walk and PDQ39. For the exercise group, quality of life improved significantly during inpatient hospitalization and this was retained at follow-up. Inpatient rehabilitation produces short term reductions in disability and improvements in quality of life in people with Parkinson's disease.

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.

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 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

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.

Effectiveness of Functional Progressive Resistance Exercise Training on Walking Ability in Children with Cerebral Palsy: A Randomized Controlled Trial

ERIC Educational Resources Information Center

Scholtes, Vanessa A.; Becher, Jules G.; Janssen-Potten, Yvonne J.; Dekkers, Hurnet; Smallenbroek, Linda; Dallmeijer, Annet J.

2012-01-01

The objective of the study was to evaluate the effectiveness of functional progressive resistance exercise (PRE) training on walking ability in children with cerebral palsy (CP). Fifty-one ambulant children with spastic CP (mean age 10 years 5 months, 29 boys) were randomized to an intervention (n=26) or control group (n=25, receiving usual care).…

Some functional limit theorems for compound Cox processes

NASA Astrophysics Data System (ADS)

Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.

2016-06-01

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Continuous Time Random Walks with memory and financial distributions

NASA Astrophysics Data System (ADS)

Montero, Miquel; Masoliver, Jaume

2017-11-01

We study financial distributions from the perspective of Continuous Time Random Walks with memory. We review some of our previous developments and apply them to financial problems. We also present some new models with memory that can be useful in characterizing tendency effects which are inherent in most markets. We also briefly study the effect on return distributions of fractional behaviors in the distribution of pausing times between successive transactions.

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.

Some functional limit theorems for compound Cox processes

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

Korolev, Victor Yu.; Institute of Informatics Problems FRC CSC RAS; Chertok, A. V.

2016-06-08

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Propagation in Striated Media

DTIC Science & Technology

1976-05-01

random walk photon scattering, geometric optics refraction at a thin phase screen, plane wave scattering from a thin screen in the Fraunhofer limit and...significant cases. In the geometric optics regime the distribution of density of allowable multipath rays is gsslanly distributed and the power...3.1 Random Walk Approach to Scattering 10 3.2 Phase Screen Approximation to Strong Scattering 13 3.3 Ray Optics and Stationary Phase Analysis 21 3,3,1

Empirical scaling of the length of the longest increasing subsequences of random walks

NASA Astrophysics Data System (ADS)

Mendonça, J. Ricardo G.

2017-02-01

We provide Monte Carlo estimates of the scaling of the length L n of the longest increasing subsequences of n-step random walks for several different distributions of step lengths, short and heavy-tailed. Our simulations indicate that, barring possible logarithmic corrections, {{L}n}∼ {{n}θ} with the leading scaling exponent 0.60≲ θ ≲ 0.69 for the heavy-tailed distributions of step lengths examined, with values increasing as the distribution becomes more heavy-tailed, and θ ≃ 0.57 for distributions of finite variance, irrespective of the particular distribution. The results are consistent with existing rigorous bounds for θ, although in a somewhat surprising manner. For random walks with step lengths of finite variance, we conjecture that the correct asymptotic behavior of L n is given by \\sqrt{n}\\ln n , and also propose the form for the subleading asymptotics. The distribution of L n was found to follow a simple scaling form with scaling functions that vary with θ. Accordingly, when the step lengths are of finite variance they seem to be universal. The nature of this scaling remains unclear, since we lack a working model, microscopic or hydrodynamic, for the behavior of the length of the longest increasing subsequences of random walks.

Ant-inspired density estimation via random walks.

PubMed

Musco, Cameron; Su, Hsin-Hao; Lynch, Nancy A

2017-10-03

Many ant species use distributed population density estimation in applications ranging from quorum sensing, to task allocation, to appraisal of enemy colony strength. It has been shown that ants estimate local population density by tracking encounter rates: The higher the density, the more often the ants bump into each other. We study distributed density estimation from a theoretical perspective. We prove that a group of anonymous agents randomly walking on a grid are able to estimate their density within a small multiplicative error in few steps by measuring their rates of encounter with other agents. Despite dependencies inherent in the fact that nearby agents may collide repeatedly (and, worse, cannot recognize when this happens), our bound nearly matches what would be required to estimate density by independently sampling grid locations. From a biological perspective, our work helps shed light on how ants and other social insects can obtain relatively accurate density estimates via encounter rates. From a technical perspective, our analysis provides tools for understanding complex dependencies in the collision probabilities of multiple random walks. We bound the strength of these dependencies using local mixing properties of the underlying graph. Our results extend beyond the grid to more general graphs, and we discuss applications to size estimation for social networks, density estimation for robot swarms, and random walk-based sampling for sensor networks.

Eigenvalue density of cross-correlations in Sri Lankan financial market

NASA Astrophysics Data System (ADS)

Nilantha, K. G. D. R.; Ranasinghe; Malmini, P. K. C.

2007-05-01

We apply the universal properties with Gaussian orthogonal ensemble (GOE) of random matrices namely spectral properties, distribution of eigenvalues, eigenvalue spacing predicted by random matrix theory (RMT) to compare cross-correlation matrix estimators from emerging market data. The daily stock prices of the Sri Lankan All share price index and Milanka price index from August 2004 to March 2005 were analyzed. Most eigenvalues in the spectrum of the cross-correlation matrix of stock price changes agree with the universal predictions of RMT. We find that the cross-correlation matrix satisfies the universal properties of the GOE of real symmetric random matrices. The eigen distribution follows the RMT predictions in the bulk but there are some deviations at the large eigenvalues. The nearest-neighbor spacing and the next nearest-neighbor spacing of the eigenvalues were examined and found that they follow the universality of GOE. RMT with deterministic correlations found that each eigenvalue from deterministic correlations is observed at values, which are repelled from the bulk distribution.

On factoring RSA modulus using random-restart hill-climbing algorithm and Pollard’s rho algorithm

NASA Astrophysics Data System (ADS)

Budiman, M. A.; Rachmawati, D.

2017-12-01

The security of the widely-used RSA public key cryptography algorithm depends on the difficulty of factoring a big integer into two large prime numbers. For many years, the integer factorization problem has been intensively and extensively studied in the field of number theory. As a result, a lot of deterministic algorithms such as Euler’s algorithm, Kraitchik’s, and variants of Pollard’s algorithms have been researched comprehensively. Our study takes a rather uncommon approach: rather than making use of intensive number theories, we attempt to factorize RSA modulus n by using random-restart hill-climbing algorithm, which belongs the class of metaheuristic algorithms. The factorization time of RSA moduli with different lengths is recorded and compared with the factorization time of Pollard’s rho algorithm, which is a deterministic algorithm. Our experimental results indicates that while random-restart hill-climbing algorithm is an acceptable candidate to factorize smaller RSA moduli, the factorization speed is much slower than that of Pollard’s rho algorithm.

Interrelation Between Safety Factors and Reliability

NASA Technical Reports Server (NTRS)

Elishakoff, Isaac; Chamis, Christos C. (Technical Monitor)

2001-01-01

An evaluation was performed to establish relationships between safety factors and reliability relationships. Results obtained show that the use of the safety factor is not contradictory to the employment of the probabilistic methods. In many cases the safety factors can be directly expressed by the required reliability levels. However, there is a major difference that must be emphasized: whereas the safety factors are allocated in an ad hoc manner, the probabilistic approach offers a unified mathematical framework. The establishment of the interrelation between the concepts opens an avenue to specify safety factors based on reliability. In cases where there are several forms of failure, then the allocation of safety factors should he based on having the same reliability associated with each failure mode. This immediately suggests that by the probabilistic methods the existing over-design or under-design can be eliminated. The report includes three parts: Part 1-Random Actual Stress and Deterministic Yield Stress; Part 2-Deterministic Actual Stress and Random Yield Stress; Part 3-Both Actual Stress and Yield Stress Are Random.

The scalable implementation of quantum walks using classical light

NASA Astrophysics Data System (ADS)

Goyal, Sandeep K.; Roux, F. S.; Forbes, Andrew; Konrad, Thomas

2014-02-01

A quantum walk is the quantum analog of the classical random walks. Despite their simple structure they form a universal platform to implement any algorithm of quantum computation. However, it is very hard to realize quantum walks with a sufficient number of iterations in quantum systems due to their sensitivity to environmental influences and subsequent loss of coherence. Here we present a scalable implementation scheme for one-dimensional quantum walks for arbitrary number of steps using the orbital angular momentum modes of classical light beams. Furthermore, we show that using the same setup with a minor adjustment we can also realize electric quantum walks.

Computer modeling of dynamic necking in bars

NASA Astrophysics Data System (ADS)

Partom, Yehuda; Lindenfeld, Avishay

2017-06-01

Necking of thin bodies (bars, plates, shells) is one form of strain localization in ductile materials that may lead to fracture. The phenomenon of necking has been studied extensively, initially for quasistatic loading and then also for dynamic loading. Nevertheless, many issues concerning necking are still unclear. Among these are: 1) is necking a random or deterministic process; 2) how does the specimen choose the final neck location; 3) to what extent do perturbations (material or geometrical) influence the neck forming process; and 4) how do various parameters (material, geometrical, loading) influence the neck forming process. Here we address these issues and others using computer simulations with a hydrocode. Among other things we find that: 1) neck formation is a deterministic process, and by changing one of the parameters influencing it monotonously, the final neck location moves monotonously as well; 2) the final neck location is sensitive to the radial velocity of the end boundaries, and as motion of these boundaries is not fully controlled in tests, this may be the reason why neck formation is sometimes regarded as a random process; and 3) neck formation is insensitive to small perturbations, which is probably why it is a deterministic process.

PCEMCAN - Probabilistic Ceramic Matrix Composites Analyzer: User's Guide, Version 1.0

NASA Technical Reports Server (NTRS)

Shah, Ashwin R.; Mital, Subodh K.; Murthy, Pappu L. N.

1998-01-01

PCEMCAN (Probabalistic CEramic Matrix Composites ANalyzer) is an integrated computer code developed at NASA Lewis Research Center that simulates uncertainties associated with the constituent properties, manufacturing process, and geometric parameters of fiber reinforced ceramic matrix composites and quantifies their random thermomechanical behavior. The PCEMCAN code can perform the deterministic as well as probabilistic analyses to predict thermomechanical properties. This User's guide details the step-by-step procedure to create input file and update/modify the material properties database required to run PCEMCAN computer code. An overview of the geometric conventions, micromechanical unit cell, nonlinear constitutive relationship and probabilistic simulation methodology is also provided in the manual. Fast probability integration as well as Monte-Carlo simulation methods are available for the uncertainty simulation. Various options available in the code to simulate probabilistic material properties and quantify sensitivity of the primitive random variables have been described. The description of deterministic as well as probabilistic results have been described using demonstration problems. For detailed theoretical description of deterministic and probabilistic analyses, the user is referred to the companion documents "Computational Simulation of Continuous Fiber-Reinforced Ceramic Matrix Composite Behavior," NASA TP-3602, 1996 and "Probabilistic Micromechanics and Macromechanics for Ceramic Matrix Composites", NASA TM 4766, June 1997.

An aerobic walking programme versus muscle strengthening programme for chronic low back pain: a randomized controlled trial.

PubMed

Shnayderman, Ilana; Katz-Leurer, Michal

2013-03-01

To assess the effect of aerobic walking training as compared to active training, which includes muscle strengthening, on functional abilities among patients with chronic low back pain. Randomized controlled clinical trial with blind assessors. Outpatient clinic. Fifty-two sedentary patients, aged 18-65 years with chronic low back pain. Patients who were post surgery, post trauma, with cardiovascular problems, and with oncological disease were excluded. Experimental 'walking' group: moderate intense treadmill walking; control 'exercise' group: specific low back exercise; both, twice a week for six weeks. Six-minute walking test, Fear-Avoidance Belief Questionnaire, back and abdomen muscle endurance tests, Oswestry Disability Questionnaire, Low Back Pain Functional Scale (LBPFS). Significant improvements were noted in all outcome measures in both groups with non-significant difference between groups. The mean distance in metres covered during 6 minutes increased by 70.7 (95% confidence interval (CI) 12.3-127.7) in the 'walking' group and by 43.8 (95% CI 19.6-68.0) in the 'exercise' group. The trunk flexor endurance test showed significant improvement in both groups, increasing by 0.6 (95% CI 0.0-1.1) in the 'walking' group and by 1.1 (95% CI 0.3-1.8) in the 'exercise' group. A six-week walk training programme was as effective as six weeks of specific strengthening exercises programme for the low back.

The implementation of a community-based aerobic walking program for mild to moderate knee osteoarthritis: A knowledge translation randomized controlled trial: Part II: Clinical outcomes

PubMed Central

2012-01-01

Background Osteoarthritis (OA) is the most common joint disorder in the world, as it is appears to be prevalent among 80% of individuals over the age of 75. Although physical activities such as walking have been scientifically proven to improve physical function and arthritic symptoms, individuals with OA tend to adopt a sedentary lifestyle. There is therefore a need to improve knowledge translation in order to influence individuals to adopt effective self-management interventions, such as an adapted walking program. Methods A single-blind, randomized control trial was conducted. Subjects (n = 222) were randomized to one of three knowledge translation groups: 1) Walking and Behavioural intervention (WB) (18 males, 57 females) which included the supervised community-based aerobic walking program combined with a behavioural intervention and an educational pamphlet on the benefits of walking; 2) Walking intervention (W) (24 males, 57 females) wherein participants only received the supervised community-based aerobic walking program intervention and the educational pamphlet; 3) Self-directed control (C) (32 males, 52 females) wherein participants only received the educational pamphlet. One-way analyses of variance were used to test for differences in quality of life, adherence, confidence, and clinical outcomes among the study groups at each 3 month assessment during the 12-month intervention period and 6-month follow-up period. Results The clinical and quality of life outcomes improved among participants in each of the three comparative groups. However, there were few statistically significant differences observed for quality of life and clinical outcomes at long-term measurements at 12-months end of intervention and at 6- months post intervention (18-month follow-up). Outcome results varied among the three groups. Conclusion The three groups were equivalent when determining the effectiveness of knowledge uptake and improvements in quality of life and other clinical outcomes. OA can be managed through the implementation of a proven effective walking program in existing community-based walking clubs. Trial registration Current Controlled Trials IRSCTNO9193542 PMID:23234575

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.

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.

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

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

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.

The Random-Effect DINA Model

ERIC Educational Resources Information Center

Huang, Hung-Yu; Wang, Wen-Chung

2014-01-01

The DINA (deterministic input, noisy, and gate) model has been widely used in cognitive diagnosis tests and in the process of test development. The outcomes known as slip and guess are included in the DINA model function representing the responses to the items. This study aimed to extend the DINA model by using the random-effect approach to allow…

Stochastic reduced order models for inverse problems under uncertainty

PubMed Central

Warner, James E.; Aquino, Wilkins; Grigoriu, Mircea D.

2014-01-01

This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well. PMID:25558115

Equivalence of Szegedy's and coined quantum walks

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2017-09-01

Szegedy's quantum walk is a quantization of a classical random walk or Markov chain, where the walk occurs on the edges of the bipartite double cover of the original graph. To search, one can simply quantize a Markov chain with absorbing vertices. Recently, Santos proposed two alternative search algorithms that instead utilize the sign-flip oracle in Grover's algorithm rather than absorbing vertices. In this paper, we show that these two algorithms are exactly equivalent to two algorithms involving coined quantum walks, which are walks on the vertices of the original graph with an internal degree of freedom. The first scheme is equivalent to a coined quantum walk with one walk step per query of Grover's oracle, and the second is equivalent to a coined quantum walk with two walk steps per query of Grover's oracle. These equivalences lie outside the previously known equivalence of Szegedy's quantum walk with absorbing vertices and the coined quantum walk with the negative identity operator as the coin for marked vertices, whose precise relationships we also investigate.

Autonomous choices among deterministic evolution-laws as source of uncertainty

NASA Astrophysics Data System (ADS)

Trujillo, Leonardo; Meyroneinc, Arnaud; Campos, Kilver; Rendón, Otto; Sigalotti, Leonardo Di G.

2018-03-01

We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these pseudo-random dynamical systems. Each chaotic system in this family exhibits a sensitivity to initial conditions that encompasses the sequence of choices of the evolution rule in some collection of maps. This opens a possibility to extend current theories of complex behaviors on the basis of intrinsic uncertainty in deterministic chaos.

The Effect of a Home-Based Walking Intervention on Quality of Life Body Composition and Estrogen Metabolism in Postmenopausal Breast Cancer Survivors

DTIC Science & Technology

2003-09-01

the effect of a 12-week home-based walking intervention on quality of life , body composition, and estrogen metabolism in survivors of breast cancer...randomized to the walking intervention will report higher levels of quality of life , experience less weight gain, and have more favorable estrogen

The Effect of a Home-Based Walking Intervention on Quality of Life, Body Composition, and Estrogen Metabolism in Postmenopausal Breast Cancer Survivors

DTIC Science & Technology

2004-09-01

the effect of a 12-week home-based walking intervention on quality of life , body composition, and estrogen metabolism in survivors of breast cancer...randomized to the walking intervention will report higher levels of quality of life , experience less weight gain, and have more favorable estrogen

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.

Random walk on p-adics and hierarchical systems

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

Lukierska-Walasek, K.; Topolski, K.; Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw

2006-02-01

We show that p-adic analysis provides a quite natural basis for the description of relaxation in hierarchical systems. For our purposes, we specify the Markov stochastic process considered by Albeverio and Karwowski. As a result we have obtained a random walk on the p-adic integer numbers, which provides the generalization of Cayley tree proposed by Ogielski and Stein. The temperature-dependent power-law decay and the Kohlrausch law are derived.

Expert Assessment of Stigmergy: A Report for the Department of National Defence

DTIC Science & Technology

2005-10-01

pheromone table may be reduced by implementing a clustering scheme. Termite can take advantage of the wireless broadcast medium, since it is possible for...comparing it with any other routing scheme. The Termite scheme [RW] differs from the source routing [ITT] by applying pheromone trails or random walks...rather than uniform or probabilistic ones. Random walk ants differ from uniform ants since they follow pheromone trails, if any. Termite [RW] also

Autocatalytic polymerization generates persistent random walk of crawling cells.

PubMed

Sambeth, R; Baumgaertner, A

2001-05-28

The autocatalytic polymerization kinetics of the cytoskeletal actin network provides the basic mechanism for a persistent random walk of a crawling cell. It is shown that network remodeling by branching processes near the cell membrane is essential for the bimodal spatial stability of the network which induces a spontaneous breaking of isotropic cell motion. Details of the phenomena are analyzed using a simple polymerization model studied by analytical and simulation methods.

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.

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 Perron-Frobenius Type of Theorem for Quantum Operations

NASA Astrophysics Data System (ADS)

Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng

2017-10-01

We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1. We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1, the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.

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.

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.

Observing random walks of atoms in buffer gas through resonant light absorption

NASA Astrophysics Data System (ADS)

Aoki, Kenichiro; Mitsui, Takahisa

2016-07-01

Using resonant light absorption, random-walk motions of rubidium atoms in nitrogen buffer gas are observed directly. The transmitted light intensity through atomic vapor is measured, and its spectrum is obtained, down to orders of magnitude below the shot-noise level to detect fluctuations caused by atomic motions. To understand the measured spectra, the spectrum for atoms performing random walks in a Gaussian light beam is computed, and its analytical form is obtained. The spectrum has 1 /f2 (f is frequency) behavior at higher frequencies, crossing over to a different, but well-defined, behavior at lower frequencies. The properties of this theoretical spectrum agree excellently with the measured spectrum. This understanding also enables us to obtain the diffusion constant, the photon cross section of atoms in buffer gas, and the atomic number density from a single spectral measurement. We further discuss other possible applications of our experimental method and analysis.

