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Sample records for dynamic random walks

  1. Fractional random walk lattice dynamics

    NASA Astrophysics Data System (ADS)

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

    2017-02-01

    We analyze time-discrete and time-continuous ‘fractional’ random walks on undirected regular networks with special focus on cubic periodic lattices in n  =  1, 2, 3,.. dimensions. The fractional random walk dynamics is governed by a master equation involving fractional powers of Laplacian matrices {{L}\\fracα{2}}} where α =2 recovers the normal walk. First we demonstrate that the interval 0<α ≤slant 2 is admissible for the fractional random walk. We derive analytical expressions for the transition matrix of the fractional random walk and closely related the average return probabilities. We further obtain the fundamental matrix {{Z}(α )} , and the mean relaxation time (Kemeny constant) for the fractional random walk. The representation for the fundamental matrix {{Z}(α )} relates fractional random walks with normal random walks. We show that the matrix elements of the transition matrix of the fractional random walk exihibit for large cubic n-dimensional lattices a power law decay of an n-dimensional infinite space Riesz fractional derivative type indicating emergence of Lévy flights. As a further footprint of Lévy flights in the n-dimensional space, the transition matrix and return probabilities of the fractional random walk are dominated for large times t by slowly relaxing long-wave modes leading to a characteristic {{t}-\\frac{n{α}} -decay. It can be concluded that, due to long range moves of fractional random walk, a small world property is emerging increasing the efficiency to explore the lattice when instead of a normal random walk a fractional random walk is chosen.

  2. Dynamic decoupling in the presence of 1D random walk

    NASA Astrophysics Data System (ADS)

    Chakrabarti, Arnab; Chakraborty, Ipsita; Bhattacharyya, Rangeet

    2016-05-01

    In the recent past, many dynamic decoupling sequences have been proposed for the suppression of decoherence of spins connected to thermal baths of various natures. Dynamic decoupling schemes for suppressing decoherence due to Gaussian diffusion have also been developed. In this work, we study the relative performances of dynamic decoupling schemes in the presence of a non-stationary Gaussian noise such as a 1D random walk. Frequency domain analysis is not suitable to determine the performances of various dynamic decoupling schemes in suppressing decoherence due to such a process. Thus, in this work, we follow a time domain calculation to arrive at the following conclusions: in the presence of such a noise, we show that (i) the traditional Carr-Purcell-Meiboom-Gill (CPMG) sequence outperforms Uhrig’s dynamic decoupling scheme, (ii) CPMG remains the optimal sequence for suppression of decoherence due to random walk in the presence of an external field gradient. Later, the theoretical predictions are experimentally verified by using nuclear magnetic resonance spectroscopy on spin 1/2 particles diffusing in a liquid medium.

  3. Complex networks: when random walk dynamics equals synchronization

    NASA Astrophysics Data System (ADS)

    Kriener, Birgit; Anand, Lishma; Timme, Marc

    2012-09-01

    Synchrony prevalently emerges from the interactions of coupled dynamical units. For simple systems such as networks of phase oscillators, the asymptotic synchronization process is assumed to be equivalent to a Markov process that models standard diffusion or random walks on the same network topology. In this paper, we analytically derive the conditions for such equivalence for networks of pulse-coupled oscillators, which serve as models for neurons and pacemaker cells interacting by exchanging electric pulses or fireflies interacting via light flashes. We find that the pulse synchronization process is less simple, but there are classes of, e.g., network topologies that ensure equivalence. In particular, local dynamical operators are required to be doubly stochastic. These results provide a natural link between stochastic processes and deterministic synchronization on networks. Tools for analyzing diffusion (or, more generally, Markov processes) may now be transferred to pin down features of synchronization in networks of pulse-coupled units such as neural circuits.