Network Dynamics of Innovation Processes.

PubMed

Iacopini, Iacopo; Milojević, Staša; Latora, Vito

2018-01-26

We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition matrix of the random walk depends on the network weights, while in turn the weight of an edge is reinforced by the passage of a walker. The presence of the network naturally accounts for the mechanism of the "adjacent possible," and the model reproduces both the rate at which novelties emerge and the correlations among them observed empirically. We show this by using synthetic networks and by studying real data sets on the growth of knowledge in different scientific disciplines. Edge-reinforced random walks on complex topologies offer a new modeling framework for the dynamics of correlated novelties and are another example of coevolution of processes and networks.

Statistical Modeling of Robotic Random Walks on Different Terrain

NASA Astrophysics Data System (ADS)

Naylor, Austin; Kinnaman, Laura

Issues of public safety, especially with crowd dynamics and pedestrian movement, have been modeled by physicists using methods from statistical mechanics over the last few years. Complex decision making of humans moving on different terrains can be modeled using random walks (RW) and correlated random walks (CRW). The effect of different terrains, such as a constant increasing slope, on RW and CRW was explored. LEGO robots were programmed to make RW and CRW with uniform step sizes. Level ground tests demonstrated that the robots had the expected step size distribution and correlation angles (for CRW). The mean square displacement was calculated for each RW and CRW on different terrains and matched expected trends. The step size distribution was determined to change based on the terrain; theoretical predictions for the step size distribution were made for various simple terrains. It's Dr. Laura Kinnaman, not sure where to put the Prefix.

Network Dynamics of Innovation Processes

NASA Astrophysics Data System (ADS)

Iacopini, Iacopo; Milojević, Staša; Latora, Vito

2018-01-01

We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition matrix of the random walk depends on the network weights, while in turn the weight of an edge is reinforced by the passage of a walker. The presence of the network naturally accounts for the mechanism of the "adjacent possible," and the model reproduces both the rate at which novelties emerge and the correlations among them observed empirically. We show this by using synthetic networks and by studying real data sets on the growth of knowledge in different scientific disciplines. Edge-reinforced random walks on complex topologies offer a new modeling framework for the dynamics of correlated novelties and are another example of coevolution of processes and networks.

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.

The implementation of a community-based aerobic walking program for mild to moderate knee osteoarthritis (OA): a knowledge translation (KT) randomized controlled trial (RCT): Part I: The Uptake of the Ottawa Panel clinical practice guidelines (CPGs)

PubMed Central

2012-01-01

Background The implementation of evidence based clinical practice guidelines on self-management interventions to patients with chronic diseases is a complex process. A multifaceted strategy may offer an effective knowledge translation (KT) intervention to promote knowledge uptake and improve adherence in an effective walking program based on the Ottawa Panel Evidence Based Clinical Practice Guidelines among individuals with moderate osteoarthritis (OA). Methods A single-blind, randomized control trial was conducted. Patients with mild to moderate (OA) of the knee (n=222) were randomized to one of three KT groups: 1) Walking and Behavioural intervention (WB) (18 males, 57 females) which included the supervised community-based aerobic walking program combined with a behavioural intervention and an educational pamphlet on the benefits of walking for OA; 2) Walking intervention (W) (24 males, 57 females) wherein participants only received the supervised community-based aerobic walking program intervention and the educational pamphlet; 3) Self-directed control (C) (32 males, 52 females) wherein participants only received the educational pamphlet. One-way analyses of variance were used to test for differences in quality of life, adherence, confidence, and clinical outcomes among the study groups at each 3 month assessment during the 12-month intervention period and 6-month follow-up period. Results Short-term program adherence was greater in WB compared to C (p<0.012) after 3 months. No statistical significance (p> 0.05) was observed for long-term adherence (6 to 12 months), and total adherence between the three groups. The three knowledge translation strategies demonstrated equivalent long-term results for the implementation of a walking program for older individuals with moderate OA. Lower dropout rates as well as higher retention rates were observed for WB at 12 and 18 months. Conclusion The additional knowledge translation behavioural component facilitated the implementation of clinical practice guidelines on walking over a short-term period. More studies are needed to improve the long-term walking adherence or longer guidelines uptake on walking among participants with OA. Particular attention should be taken into account related to patient’s characteristic and preference. OA can be managed through the implementation of a walking program based on clinical practice guidelines in existing community-based walking clubs as well as at home with the minimal support of an exercise therapist or a trained volunteer. Trial Registration Current Controlled Trials IRSCTNO9193542 PMID:23061875

A new method for predicting response in complex linear systems. II. [under random or deterministic steady state excitation

NASA Technical Reports Server (NTRS)

Bogdanoff, J. L.; Kayser, K.; Krieger, W.

1977-01-01

The paper describes convergence and response studies in the low frequency range of complex systems, particularly with low values of damping of different distributions, and reports on the modification of the relaxation procedure required under these conditions. A new method is presented for response estimation in complex lumped parameter linear systems under random or deterministic steady state excitation. The essence of the method is the use of relaxation procedures with a suitable error function to find the estimated response; natural frequencies and normal modes are not computed. For a 45 degree of freedom system, and two relaxation procedures, convergence studies and frequency response estimates were performed. The low frequency studies are considered in the framework of earlier studies (Kayser and Bogdanoff, 1975) involving the mid to high frequency range.

Performance Analysis of Combined Methods of Genetic Algorithm and K-Means Clustering in Determining the Value of Centroid

NASA Astrophysics Data System (ADS)

Adya Zizwan, Putra; Zarlis, Muhammad; Budhiarti Nababan, Erna

2017-12-01

The determination of Centroid on K-Means Algorithm directly affects the quality of the clustering results. Determination of centroid by using random numbers has many weaknesses. The GenClust algorithm that combines the use of Genetic Algorithms and K-Means uses a genetic algorithm to determine the centroid of each cluster. The use of the GenClust algorithm uses 50% chromosomes obtained through deterministic calculations and 50% is obtained from the generation of random numbers. This study will modify the use of the GenClust algorithm in which the chromosomes used are 100% obtained through deterministic calculations. The results of this study resulted in performance comparisons expressed in Mean Square Error influenced by centroid determination on K-Means method by using GenClust method, modified GenClust method and also classic K-Means.

When human walking becomes random walking: fractal analysis and modeling of gait rhythm fluctuations

NASA Astrophysics Data System (ADS)

Hausdorff, Jeffrey M.; Ashkenazy, Yosef; Peng, Chang-K.; Ivanov, Plamen Ch.; Stanley, H. Eugene; Goldberger, Ary L.

2001-12-01

We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases. Stochastic modeling of the gait rhythm dynamics, based on transitions between different “neural centers”, reproduces distinctive statistical properties of the gait pattern. By tuning one model parameter, the hopping (transition) range, the model can describe alterations in gait dynamics from childhood to adulthood - including a decrease in the correlation and volatility exponents with maturation.

A theoretical and experimental study of turbulent evaporating sprays

NASA Technical Reports Server (NTRS)

Solomon, A. S. P.; Shuen, J. S.; Zhang, Q. F.; Faeth, G. M.

1984-01-01

Measurements and analysis limited to the dilute portions of turbulent evaporating sprays, injected into a still air environment were completed. Mean and fluctuating velocities and Reynolds stress were measured in the continuous phase. Liquid phase measurements included liquid mass fluxes, drop sizes and drop size and velocity correlation. Initial conditions needed for model evaluation were measured at a location as close to the injector exit as possible. The test sprays showed significant effects of slip and turbulent dispersion of the discrete phase. The measurements were used to evaluate three typical models of these processes: (1) a locally homogeneous flow (LHF) model, where slip between the phases were neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of drop dispersion by turbulence were ignored; and (3) a stochastic separated flow (SSF) model, where effects of interphase slip and turbulent dispersion were considered using random-walk computations for drop motion. For all three models, a k-epsilon model as used to find the properties of the continuous phase. The LHF and DSF models did not provide very satisfactory predictions for the present measurements. In contrast, the SSF model performed reasonably well--with no modifications in the prescription of eddy properties from its original calibration.

Stochastic simulation of biological reactions, and its applications for studying actin polymerization.

PubMed

Ichikawa, Kazuhisa; Suzuki, Takashi; Murata, Noboru

2010-11-30

Molecular events in biological cells occur in local subregions, where the molecules tend to be small in number. The cytoskeleton, which is important for both the structural changes of cells and their functions, is also a countable entity because of its long fibrous shape. To simulate the local environment using a computer, stochastic simulations should be run. We herein report a new method of stochastic simulation based on random walk and reaction by the collision of all molecules. The microscopic reaction rate P(r) is calculated from the macroscopic rate constant k. The formula involves only local parameters embedded for each molecule. The results of the stochastic simulations of simple second-order, polymerization, Michaelis-Menten-type and other reactions agreed quite well with those of deterministic simulations when the number of molecules was sufficiently large. An analysis of the theory indicated a relationship between variance and the number of molecules in the system, and results of multiple stochastic simulation runs confirmed this relationship. We simulated Ca²(+) dynamics in a cell by inward flow from a point on the cell surface and the polymerization of G-actin forming F-actin. Our results showed that this theory and method can be used to simulate spatially inhomogeneous events.

The effects of demand uncertainty on strategic gaming in the merit-order electricity pool market

NASA Astrophysics Data System (ADS)

Frem, Bassam

In a merit-order electricity pool market, generating companies (Gencos) game with their offered incremental cost to meet the electricity demand and earn bigger market shares and higher profits. However when the demand is treated as a random variable instead of as a known constant, these Genco gaming strategies become more complex. After a brief introduction of electricity markets and gaming, the effects of demand uncertainty on strategic gaming are studied in two parts: (1) Demand modelled as a discrete random variable (2) Demand modelled as a continuous random variable. In the first part, we proposed an algorithm, the discrete stochastic strategy (DSS) algorithm that generates a strategic set of offers from the perspective of the Gencos' profits. The DSS offers were tested and compared to the deterministic Nash equilibrium (NE) offers based on the predicted demand. This comparison, based on the expected Genco profits, showed the DSS to be a better strategy in a probabilistic sense than the deterministic NE. In the second part, we presented three gaming strategies: (1) Deterministic NE (2) No-Risk (3) Risk-Taking. The strategies were then tested and their profit performances were compared using two assessment tools: (a) Expected value and standard deviation (b) Inverse cumulative distribution. We concluded that despite yielding higher profit performance under the right conjectures, Risk-Taking strategies are very sensitive to incorrect conjectures on the competitors' gaming decisions. As such, despite its lower profit performance, the No-Risk strategy was deemed preferable.

Random-walk approach to the d -dimensional disordered Lorentz gas

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2008-02-01

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3 . Extensive numerical simulations were also performed to elucidate the role of the approximations involved.

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.

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.

Conflicting results of robot-assisted versus usual gait training during postacute rehabilitation of stroke patients: a randomized clinical trial

PubMed Central

Taveggia, Giovanni; Borboni, Alberto; Mulé, Chiara; Negrini, Stefano

2016-01-01

Robot gait training has the potential to increase the effectiveness of walking therapy. Clinical outcomes after robotic training are often not superior to conventional therapy. We evaluated the effectiveness of a robot training compared with a usual gait training physiotherapy during a standardized rehabilitation protocol in inpatient participants with poststroke hemiparesis. This was a randomized double-blind clinical trial in a postacute physical and rehabilitation medicine hospital. Twenty-eight patients, 39.3% women (72±6 years), with hemiparesis (<6 months after stroke) receiving a conventional treatment according to the Bobath approach were assigned randomly to an experimental or a control intervention of robot gait training to improve walking (five sessions a week for 5 weeks). Outcome measures included the 6-min walk test, the 10 m walk test, Functional Independence Measure, SF-36 physical functioning and the Tinetti scale. Outcomes were collected at baseline, immediately following the intervention period and 3 months following the end of the intervention. The experimental group showed a significant increase in functional independence and gait speed (10 m walk test) at the end of the treatment and follow-up, higher than the minimal detectable change. The control group showed a significant increase in the gait endurance (6-min walk test) at the follow-up, higher than the minimal detectable change. Both treatments were effective in the improvement of gait performances, although the statistical analysis of functional independence showed a significant improvement in the experimental group, indicating possible advantages during generic activities of daily living compared with overground treatment. PMID:26512928

Effects of mirror therapy combined with neuromuscular electrical stimulation on motor recovery of lower limbs and walking ability of patients with stroke: a randomized controlled study.

PubMed

Xu, Qun; Guo, Feng; Salem, Hassan M Abo; Chen, Hong; Huang, Xiaolin

2017-12-01

To investigate the effectiveness of mirror therapy combined with neuromuscular electrical stimulation in promoting motor recovery of the lower limbs and walking ability in patients suffering from foot drop after stroke. Randomized controlled study. Inpatient rehabilitation center of a teaching hospital. Sixty-nine patients with foot drop. Patients were randomly divided into three groups: control, mirror therapy, and mirror therapy + neuromuscular electrical stimulation. All groups received interventions for 0.5 hours/day and five days/week for four weeks. 10-Meter walk test, Brunnstrom stage of motor recovery of the lower limbs, Modified Ashworth Scale score of plantar flexor spasticity, and passive ankle joint dorsiflexion range of motion were assessed before and after the four-week period. After four weeks of intervention, Brunnstrom stage ( P = 0.04), 10-meter walk test ( P < 0.05), and passive range of motion ( P < 0.05) showed obvious improvements between patients in the mirror therapy and control groups. Patients in the mirror therapy + neuromuscular electrical stimulation group showed better results than those in the mirror therapy group in the 10-meter walk test ( P < 0.05). There was no significant difference in spasticity between patients in the two intervention groups. However, compared with patients in the control group, patients in the mirror therapy + neuromuscular electrical stimulation group showed a significant decrease in spasticity ( P < 0.001). Therapy combining mirror therapy and neuromuscular electrical stimulation may help improve walking ability and reduce spasticity in stroke patients with foot drop.

A random walk model for evaluating clinical trials involving serial observations.

PubMed

Hopper, J L; Young, G P

1988-05-01

For clinical trials where the variable of interest is ordered and categorical (for example, disease severity, symptom scale), and where measurements are taken at intervals, it might be possible to achieve a greater discrimination between the efficacy of treatments by modelling each patient's progress as a stochastic process. The random walk is a simple, easily interpreted model that can be fitted by maximum likelihood using a maximization routine with inference based on standard likelihood theory. In general the model can allow for randomly censored data, incorporates measured prognostic factors, and inference is conditional on the (possibly non-random) allocation of patients. Tests of fit and of model assumptions are proposed, and application to two therapeutic trials of gastroenterological disorders are presented. The model gave measures of the rate of, and variability in, improvement for patients under different treatments. A small simulation study suggested that the model is more powerful than considering the difference between initial and final scores, even when applied to data generated by a mechanism other than the random walk model assumed in the analysis. It thus provides a useful additional statistical method for evaluating clinical trials.

Varied overground walking-task practice versus body-weight-supported treadmill training in ambulatory adults within one year of stroke: a randomized controlled trial protocol.

PubMed

DePaul, Vincent G; Wishart, Laurie R; Richardson, Julie; Lee, Timothy D; Thabane, Lehana

2011-10-21

Although task-oriented training has been shown to improve walking outcomes after stroke, it is not yet clear whether one task-oriented approach is superior to another. The purpose of this study is to compare the effectiveness of the Motor Learning Walking Program (MLWP), a varied overground walking task program consistent with key motor learning principles, to body-weight-supported treadmill training (BWSTT) in community-dwelling, ambulatory, adults within 1 year of stroke. A parallel, randomized controlled trial with stratification by baseline gait speed will be conducted. Allocation will be controlled by a central randomization service and participants will be allocated to the two active intervention groups (1:1) using a permuted block randomization process. Seventy participants will be assigned to one of two 15-session training programs. In MLWP, one physiotherapist will supervise practice of various overground walking tasks. Instructions, feedback, and guidance will be provided in a manner that facilitates self-evaluation and problem solving. In BWSTT, training will emphasize repetition of the normal gait cycle while supported over a treadmill, assisted by up to three physiotherapists. Outcomes will be assessed by a blinded assessor at baseline, post-intervention and at 2-month follow-up. The primary outcome will be post-intervention comfortable gait speed. Secondary outcomes include fast gait speed, walking endurance, balance self-efficacy, participation in community mobility, health-related quality of life, and goal attainment. Groups will be compared using analysis of covariance with baseline gait speed strata as the single covariate. Intention-to-treat analysis will be used. In order to direct clinicians, patients, and other health decision-makers, there is a need for a head-to-head comparison of different approaches to active, task-related walking training after stroke. We hypothesize that outcomes will be optimized through the application of a task-related training program that is consistent with key motor learning principles related to practice, guidance and feedback. ClinicalTrials.gov # NCT00561405.

Varied overground walking-task practice versus body-weight-supported treadmill training in ambulatory adults within one year of stroke: a randomized controlled trial protocol

PubMed Central

2011-01-01

Background Although task-oriented training has been shown to improve walking outcomes after stroke, it is not yet clear whether one task-oriented approach is superior to another. The purpose of this study is to compare the effectiveness of the Motor Learning Walking Program (MLWP), a varied overground walking task program consistent with key motor learning principles, to body-weight-supported treadmill training (BWSTT) in community-dwelling, ambulatory, adults within 1 year of stroke. Methods/Design A parallel, randomized controlled trial with stratification by baseline gait speed will be conducted. Allocation will be controlled by a central randomization service and participants will be allocated to the two active intervention groups (1:1) using a permuted block randomization process. Seventy participants will be assigned to one of two 15-session training programs. In MLWP, one physiotherapist will supervise practice of various overground walking tasks. Instructions, feedback, and guidance will be provided in a manner that facilitates self-evaluation and problem solving. In BWSTT, training will emphasize repetition of the normal gait cycle while supported over a treadmill, assisted by up to three physiotherapists. Outcomes will be assessed by a blinded assessor at baseline, post-intervention and at 2-month follow-up. The primary outcome will be post-intervention comfortable gait speed. Secondary outcomes include fast gait speed, walking endurance, balance self-efficacy, participation in community mobility, health-related quality of life, and goal attainment. Groups will be compared using analysis of covariance with baseline gait speed strata as the single covariate. Intention-to-treat analysis will be used. Discussion In order to direct clinicians, patients, and other health decision-makers, there is a need for a head-to-head comparison of different approaches to active, task-related walking training after stroke. We hypothesize that outcomes will be optimized through the application of a task-related training program that is consistent with key motor learning principles related to practice, guidance and feedback. Trial Registration ClinicalTrials.gov # NCT00561405 PMID:22018267

The "Interval Walking in Colorectal Cancer" (I-WALK-CRC) study: Design, methods and recruitment results of a randomized controlled feasibility trial.

PubMed

Banck-Petersen, Anna; Olsen, Cecilie K; Djurhuus, Sissal S; Herrstedt, Anita; Thorsen-Streit, Sarah; Ried-Larsen, Mathias; Østerlind, Kell; Osterkamp, Jens; Krarup, Peter-Martin; Vistisen, Kirsten; Mosgaard, Camilla S; Pedersen, Bente K; Højman, Pernille; Christensen, Jesper F

2018-03-01

Low physical activity level is associated with poor prognosis in patients with colorectal cancer (CRC). To increase physical activity, technology-based platforms are emerging and provide intriguing opportunities to prescribe and monitor active lifestyle interventions. The "Interval Walking in Colorectal Cancer"(I-WALK-CRC) study explores the feasibility and efficacy a home-based interval-walking intervention delivered by a smart-phone application in order to improve cardio-metabolic health profile among CRC survivors. The aim of the present report is to describe the design, methods and recruitment results of the I-WALK-CRC study.Methods/Results: The I-WALK-CRC study is a randomized controlled trial designed to evaluate the feasibility and efficacy of a home-based interval walking intervention compared to a waiting-list control group for physiological and patient-reported outcomes. Patients who had completed surgery for local stage disease and patients who had completed surgery and any adjuvant chemotherapy for locally advanced stage disease were eligible for inclusion. Between October 1st , 2015, and February 1st , 2017, 136 inquiries were recorded; 83 patients were eligible for enrollment, and 42 patients accepted participation. Age and employment status were associated with participation, as participants were significantly younger (60.5 vs 70.8 years, P < 0.001) and more likely to be working (OR 5.04; 95%CI 1.96-12.98, P < 0.001) than non-participants. In the present study, recruitment of CRC survivors was feasible but we aim to better the recruitment rate in future studies. Further, the study clearly favored younger participants. The I-WALK-CRC study will provide important information regarding feasibility and efficacy of a home-based walking exercise program in CRC survivors.

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.

Nordic Walking as an Exercise Intervention to Reduce Pain in Women With Aromatase Inhibitor-Associated Arthralgia: A Feasibility Study.

PubMed

Fields, Jo; Richardson, Alison; Hopkinson, Jane; Fenlon, Deborah

2016-10-01

Women taking aromatase inhibitors as treatment for breast cancer commonly experience joint pain and stiffness (aromatase inhibitor-associated arthralgia [AIAA]), which can cause problems with adherence. There is evidence that exercise might be helpful, and Nordic walking could reduce joint pain compared to normal walking. To determine the feasibility of a trial of Nordic walking as an exercise intervention for women with AIAA. A feasibility study was carried out in a sample of women with AIAA using a randomized control design. Women were randomized to exercise (six-week supervised group Nordic walking training once per week with an increasing independent element, followed by six weeks 4 × 30 minutes/week independent Nordic walking); or enhanced usual care. Data were collected on recruitment, retention, exercise adherence, safety, and acceptability. The Brief Pain Inventory, GP Physical Activity Questionnaire, and biopsychosocial measures were completed at baseline, six and 12 weeks. Forty of 159 eligible women were recruited and attrition was 10%. There was no increased lymphedema and no long-term or serious injury. Adherence was >90% for weekly supervised group Nordic walking, and during independent Nordic walking, >80% women managed one to two Nordic walking sessions per week. From baseline to study end point, overall activity levels increased and pain reduced in both the intervention and control groups. Our findings indicate that women with AIAA are prepared to take up Nordic walking, complete a six-week supervised course and maintain increased activity levels over a 12-week period with no adverse effects. Copyright © 2016 American Academy of Hospice and Palliative Medicine. Published by Elsevier Inc. All rights reserved.

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.

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

NASA Astrophysics Data System (ADS)

Nazé, Pierre

2018-03-01

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel-Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag-Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.

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.

Adults' Daily Walking for Travel and Leisure: Interaction Between Attitude Toward Walking and the Neighborhood Environment.

PubMed

Yang, Yong; Diez-Roux, Ana V

2017-09-01

Studies on how the interaction of psychological and environmental characteristics influences walking are limited, and the results are inconsistent. Our aim is to examine how the attitude toward walking and neighborhood environments interacts to influence walking. Cross-sectional phone and mail survey. Participants randomly sampled from 6 study sites including Los Angeles, Chicago, Baltimore, Minneapolis, Manhattan, and Bronx Counties in New York City, and Forsyth and Davidson Counties in North Carolina. The final sample consisted of 2621 persons from 2011 to 2012. Total minutes of walking for travel or leisure, attitude toward walking, and perceptions of the neighborhood environments were self-reported. Street Smart (SS) Walk Score (a measure of walkability derived from a variety of geographic data) was obtained for each residential location. Linear regression models adjusting for age, gender, race/ethnicity, education, and income. Attitude toward walking was positively associated with walking for both purposes. Walking for travel was significantly associated with SS Walk Score, whereas walking for leisure was not. The SS Walk Score and selected perceived environment characteristics were associated with walking in people with a very positive attitude toward walking but were not associated with walking in people with a less positive attitude. Attitudes toward walking and neighborhood environments interact to affect walking behavior.

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

Continuous-time random-walk model for financial distributions

NASA Astrophysics Data System (ADS)

Masoliver, Jaume; Montero, Miquel; Weiss, George H.

2003-02-01

We apply the formalism of the continuous-time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump. We have applied the formalism to data on the U.S. dollar deutsche mark future exchange, finding good agreement between theory and the observed data.

Superimposed Code Theorectic Analysis of DNA Codes and DNA Computing

DTIC Science & Technology

2010-03-01

because only certain collections (partitioned by font type) of sequences are allowed to be in each position (e.g., Arial = position 0, Comic ...rigidity of short oligos and the shape of the polar charge. Oligo movement was modeled by a Brownian motion 3 dimensional random walk. The one...temperature, kB is Boltz he viscosity of the medium. The random walk motion is modeled by assuming the oligo is on a three dimensional lattice and may

Physical interrelation between Fokker-Planck and random walk models with application to Coulomb interactions.

NASA Technical Reports Server (NTRS)

Englert, G. W.

1971-01-01

A model of the random walk is formulated to allow a simple computing procedure to replace the difficult problem of solution of the Fokker-Planck equation. The step sizes and probabilities of taking steps in the various directions are expressed in terms of Fokker-Planck coefficients. Application is made to many particle systems with Coulomb interactions. The relaxation of a highly peaked velocity distribution of particles to equilibrium conditions is illustrated.

Ant-inspired density estimation via random walks

PubMed Central

Musco, Cameron; Su, Hsin-Hao

2017-01-01

Many ant species use distributed population density estimation in applications ranging from quorum sensing, to task allocation, to appraisal of enemy colony strength. It has been shown that ants estimate local population density by tracking encounter rates: The higher the density, the more often the ants bump into each other. We study distributed density estimation from a theoretical perspective. We prove that a group of anonymous agents randomly walking on a grid are able to estimate their density within a small multiplicative error in few steps by measuring their rates of encounter with other agents. Despite dependencies inherent in the fact that nearby agents may collide repeatedly (and, worse, cannot recognize when this happens), our bound nearly matches what would be required to estimate density by independently sampling grid locations. From a biological perspective, our work helps shed light on how ants and other social insects can obtain relatively accurate density estimates via encounter rates. From a technical perspective, our analysis provides tools for understanding complex dependencies in the collision probabilities of multiple random walks. We bound the strength of these dependencies using local mixing properties of the underlying graph. Our results extend beyond the grid to more general graphs, and we discuss applications to size estimation for social networks, density estimation for robot swarms, and random walk-based sampling for sensor networks. PMID:28928146

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.

Central limit theorem for recurrent random walks on a strip with bounded potential

NASA Astrophysics Data System (ADS)

Dolgopyat, D.; Goldsheid, I.

2018-07-01

We prove that the recurrent random walk (RW) in random environment (RE) on a strip in bounded potential satisfies the central limit theorem (CLT). The key ingredients of the proof are the analysis of the invariant measure equation and construction of a linearly growing martingale for walks in bounded potential. Our main result implies a complete classification of recurrent i.i.d. RWRE on the strip. Namely the walk either exhibits the Sinai behaviour in the sense that converges, as , to a (random) limit (the Sinai law) or, it satisfies the CLT. Another application of our main result is the CLT for the quasiperiodic environments with Diophantine frequencies in the recurrent case. We complement this result by proving that in the transient case the CLT holds for all uniquely ergodic environments. We also investigate the algebraic structure of the environments satisfying the CLT. In particular, we show that there exists a collection of proper algebraic subvarieties in the space of transition probabilities, such that: • If RE is stationary and ergodic and the transition probabilities are con-centrated on one of subvarieties from our collection then the CLT holds. • If the environment is i.i.d then the above condition is also necessary forthe CLT. All these results are valid for one-dimensional RWRE with bounded jumps as a particular case of the strip model.

Distributed clone detection in static wireless sensor networks: random walk with network division.

PubMed

Khan, Wazir Zada; Aalsalem, Mohammed Y; Saad, N M

2015-01-01

Wireless Sensor Networks (WSNs) are vulnerable to clone attacks or node replication attacks as they are deployed in hostile and unattended environments where they are deprived of physical protection, lacking physical tamper-resistance of sensor nodes. As a result, an adversary can easily capture and compromise sensor nodes and after replicating them, he inserts arbitrary number of clones/replicas into the network. If these clones are not efficiently detected, an adversary can be further capable to mount a wide variety of internal attacks which can emasculate the various protocols and sensor applications. Several solutions have been proposed in the literature to address the crucial problem of clone detection, which are not satisfactory as they suffer from some serious drawbacks. In this paper we propose a novel distributed solution called Random Walk with Network Division (RWND) for the detection of node replication attack in static WSNs which is based on claimer-reporter-witness framework and combines a simple random walk with network division. RWND detects clone(s) by following a claimer-reporter-witness framework and a random walk is employed within each area for the selection of witness nodes. Splitting the network into levels and areas makes clone detection more efficient and the high security of witness nodes is ensured with moderate communication and memory overheads. Our simulation results show that RWND outperforms the existing witness node based strategies with moderate communication and memory overheads.

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.

Changes in work affect in response to lunchtime walking in previously physically inactive employees: A randomized trial.

PubMed

Thøgersen-Ntoumani, C; Loughren, E A; Kinnafick, F-E; Taylor, I M; Duda, J L; Fox, K R

2015-12-01

Physical activity may regulate affective experiences at work, but controlled studies are needed and there has been a reliance on retrospective accounts of experience. The purpose of the present study was to examine the effect of lunchtime walks on momentary work affect at the individual and group levels. Physically inactive employees (N = 56; M age = 47.68; 92.86% female) from a large university in the UK were randomized to immediate treatment or delayed treatment (DT). The DT participants completed both a control and intervention period. During the intervention period, participants partook in three weekly 30-min lunchtime group-led walks for 10 weeks. They completed twice daily affective reports at work (morning and afternoon) using mobile phones on two randomly chosen days per week. Multilevel modeling was used to analyze the data. Lunchtime walks improved enthusiasm, relaxation, and nervousness at work, although the pattern of results differed depending on whether between-group or within-person analyses were conducted. The intervention was effective in changing some affective states and may have broader implications for public health and workplace performance. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Dual Roles for Spike Signaling in Cortical Neural Populations

PubMed Central

Ballard, Dana H.; Jehee, Janneke F. M.

2011-01-01

A prominent feature of signaling in cortical neurons is that of randomness in the action potential. The output of a typical pyramidal cell can be well fit with a Poisson model, and variations in the Poisson rate repeatedly have been shown to be correlated with stimuli. However while the rate provides a very useful characterization of neural spike data, it may not be the most fundamental description of the signaling code. Recent data showing γ frequency range multi-cell action potential correlations, together with spike timing dependent plasticity, are spurring a re-examination of the classical model, since precise timing codes imply that the generation of spikes is essentially deterministic. Could the observed Poisson randomness and timing determinism reflect two separate modes of communication, or do they somehow derive from a single process? We investigate in a timing-based model whether the apparent incompatibility between these probabilistic and deterministic observations may be resolved by examining how spikes could be used in the underlying neural circuits. The crucial component of this model draws on dual roles for spike signaling. In learning receptive fields from ensembles of inputs, spikes need to behave probabilistically, whereas for fast signaling of individual stimuli, the spikes need to behave deterministically. Our simulations show that this combination is possible if deterministic signals using γ latency coding are probabilistically routed through different members of a cortical cell population at different times. This model exhibits standard features characteristic of Poisson models such as orientation tuning and exponential interval histograms. In addition, it makes testable predictions that follow from the γ latency coding. PMID:21687798

Lyapunov exponents for one-dimensional aperiodic photonic bandgap structures

NASA Astrophysics Data System (ADS)

Kissel, Glen J.

2011-10-01

Existing in the "gray area" between perfectly periodic and purely randomized photonic bandgap structures are the socalled aperoidic structures whose layers are chosen according to some deterministic rule. We consider here a onedimensional photonic bandgap structure, a quarter-wave stack, with the layer thickness of one of the bilayers subject to being either thin or thick according to five deterministic sequence rules and binary random selection. To produce these aperiodic structures we examine the following sequences: Fibonacci, Thue-Morse, Period doubling, Rudin-Shapiro, as well as the triadic Cantor sequence. We model these structures numerically with a long chain (approximately 5,000,000) of transfer matrices, and then use the reliable algorithm of Wolf to calculate the (upper) Lyapunov exponent for the long product of matrices. The Lyapunov exponent is the statistically well-behaved variable used to characterize the Anderson localization effect (exponential confinement) when the layers are randomized, so its calculation allows us to more precisely compare the purely randomized structure with its aperiodic counterparts. It is found that the aperiodic photonic systems show much fine structure in their Lyapunov exponents as a function of frequency, and, in a number of cases, the exponents are quite obviously fractal.

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.

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.

Factors Influencing the Efficacy of Aerobic Exercise for Improving Fitness and Walking Capacity After Stroke: A Meta-Analysis With Meta-Regression.

PubMed

Boyne, Pierce; Welge, Jeffrey; Kissela, Brett; Dunning, Kari

2017-03-01

To assess the influence of dosing parameters and patient characteristics on the efficacy of aerobic exercise (AEX) poststroke. A systematic review was conducted using PubMed, MEDLINE, Cumulative Index of Nursing and Allied Health Literature, Physiotherapy Evidence Database, and Academic Search Complete. Studies were selected that compared an AEX group with a nonaerobic control group among ambulatory persons with stroke. Extracted outcome data included peak oxygen consumption (V˙o 2 peak) during exercise testing, walking speed, and walking endurance (6-min walk test). Independent variables of interest were AEX mode (seated or walking), AEX intensity (moderate or vigorous), AEX volume (total hours), stroke chronicity, and baseline outcome scores. Significant between-study heterogeneity was confirmed for all outcomes. Pooled AEX effect size estimates (AEX group change minus control group change) from random effects models were V˙o 2 peak, 2.2mL⋅kg -1 ⋅min -1 (95% confidence interval [CI], 1.3-3.1mL⋅kg -1 ⋅min -1 ); walking speed, .06m/s (95% CI, .01-.11m/s); and 6-minute walk test distance, 29m (95% CI, 15-42m). In meta-regression, larger V˙o 2 peak effect sizes were significantly associated with higher AEX intensity and higher baseline V˙o 2 peak. Larger effect sizes for walking speed and the 6-minute walk test were significantly associated with a walking AEX mode. In contrast, seated AEX did not have a significant effect on walking outcomes. AEX significantly improves aerobic capacity poststroke, but may need to be task specific to affect walking speed and endurance. Higher AEX intensity is associated with better outcomes. Future randomized studies are needed to confirm these results. Copyright © 2016 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

Inferring Lévy walks from curved trajectories: A rescaling method

NASA Astrophysics Data System (ADS)

Tromer, R. M.; Barbosa, M. B.; Bartumeus, F.; Catalan, J.; da Luz, M. G. E.; Raposo, E. P.; Viswanathan, G. M.

2015-08-01

An important problem in the study of anomalous diffusion and transport concerns the proper analysis of trajectory data. The analysis and inference of Lévy walk patterns from empirical or simulated trajectories of particles in two and three-dimensional spaces (2D and 3D) is much more difficult than in 1D because path curvature is nonexistent in 1D but quite common in higher dimensions. Recently, a new method for detecting Lévy walks, which considers 1D projections of 2D or 3D trajectory data, has been proposed by Humphries et al. The key new idea is to exploit the fact that the 1D projection of a high-dimensional Lévy walk is itself a Lévy walk. Here, we ask whether or not this projection method is powerful enough to cleanly distinguish 2D Lévy walk with added curvature from a simple Markovian correlated random walk. We study the especially challenging case in which both 2D walks have exactly identical probability density functions (pdf) of step sizes as well as of turning angles between successive steps. Our approach extends the original projection method by introducing a rescaling of the projected data. Upon projection and coarse-graining, the renormalized pdf for the travel distances between successive turnings is seen to possess a fat tail when there is an underlying Lévy process. We exploit this effect to infer a Lévy walk process in the original high-dimensional curved trajectory. In contrast, no fat tail appears when a (Markovian) correlated random walk is analyzed in this way. We show that this procedure works extremely well in clearly identifying a Lévy walk even when there is noise from curvature. The present protocol may be useful in realistic contexts involving ongoing debates on the presence (or not) of Lévy walks related to animal movement on land (2D) and in air and oceans (3D).

Comparison of Deterministic and Probabilistic Radial Distribution Systems Load Flow

NASA Astrophysics Data System (ADS)

Gupta, Atma Ram; Kumar, Ashwani

2017-12-01

Distribution system network today is facing the challenge of meeting increased load demands from the industrial, commercial and residential sectors. The pattern of load is highly dependent on consumer behavior and temporal factors such as season of the year, day of the week or time of the day. For deterministic radial distribution load flow studies load is taken as constant. But, load varies continually with a high degree of uncertainty. So, there is a need to model probable realistic load. Monte-Carlo Simulation is used to model the probable realistic load by generating random values of active and reactive power load from the mean and standard deviation of the load and for solving a Deterministic Radial Load Flow with these values. The probabilistic solution is reconstructed from deterministic data obtained for each simulation. The main contribution of the work is: Finding impact of probable realistic ZIP load modeling on balanced radial distribution load flow. Finding impact of probable realistic ZIP load modeling on unbalanced radial distribution load flow. Compare the voltage profile and losses with probable realistic ZIP load modeling for balanced and unbalanced radial distribution load flow.

Pilot study of a dog walking randomized intervention: effects of a focus on canine exercise.

PubMed

Rhodes, Ryan E; Murray, Holly; Temple, Viviene A; Tuokko, Holly; Higgins, Joan Wharf

2012-05-01

The promotion of dog walking among owners who do not walk their dogs regularly may be a viable physical activity intervention aperture, yet research is very limited and no intervention studies have employed control groups. Therefore, the purpose of this pilot study was to examine the viability of dog walking for physical activity intervention using messages targeting canine exercise. Inactive dog owners (n=58) were randomized to either a standard control condition or the intervention (persuasive material about canine health from walking and a calendar to mark walks) after completing a baseline questionnaire package and wearing a pedometer for one week. Participants (standard condition n=28; intervention condition n=30) completed the six and 12 week follow-up questionnaire packages. Intention to treat analyses showed that both groups increased physical activity significantly across the 12 weeks (η(2)=0.09 to 0.21). The intervention group resulted in significantly higher step-counts compared to the control group (Δ 1823 steps) and showed significantly higher trajectories from baseline to 12 weeks in the self-reported physical activity measures (η(2)=0.11 to 0.27). The results are promising for the viability of increasing dog walking as a means for physical activity promotion and suggest that theoretical fidelity targeting canine exercise may be a helpful approach. Copyright © 2012 Elsevier Inc. All rights reserved.