  4. On the pertinence to Physics of random walks induced by random dynamical systems: a survey

    NASA Astrophysics Data System (ADS)

    Petritis, Dimitri

    2016-08-01

    Let be an abstract space and a denumerable (finite or infinite) alphabet. Suppose that is a family of functions such that for all we have and a family of transformations . The pair ((Sa)a , (pa)a ) is termed an iterated function system with place dependent probabilities. Such systems can be thought as generalisations of random dynamical systems. As a matter of fact, suppose we start from a given ; we pick then randomly, with probability pa (x), the transformation Sa and evolve to Sa (x). We are interested in the behaviour of the system when the iteration continues indefinitely. Random walks of the above type are omnipresent in both classical and quantum Physics. To give a small sample of occurrences we mention: random walks on the affine group, random walks on Penrose lattices, random walks on partially directed lattices, evolution of density matrices induced by repeated quantum measurements, quantum channels, quantum random walks, etc. In this article, we review some basic properties of such systems and provide with a pathfinder in the extensive bibliography (both on mathematical and physical sides) where the main results have been originally published.

  5. Quantum random walks without walking

    SciTech Connect

    Manouchehri, K.; Wang, J. B.

    2009-12-15

    Quantum random walks have received much interest due to their nonintuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable and not limited to special connectivity criteria. We present a scheme for walking on arbitrarily complex graphs, which can be realized using a variety of quantum systems such as a Bose-Einstein condensate trapped inside an optical lattice. This scheme is particularly elegant since the walker is not required to physically step between the nodes; only flipping coins is sufficient.

  6. Correlated random walks caused by dynamical wavefunction collapse

    NASA Astrophysics Data System (ADS)

    Bedingham, D. J.; Ulbricht, H.

    2015-08-01

    Wavefunction collapse models modify Schrödinger’s equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum measurement problem. An additional generic consequence of the collapse mechanism is that it causes particles to exhibit a tiny random diffusive motion. Here it is shown that for the continuous spontaneous localization (CSL) model—one of the most well developed collapse models—the diffusions of two sufficiently nearby particles are positively correlated. An experimental test of this effect is proposed in which random displacements of pairs of free nanoparticles are measured after they have been simultaneously released from nearby traps. The experiment must be carried out at sufficiently low temperature and pressure in order for the collapse effects to dominate over the ambient environmental noise. It is argued that these constraints can be satisfied by current technologies for a large region of the viable parameter space of the CSL model. The effect disappears as the separation between particles exceeds the CSL length scale. The test therefore provides a means of bounding this length scale.

  7. Correlated random walks caused by dynamical wavefunction collapse

    PubMed Central

    Bedingham, D. J.; Ulbricht, H.

    2015-01-01

    Wavefunction collapse models modify Schrödinger’s equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum measurement problem. An additional generic consequence of the collapse mechanism is that it causes particles to exhibit a tiny random diffusive motion. Here it is shown that for the continuous spontaneous localization (CSL) model—one of the most well developed collapse models—the diffusions of two sufficiently nearby particles are positively correlated. An experimental test of this effect is proposed in which random displacements of pairs of free nanoparticles are measured after they have been simultaneously released from nearby traps. The experiment must be carried out at sufficiently low temperature and pressure in order for the collapse effects to dominate over the ambient environmental noise. It is argued that these constraints can be satisfied by current technologies for a large region of the viable parameter space of the CSL model. The effect disappears as the separation between particles exceeds the CSL length scale. The test therefore provides a means of bounding this length scale. PMID:26303388

  8. The adaptive dynamic community detection algorithm based on the non-homogeneous random walking

    NASA Astrophysics Data System (ADS)

    Xin, Yu; Xie, Zhi-Qiang; Yang, Jing

    2016-05-01

    With the changing of the habit and custom, people's social activity tends to be changeable. It is required to have a community evolution analyzing method to mine the dynamic information in social network. For that, we design the random walking possibility function and the topology gain function to calculate the global influence matrix of the nodes. By the analysis of the global influence matrix, the clustering directions of the nodes can be obtained, thus the NRW (Non-Homogeneous Random Walk) method for detecting the static overlapping communities can be established. We design the ANRW (Adaptive Non-Homogeneous Random Walk) method via adapting the nodes impacted by the dynamic events based on the NRW. The ANRW combines the local community detection with dynamic adaptive adjustment to decrease the computational cost for ANRW. Furthermore, the ANRW treats the node as the calculating unity, thus the running manner of the ANRW is suitable to the parallel computing, which could meet the requirement of large dataset mining. Finally, by the experiment analysis, the efficiency of ANRW on dynamic community detection is verified.

  9. All-time dynamics of continuous-time random walks on complex networks

    NASA Astrophysics Data System (ADS)

    Teimouri, Hamid; Kolomeisky, Anatoly B.