Quantifying the dose-response of walking in reducing coronary heart disease risk: meta-analysis.

PubMed

Zheng, Henry; Orsini, Nicola; Amin, Janaki; Wolk, Alicja; Nguyen, Van Thi Thuy; Ehrlich, Fred

2009-01-01

The evidence for the efficacy of walking in reducing the risk of and preventing coronary heart disease (CHD) is not completely understood. This meta-analysis aimed to quantify the dose-response relationship between walking and CHD risk reduction for both men and women in the general population. Studies on walking and CHD primary prevention between 1954 and 2007 were identified through Medline, SportDiscus and the Cochrane Database of Systematic Reviews. Random-effect meta-regression models were used to pool the relative risks from individual studies. A total of 11 prospective cohort studies and one randomized control trial study met the inclusion criteria, with 295,177 participants free of CHD at baseline and 7,094 cases at follow-up. The meta-analysis indicated that an increment of approximately 30 min of normal walking a day for 5 days a week was associated with 19% CHD risk reduction (95% CI = 14-23%; P-heterogeneity = 0.56; I (2) = 0%). We found no evidence of heterogeneity between subgroups of studies defined by gender (P = 0.67); age of the study population (P = 0.52); or follow-up duration (P = 0.77). The meta-analysis showed that the risk for developing CHD decreases as walking dose increases. Walking should be prescribed as an evidence-based effective exercise modality for CHD prevention in the general population.

Effect of multilayer high-compression bandaging on ankle range of motion and oxygen cost of walking

PubMed Central

Roaldsen, K S; Elfving, B; Stanghelle, J K; Mattsson, E

2012-01-01

Objective To evaluate the effects of multilayer high-compression bandaging on ankle range of motion, oxygen consumption and subjective walking ability in healthy subjects. Method A volunteer sample of 22 healthy subjects (10 women and 12 men; aged 67 [63–83] years) were studied. The intervention included treadmill-walking at self-selected speed with and without multilayer high-compression bandaging (Proforeº), randomly selected. The primary outcome variables were ankle range of motion, oxygen consumption and subjective walking ability. Results Total ankle range of motion decreased 4% with compression. No change in oxygen cost of walking was observed. Less than half the subjects reported that walking-shoe comfort or walking distance was negatively affected. Conclusion Ankle range of motion decreased with compression but could probably be counteracted with a regular exercise programme. There were no indications that walking with compression was more exhausting than walking without. Appropriate walking shoes could seem important to secure gait efficiency when using compression garments. PMID:21810941

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

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.

SU-D-201-06: Random Walk Algorithm Seed Localization Parameters in Lung Positron Emission Tomography (PET) Images

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

Soufi, M; Asl, A Kamali; Geramifar, P

2015-06-15

Purpose: The objective of this study was to find the best seed localization parameters in random walk algorithm application to lung tumor delineation in Positron Emission Tomography (PET) images. Methods: PET images suffer from statistical noise and therefore tumor delineation in these images is a challenging task. Random walk algorithm, a graph based image segmentation technique, has reliable image noise robustness. Also its fast computation and fast editing characteristics make it powerful for clinical purposes. We implemented the random walk algorithm using MATLAB codes. The validation and verification of the algorithm have been done by 4D-NCAT phantom with spherical lungmore » lesions in different diameters from 20 to 90 mm (with incremental steps of 10 mm) and different tumor to background ratios of 4:1 and 8:1. STIR (Software for Tomographic Image Reconstruction) has been applied to reconstruct the phantom PET images with different pixel sizes of 2×2×2 and 4×4×4 mm{sup 3}. For seed localization, we selected pixels with different maximum Standardized Uptake Value (SUVmax) percentages, at least (70%, 80%, 90% and 100%) SUVmax for foreground seeds and up to (20% to 55%, 5% increment) SUVmax for background seeds. Also, for investigation of algorithm performance on clinical data, 19 patients with lung tumor were studied. The resulted contours from algorithm have been compared with nuclear medicine expert manual contouring as ground truth. Results: Phantom and clinical lesion segmentation have shown that the best segmentation results obtained by selecting the pixels with at least 70% SUVmax as foreground seeds and pixels up to 30% SUVmax as background seeds respectively. The mean Dice Similarity Coefficient of 94% ± 5% (83% ± 6%) and mean Hausdorff Distance of 1 (2) pixels have been obtained for phantom (clinical) study. Conclusion: The accurate results of random walk algorithm in PET image segmentation assure its application for radiation treatment planning and diagnosis.« less

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

Simulating intrafraction prostate motion with a random walk model.

PubMed

Pommer, Tobias; Oh, Jung Hun; Munck Af Rosenschöld, Per; Deasy, Joseph O

2017-01-01

Prostate motion during radiation therapy (ie, intrafraction motion) can cause unwanted loss of radiation dose to the prostate and increased dose to the surrounding organs at risk. A compact but general statistical description of this motion could be useful for simulation of radiation therapy delivery or margin calculations. We investigated whether prostate motion could be modeled with a random walk model. Prostate motion recorded during 548 radiation therapy fractions in 17 patients was analyzed and used for input in a random walk prostate motion model. The recorded motion was categorized on the basis of whether any transient excursions (ie, rapid prostate motion in the anterior and superior direction followed by a return) occurred in the trace and transient motion. This was separately modeled as a large step in the anterior/superior direction followed by a returning large step. Random walk simulations were conducted with and without added artificial transient motion using either motion data from all observed traces or only traces without transient excursions as model input, respectively. A general estimate of motion was derived with reasonable agreement between simulated and observed traces, especially during the first 5 minutes of the excursion-free simulations. Simulated and observed diffusion coefficients agreed within 0.03, 0.2 and 0.3 mm 2 /min in the left/right, superior/inferior, and anterior/posterior directions, respectively. A rapid increase in variance at the start of observed traces was difficult to reproduce and seemed to represent the patient's need to adjust before treatment. This could be estimated somewhat using artificial transient motion. Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during delivery of radiation therapy.

History dependent quantum random walks as quantum lattice gas automata

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

Shakeel, Asif, E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu; Love, Peter J., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu; Meyer, David A., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu

Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the historymore » information arise naturally as geometrical degrees of freedom on the lattice.« less

First-passage problems: A probabilistic dynamic analysis for degraded structures

NASA Technical Reports Server (NTRS)

Shiao, Michael C.; Chamis, Christos C.

1990-01-01

Structures subjected to random excitations with uncertain system parameters degraded by surrounding environments (a random time history) are studied. Methods are developed to determine the statistics of dynamic responses, such as the time-varying mean, the standard deviation, the autocorrelation functions, and the joint probability density function of any response and its derivative. Moreover, the first-passage problems with deterministic and stationary/evolutionary random barriers are evaluated. The time-varying (joint) mean crossing rate and the probability density function of the first-passage time for various random barriers are derived.

Comparison of three controllers applied to helicopter vibration

NASA Technical Reports Server (NTRS)

Leyland, Jane A.

1992-01-01

A comparison was made of the applicability and suitability of the deterministic controller, the cautious controller, and the dual controller for the reduction of helicopter vibration by using higher harmonic blade pitch control. A randomly generated linear plant model was assumed and the performance index was defined to be a quadratic output metric of this linear plant. A computer code, designed to check out and evaluate these controllers, was implemented and used to accomplish this comparison. The effects of random measurement noise, the initial estimate of the plant matrix, and the plant matrix propagation rate were determined for each of the controllers. With few exceptions, the deterministic controller yielded the greatest vibration reduction (as characterized by the quadratic output metric) and operated with the greatest reliability. Theoretical limitations of these controllers were defined and appropriate candidate alternative methods, including one method particularly suitable to the cockpit, were identified.

Extracting Information about the Rotator Cuff from Magnetic Resonance Images Using Deterministic and Random Techniques

PubMed Central

De Los Ríos, F. A.; Paluszny, M.

2015-01-01

We consider some methods to extract information about the rotator cuff based on magnetic resonance images; the study aims to define an alternative method of display that might facilitate the detection of partial tears in the supraspinatus tendon. Specifically, we are going to use families of ellipsoidal triangular patches to cover the humerus head near the affected area. These patches are going to be textured and displayed with the information of the magnetic resonance images using the trilinear interpolation technique. For the generation of points to texture each patch, we propose a new method that guarantees the uniform distribution of its points using a random statistical method. Its computational cost, defined as the average computing time to generate a fixed number of points, is significantly lower as compared with deterministic and other standard statistical techniques. PMID:25650281

Deterministic binary vectors for efficient automated indexing of MEDLINE/PubMed abstracts.

PubMed

Wahle, Manuel; Widdows, Dominic; Herskovic, Jorge R; Bernstam, Elmer V; Cohen, Trevor

2012-01-01

The need to maintain accessibility of the biomedical literature has led to development of methods to assist human indexers by recommending index terms for newly encountered articles. Given the rapid expansion of this literature, it is essential that these methods be scalable. Document vector representations are commonly used for automated indexing, and Random Indexing (RI) provides the means to generate them efficiently. However, RI is difficult to implement in real-world indexing systems, as (1) efficient nearest-neighbor search requires retaining all document vectors in RAM, and (2) it is necessary to maintain a store of randomly generated term vectors to index future documents. Motivated by these concerns, this paper documents the development and evaluation of a deterministic binary variant of RI. The increased capacity demonstrated by binary vectors has implications for information retrieval, and the elimination of the need to retain term vectors facilitates distributed implementations, enhancing the scalability of RI.

Deterministic Binary Vectors for Efficient Automated Indexing of MEDLINE/PubMed Abstracts

PubMed Central

Wahle, Manuel; Widdows, Dominic; Herskovic, Jorge R.; Bernstam, Elmer V.; Cohen, Trevor

2012-01-01

The need to maintain accessibility of the biomedical literature has led to development of methods to assist human indexers by recommending index terms for newly encountered articles. Given the rapid expansion of this literature, it is essential that these methods be scalable. Document vector representations are commonly used for automated indexing, and Random Indexing (RI) provides the means to generate them efficiently. However, RI is difficult to implement in real-world indexing systems, as (1) efficient nearest-neighbor search requires retaining all document vectors in RAM, and (2) it is necessary to maintain a store of randomly generated term vectors to index future documents. Motivated by these concerns, this paper documents the development and evaluation of a deterministic binary variant of RI. The increased capacity demonstrated by binary vectors has implications for information retrieval, and the elimination of the need to retain term vectors facilitates distributed implementations, enhancing the scalability of RI. PMID:23304369

Tests of peak flow scaling in simulated self-similar river networks

USGS Publications Warehouse

Menabde, M.; Veitzer, S.; Gupta, V.; Sivapalan, M.

2001-01-01

The effect of linear flow routing incorporating attenuation and network topology on peak flow scaling exponent is investigated for an instantaneously applied uniform runoff on simulated deterministic and random self-similar channel networks. The flow routing is modelled by a linear mass conservation equation for a discrete set of channel links connected in parallel and series, and having the same topology as the channel network. A quasi-analytical solution for the unit hydrograph is obtained in terms of recursion relations. The analysis of this solution shows that the peak flow has an asymptotically scaling dependence on the drainage area for deterministic Mandelbrot-Vicsek (MV) and Peano networks, as well as for a subclass of random self-similar channel networks. However, the scaling exponent is shown to be different from that predicted by the scaling properties of the maxima of the width functions. ?? 2001 Elsevier Science Ltd. All rights reserved.

Unifying Complexity and Information

NASA Astrophysics Data System (ADS)

Ke, Da-Guan

2013-04-01

Complex systems, arising in many contexts in the computer, life, social, and physical sciences, have not shared a generally-accepted complexity measure playing a fundamental role as the Shannon entropy H in statistical mechanics. Superficially-conflicting criteria of complexity measurement, i.e. complexity-randomness (C-R) relations, have given rise to a special measure intrinsically adaptable to more than one criterion. However, deep causes of the conflict and the adaptability are not much clear. Here I trace the root of each representative or adaptable measure to its particular universal data-generating or -regenerating model (UDGM or UDRM). A representative measure for deterministic dynamical systems is found as a counterpart of the H for random process, clearly redefining the boundary of different criteria. And a specific UDRM achieving the intrinsic adaptability enables a general information measure that ultimately solves all major disputes. This work encourages a single framework coving deterministic systems, statistical mechanics and real-world living organisms.

Quantum Algorithms Based on Physical Processes

DTIC Science & Technology

2013-12-03

quantum walks with hard-core bosons and the graph isomorphism problem,” American Physical Society March meeting, March 2011 Kenneth Rudinger, John...King Gamble, Mark Wellons, Mark Friesen, Dong Zhou, Eric Bach, Robert Joynt, and S.N. Coppersmith, “Quantum random walks of non-interacting bosons on...and noninteracting Bosons to distinguish nonisomorphic graphs. 1) We showed that quantum walks of two hard-core Bosons can distinguish all pairs of

Quantum Algorithms Based on Physical Processes

DTIC Science & Technology

2013-12-02

quantum walks with hard-core bosons and the graph isomorphism problem,” American Physical Society March meeting, March 2011 Kenneth Rudinger, John...King Gamble, Mark Wellons, Mark Friesen, Dong Zhou, Eric Bach, Robert Joynt, and S.N. Coppersmith, “Quantum random walks of non-interacting bosons on...and noninteracting Bosons to distinguish nonisomorphic graphs. 1) We showed that quantum walks of two hard-core Bosons can distinguish all pairs of

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.

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.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

Superimposed Code Theoretic Analysis of Deoxyribonucleic Acid (DNA) Codes and DNA Computing

DTIC Science & Technology

2010-01-01

partitioned by font type) of sequences are allowed to be in each position (e.g., Arial = position 0, Comic = position 1, etc. ) and within each collection...movement was modeled by a Brownian motion 3 dimensional random walk. The one dimensional diffusion coefficient D for the ellipsoid shape with 3...temperature, kB is Boltzmann’s constant, and η is the viscosity of the medium. The random walk motion is modeled by assuming the oligo is on a three

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.

The Effect of a Home-Based Walking Intervention on Quality of Life, Body Composition, and Estrogen Metabolism in Postmenopausal Breast Cancer Survivors

DTIC Science & Technology

2006-09-01

Effect sizes are also shown for each randomization group (i.e., effect size from pretest to posttest ) and for the comparison of the two randomization...questions were answered. This study was designed to be a pilot study to quantify effect sizes of the effect of walking on quality of life...physical activity, body composition, and depending on inclusion criteria, estrogen metabolism. Second, this study was designed to assess the degree to

Evaluating the Bias of Alternative Cost Progress Models: Tests Using Aerospace Industry Acquisition Programs

DTIC Science & Technology

1992-12-01

suspect :mat, -n2 extent predict:.on cas jas ccsiziveiv crrei:=e amonc e v:arious models, :he fandom *.;aik, learn ha r ur e, i;<ea- variable and Bemis...Functions, Production Rate Adjustment Model, Learning Curve Model. Random Walk Model. Bemis Model. Evaluating Model Bias, Cost Prediction Bias. Cost...of four cost progress models--a random walk model, the tradiuonai learning curve model, a production rate model Ifixed-variable model). and a model

On Connected Diagrams and Cumulants of Erdős-Rényi Matrix Models

NASA Astrophysics Data System (ADS)

Khorunzhiy, O.

2008-08-01

Regarding the adjacency matrices of n-vertex graphs and related graph Laplacian we introduce two families of discrete matrix models constructed both with the help of the Erdős-Rényi ensemble of random graphs. Corresponding matrix sums represent the characteristic functions of the average number of walks and closed walks over the random graph. These sums can be considered as discrete analogues of the matrix integrals of random matrix theory. We study the diagram structure of the cumulant expansions of logarithms of these matrix sums and analyze the limiting expressions as n → ∞ in the cases of constant and vanishing edge probabilities.

Effect of a Home-Based Exercise Intervention of Wearable Technology and Telephone Coaching on Walking Performance in Peripheral Artery Disease: The HONOR Randomized Clinical Trial.

PubMed

McDermott, Mary M; Spring, Bonnie; Berger, Jeffrey S; Treat-Jacobson, Diane; Conte, Michael S; Creager, Mark A; Criqui, Michael H; Ferrucci, Luigi; Gornik, Heather L; Guralnik, Jack M; Hahn, Elizabeth A; Henke, Peter; Kibbe, Melina R; Kohlman-Trighoff, Debra; Li, Lingyu; Lloyd-Jones, Donald; McCarthy, Walter; Polonsky, Tamar S; Skelly, Christopher; Tian, Lu; Zhao, Lihui; Zhang, Dongxue; Rejeski, W Jack

2018-04-24

Clinical practice guidelines support home-based exercise for patients with peripheral artery disease (PAD), but no randomized trials have tested whether an exercise intervention without periodic medical center visits improves walking performance. To determine whether a home-based exercise intervention consisting of a wearable activity monitor and telephone coaching improves walking ability over 9 months in patients with PAD. Randomized clinical trial conducted at 3 US medical centers. Patients with PAD were randomized between June 18, 2015, and April 4, 2017, to home-based exercise vs usual care for 9 months. Final follow-up was on December 5, 2017. The exercise intervention group (n = 99) received 4 weekly medical center visits during the first month followed by 8 months of a wearable activity monitor and telephone coaching. The usual care group (n = 101) received no onsite sessions, active exercise, or coaching intervention. The primary outcome was change in 6-minute walk distance at 9-month follow-up (minimal clinically important difference [MCID], 20 m). Secondary outcomes included 9-month change in subcomponents of the Walking Impairment Questionnaire (WIQ) (0-100 score; 100, best), SF-36 physical functioning score, Patient-Reported Outcomes Measurement Information System (PROMIS) mobility questionnaire (higher = better; MCID, 2 points), PROMIS satisfaction with social roles questionnaire, PROMIS pain interference questionnaire (lower = better; MCID range, 3.5-4.5 points), and objectively measured physical activity. Among 200 randomized participants (mean [SD] age, 70.2 [10.4] years; 105 [52.5%] women), 182 (91%) completed 9-month follow-up. The mean change from baseline to 9-month follow-up in the 6-minute walk distance was 5.5 m in the intervention group vs 14.4 m in the usual care group (difference, -8.9 m; 95% CI, -26.0 to 8.2 m; P = .31). The exercise intervention worsened the PROMIS pain interference score, mean change from baseline to 9 months was 0.7 in the intervention group vs -2.8 in the usual care group (difference, 3.5; 95% CI, 1.3 to 5.8; P = .002). There were no significant between-group differences in the WIQ score, the SF-36 physical functioning score, or the PROMIS mobility or satisfaction with social roles scores. Among patients with PAD, a home-based exercise intervention consisting of a wearable activity monitor and telephone coaching, compared with usual care, did not improve walking performance at 9-month follow-up. These results do not support home-based exercise interventions of wearable devices and telephone counseling without periodic onsite visits to improve walking performance in patients with PAD. clinicaltrials.gov Identifier: NCT02462824.