    2013-02-01

    The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social, and economic sciences. Recently, several theoretical approaches have been developed that allowed to analyze explicitly dynamics of CTRW at all times, which is critically important for understanding mechanisms of underlying phenomena. However, theoretical analysis has been done mostly for systems with a simple geometry. Here we extend the original method based on generalized master equations to analyze all-time dynamics of CTRW models on complex networks. Specific calculations are performed for models on lattices with branches and for models on coupled parallel-chain lattices. Exact expressions for velocities and dispersions are obtained. Generalized fluctuations theorems for CTRW models on complex networks are discussed.

  10. Noisy continuous time random walks

    NASA Astrophysics Data System (ADS)

    Jeon, Jae-Hyung; Barkai, Eli; Metzler, Ralf

    2013-09-01

    Experimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time random walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time random walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time random walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time random walks may appear ergodic, while the bare continuous time random walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.

  11. When Human Walking is a Random Walk

    NASA Astrophysics Data System (ADS)

    Hausdorff, J. M.

    1998-03-01

    The complex, hierarchical locomotor system normally does a remarkable job of controlling an inherently unstable, multi-joint system. Nevertheless, the stride interval --- the duration of a gait cycle --- fluctuates from one stride to the next, even under stationary conditions. We used random walk analysis to study the dynamical properties of these fluctuations under normal conditions and how they change with disease and aging. Random walk analysis of the stride-to-stride fluctuations of healthy, young adult men surprisingly reveals a self-similar pattern: fluctuations at one time scale are statistically similar to those at multiple other time scales (Hausdorff et al, J Appl Phsyiol, 1995). To study the stability of this fractal property, we analyzed data obtained from healthy subjects who walked for 1 hour at their usual pace, as well as at slower and faster speeds. The stride interval fluctuations exhibited long-range correlations with power-law decay for up to a thousand strides at all three walking rates. In contrast, during metronomically-paced walking, these long-range correlations disappeared; variations in the stride interval were uncorrelated and non-fractal (Hausdorff et al, J Appl Phsyiol, 1996). To gain insight into the mechanism(s) responsible for this fractal property, we examined the effects of aging and neurological impairment. Using detrended fluctuation analysis (DFA), we computed α, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. α was significantly lower in healthy elderly subjects compared to young adults (p < .003) and in subjects with Huntington's disease, a neuro-degenerative disorder of the central nervous system, compared to disease-free controls (p < 0.005) (Hausdorff et al, J Appl Phsyiol, 1997). α was also significantly related to degree of functional impairment in subjects with Huntington's disease (r=0.78). Recently, we have observed that just as

  12. Magnetic field line random walk in two-dimensional dynamical turbulence

    NASA Astrophysics Data System (ADS)

    Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.

    2017-08-01

    The field line random walk (FLRW) of magnetic turbulence is one of the important topics in plasma physics and astrophysics. In this article, by using the field line tracing method, the mean square displacement (MSD) of FLRW is calculated on all possible length scales for pure two-dimensional turbulence with the damping dynamical model. We demonstrate that in order to describe FLRW with the damping dynamical model, a new dimensionless quantity R is needed to be introduced. On different length scales, dimensionless MSD shows different relationships with the dimensionless quantity R. Although the temporal effect affects the MSD of FLRW and even changes regimes of FLRW, it does not affect the relationship between the dimensionless MSD and dimensionless quantity R on all possible length scales.

  13. Memory-induced anomalous dynamics in a minimal random walk model

    NASA Astrophysics Data System (ADS)

    Harbola, Upendra; Kumar, Niraj; Lindenberg, Katja

    2014-08-01

    A discrete-time dynamics of a non-Markovian random walker is analyzed using a minimal model where memory of the past drives the present dynamics. In recent work [N. Kumar et al., Phys. Rev. E 82, 021101 (2010), 10.1103/PhysRevE.82.021101] we proposed a model that exhibits asymptotic superdiffusion, normal diffusion, and subdiffusion with the sweep of a single parameter. Here we propose an even simpler model, with minimal options for the walker: either move forward or stay at rest. We show that this model can also give rise to diffusive, subdiffusive, and superdiffusive dynamics at long times as a single parameter is varied. We show that in order to have subdiffusive dynamics, the memory of the rest states must be perfectly correlated with the present dynamics. We show explicitly that if this condition is not satisfied in a unidirectional walk, the dynamics is only either diffusive or superdiffusive (but not subdiffusive) at long times.

  14. The random walk function in the analysis of time-activity curves from dynamic radionuclide studies.

    PubMed

    Hart, G C; Bunday, B; Kiri, V

    1987-04-01

    The random walk function is a mathematical function derived from studies of the mass transport and flow of diffusible materials through tubes. Approximations to the function were first used some time ago in the field of cardiac tracer dilution curves, but in the absence of rapid and reproducible curve fitting the method never became commonplace. The current study uses the latest curve-fitting techniques and shows how the method may be used with precision in the analysis of time-activity curves from dynamic oesophageal and blood flow studies. The physiological basis of the method is given and parameters obtained which relate to both the rate of flow and the local dispersion of the bolus.

  15. Quantum walks with random phase shifts

    SciTech Connect

    Kosik, Jozef; Buzek, Vladimir; Hillery, Mark

    2006-08-15

    We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail the role of decoherence in quantum walks and to investigate the quantum-to-classical transition. We also provide classical analog of the quantum random walks studied. Interestingly enough, it turns out that the classical counterparts of some quantum random walks are classical random walks with a memory and biased coin. In addition random phase shifts 'simplify' the dynamics (the cross-interference terms of different paths vanish on average) and enable us to give a compact formula for the dispersion of such walks.

  16. Distribution of dynamical quantities in the contact process, random walks, and quantum spin chains in random environments

    NASA Astrophysics Data System (ADS)

    Juhász, Róbert

    2014-03-01

    We study the distribution of dynamical quantities in various one-dimensional disordered models, the critical behavior of which is described by an infinite randomness fixed point. In the disordered contact process, the survival probability P (t) is found to show multiscaling in the critical point, meaning that P(t )=t-δ, where the (environment and time-dependent) exponent δ has a universal limit distribution when t →∞. The limit distribution is determined by the strong disorder renormalization group method analytically in the end point of a semi-infinite lattice, where it is found to be exponential, while, in the infinite system, conjectures on its limiting behaviors for small and large δ, which are based on numerical results, are formulated. By the same method, the survival probability in the problem of random walks in random environments is also shown to exhibit multiscaling with an exponential limit distribution. In addition to this, the (imaginary-time) spin-spin autocorrelation function of the random transverse-field Ising chain is found to have a form similar to that of survival probability of the contact process at the level of the renormalization approach. Consequently, a relationship between the corresponding limit distributions in the two problems can be established. Finally, the distribution of the spontaneous magnetization in this model is also discussed.

  17. Quantum random walk polynomial and quantum random walk measure

    NASA Astrophysics Data System (ADS)

    Kang, Yuanbao; Wang, Caishi

    2014-05-01

    In the paper, we introduce a quantum random walk polynomial (QRWP) that can be defined as a polynomial , which is orthogonal with respect to a quantum random walk measure (QRWM) on , such that the parameters are in the recurrence relations and satisfy . We firstly obtain some results of QRWP and QRWM, in which case the correspondence between measures and orthogonal polynomial sequences is one-to-one. It shows that any measure with respect to which a quantum random walk polynomial sequence is orthogonal is a quantum random walk measure. We next collect some properties of QRWM; moreover, we extend Karlin and McGregor's representation formula for the transition probabilities of a quantum random walk (QRW) in the interacting Fock space, which is a parallel result with the CGMV method. Using these findings, we finally obtain some applications for QRWM, which are of interest in the study of quantum random walk, highlighting the role played by QRWP and QRWM.

  18. Directed random walk with random restarts: The Sisyphus random walk

    NASA Astrophysics Data System (ADS)

    Montero, Miquel; Villarroel, Javier

    2016-09-01

    In this paper we consider a particular version of the random walk with restarts: random reset events which suddenly bring the system to the starting value. We analyze its relevant statistical properties, like the transition probability, and show how an equilibrium state appears. Formulas for the first-passage time, high-water marks, and other extreme statistics are also derived; we consider counting problems naturally associated with the system. Finally we indicate feasible generalizations useful for interpreting different physical effects.