3D exemplar-based random walks for tooth segmentation from cone-beam computed tomography images

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

Pei, Yuru, E-mail: peiyuru@cis.pku.edu.cn; Ai, Xin

Purpose: Tooth segmentation is an essential step in acquiring patient-specific dental geometries from cone-beam computed tomography (CBCT) images. Tooth segmentation from CBCT images is still a challenging task considering the comparatively low image quality caused by the limited radiation dose, as well as structural ambiguities from intercuspation and nearby alveolar bones. The goal of this paper is to present and discuss the latest accomplishments in semisupervised tooth segmentation with adaptive 3D shape constraints. Methods: The authors propose a 3D exemplar-based random walk method of tooth segmentation from CBCT images. The proposed method integrates semisupervised label propagation and regularization by 3Dmore » exemplar registration. To begin with, the pure random walk method is to get an initial segmentation of the teeth, which tends to be erroneous because of the structural ambiguity of CBCT images. And then, as an iterative refinement, the authors conduct a regularization by using 3D exemplar registration, as well as label propagation by random walks with soft constraints, to improve the tooth segmentation. In the first stage of the iteration, 3D exemplars with well-defined topologies are adapted to fit the tooth contours, which are obtained from the random walks based segmentation. The soft constraints on voxel labeling are defined by shape-based foreground dentine probability acquired by the exemplar registration, as well as the appearance-based probability from a support vector machine (SVM) classifier. In the second stage, the labels of the volume-of-interest (VOI) are updated by the random walks with soft constraints. The two stages are optimized iteratively. Instead of the one-shot label propagation in the VOI, an iterative refinement process can achieve a reliable tooth segmentation by virtue of exemplar-based random walks with adaptive soft constraints. Results: The proposed method was applied for tooth segmentation of twenty clinically captured CBCT images. Three metrics, including the Dice similarity coefficient (DSC), the Jaccard similarity coefficient (JSC), and the mean surface deviation (MSD), were used to quantitatively analyze the segmentation of anterior teeth including incisors and canines, premolars, and molars. The segmentation of the anterior teeth achieved a DSC up to 98%, a JSC of 97%, and an MSD of 0.11 mm compared with manual segmentation. For the premolars, the average values of DSC, JSC, and MSD were 98%, 96%, and 0.12 mm, respectively. The proposed method yielded a DSC of 95%, a JSC of 89%, and an MSD of 0.26 mm for molars. Aside from the interactive definition of label priors by the user, automatic tooth segmentation can be achieved in an average of 1.18 min. Conclusions: The proposed technique enables an efficient and reliable tooth segmentation from CBCT images. This study makes it clinically practical to segment teeth from CBCT images, thus facilitating pre- and interoperative uses of dental morphologies in maxillofacial and orthodontic treatments.« less

3D exemplar-based random walks for tooth segmentation from cone-beam computed tomography images.

PubMed

Pei, Yuru; Ai, Xingsheng; Zha, Hongbin; Xu, Tianmin; Ma, Gengyu

2016-09-01

Tooth segmentation is an essential step in acquiring patient-specific dental geometries from cone-beam computed tomography (CBCT) images. Tooth segmentation from CBCT images is still a challenging task considering the comparatively low image quality caused by the limited radiation dose, as well as structural ambiguities from intercuspation and nearby alveolar bones. The goal of this paper is to present and discuss the latest accomplishments in semisupervised tooth segmentation with adaptive 3D shape constraints. The authors propose a 3D exemplar-based random walk method of tooth segmentation from CBCT images. The proposed method integrates semisupervised label propagation and regularization by 3D exemplar registration. To begin with, the pure random walk method is to get an initial segmentation of the teeth, which tends to be erroneous because of the structural ambiguity of CBCT images. And then, as an iterative refinement, the authors conduct a regularization by using 3D exemplar registration, as well as label propagation by random walks with soft constraints, to improve the tooth segmentation. In the first stage of the iteration, 3D exemplars with well-defined topologies are adapted to fit the tooth contours, which are obtained from the random walks based segmentation. The soft constraints on voxel labeling are defined by shape-based foreground dentine probability acquired by the exemplar registration, as well as the appearance-based probability from a support vector machine (SVM) classifier. In the second stage, the labels of the volume-of-interest (VOI) are updated by the random walks with soft constraints. The two stages are optimized iteratively. Instead of the one-shot label propagation in the VOI, an iterative refinement process can achieve a reliable tooth segmentation by virtue of exemplar-based random walks with adaptive soft constraints. The proposed method was applied for tooth segmentation of twenty clinically captured CBCT images. Three metrics, including the Dice similarity coefficient (DSC), the Jaccard similarity coefficient (JSC), and the mean surface deviation (MSD), were used to quantitatively analyze the segmentation of anterior teeth including incisors and canines, premolars, and molars. The segmentation of the anterior teeth achieved a DSC up to 98%, a JSC of 97%, and an MSD of 0.11 mm compared with manual segmentation. For the premolars, the average values of DSC, JSC, and MSD were 98%, 96%, and 0.12 mm, respectively. The proposed method yielded a DSC of 95%, a JSC of 89%, and an MSD of 0.26 mm for molars. Aside from the interactive definition of label priors by the user, automatic tooth segmentation can be achieved in an average of 1.18 min. The proposed technique enables an efficient and reliable tooth segmentation from CBCT images. This study makes it clinically practical to segment teeth from CBCT images, thus facilitating pre- and interoperative uses of dental morphologies in maxillofacial and orthodontic treatments.

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.

The effect of walking and vitamin B supplementation on quality of life in community-dwelling adults with mild cognitive impairment: a randomized, controlled trial

PubMed Central

van Uffelen, Jannique G. Z.; Hopman-Rock, Marijke; van Mechelen, Willem

2007-01-01

Objectives To examine the effect of walking and vitamin B supplementation on quality-of-life (QoL) in community-dwelling adults with mild cognitive impairment. Methods One year, double-blind, placebo-controlled trial. Participants were randomized to: (1) twice-weekly, group-based, moderate-intensity walking program (n = 77) or a light-intensity placebo activity program (n = 75); and (2) daily vitamin B pills containing 5 mg folic acid, 0.4 mg B12, 50 mg B6 (n = 78) or placebo pills (n = 74). QoL was measured at baseline, after six and 12 months using the population-specific Dementia Quality-of-Life (D-QoL) to assess overall QoL and the generic Short-Form 12 mental and physical component scales (SF12-MCS and SF12-PCS) to assess health-related QoL. Results Baseline levels of QoL were relatively high. Modified intention-to-treat analyses revealed no positive main intervention effect of walking or vitamin supplementation. In both men and women, ratings of D-QoL-belonging and D-QoL-positive affect subscales improved with 0.003 (P = 0.04) and 0.002 points (P = 0.06) with each percent increase in attendance to the walking program. Only in men, SF12-MCS increased with 0.03 points with each percent increase in attendance (P = 0.08). Conclusion Several small but significant improvements in QoL were observed with increasing attendance to the walking program. No effect of vitamin B supplementation was observed. Trial Registration International Standard Randomized Controlled Trial Number Register, 19227688, http://www.controlled-trials.com/isrctn/. PMID:17616840

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 .

Reducing The Cost of Transport and Increasing Walking Distance After Stroke: A Randomized Controlled Trial on Fast Locomotor Training Combined With Functional Electrical Stimulation

PubMed Central

Awad, Louis N.; Reisman, Darcy S.; Pohlig, Ryan T.; Binder-Macleod, Stuart A.

2015-01-01

Background Neurorehabilitation efforts have been limited in their ability to restore walking function after stroke. Recent work has demonstrated proof-of-concept for a Functional Electrical Stimulation (FES)-based combination therapy designed to improve poststroke walking by targeting deficits in paretic propulsion. Objectives To determine the effects on the energy cost of walking (EC) and long-distance walking ability of locomotor training that combines fast walking with FES to the paretic ankle musculature (FastFES). Methods Fifty participants >6 months poststroke were randomized to 12 weeks of gait training at self-selected speeds (SS), fast speeds (Fast), or FastFES. Participants’ 6-Minute Walk Test (6MWT) distance and EC at comfortable (EC-CWS) and fast (EC-Fast) walking speeds were measured pretraining, posttraining, and at a 3-month follow-up. A reduction in EC-CWS, independent of changes in speed, was the primary outcome. Also evaluated were group differences in the number of 6MWT responders and moderation by baseline speed. Results When compared with SS and Fast, FastFES produced larger reductions in EC (p’s ≤0.03). FastFES produced reductions of 24% and 19% in EC-CWS and EC-Fast (p’s <0.001), whereas neither Fast nor SS influenced EC. Between-group 6MWT differences were not observed; however, 73% of FastFES and 68% of Fast participants were responders, in contrast to 35% of SS participants. Conclusions Combining fast locomotor training with FES is an effective approach to reducing the high EC of persons poststroke. Surprisingly, differences in 6MWT gains were not observed between groups. Closer inspection of the 6MWT and EC relationship and elucidation of how reduced EC may influence walking-related disability is warranted. PMID:26621366

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.

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects.

PubMed

Kang, Yun; Lanchier, Nicolas

2011-06-01

We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart. The deterministic model has either two, three or four attractors. The existence of a regime with exactly three attractors only appears when patches have distinct Allee thresholds. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either a global expansion or a global extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the global extinction and the basin of attraction of the global expansion. Above this threshold, for both the deterministic and the stochastic models, the patches tend to synchronize as the intensity of the dispersal increases. This results in either a global expansion or a global extinction. For the deterministic model, there are only two attractors, while the stochastic model no longer exhibits a metastable behavior. In the presence of strong dispersal, the limiting behavior is entirely determined by the value of the Allee thresholds as the global population size in the deterministic and the stochastic models evolves as dictated by their single-patch counterparts. For all values of the dispersal parameter, Allee effects promote global extinction in terms of an expansion of the basin of attraction of the extinction equilibrium for the deterministic model and an increase of the probability of extinction for the stochastic model.

Effect of pretesting on intentions and behaviour: a pedometer and walking intervention.

PubMed

Spence, John C; Burgess, Jenny; Rodgers, Wendy; Murray, Terra

2009-09-01

This study addressed the influence of pedometers and a pretest on walking intentions and behaviour. Using a Solomon four-group design, 63 female university students were randomly assigned to one of four conditions: pedometer and pretest (n = 16), pedometer and no pretest (n = 16), no pedometer and pretest (n = 15), no pedometer and no pretest (n = 16). The pretest conditions included questions on walking, intentions to walk 12,500 steps per day, and self-efficacy for walking 12,500 steps per day. In the pedometer conditions a Yamax Digi-Walker SW-650 pedometer was worn for one week. All participants completed posttest questions. While significant pretest x pedometer interactions would have indicated the presence of pretest sensitisation, no such interactions were observed for either intention or self-reported walking. Wearing pedometers reduced intentions for future walking and coping self-efficacy. However, after controlling for pretest self-reported walking, pedometer use resulted in more self-reported walking. We conclude that wearing a pedometer increased self-reported walking behaviour but that a pretest did not differentially influence walking intentions, behaviour, or self-efficacy.

Scattering from binary optics

NASA Technical Reports Server (NTRS)

Ricks, Douglas W.

1993-01-01

There are a number of sources of scattering in binary optics: etch depth errors, line edge errors, quantization errors, roughness, and the binary approximation to the ideal surface. These sources of scattering can be systematic (deterministic) or random. In this paper, scattering formulas for both systematic and random errors are derived using Fourier optics. These formulas can be used to explain the results of scattering measurements and computer simulations.

Symmetry Breaking in a random passive scalar

NASA Astrophysics Data System (ADS)

Kilic, Zeliha; McLaughlin, Richard; Camassa, Roberto

2017-11-01

We consider the evolution of a decaying passive scalar in the presence of a gaussian white noise fluctuating shear flow. We focus on deterministic initial data and establish the short, intermediate, and long time symmetry properties of the evolving point wise probability measure for the random passive scalar. Analytical results are compared directly to Monte Carlo simulations. Time permitting we will compare the predictions to experimental observations.

Comparative Effectiveness of Two Walking Interventions on Participation, Step Counts, and Health.

PubMed

Smith-McLallen, Aaron; Heller, Debbie; Vernisi, Kristin; Gulick, Diana; Cruz, Samantha; Snyder, Richard L

2017-03-01

To (1) compare the effects of two worksite-based walking interventions on employee participation rates; (2) compare average daily step counts between conditions, and; (3) examine the effects of increases in average daily step counts on biometric and psychologic outcomes. We conducted a cluster-randomized trial in which six employer groups were randomly selected and randomly assigned to condition. Four manufacturing worksites and two office-based worksite served as the setting. A total of 474 employees from six employer groups were included. A standard walking program was compared to an enhanced program that included incentives, feedback, competitive challenges, and monthly wellness workshops. Walking was measured by self-reported daily step counts. Survey measures and biometric screenings were administered at baseline and 3, 6, and 9 months after baseline. Analysis used linear mixed models with repeated measures. During 9 months, participants in the enhanced condition averaged 726 more steps per day compared with those in the standard condition (p < .001). A 1000-step increase in average daily steps was associated with significant weight loss for both men (-3.8 lbs.) and women (-2.1 lbs.), and reductions in body mass index (-0.41 men, -0.31 women). Higher step counts were also associated with improvements in mood, having more energy, and higher ratings of overall health. An enhanced walking program significantly increases participation rates and daily step counts, which were associated with weight loss and reductions in body mass index.

Hybrid stochastic and deterministic simulations of calcium blips.

PubMed

Rüdiger, S; Shuai, J W; Huisinga, W; Nagaiah, C; Warnecke, G; Parker, I; Falcke, M

2007-09-15

Intracellular calcium release is a prime example for the role of stochastic effects in cellular systems. Recent models consist of deterministic reaction-diffusion equations coupled to stochastic transitions of calcium channels. The resulting dynamics is of multiple time and spatial scales, which complicates far-reaching computer simulations. In this article, we introduce a novel hybrid scheme that is especially tailored to accurately trace events with essential stochastic variations, while deterministic concentration variables are efficiently and accurately traced at the same time. We use finite elements to efficiently resolve the extreme spatial gradients of concentration variables close to a channel. We describe the algorithmic approach and we demonstrate its efficiency compared to conventional methods. Our single-channel model matches experimental data and results in intriguing dynamics if calcium is used as charge carrier. Random openings of the channel accumulate in bursts of calcium blips that may be central for the understanding of cellular calcium dynamics.

A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence.

PubMed

Maliyoni, Milliward; Chirove, Faraimunashe; Gaff, Holly D; Govinder, Keshlan S

2017-09-01

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton-Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.

Adaptation to Temporally Fluctuating Environments by the Evolution of Maternal Effects.

PubMed

Dey, Snigdhadip; Proulx, Stephen R; Teotónio, Henrique

2016-02-01

All organisms live in temporally fluctuating environments. Theory predicts that the evolution of deterministic maternal effects (i.e., anticipatory maternal effects or transgenerational phenotypic plasticity) underlies adaptation to environments that fluctuate in a predictably alternating fashion over maternal-offspring generations. In contrast, randomizing maternal effects (i.e., diversifying and conservative bet-hedging), are expected to evolve in response to unpredictably fluctuating environments. Although maternal effects are common, evidence for their adaptive significance is equivocal since they can easily evolve as a correlated response to maternal selection and may or may not increase the future fitness of offspring. Using the hermaphroditic nematode Caenorhabditis elegans, we here show that the experimental evolution of maternal glycogen provisioning underlies adaptation to a fluctuating normoxia-anoxia hatching environment by increasing embryo survival under anoxia. In strictly alternating environments, we found that hermaphrodites evolved the ability to increase embryo glycogen provisioning when they experienced normoxia and to decrease embryo glycogen provisioning when they experienced anoxia. At odds with existing theory, however, populations facing irregularly fluctuating normoxia-anoxia hatching environments failed to evolve randomizing maternal effects. Instead, adaptation in these populations may have occurred through the evolution of fitness effects that percolate over multiple generations, as they maintained considerably high expected growth rates during experimental evolution despite evolving reduced fecundity and reduced embryo survival under one or two generations of anoxia. We develop theoretical models that explain why adaptation to a wide range of patterns of environmental fluctuations hinges on the existence of deterministic maternal effects, and that such deterministic maternal effects are more likely to contribute to adaptation than randomizing maternal effects.

Adaptation to Temporally Fluctuating Environments by the Evolution of Maternal Effects

PubMed Central

Dey, Snigdhadip; Proulx, Stephen R.; Teotónio, Henrique

2016-01-01

All organisms live in temporally fluctuating environments. Theory predicts that the evolution of deterministic maternal effects (i.e., anticipatory maternal effects or transgenerational phenotypic plasticity) underlies adaptation to environments that fluctuate in a predictably alternating fashion over maternal-offspring generations. In contrast, randomizing maternal effects (i.e., diversifying and conservative bet-hedging), are expected to evolve in response to unpredictably fluctuating environments. Although maternal effects are common, evidence for their adaptive significance is equivocal since they can easily evolve as a correlated response to maternal selection and may or may not increase the future fitness of offspring. Using the hermaphroditic nematode Caenorhabditis elegans, we here show that the experimental evolution of maternal glycogen provisioning underlies adaptation to a fluctuating normoxia–anoxia hatching environment by increasing embryo survival under anoxia. In strictly alternating environments, we found that hermaphrodites evolved the ability to increase embryo glycogen provisioning when they experienced normoxia and to decrease embryo glycogen provisioning when they experienced anoxia. At odds with existing theory, however, populations facing irregularly fluctuating normoxia–anoxia hatching environments failed to evolve randomizing maternal effects. Instead, adaptation in these populations may have occurred through the evolution of fitness effects that percolate over multiple generations, as they maintained considerably high expected growth rates during experimental evolution despite evolving reduced fecundity and reduced embryo survival under one or two generations of anoxia. We develop theoretical models that explain why adaptation to a wide range of patterns of environmental fluctuations hinges on the existence of deterministic maternal effects, and that such deterministic maternal effects are more likely to contribute to adaptation than randomizing maternal effects. PMID:26910440

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.

Longitudinal Relationship Among Physical Fitness, Walking-Related Physical Activity, and Fatigue in Children With Cerebral Palsy.

PubMed

Balemans, Astrid C J; van Wely, Leontien; Becher, Jules G; Dallmeijer, Annet J

2015-07-01

A vicious circle of decreased physical fitness, early fatigue, and low physical activity levels (PAL) is thought to affect children with cerebral palsy (CP). However, the relationship of changes in physical fitness to changes in PAL and fatigue is unclear. The objective of this study was to investigate the associations among changes in physical fitness, walking-related PAL, and fatigue in children with CP. This study was a secondary analysis of a randomized controlled trial with measurements at baseline, 6 months (after the intervention period), and 12 months. Twenty-four children with bilateral spastic CP and 22 with unilateral spastic CP, aged 7 to 13 years, all walking, participated in this study. Physical fitness was measured by aerobic capacity, anaerobic threshold, anaerobic capacity, and isometric and functional muscle strength. Walking-related PAL was measured using an ankle-worn activity monitor for 1 week. Fatigue was determined with the Pediatric Quality of Life (PedsQL) Multidimensional Fatigue Scale. Longitudinal associations were analyzed by random coefficient regression analysis. In children with bilateral CP, all fitness parameters showed a positive, significant association with walking-related PAL, whereas no associations between physical fitness and walking-related PAL were seen in children with unilateral CP. No clinically relevant association between physical fitness and fatigue was found. Although random coefficient regression analysis can be used to investigate longitudinal associations between parameters, a causal relationship cannot be determined. The actual direction of the association between physical fitness and walking-related PAL, therefore, remains inconclusive. Children with bilateral spastic CP might benefit from improved physical fitness to increase their PAL or vice versa, although this is not the case in children with unilateral CP. There appears to be no relationship between physical fitness and self-reported fatigue in children with CP. Interventions aimed at improving PAL may be differently targeted in children with either bilateral or unilateral CP. © 2015 American Physical Therapy Association.