  19. Directed random walk with random restarts: The Sisyphus random walk.

    PubMed

    Montero, Miquel; Villarroel, Javier

    2016-09-01

    In this paper we consider a particular version of the random walk with restarts: random reset events which suddenly bring the system to the starting value. We analyze its relevant statistical properties, like the transition probability, and show how an equilibrium state appears. Formulas for the first-passage time, high-water marks, and other extreme statistics are also derived; we consider counting problems naturally associated with the system. Finally we indicate feasible generalizations useful for interpreting different physical effects.

  20. Random-walk enzymes

    PubMed Central

    Mak, Chi H.; Pham, Phuong; Afif, Samir A.; Goodman, Myron F.

    2015-01-01

    Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C → U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics. PMID:26465508

  1. Random-walk enzymes.

    PubMed

    Mak, Chi H; Pham, Phuong; Afif, Samir A; Goodman, Myron F

    2015-09-01

    Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C→U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics.

  2. Random-walk enzymes

    NASA Astrophysics Data System (ADS)

    Mak, Chi H.; Pham, Phuong; Afif, Samir A.; Goodman, Myron F.

    2015-09-01

    Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C →U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics.

  3. A relativistically covariant random walk

    NASA Astrophysics Data System (ADS)

    Almaguer, J.; Larralde, H.

    2007-08-01

    In this work we present and analyze an extremely simple relativistically covariant random walk model. In our approach, the probability density and the flow of probability arise naturally as the components of a four-vector and they are related to one another via a tensorial constitutive equation. We show that the system can be described in terms of an underlying invariant space time random walk parameterized by the number of sojourns. Finally, we obtain explicit expressions for the moments of the covariant random walk as well as for the underlying invariant random walk.

  4. Dynamics of technological evolution: Random walk model for the research enterprise.

    PubMed

    Montroll, E W; Shuler, K E

    1979-12-01

    Technological evolution is a consequence of a sequence of replacements. The development of a new technology generally follows from model testing of the basic ideas on a small scale. Traditional technologies such as aerodynamics and naval architecture involved feasibility experiments on systems characterized by only one or two dimensionless constants. Technologies of the "future" such as magnetically confined fusion depend upon many coupled dimensionless constants. Research and development is modeled and analyzed in terms of random walks in appropriate dimensionless constant space.

  5. Molecular dynamics simulation for PBR pebble tracking simulation via a random walk approach using Monte Carlo simulation.

    PubMed

    Lee, Kyoung O; Holmes, Thomas W; Calderon, Adan F; Gardner, Robin P

    2012-05-01

    Using a Monte Carlo (MC) simulation, random walks were used for pebble tracking in a two-dimensional geometry in the presence of a biased gravity field. We investigated the effect of viscosity damping in the presence of random Gaussian fluctuations. The particle tracks were generated by Molecular Dynamics (MD) simulation for a Pebble Bed Reactor. The MD simulations were conducted in the interaction of noncohesive Hertz-Mindlin theory where the random walk MC simulation has a correlation with the MD simulation. This treatment can easily be extended to include the generation of transient gamma-ray spectra from a single pebble that contains a radioactive tracer. Then the inverse analysis thereof could be made to determine the uncertainty of the realistic measurement of transient positions of that pebble by any given radiation detection system designed for that purpose.

  6. Epidemic spreading driven by biased random walks

    NASA Astrophysics Data System (ADS)

    Pu, Cunlai; Li, Siyuan; Yang, Jian

    2015-08-01

    Random walk is one of the basic mechanisms of many network-related applications. In this paper, we study the dynamics of epidemic spreading driven by biased random walks in complex networks. In our epidemic model, infected nodes send out infection packets by biased random walks to their neighbor nodes, and this causes the infection of susceptible nodes that receive the packets. Infected nodes recover from the infection at a constant rate λ, and will not be infected again after recovery. We obtain the largest instantaneous number of infected nodes and the largest number of ever-infected nodes respectively, by tuning the parameter α of the biased random walks. Simulation results on model and real-world networks show that spread of the epidemic becomes intense and widespread with increase of either delivery capacity of infected nodes, average node degree, or homogeneity of node degree distribution.

  7. Dynamics of technological evolution: Random walk model for the research enterprise

    PubMed Central

    Montroll, Elliott W.; Shuler, Kurt E.

    1979-01-01

    Technological evolution is a consequence of a sequence of replacements. The development of a new technology generally follows from model testing of the basic ideas on a small scale. Traditional technologies such as aerodynamics and naval architecture involved feasibility experiments on systems characterized by only one or two dimensionless constants. Technologies of the “future” such as magnetically confined fusion depend upon many coupled dimensionless constants. Research and development is modeled and analyzed in terms of random walks in appropriate dimensionless constant space. PMID:16592727

  8. Persistence of random walk records

    NASA Astrophysics Data System (ADS)

    Ben-Naim, E.; Krapivsky, P. L.

    2014-06-01

    We study records generated by Brownian particles in one dimension. Specifically, we investigate an ordinary random walk and define the record as the maximal position of the walk. We compare the record of an individual random walk with the mean record, obtained as an average over infinitely many realizations. We term the walk ‘superior’ if the record is always above average, and conversely, the walk is said to be ‘inferior’ if the record is always below average. We find that the fraction of superior walks, S, decays algebraically with time, S ˜ t-β, in the limit t → ∞, and that the persistence exponent is nontrivial, β = 0.382 258…. The fraction of inferior walks, I, also decays as a power law, I ˜ t-α, but the persistence exponent is smaller, α = 0.241 608…. Both exponents are roots of transcendental equations involving the parabolic cylinder function. To obtain these theoretical results, we analyze the joint density of superior walks with a given record and position, while for inferior walks it suffices to study the density as a function of position.

  9. Rare events statistics of random walks on networks: localisation and other dynamical phase transitions

    NASA Astrophysics Data System (ADS)

    De Bacco, Caterina; Guggiola, Alberto; Kühn, Reimer; Paga, Pierre

    2016-05-01

    Rare event statistics for random walks on complex networks are investigated using the large deviation formalism. Within this formalism, rare events are realised as typical events in a suitably deformed path-ensemble, and their statistics can be studied in terms of spectral properties of a deformed Markov transition matrix. We observe two different types of phase transition in such systems: (i) rare events which are singled out for sufficiently large values of the deformation parameter may correspond to localised modes of the deformed transition matrix; (ii) ‘mode-switching transitions’ may occur as the deformation parameter is varied. Details depend on the nature of the observable for which the rare event statistics is studied, as well as on the underlying graph ensemble. In the present paper we report results on rare events statistics for path averages of random walks in Erdős-Rényi and scale free networks. Large deviation rate functions and localisation properties are studied numerically. For observables of the type considered here, we also derive an analytical approximation for the Legendre transform of the large deviation rate function, which is valid in the large connectivity limit. It is found to agree well with simulations.

  10. Crossover from random walk to self-avoiding walk

    NASA Astrophysics Data System (ADS)

    Rieger, Jens

    1988-11-01

    A one-dimensional n-step random walk on openZ1 which must not visit a vertex more than k times is studied via Monte Carlo methods. The dependences of the mean-square end-to-end distance of the walk and of the fraction of trapped walks on λ=(k-1)/n will be given for the range from λ=0 (self-avoiding walk) to λ=1 (unrestricted random walk). From the results it is conjectured that in the limit n-->∞ the walk obeys simple random walk statistics with respect to its static properties for all λ>0.

  11. 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.

  12. 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.

  13. Socially informed random walks: incorporating group dynamics into models of population spread and growth

    PubMed Central

    Haydon, Daniel T; Morales, Juan M; Yott, Adelle; Jenkins, Deborah A; Rosatte, Rick; Fryxell, John M

    2008-01-01

    Simple correlated random walk (CRW) models are rarely sufficient to describe movement of animals over more than the shortest time scales. However, CRW approaches can be used to model more complex animal movement trajectories by assuming individuals move in one of several different behavioural or movement states, each characterized by a different CRW. The spatial and social context an individual experiences may influence the proportion of time spent in different movement states, with subsequent effects on its spatial distribution, survival and fecundity. While methods to study habitat influences on animal movement have been previously developed, social influences have been largely neglected. Here, we fit a ‘socially informed’ movement model to data from a population of over 100 elk (Cervus canadensis) reintroduced into a new environment, radio-collared and subsequently tracked over a 4-year period. The analysis shows how elk move further when they are solitary than when they are grouped and incur a higher rate of mortality the further they move away from the release area. We use the model to show how the spatial distribution and growth rate of the population depend on the balance of fission and fusion processes governing the group structure of the population. The results are briefly discussed with respect to the design of species reintroduction programmes. PMID:18270158

  14. Random walk with barriers

    PubMed Central

    Novikov, Dmitry S.; Fieremans, Els; Jensen, Jens H.; Helpern, Joseph A.