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).

Robot-assisted gait training in multiple sclerosis: a pilot randomized trial.

PubMed

Beer, S; Aschbacher, B; Manoglou, D; Gamper, E; Kool, J; Kesselring, J

2008-03-01

To evaluate feasibility and perform an explanatory analysis of the efficacy of robot-assisted gait training (RAGT) in MS patients with severe walking disabilities (Expanded Disability Status Scale [EDSS] 6.0-7.5) in a pilot trial. Prospective, randomized, controlled clinical trial comparing RAGT with conventional walking training (CWT) in a group of stable MS patients (n = 35) during an inpatient rehabilitation stay, 15 sessions over three weeks. All patients participated additionally in a multimodal rehabilitation program. The primary outcome measure was walking velocity and secondary measures were 6-min-walking distance, stride length and knee-extensor strength. All tests were performed by an external blinded assessor at baseline after three weeks and at follow-up after six months. Additionally, Extended Barthel Index (EBI) at entry and discharge was assessed (not blinded), and acceptance/convenience of RAGT rated by patients (Visual Analogue Scale [VAS]) was recorded. Nineteen patients were randomly allocated to RAGT and 16 patients to CWT. Groups were comparable at baseline. There were 5 drop-outs (2 related directly to treatment) in the RAGT group and 1 in the CWT group, leaving 14 RAGT patients and 15 CWT patients for final analysis. Acceptance and convenience of RAGT as rated by patients were high. Effect sizes were moderate to large, although not significant, for walking velocity (0.700, 95% CI -0.089 to 1.489), walking distance (0.401, 95% CI - 0.370 to 1.172) and knee-extensor strength (right: 1.105, 95% CI 0.278 to 1.932, left 0.650, 95% CI -0.135 to 1.436) favouring RAGT. Prepost within-group analysis revealed an increase of walking velocity, walking distance and knee-extensor strength in the RAGT group, whereas in CWT group only walking velocity was improved. In both groups outcome values returned to baseline at follow-up after six months (n = 23). Robot-assisted gait training is feasible and may be an effective therapeutic option in MS patients with severe walking disabilities. Effect size calculation and prepost analysis suggest a higher benefit on walking velocity and knee-extensor strength by RAGT compared to CWT. Due to several limitations, however, our results should be regarded as preliminary. Post hoc power calculation showed that two groups of 106 patients are needed to demonstrate a significant moderate effect size of 0.4 after three weeks of RAGT. Thus, further studies with a larger number of patients are needed to investigate the impact of this new treatment option in MS patients.

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.

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.

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.

[Plaque segmentation of intracoronary optical coherence tomography images based on K-means and improved random walk algorithm].

PubMed

Wang, Guanglei; Wang, Pengyu; Han, Yechen; Liu, Xiuling; Li, Yan; Lu, Qian

2017-06-01

In recent years, optical coherence tomography (OCT) has developed into a popular coronary imaging technology at home and abroad. The segmentation of plaque regions in coronary OCT images has great significance for vulnerable plaque recognition and research. In this paper, a new algorithm based on K -means clustering and improved random walk is proposed and Semi-automated segmentation of calcified plaque, fibrotic plaque and lipid pool was achieved. And the weight function of random walk is improved. The distance between the edges of pixels in the image and the seed points is added to the definition of the weight function. It increases the weak edge weights and prevent over-segmentation. Based on the above methods, the OCT images of 9 coronary atherosclerotic patients were selected for plaque segmentation. By contrasting the doctor's manual segmentation results with this method, it was proved that this method had good robustness and accuracy. It is hoped that this method can be helpful for the clinical diagnosis of coronary heart disease.

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.

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.

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.

TemperSAT: A new efficient fair-sampling random k-SAT solver

NASA Astrophysics Data System (ADS)

Fang, Chao; Zhu, Zheng; Katzgraber, Helmut G.

The set membership problem is of great importance to many applications and, in particular, database searches for target groups. Recently, an approach to speed up set membership searches based on the NP-hard constraint-satisfaction problem (random k-SAT) has been developed. However, the bottleneck of the approach lies in finding the solution to a large SAT formula efficiently and, in particular, a large number of independent solutions is needed to reduce the probability of false positives. Unfortunately, traditional random k-SAT solvers such as WalkSAT are biased when seeking solutions to the Boolean formulas. By porting parallel tempering Monte Carlo to the sampling of binary optimization problems, we introduce a new algorithm (TemperSAT) whose performance is comparable to current state-of-the-art SAT solvers for large k with the added benefit that theoretically it can find many independent solutions quickly. We illustrate our results by comparing to the currently fastest implementation of WalkSAT, WalkSATlm.

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 effect of an arm sling used for shoulder support on gait efficiency in hemiplegic patients with stroke using walking aids.

PubMed

Jeong, Yeon-Gyu; Jeong, Yeon-Jae; Koo, Jung-Wan

2017-06-01

The effects of an arm sling on the physiological costs of walking are not known. Even though a previous study reported that an arm sling can improve gait efficiency, its entrance criteria was only hemiparetic patients able to walk without walking aids independently. The aim of this study was to investigate the effect of shoulder support by an arm sling on gait efficiency in hemiplegic stroke patients using walking aids. Randomized crossover design. Rehabilitation department of a university hospital. A total of 57 hemiplegic patients with shoulder subluxation dependent on canes were grouped into single cane (N.=30) and quad cane groups (N.=27) as walking aids. All patients performed a walk with their own walking aid with and without an arm sling in randomized order, on the same day. We measured the energy cost and energy expenditure using a portable gas analyzer and heart rate during a 6-minutes Walk Test and a 10-m Walk Test. We analyzed all outcomes measures with and without an arm sling between the patients who were grouped according to their walking aids using 2-way repeated ANOVA. The energy cost (0.068±0.023 mL/kg/m) and oxygen expenditure (8.609±2.155 mL/kg/minutes) were lower with the arm sling (P<0.05) than without the arm sling (0.074±0.029 mL/kg/m, and 9.109±2.406 mL/kg/minutes, respectively), and the walking endurance (138.942±47.043 m) were longer (P<0.05) with the arm sling among the hemiplegic patients with single cane. Among the hemiplegic patients with a single cane, the walking endurance achieved with an arm sling significantly improved than those achieved without an arm sling, and the energy expenditure and energy cost was significantly lower. The hemiplegic arm support with an arm sling may be beneficial for gait efficiency in hemiplegic patients using a single cane, which lead to decreased oxygen use at a given speed.

Nordic Walking and chronic low back pain: design of a randomized clinical trial

PubMed Central

Morsø, Lars; Hartvigsen, Jan; Puggaard, Lis; Manniche, Claus

2006-01-01

Background Low Back Pain is a major public health problem all over the western world. Active approaches including exercise in the treatment of low back pain results in better outcomes for patients, but it is not known exactly which types of back exercises are most beneficial or whether general physical activity provide similar benefits. Nordic Walking is a popular and fast growing type of exercise in Northern Europe. Initial studies have demonstrated that persons performing Nordic Walking are able to exercise longer and harder compared to normal walking thereby increasing their cardiovascular metabolism. Until now no studies have been performed to investigate whether Nordic Walking has beneficial effects in relation to low back pain. The primary aim of this study is to investigate whether supervised Nordic Walking can reduce pain and improve function in a population of chronic low back pain patients when compared to unsupervised Nordic Walking and advice to stay active. In addition we investigate whether there is an increase in the cardiovascular metabolism in persons performing supervised Nordic Walking compared to persons who are advised to stay active. Finally, we investigate whether there is a difference in compliance between persons receiving supervised Nordic Walking and persons doing unsupervised Nordic Walking. Methods One hundred and fifty patients with low back pain for at least eight weeks and referred to a specialized secondary sector outpatient back pain clinic are included in the study. After completion of the standard back centre treatment patients are randomized into one of three groups: A) Nordic Walking twice a week for eight weeks under supervision of a specially trained instructor; B) Unsupervised Nordic Walking for eight weeks after one training session with an instructor; C) A one hour motivational talk including advice to stay active. Outcome measures are pain, function, overall health, cardiovascular ability and activity level. Results No results available at this point. Discussion This study will investigate the effect of Nordic Walking on pain and function in a population of people with chronic LBP. Trial Registration registration # NCT00209820 PMID:17014731

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.

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.

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.

Interpolating between random walks and optimal transportation routes: Flow with multiple sources and targets

NASA Astrophysics Data System (ADS)

Guex, Guillaume

2016-05-01

In recent articles about graphs, different models proposed a formalism to find a type of path between two nodes, the source and the target, at crossroads between the shortest-path and the random-walk path. These models include a freely adjustable parameter, allowing to tune the behavior of the path toward randomized movements or direct routes. This article presents a natural generalization of these models, namely a model with multiple sources and targets. In this context, source nodes can be viewed as locations with a supply of a certain good (e.g. people, money, information) and target nodes as locations with a demand of the same good. An algorithm is constructed to display the flow of goods in the network between sources and targets. With again a freely adjustable parameter, this flow can be tuned to follow routes of minimum cost, thus displaying the flow in the context of the optimal transportation problem or, by contrast, a random flow, known to be similar to the electrical current flow if the random-walk is reversible. Moreover, a source-targetcoupling can be retrieved from this flow, offering an optimal assignment to the transportation problem. This algorithm is described in the first part of this article and then illustrated with case studies.

Unsupervised Metric Fusion Over Multiview Data by Graph Random Walk-Based Cross-View Diffusion.

PubMed

Wang, Yang; Zhang, Wenjie; Wu, Lin; Lin, Xuemin; Zhao, Xiang

2017-01-01

Learning an ideal metric is crucial to many tasks in computer vision. Diverse feature representations may combat this problem from different aspects; as visual data objects described by multiple features can be decomposed into multiple views, thus often provide complementary information. In this paper, we propose a cross-view fusion algorithm that leads to a similarity metric for multiview data by systematically fusing multiple similarity measures. Unlike existing paradigms, we focus on learning distance measure by exploiting a graph structure of data samples, where an input similarity matrix can be improved through a propagation of graph random walk. In particular, we construct multiple graphs with each one corresponding to an individual view, and a cross-view fusion approach based on graph random walk is presented to derive an optimal distance measure by fusing multiple metrics. Our method is scalable to a large amount of data by enforcing sparsity through an anchor graph representation. To adaptively control the effects of different views, we dynamically learn view-specific coefficients, which are leveraged into graph random walk to balance multiviews. However, such a strategy may lead to an over-smooth similarity metric where affinities between dissimilar samples may be enlarged by excessively conducting cross-view fusion. Thus, we figure out a heuristic approach to controlling the iteration number in the fusion process in order to avoid over smoothness. Extensive experiments conducted on real-world data sets validate the effectiveness and efficiency of our approach.

Distributed Clone Detection in Static Wireless Sensor Networks: Random Walk with Network Division

PubMed Central

Khan, Wazir Zada; Aalsalem, Mohammed Y.; Saad, N. M.

2015-01-01

Wireless Sensor Networks (WSNs) are vulnerable to clone attacks or node replication attacks as they are deployed in hostile and unattended environments where they are deprived of physical protection, lacking physical tamper-resistance of sensor nodes. As a result, an adversary can easily capture and compromise sensor nodes and after replicating them, he inserts arbitrary number of clones/replicas into the network. If these clones are not efficiently detected, an adversary can be further capable to mount a wide variety of internal attacks which can emasculate the various protocols and sensor applications. Several solutions have been proposed in the literature to address the crucial problem of clone detection, which are not satisfactory as they suffer from some serious drawbacks. In this paper we propose a novel distributed solution called Random Walk with Network Division (RWND) for the detection of node replication attack in static WSNs which is based on claimer-reporter-witness framework and combines a simple random walk with network division. RWND detects clone(s) by following a claimer-reporter-witness framework and a random walk is employed within each area for the selection of witness nodes. Splitting the network into levels and areas makes clone detection more efficient and the high security of witness nodes is ensured with moderate communication and memory overheads. Our simulation results show that RWND outperforms the existing witness node based strategies with moderate communication and memory overheads. PMID:25992913

Investigation of random walks knee cartilage segmentation model using inter-observer reproducibility: Data from the osteoarthritis initiative.

PubMed

Hong-Seng, Gan; Sayuti, Khairil Amir; Karim, Ahmad Helmy Abdul

2017-01-01

Existing knee cartilage segmentation methods have reported several technical drawbacks. In essence, graph cuts remains highly susceptible to image noise despite extended research interest; active shape model is often constraint by the selection of training data while shortest path have demonstrated shortcut problem in the presence of weak boundary, which is a common problem in medical images. The aims of this study is to investigate the capability of random walks as knee cartilage segmentation method. Experts would scribble on knee cartilage image to initialize random walks segmentation. Then, reproducibility of the method is assessed against manual segmentation by using Dice Similarity Index. The evaluation consists of normal cartilage and diseased cartilage sections which is divided into whole and single cartilage categories. A total of 15 normal images and 10 osteoarthritic images were included. The results showed that random walks method has demonstrated high reproducibility in both normal cartilage (observer 1: 0.83±0.028 and observer 2: 0.82±0.026) and osteoarthritic cartilage (observer 1: 0.80±0.069 and observer 2: 0.83±0.029). Besides, results from both experts were found to be consistent with each other, suggesting the inter-observer variation is insignificant (Normal: P=0.21; Diseased: P=0.15). The proposed segmentation model has overcame technical problems reported by existing semi-automated techniques and demonstrated highly reproducible and consistent results against manual segmentation method.

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

Robustness of the non-Markovian Alzheimer walk under stochastic perturbation

NASA Astrophysics Data System (ADS)

Cressoni, J. C.; da Silva, L. R.; Viswanathan, G. M.; da Silva, M. A. A.

2012-12-01

The elephant walk model originally proposed by Schütz and Trimper to investigate non-Markovian processes led to the investigation of a series of other random-walk models. Of these, the best known is the Alzheimer walk model, because it was the first model shown to have amnestically induced persistence —i.e. superdiffusion caused by loss of memory. Here we study the robustness of the Alzheimer walk by adding a memoryless stochastic perturbation. Surprisingly, the solution of the perturbed model can be formally reduced to the solutions of the unperturbed model. Specifically, we give an exact solution of the perturbed model by finding a surjective mapping to the unperturbed model.

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.

Robot-assisted gait training in patients with Parkinson disease: a randomized controlled trial.

PubMed

Picelli, Alessandro; Melotti, Camilla; Origano, Francesca; Waldner, Andreas; Fiaschi, Antonio; Santilli, Valter; Smania, Nicola

2012-05-01

. Gait impairment is a common cause of disability in Parkinson disease (PD). Electromechanical devices to assist stepping have been suggested as a potential intervention. . To evaluate whether a rehabilitation program of robot-assisted gait training (RAGT) is more effective than conventional physiotherapy to improve walking. . A total of 41 patients with PD were randomly assigned to 45-minute treatment sessions (12 in all), 3 days a week, for 4 consecutive weeks of either robotic stepper training (RST; n = 21) using the Gait Trainer or physiotherapy (PT; n = 20) with active joint mobilization and a modest amount of conventional gait training. Participants were evaluated before, immediately after, and 1 month after treatment. Primary outcomes were 10-m walking speed and distance walked in 6 minutes. . Baseline measures revealed no statistical differences between groups, but the PT group walked 0.12 m/s slower; 5 patients withdrew. A statistically significant improvement was found in favor of the RST group (walking speed 1.22 ± 0.19 m/s [P = .035]; distance 366.06 ± 78.54 m [P < .001]) compared with the PT group (0.98 ± 0.32 m/s; 280.11 ± 106.61 m). The RAGT mean speed increased by 0.13 m/s, which is probably not clinically important. Improvements were maintained 1 month later. . RAGT may improve aspects of walking ability in patients with PD. Future trials should compare robotic assistive training with treadmill or equal amounts of overground walking practice.

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.

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.

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.

Zooplankton intermittency and turbulence

NASA Astrophysics Data System (ADS)

Schmitt, François G.

2010-05-01

Planktonic organisms usually live in a turbulent world. Since marine turbulence is characterized by very high Reynolds numbers, it possesses very intermittent fluctuations which in turn affect marine life. We consider here such influence on zooplankton on 2 aspects. First we consider zooplankton motion in the lab. Many copepods display swimming abilities. More and more species have been recently recorded using normal or high speed cameras, and many trajectories have been extracted from these movies and are now available for analysis. These trajectories can be complex, stochastic, with random switching from low velocity to high velocity events and even jumps. These complex trajectories show that an adequate modeling is necessary to understand and characterize them. Here we review the results published in the literature on copepod trajectories. We discuss the random walk, Levy walk modeling and introduce also multifractal random walks. We discuss the way to discriminate between these different walks using experimental data. Stochastic simulations will be performed to illustrate the different families. Second, we consider zooplankton contact rates in the framework of intermittent turbulence. Intermittency may have influence on plankton contact rates. We consider the Particle Stokes number of copepods, in a intermediate dissipation range affected by intermittent fluctuations. We show that they may display preferential concentration effects, and we consider the influence on contact rates of this effect in the intermediate dissipation range.

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.

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.

Chance of Necessity: Modeling Origins of Life

NASA Technical Reports Server (NTRS)

Pohorille, Andrew

2006-01-01

The fundamental nature of processes that led to the emergence of life has been a subject of long-standing debate. One view holds that the origin of life is an event governed by chance, and the result of so many random events is unpredictable. This view was eloquently expressed by Jacques Monod in his book Chance or Necessity. In an alternative view, the origin of life is considered a deterministic event. Its details need not be deterministic in every respect, but the overall behavior is predictable. A corollary to the deterministic view is that the emergence of life must have been determined primarily by universal chemistry and biochemistry rather than by subtle details of environmental conditions. In my lecture I will explore two different paradigms for the emergence of life and discuss their implications for predictability and universality of life-forming processes. The dominant approach is that the origin of life was guided by information stored in nucleic acids (the RNA World hypothesis). In this view, selection of improved combinations of nucleic acids obtained through random mutations drove evolution of biological systems from their conception. An alternative hypothesis states that the formation of protocellular metabolism was driven by non-genomic processes. Even though these processes were highly stochastic the outcome was largely deterministic, strongly constrained by laws of chemistry. I will argue that self-replication of macromolecules was not required at the early stages of evolution; the reproduction of cellular functions alone was sufficient for self-maintenance of protocells. In fact, the precise transfer of information between successive generations of the earliest protocells was unnecessary and could have impeded the discovery of cellular metabolism. I will also show that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution also hold in the absence of a genome.

Greek classicism in living structure? Some deductive pathways in animal morphology.

PubMed

Zweers, G A

1985-01-01

Classical temples in ancient Greece show two deterministic illusionistic principles of architecture, which govern their functional design: geometric proportionalism and a set of illusion-strengthening rules in the proportionalism's "stochastic margin". Animal morphology, in its mechanistic-deductive revival, applies just one architectural principle, which is not always satisfactory. Whether a "Greek Classical" situation occurs in the architecture of living structure is to be investigated by extreme testing with deductive methods. Three deductive methods for explanation of living structure in animal morphology are proposed: the parts, the compromise, and the transformation deduction. The methods are based upon the systems concept for an organism, the flow chart for a functionalistic picture, and the network chart for a structuralistic picture, whereas the "optimal design" serves as the architectural principle for living structure. These methods show clearly the high explanatory power of deductive methods in morphology, but they also make one open end most explicit: neutral issues do exist. Full explanation of living structure asks for three entries: functional design within architectural and transformational constraints. The transformational constraint brings necessarily in a stochastic component: an at random variation being a sort of "free management space". This variation must be a variation from the deterministic principle of the optimal design, since any transformation requires space for plasticity in structure and action, and flexibility in role fulfilling. Nevertheless, finally the question comes up whether for animal structure a similar situation exists as in Greek Classical temples. This means that the at random variation, that is found when the optimal design is used to explain structure, comprises apart from a stochastic part also real deviations being yet another deterministic part. This deterministic part could be a set of rules that governs actualization in the "free management space".

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

Dynamical Localization for Unitary Anderson Models

NASA Astrophysics Data System (ADS)

Hamza, Eman; Joye, Alain; Stolz, Günter

2009-11-01

This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum transport and draw their name from the analogy with the discrete Anderson model of solid state physics. They consist in a product of a deterministic unitary operator and a random unitary operator. The deterministic operator has a band structure, is absolutely continuous and plays the role of the discrete Laplacian. The random operator is diagonal with elements given by i.i.d. random phases distributed according to some absolutely continuous measure and plays the role of the random potential. In dimension one, these operators belong to the family of CMV-matrices in the theory of orthogonal polynomials on the unit circle. We implement the method of Aizenman-Molchanov to prove exponential decay of the fractional moments of the Green function for the unitary Anderson model in the following three regimes: In any dimension, throughout the spectrum at large disorder and near the band edges at arbitrary disorder and, in dimension one, throughout the spectrum at arbitrary disorder. We also prove that exponential decay of fractional moments of the Green function implies dynamical localization, which in turn implies spectral localization. These results complete the analogy with the self-adjoint case where dynamical localization is known to be true in the same three regimes.

Lévy Walks Suboptimal under Predation Risk

PubMed Central

Abe, Masato S.; Shimada, Masakazu

2015-01-01

A key challenge in movement ecology is to understand how animals move in nature. Previous studies have predicted that animals should perform a special class of random walks, called Lévy walk, to obtain more targets. However, some empirical studies did not support this hypothesis, and the relationship between search strategy and ecological factors is still unclear. We focused on ecological factors, such as predation risk, and analyzed whether Lévy walk may not be favored. It was remarkable that the ecological factors often altered an optimal search strategy from Lévy walk to Brownian walk, depending on the speed of the predator’s movement, density of predators, etc. This occurred because higher target encounter rates simultaneously led searchers to higher predation risks. Our findings indicate that animals may not perform Lévy walks often, and we suggest that it is crucial to consider the ecological context for evaluating the search strategy performed by animals in the field. PMID:26544687

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.

Magnetic field line random walk in models and simulations of reduced magnetohydrodynamic turbulence

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

Snodin, A. P.; Ruffolo, D.; Oughton, S.

2013-12-10

The random walk of magnetic field lines is examined numerically and analytically in the context of reduced magnetohydrodynamic (RMHD) turbulence, which provides a useful description of plasmas dominated by a strong mean field, such as in the solar corona. A recently developed non-perturbative theory of magnetic field line diffusion is compared with the diffusion coefficients obtained by accurate numerical tracing of magnetic field lines for both synthetic models and direct numerical simulations of RMHD. Statistical analysis of an ensemble of trajectories confirms the applicability of the theory, which very closely matches the numerical field line diffusion coefficient as a functionmore » of distance z along the mean magnetic field for a wide range of the Kubo number R. This theory employs Corrsin's independence hypothesis, sometimes thought to be valid only at low R. However, the results demonstrate that it works well up to R = 10, both for a synthetic RMHD model and an RMHD simulation. The numerical results from the RMHD simulation are compared with and without phase randomization, demonstrating a clear effect of coherent structures on the field line random walk for a very low Kubo number.« less

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.

A randomized, controlled trial of aerobic exercise for treatment-related fatigue in men receiving radical external beam radiotherapy for localized prostate carcinoma.

PubMed

Windsor, Phyllis M; Nicol, Kathleen F; Potter, Joan

2004-08-01

Advice to rest and take things easy if patients become fatigued during radiotherapy may be detrimental. Aerobic walking improves physical functioning and has been an intervention for chemotherapy-related fatigue. A prospective, randomized, controlled trial was performed to determine whether aerobic exercise would reduce the incidence of fatigue and prevent deterioration in physical functioning during radiotherapy for localized prostate carcinoma. Sixty-six men were randomized before they received radical radiotherapy for localized prostate carcinoma, with 33 men randomized to an exercise group and 33 men randomized to a control group. Outcome measures were fatigue and distance walked in a modified shuttle test before and after radiotherapy. There were no significant between group differences noted with regard to fatigue scores at baseline (P = 0.55) or after 4 weeks of radiotherapy (P = 0.18). Men in the control group had significant increases in fatigue scores from baseline to the end of radiotherapy (P = 0.013), with no significant increases observed in the exercise group (P = 0.203). A nonsignificant reduction (2.4%) in shuttle test distance at the end of radiotherapy was observed in the control group; however, in the exercise group, there was a significant increase (13.2%) in distance walked (P = 0.0003). Men who followed advice to rest and take things easy if they became fatigued demonstrated a slight deterioration in physical functioning and a significant increase in fatigue at the end of radiotherapy. Home-based, moderate-intensity walking produced a significant improvement in physical functioning with no significant increase in fatigue. Improved physical functioning may be necessary to combat radiation fatigue.

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).

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.

Walking training associated with virtual reality-based training increases walking speed of individuals with chronic stroke: systematic review with meta-analysis.

PubMed

Rodrigues-Baroni, Juliana M; Nascimento, Lucas R; Ada, Louise; Teixeira-Salmela, Luci F

2014-01-01

To systematically review the available evidence on the efficacy of walking training associated with virtual reality-based training in patients with stroke. The specific questions were: Is walking training associated with virtual reality-based training effective in increasing walking speed after stroke? Is this type of intervention more effective in increasing walking speed, than non-virtual reality-based walking interventions? A systematic review with meta-analysis of randomized clinical trials was conducted. Participants were adults with chronic stroke and the experimental intervention was walking training associated with virtual reality-based training to increase walking speed. The outcome data regarding walking speed were extracted from the eligible trials and were combined using a meta-analysis approach. Seven trials representing eight comparisons were included in this systematic review. Overall, the virtual reality-based training increased walking speed by 0.17 m/s (IC 95% 0.08 to 0.26), compared with placebo/nothing or non-walking interventions. In addition, the virtual reality-based training increased walking speed by 0.15 m/s (IC 95% 0.05 to 0.24), compared with non-virtual reality walking interventions. This review provided evidence that walking training associated with virtual reality-based training was effective in increasing walking speed after stroke, and resulted in better results than non-virtual reality interventions.

Who walks? Factors associated with walking behavior in disabled older women with and without self-reported walking difficulty.

PubMed

Simonsick, E M; Guralnik, J M; Fried, L P

1999-06-01

To determine how severity of walking difficulty and sociodemographic, psychosocial, and health-related factors influence walking behavior in disabled older women. Cross-sectional analyses of baseline data from the Women's Health and Aging Study (WHAS). An urban community encompassing 12 contiguous zip code areas in the eastern portion of Baltimore City and part of Baltimore County, Maryland. A total of 920 moderately to severely disabled community-resident women, aged 65 years and older, identified from an age-stratified random sample of Medicare beneficiaries. Walking behavior was defined as minutes walked for exercise and total blocks walked per week. Independent variables included self-reported walking difficulty, sociodemographic factors, psychological status (depression, mastery, anxiety, and cognition), and health-related factors (falls and fear of falling, fatigue, vision and balance problems, weight, smoking, and cane use). Walking at least 8 blocks per week was strongly negatively related to severity of walking difficulty. Independent of difficulty level, older age, black race, fatigue, obesity, and cane use were also negatively associated with walking; living alone and high mastery had a positive association with walking. Even among functionally limited women, sociocultural, psychological, and health-related factors were independently associated with walking behavior. Thus, programs aimed at improving walking ability need to address these factors in addition to walking difficulties to maximize participation and compliance.

Walking training associated with virtual reality-based training increases walking speed of individuals with chronic stroke: systematic review with meta-analysis

PubMed Central

Rodrigues-Baroni, Juliana M.; Nascimento, Lucas R.; Ada, Louise; Teixeira-Salmela, Luci F.

2014-01-01

OBJECTIVE: To systematically review the available evidence on the efficacy of walking training associated with virtual reality-based training in patients with stroke. The specific questions were: Is walking training associated with virtual reality-based training effective in increasing walking speed after stroke? Is this type of intervention more effective in increasing walking speed, than non-virtual reality-based walking interventions? METHOD: A systematic review with meta-analysis of randomized clinical trials was conducted. Participants were adults with chronic stroke and the experimental intervention was walking training associated with virtual reality-based training to increase walking speed. The outcome data regarding walking speed were extracted from the eligible trials and were combined using a meta-analysis approach. RESULTS: Seven trials representing eight comparisons were included in this systematic review. Overall, the virtual reality-based training increased walking speed by 0.17 m/s (IC 95% 0.08 to 0.26), compared with placebo/nothing or non-walking interventions. In addition, the virtual reality-based training increased walking speed by 0.15 m/s (IC 95% 0.05 to 0.24), compared with non-virtual reality walking interventions. CONCLUSIONS: This review provided evidence that walking training associated with virtual reality-based training was effective in increasing walking speed after stroke, and resulted in better results than non-virtual reality interventions. PMID:25590442

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

Random elements on lattices: Review and statistical applications

NASA Astrophysics Data System (ADS)

Potocký, Rastislav; Villarroel, Claudia Navarro; Sepúlveda, Maritza; Luna, Guillermo; Stehlík, Milan

2017-07-01

We discuss important contributions to random elements on lattices. We relate to both algebraic and probabilistic properties. Several applications and concepts are discussed, e.g. positive dependence, Random walks and distributions on lattices, Super-lattices, learning. The application to Chilean Ecology is given.

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.

Approximated maximum likelihood estimation in multifractal random walks

NASA Astrophysics Data System (ADS)

Løvsletten, O.; Rypdal, M.

2012-04-01

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry , Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.64.026103 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the r computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.

Representation of Reserves Through a Brownian Motion Model

NASA Astrophysics Data System (ADS)

Andrade, M.; Ferreira, M. A. M.; Filipe, J. A.

2012-11-01

The Brownian Motion is commonly used as an approximation for some Random Walks and also for the Classic Risk Process. As the Random Walks and the Classic Risk Process are used frequently as stochastic models to represent reserves, it is natural to consider the Brownian Motion with the same purpose. In this study a model, based on the Brownian Motion, is presented to represent reserves. The Brownian Motion is used in this study to estimate the ruin probability of a fund. This kind of models is considered often in the study of pensions funds.

Analytic model for low-frequency noise in nanorod devices.

PubMed

Lee, Jungil; Yu, Byung Yong; Han, Ilki; Choi, Kyoung Jin; Ghibaudo, Gerard

2008-10-01

In this work analytic model for generation of excess low-frequency noise in nanorod devices such as field-effect transistors are developed. In back-gate field-effect transistors where most of the surface area of the nanorod is exposed to the ambient, the surface states could be the major noise source via random walk of electrons for the low-frequency or 1/f noise. In dual gate transistors, the interface states and oxide traps can compete with each other as the main noise source via random walk and tunneling, respectively.

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.

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.

A stylistic classification of Russian-language texts based on the random walk model

NASA Astrophysics Data System (ADS)

Kramarenko, A. A.; Nekrasov, K. A.; Filimonov, V. V.; Zhivoderov, A. A.; Amieva, A. A.

2017-09-01

A formal approach to text analysis is suggested that is based on the random walk model. The frequencies and reciprocal positions of the vowel letters are matched up by a process of quasi-particle migration. Statistically significant difference in the migration parameters for the texts of different functional styles is found. Thus, a possibility of classification of texts using the suggested method is demonstrated. Five groups of the texts are singled out that can be distinguished from one another by the parameters of the quasi-particle migration process.

Modeling of Thermal Phase Noise in a Solid Core Photonic Crystal Fiber-Optic Gyroscope.

PubMed

Song, Ningfang; Ma, Kun; Jin, Jing; Teng, Fei; Cai, Wei

2017-10-26

A theoretical model of the thermal phase noise in a square-wave modulated solid core photonic crystal fiber-optic gyroscope has been established, and then verified by measurements. The results demonstrate a good agreement between theory and experiment. The contribution of the thermal phase noise to the random walk coefficient of the gyroscope is derived. A fiber coil with 2.8 km length is used in the experimental solid core photonic crystal fiber-optic gyroscope, showing a random walk coefficient of 9.25 × 10 -5 deg/√h.

Adaptive Path Control of Surface Ships in Restricted Waters.

DTIC Science & Technology

1980-08-01

and Fn=0.116-- Random Walk Disturbance Model 31 6. Optimal Gains for Tokyo Mazu at H/T=- and Fn=0.116-- Random Walk Disturbance Model 39 7. RMS Cost J...yaw mass moment of inertia [kgm 2 V =21 /pL nondimensional yaw mass moment of inertia zz zz J optimal control or Weighted Least-Squares cost function...J RMS cost , eq. (70) J 5yaw added mass moment of inertia [kgm 2 iz=2Jz/pL nondimensional yaw added mass moment of inertia zz zz K Kalman-Bucy state

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.

A comparative controlled trial comparing the effects of yoga and walking for overweight and obese adults

PubMed Central

Telles, Shirley; Sharma, Sachin Kr.; Yadav, Arti; Singh, Nilkamal; Balkrishna, Acharya

2014-01-01

Background Walking and yoga have been independently evaluated for weight control; however, there are very few studies comparing the 2 with randomization. Material/Methods The present study compared the effects of 90 minutes/day for 15 days of supervised yoga or supervised walking on: (i) related biochemistry, (ii) anthropometric variables, (iii) body composition, (iv) postural stability, and (v) bilateral hand grip strength in overweight and obese persons. Sixty-eight participants, of whom 5 were overweight (BMI ≥25 kg/m2) and 63 were obese (BMI ≥30 kg/m2; group mean age ±S.D., 36.4±11.2 years; 35 females), were randomized as 2 groups – (i) a yoga group and (ii) a walking group – given the same diet. Results All differences were pre-post changes within each group. Both groups showed a significant (p<0.05; repeated measures ANOVA, post-hoc analyses) decrease in: BMI, waist circumference, hip circumference, lean mass, body water, and total cholesterol. The yoga group increased serum leptin (p<0.01) and decreased LDL cholesterol (p<0.05). The walking group decreased serum adiponectin (p<0.05) and triglycerides (p<0.05). Conclusions Both yoga and walking improved anthropometric variables and serum lipid profile in overweight and obese persons. The possible implications are discussed. PMID:24878827

Evidence of Levy walk foraging patterns in human hunter-gatherers.

PubMed

Raichlen, David A; Wood, Brian M; Gordon, Adam D; Mabulla, Audax Z P; Marlowe, Frank W; Pontzer, Herman

2014-01-14

When searching for food, many organisms adopt a superdiffusive, scale-free movement pattern called a Lévy walk, which is considered optimal when foraging for heterogeneously located resources with little prior knowledge of distribution patterns [Viswanathan GM, da Luz MGE, Raposo EP, Stanley HE (2011) The Physics of Foraging: An Introduction to Random Searches and Biological Encounters]. Although memory of food locations and higher cognition may limit the benefits of random walk strategies, no studies to date have fully explored search patterns in human foraging. Here, we show that human hunter-gatherers, the Hadza of northern Tanzania, perform Lévy walks in nearly one-half of all foraging bouts. Lévy walks occur when searching for a wide variety of foods from animal prey to underground tubers, suggesting that, even in the most cognitively complex forager on Earth, such patterns are essential to understanding elementary foraging mechanisms. This movement pattern may be fundamental to how humans experience and interact with the world across a wide range of ecological contexts, and it may be adaptive to food distribution patterns on the landscape, which previous studies suggested for organisms with more limited cognition. Additionally, Lévy walks may have become common early in our genus when hunting and gathering arose as a major foraging strategy, playing an important role in the evolution of human mobility.

Habitat connectivity and in-stream vegetation control temporal variability of benthic invertebrate communities.

PubMed

Huttunen, K-L; Mykrä, H; Oksanen, J; Astorga, A; Paavola, R; Muotka, T

2017-05-03

One of the key challenges to understanding patterns of β diversity is to disentangle deterministic patterns from stochastic ones. Stochastic processes may mask the influence of deterministic factors on community dynamics, hindering identification of the mechanisms causing variation in community composition. We studied temporal β diversity (among-year dissimilarity) of macroinvertebrate communities in near-pristine boreal streams across 14 years. To assess whether the observed β diversity deviates from that expected by chance, and to identify processes (deterministic vs. stochastic) through which different explanatory factors affect community variability, we used a null model approach. We observed that at the majority of sites temporal β diversity was low indicating high community stability. When stochastic variation was unaccounted for, connectivity was the only variable explaining temporal β diversity, with weakly connected sites exhibiting higher community variability through time. After accounting for stochastic effects, connectivity lost importance, suggesting that it was related to temporal β diversity via random colonization processes. Instead, β diversity was best explained by in-stream vegetation, community variability decreasing with increasing bryophyte cover. These results highlight the potential of stochastic factors to dampen the influence of deterministic processes, affecting our ability to understand and predict changes in biological communities through time.

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.

Parallelizing quantum circuit synthesis

NASA Astrophysics Data System (ADS)

Di Matteo, Olivia; Mosca, Michele

2016-03-01

Quantum circuit synthesis is the process in which an arbitrary unitary operation is decomposed into a sequence of gates from a universal set, typically one which a quantum computer can implement both efficiently and fault-tolerantly. As physical implementations of quantum computers improve, the need is growing for tools that can effectively synthesize components of the circuits and algorithms they will run. Existing algorithms for exact, multi-qubit circuit synthesis scale exponentially in the number of qubits and circuit depth, leaving synthesis intractable for circuits on more than a handful of qubits. Even modest improvements in circuit synthesis procedures may lead to significant advances, pushing forward the boundaries of not only the size of solvable circuit synthesis problems, but also in what can be realized physically as a result of having more efficient circuits. We present a method for quantum circuit synthesis using deterministic walks. Also termed pseudorandom walks, these are walks in which once a starting point is chosen, its path is completely determined. We apply our method to construct a parallel framework for circuit synthesis, and implement one such version performing optimal T-count synthesis over the Clifford+T gate set. We use our software to present examples where parallelization offers a significant speedup on the runtime, as well as directly confirm that the 4-qubit 1-bit full adder has optimal T-count 7 and T-depth 3.

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.

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

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

An Indoor Pedestrian Positioning Method Using HMM with a Fuzzy Pattern Recognition Algorithm in a WLAN Fingerprint System

PubMed Central

Ni, Yepeng; Liu, Jianbo; Liu, Shan; Bai, Yaxin

2016-01-01

With the rapid development of smartphones and wireless networks, indoor location-based services have become more and more prevalent. Due to the sophisticated propagation of radio signals, the Received Signal Strength Indicator (RSSI) shows a significant variation during pedestrian walking, which introduces critical errors in deterministic indoor positioning. To solve this problem, we present a novel method to improve the indoor pedestrian positioning accuracy by embedding a fuzzy pattern recognition algorithm into a Hidden Markov Model. The fuzzy pattern recognition algorithm follows the rule that the RSSI fading has a positive correlation to the distance between the measuring point and the AP location even during a dynamic positioning measurement. Through this algorithm, we use the RSSI variation trend to replace the specific RSSI value to achieve a fuzzy positioning. The transition probability of the Hidden Markov Model is trained by the fuzzy pattern recognition algorithm with pedestrian trajectories. Using the Viterbi algorithm with the trained model, we can obtain a set of hidden location states. In our experiments, we demonstrate that, compared with the deterministic pattern matching algorithm, our method can greatly improve the positioning accuracy and shows robust environmental adaptability. PMID:27618053

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.

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.

Gait training strategies to optimize walking ability in people with stroke: A synthesis of the evidence

PubMed Central

Tang, Pei Fang

2011-01-01

Stroke is a leading cause of long-term disability. Impairments resulting from stroke lead to persistent difficulties with walking and subsequently, improved walking ability is one of the highest priorities for people living with a stroke. In addition, walking ability has important health implications in providing protective effects against secondary complications common after a stroke such as heart disease or osteoporosis. This paper systematically reviews common gait training strategies (neurodevelopmental techniques, muscle strengthening, treadmill training, intensive mobility exercises) to improve walking ability. The results (descriptive summaries as well as pooled effect sizes) from randomized controlled trials are presented and implications for optimal gait training strategies are discussed. Novel and emerging gait training strategies are highlighted and research directions proposed to enable the optimal recovery and maintenance of walking ability. PMID:17939776

Evaluating physical capacity in patients with chronic obstructive pulmonary disease: comparing the shuttle walk test with the encouraged 6-minute walk test.

PubMed

Rosa, Fernanda Warken; Camelier, Aquiles; Mayer, Anamaria; Jardim, José Roberto

2006-01-01

To evaluate the applicability of the incremental (shuttle) walk test in patients with chronic obstructive pulmonary disease and compare the performance of those patients on the shuttle walk test to that of the same patients on the encouraged 6-minute walk test. A cross-sectional study was conducted, in which 24 patients with chronic obstructive pulmonary disease were selected. In random order, patients were, after an initial practice period, submitted to a shuttle walk test and an encouraged 6-minute walk test. The patients obtained a higher heart rate (expressed as a percentage of that predicted based on gender and age) on the encouraged 6-minute walk test (84.1 +/- 11.4%) than on the shuttle walk test (76.4 +/- 9.7%) (p = 0.003). The post-test sensation of dyspnea (Borg scale) was also higher on the encouraged 6-minute walk test. On average, the patients walked 307.0 +/- 89.3 meters on the shuttle walk test and 515.5 +/- 102.3 meters on the encouraged 6-minute walk test (p < 0.001). There was a good correlation between the two tests in terms of the distance walked (r = 0.80, p < 0.001). The shuttle walk test is simple and easy to implement in patients with chronic obstructive pulmonary disease. The encouraged 6-minute walk test produced higher post-test heart rate and greater post-test sensation of dyspnea than did the shuttle walk test.

The Results of the "Positive Action for Today's Health" (PATH) Trial for Increasing Walking and Physical Activity in Underserved African-American Communities.

PubMed

Wilson, Dawn K; Van Horn, M Lee; Siceloff, E Rebekah; Alia, Kassandra A; St George, Sara M; Lawman, Hannah G; Trumpeter, Nevelyn N; Coulon, Sandra M; Griffin, Sarah F; Wandersman, Abraham; Egan, Brent; Colabianchi, Natalie; Forthofer, Melinda; Gadson, Barney

2015-06-01

The "Positive Action for Today's Health" (PATH) trial tested an environmental intervention to increase walking in underserved communities. Three matched communities were randomized to a police-patrolled walking plus social marketing, a police-patrolled walking-only, or a no-walking intervention. The 24-month intervention addressed safety and access for physical activity (PA) and utilized social marketing to enhance environmental supports for PA. African-Americans (N=434; 62% females; aged 51±16 years) provided accelerometry and psychosocial measures at baseline and 12, 18, and 24 months. Walking attendance and trail use were obtained over 24 months. There were no significant differences across communities over 24 months for moderate-to-vigorous PA. Walking attendance in the social marketing community showed an increase from 40 to 400 walkers per month at 9 months and sustained ~200 walkers per month through 24 months. No change in attendance was observed in the walking-only community. Findings support integrating social marketing strategies to increase walking in underserved African-Americans (ClinicalTrials.gov #NCT01025726).

Nordic walking in fibromyalgia: a means of promoting fitness that is easy for busy clinicians to recommend

PubMed Central

2011-01-01

A total of 67 women with fibromyalgia were recruited to an exercise study and were randomized to moderate-to-high-intensity Nordic walking (age 48 ± 7.8 years) or to a control group engaging in supervised low-intensity walking (age 50 ± 7.6 years). A total of 58 patients completed. Significantly greater improvement in the 6-minute walk test was found in the Nordic walking group (P = 0.009), compared with the low-intensity walking group. A significantly larger decrease in exercise heart rate (P = 0.020) and significantly improved scores on the Fibromyalgia Impact Questionnaire Physical function (P = 0.027) were found in the Nordic walking group as compared with the low-intensity walking group. No between-group difference was found for the Fibromyalgia Impact Questionnaire total or pain scores. The authors conclude that moderate-to-high intensity aerobic exercise by means of Nordic walking twice a week for 15 weeks was found to be a feasible mode of exercise, resulting in improved functional capacity and a decreased level of activity limitations. PMID:21345243

Capture of fixation by rotational flow; a deterministic hypothesis regarding scaling and stochasticity in fixational eye movements

PubMed Central

Wilkinson, Nicholas M.; Metta, Giorgio

2014-01-01

Visual scan paths exhibit complex, stochastic dynamics. Even during visual fixation, the eye is in constant motion. Fixational drift and tremor are thought to reflect fluctuations in the persistent neural activity of neural integrators in the oculomotor brainstem, which integrate sequences of transient saccadic velocity signals into a short term memory of eye position. Despite intensive research and much progress, the precise mechanisms by which oculomotor posture is maintained remain elusive. Drift exhibits a stochastic statistical profile which has been modeled using random walk formalisms. Tremor is widely dismissed as noise. Here we focus on the dynamical profile of fixational tremor, and argue that tremor may be a signal which usefully reflects the workings of oculomotor postural control. We identify signatures reminiscent of a certain flavor of transient neurodynamics; toric traveling waves which rotate around a central phase singularity. Spiral waves play an organizational role in dynamical systems at many scales throughout nature, though their potential functional role in brain activity remains a matter of educated speculation. Spiral waves have a repertoire of functionally interesting dynamical properties, including persistence, which suggest that they could in theory contribute to persistent neural activity in the oculomotor postural control system. Whilst speculative, the singularity hypothesis of oculomotor postural control implies testable predictions, and could provide the beginnings of an integrated dynamical framework for eye movements across scales. PMID:24616670

Large-Scale CTRW Analysis of Push-Pull Tracer Tests and Other Transport in Heterogeneous Porous Media

NASA Astrophysics Data System (ADS)

Hansen, S. K.; Berkowitz, B.

2014-12-01

Recently, we developed an alternative CTRW formulation which uses a "latching" upscaling scheme to rigorously map continuous or fine-scale stochastic solute motion onto discrete transitions on an arbitrarily coarse lattice (with spacing potentially on the meter scale or more). This approach enables model simplification, among many other things. Under advection, for example, we see that many relevant anomalous transport problems may be mapped into 1D, with latching to a sequence of successive, uniformly spaced planes. On this formulation (which we term RP-CTRW), the spatial transition vector may generally be made deterministic, with CTRW waiting time distributions encapsulating all the stochastic behavior. We demonstrate the excellent performance of this technique alongside Pareto-distributed waiting times in explaining experiments across a variety of scales using only two degrees of freedom. An interesting new application of the RP-CTRW technique is the analysis of radial (push-pull) tracer tests. Given modern computational power, random walk simulations are a natural fit for the inverse problem of inferring subsurface parameters from push-pull test data, and we propose them as an alternative to the classical type curve approach. In particular, we explore the visibility of heterogeneity through non-Fickian behavior in push-pull tests, and illustrate the ability of a radial RP-CTRW technique to encapsulate this behavior using a sparse parameterization which has predictive value.

Evaluating random search strategies in three mammals from distinct feeding guilds.

PubMed

Auger-Méthé, Marie; Derocher, Andrew E; DeMars, Craig A; Plank, Michael J; Codling, Edward A; Lewis, Mark A

2016-09-01

Searching allows animals to find food, mates, shelter and other resources essential for survival and reproduction and is thus among the most important activities performed by animals. Theory predicts that animals will use random search strategies in highly variable and unpredictable environments. Two prominent models have been suggested for animals searching in sparse and heterogeneous environments: (i) the Lévy walk and (ii) the composite correlated random walk (CCRW) and its associated area-restricted search behaviour. Until recently, it was difficult to differentiate between the movement patterns of these two strategies. Using a new method that assesses whether movement patterns are consistent with these two strategies and two other common random search strategies, we investigated the movement behaviour of three species inhabiting sparse northern environments: woodland caribou (Rangifer tarandus caribou), barren-ground grizzly bear (Ursus arctos) and polar bear (Ursus maritimus). These three species vary widely in their diets and thus allow us to contrast the movement patterns of animals from different feeding guilds. Our results showed that although more traditional methods would have found evidence for the Lévy walk for some individuals, a comparison of the Lévy walk to CCRWs showed stronger support for the latter. While a CCRW was the best model for most individuals, there was a range of support for its absolute fit. A CCRW was sufficient to explain the movement of nearly half of herbivorous caribou and a quarter of omnivorous grizzly bears, but was insufficient to explain the movement of all carnivorous polar bears. Strong evidence for CCRW movement patterns suggests that many individuals may use a multiphasic movement strategy rather than one-behaviour strategies such as the Lévy walk. The fact that the best model was insufficient to describe the movement paths of many individuals suggests that some animals living in sparse environments may use strategies that are more complicated than those described by the standard random search models. Thus, our results indicate a need to develop movement models that incorporate factors such as the perceptual and cognitive capacities of animals. © 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society.

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.

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.

Anderson transition in a three-dimensional kicked rotor

NASA Astrophysics Data System (ADS)

Wang, Jiao; García-García, Antonio M.

2009-03-01

We investigate Anderson localization in a three-dimensional (3D) kicked rotor. By a finite-size scaling analysis we identify a mobility edge for a certain value of the kicking strength k=kc . For k>kc dynamical localization does not occur, all eigenstates are delocalized and the spectral correlations are well described by Wigner-Dyson statistics. This can be understood by mapping the kicked rotor problem onto a 3D Anderson model (AM) where a band of metallic states exists for sufficiently weak disorder. Around the critical region k≈kc we carry out a detailed study of the level statistics and quantum diffusion. In agreement with the predictions of the one parameter scaling theory (OPT) and with previous numerical simulations, the number variance is linear, level repulsion is still observed, and quantum diffusion is anomalous with ⟨p2⟩∝t2/3 . We note that in the 3D kicked rotor the dynamics is not random but deterministic. In order to estimate the differences between these two situations we have studied a 3D kicked rotor in which the kinetic term of the associated evolution matrix is random. A detailed numerical comparison shows that the differences between the two cases are relatively small. However in the deterministic case only a small set of irrational periods was used. A qualitative analysis of a much larger set suggests that deviations between the random and the deterministic kicked rotor can be important for certain choices of periods. Heuristically it is expected that localization effects will be weaker in a nonrandom potential since destructive interference will be less effective to arrest quantum diffusion. However we have found that certain choices of irrational periods enhance Anderson localization effects.

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.

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.

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.

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

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.

Random walk and graph cut based active contour model for three-dimension interactive pituitary adenoma segmentation from MR images

NASA Astrophysics Data System (ADS)

Sun, Min; Chen, Xinjian; Zhang, Zhiqiang; Ma, Chiyuan

2017-02-01

Accurate volume measurements of pituitary adenoma are important to the diagnosis and treatment for this kind of sellar tumor. The pituitary adenomas have different pathological representations and various shapes. Particularly, in the case of infiltrating to surrounding soft tissues, they present similar intensities and indistinct boundary in T1-weighted (T1W) magnetic resonance (MR) images. Then the extraction of pituitary adenoma from MR images is still a challenging task. In this paper, we propose an interactive method to segment the pituitary adenoma from brain MR data, by combining graph cuts based active contour model (GCACM) and random walk algorithm. By using the GCACM method, the segmentation task is formulated as an energy minimization problem by a hybrid active contour model (ACM), and then the problem is solved by the graph cuts method. The region-based term in the hybrid ACM considers the local image intensities as described by Gaussian distributions with different means and variances, expressed as maximum a posteriori probability (MAP). Random walk is utilized as an initialization tool to provide initialized surface for GCACM. The proposed method is evaluated on the three-dimensional (3-D) T1W MR data of 23 patients and compared with the standard graph cuts method, the random walk method, the hybrid ACM method, a GCACM method which considers global mean intensity in region forces, and a competitive region-growing based GrowCut method planted in 3D Slicer. Based on the experimental results, the proposed method is superior to those methods.

A dual-docking microfluidic cell migration assay (D2-Chip) for testing neutrophil chemotaxis and the memory effect.

PubMed

Yang, Ke; Wu, Jiandong; Xu, Guoqing; Xie, Dongxue; Peretz-Soroka, Hagit; Santos, Susy; Alexander, Murray; Zhu, Ling; Zhang, Michael; Liu, Yong; Lin, Francis

2017-04-18

Chemotaxis is a classic mechanism for guiding cell migration and an important topic in both fundamental cell biology and health sciences. Neutrophils are a widely used model to study eukaryotic cell migration and neutrophil chemotaxis itself can lead to protective or harmful immune actions to the body. While much has been learnt from past research about how neutrophils effectively navigate through a chemoattractant gradient, many interesting questions remain unclear. For example, while it is tempting to model neutrophil chemotaxis using the well-established biased random walk theory, the experimental proof was challenged by the cell's highly persistent migrating nature. A special experimental design is required to test the key predictions from the random walk model. Another question that has interested the cell migration community for decades concerns the existence of chemotactic memory and its underlying mechanism. Although chemotactic memory has been suggested in various studies, a clear quantitative experimental demonstration will improve our understanding of the migratory memory effect. Motivated by these questions, we developed a microfluidic cell migration assay (so-called dual-docking chip or D 2 -Chip) that can test both the biased random walk model and the memory effect for neutrophil chemotaxis on a single chip enabled by multi-region gradient generation and dual-region cell alignment. Our results provide experimental support for the biased random walk model and chemotactic memory for neutrophil chemotaxis. Quantitative data analyses provide new insights into neutrophil chemotaxis and memory by making connections to entropic disorder, cell morphology and oscillating migratory response.

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.

ENabling Reduction of Low-grade Inflammation in SEniors Pilot Study: Concept, Rationale, and Design.

PubMed

Manini, Todd M; Anton, Stephen D; Beavers, Daniel P; Cauley, Jane A; Espeland, Mark A; Fielding, Roger A; Kritchevsky, Stephen B; Leeuwenburgh, Christiaan; Lewis, Kristina H; Liu, Christine; McDermott, Mary M; Miller, Michael E; Tracy, Russell P; Walston, Jeremy D; Radziszewska, Barbara; Lu, Jane; Stowe, Cindy; Wu, Samuel; Newman, Anne B; Ambrosius, Walter T; Pahor, Marco

2017-09-01

To test two interventions to reduce interleukin (IL)-6 levels, an indicator of low-grade chronic inflammation and an independent risk factor for impaired mobility and slow walking speed in older adults. The ENabling Reduction of low-Grade Inflammation in SEniors (ENRGISE) Pilot Study was a multicenter, double-blind, placebo-controlled randomized pilot trial of two interventions to reduce IL-6 levels. Five university-based research centers. Target enrollment was 300 men and women aged 70 and older with an average plasma IL-6 level between 2.5 and 30 pg/mL measured twice at least 1 week apart. Participants had low to moderate physical function, defined as self-reported difficulty walking one-quarter of a mile or climbing a flight of stairs and usual walk speed of less than 1 m/s on a 4-m usual-pace walk. Participants were randomized to losartan, omega-3 fish oil (ω-3), combined losartan and ω-3, or placebo. Randomization was stratified depending on eligibility for each group. A titration schedule was implemented to reach a dose that was safe and effective for IL-6 reduction. Maximal doses were 100 mg/d for losartan and 2.8 g/d for ω-3. IL-6, walking speed over 400 m, physical function (Short Physical Performance Battery), other inflammatory markers, safety, tolerability, frailty domains, and maximal leg strength were measured. Results from the ENRGISE Pilot Study will provide recruitment yields, feasibility, medication tolerance and adherence, and preliminary data to help justify a sample size for a more definitive randomized trial. The ENRGISE Pilot Study will inform a larger subsequent trial that is expected to have important clinical and public health implications for the growing population of older adults with low-grade chronic inflammation and mobility limitations. © 2017, Copyright the Authors Journal compilation © 2017, The American Geriatrics Society.

Effects of a 6-month exercise program pilot study on walking economy, peak physiological characteristics, and walking performance in patients with peripheral arterial disease.

PubMed

Crowther, Robert G; Leicht, Anthony S; Spinks, Warwick L; Sangla, Kunwarjit; Quigley, Frank; Golledge, Jonathan

2012-01-01

The purpose of this study was to examine the effects of a 6-month exercise program on submaximal walking economy in individuals with peripheral arterial disease and intermittent claudication (PAD-IC). Participants (n = 16) were randomly allocated to either a control PAD-IC group (CPAD-IC, n = 6) which received standard medical therapy, or a treatment PAD-IC group (TPAD-IC; n = 10) which took part in a supervised exercise program. During a graded treadmill test, physiological responses, including oxygen consumption, were assessed to calculate walking economy during submaximal and maximal walking performance. Differences between groups at baseline and post-intervention were analyzed via Kruskal-Wallis tests. At baseline, CPAD-IC and TPAD-IC groups demonstrated similar walking performance and physiological responses. Postintervention, TPAD-IC patients demonstrated significantly lower oxygen consumption during the graded exercise test, and greater maximal walking performance compared to CPAD-IC. These preliminary results indicate that 6 months of regular exercise improves both submaximal walking economy and maximal walking performance, without significant changes in maximal walking economy. Enhanced walking economy may contribute to physiological efficiency, which in turn may improve walking performance as demonstrated by PAD-IC patients following regular exercise programs.

Phenotypic switching of populations of cells in a stochastic environment

NASA Astrophysics Data System (ADS)

Hufton, Peter G.; Lin, Yen Ting; Galla, Tobias

2018-02-01

In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response. We focus on the case in which the environment switches randomly between discrete states. Starting from an individual-based model we derive stochastic differential equations to describe the dynamics, and obtain analytical expressions for the mean instantaneous growth rates based on the theory of piecewise-deterministic Markov processes. We show that optimal phenotypic responses are non-trivial for slow and intermediate environmental processes, and systematically compare the cases of periodic and random environments. The best response to random switching is more likely to be heterogeneity than in the case of deterministic periodic environments, net growth rates tend to be higher under stochastic environmental dynamics. The combined system of environment and population of cells can be interpreted as host-pathogen interaction, in which the host tries to choose environmental switching so as to minimise growth of the pathogen, and in which the pathogen employs a phenotypic switching optimised to increase its growth rate. We discuss the existence of Nash-like mutual best-response scenarios for such host-pathogen games.