    2011-01-01

    Restrictions to molecular motion by barriers (membranes) are ubiquitous in porous media, composite materials and biological tissues. A major challenge is to characterize the microstructure of a material or an organism nondestructively using a bulk transport measurement. Here we demonstrate how the long-range structural correlations introduced by permeable membranes give rise to distinct features of transport. We consider Brownian motion restricted by randomly placed and oriented membranes (d − 1 dimensional planes in d dimensions) and focus on the disorder-averaged diffusion propagator using a scattering approach. The renormalization group solution reveals a scaling behavior of the diffusion coefficient for large times, with a characteristically slow inverse square root time dependence for any d. Its origin lies in the strong structural fluctuations introduced by the spatially extended random restrictions, representing a novel universality class of the structural disorder. Our results agree well with Monte Carlo simulations in two dimensions. They can be used to identify permeable barriers as restrictions to transport, and to quantify their permeability and surface area. PMID:21686083

  15. Random walk approach to spin dynamics in a two-dimensional electron gas with spin-orbit coupling

    SciTech Connect

    Yang, Luyi; Orenstein, J.; Lee, Dung-Hai

    2010-09-27

    We introduce and solve a semiclassical random walk (RW) model that describes the dynamics of spin polarization waves in zinc-blende semiconductor quantum wells. We derive the dispersion relations for these waves, including the Rashba, linear and cubic Dresselhaus spin-orbit interactions, as well as the effects of an electric field applied parallel to the spin polarization wave vector. In agreement with calculations based on quantum kinetic theory [P. Kleinert and V. V. Bryksin, Phys. Rev. B 76, 205326 (2007)], the RW approach predicts that spin waves acquire a phase velocity in the presence of the field that crosses zero at a nonzero wave vector, q{sub 0}. In addition, we show that the spin-wave decay rate is independent of field at q{sub 0} but increases as (q-q{sub 0}){sup 2} for q {ne} q{sub 0}. These predictions can be tested experimentally by suitable transient spin grating experiments.

  16. Random walk centrality for temporal networks

    NASA Astrophysics Data System (ADS)

    Rocha, Luis E. C.; Masuda, Naoki

    2014-06-01

    Nodes can be ranked according to their relative importance within a network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based on random walks, for example the PageRank, have focused on static structures. However, several realistic networks are indeed dynamic, meaning that their structure changes in time. In this paper, we propose a centrality measure for temporal networks based on random walks under periodic boundary conditions that we call TempoRank. It is known that, in static networks, the stationary density of the random walk is proportional to the degree or the strength of a node. In contrast, we find that, in temporal networks, the stationary density is proportional to the in-strength of the so-called effective network, a weighted and directed network explicitly constructed from the original sequence of transition matrices. The stationary density also depends on the sojourn probability q, which regulates the tendency of the walker to stay in the node, and on the temporal resolution of the data. We apply our method to human interaction networks and show that although it is important for a node to be connected to another node with many random walkers (one of the principles of the PageRank) at the right moment, this effect is negligible in practice when the time order of link activation is included.

  17. Theory of Random Walks.

    NASA Astrophysics Data System (ADS)

    Sokol, M.

    1996-11-01

    We develope a mathematical analysis derived from a simple vector-kick model of the evolution of a laser field due to strictly phase diffusion and having arbitrary average photon number barn. We write the exact-coupled, nonlinear equations in two dynamical variables, namely the magnitude of the new field E_0^' and the differential change in angle δ φ. A closed form approximate solution to find the variance in the tangent of phase, for small angles, has yielded the theoretical lower limit for large photon number √n=E_0>> 1. The exact solution to the variance in the tangent of phase angle δ φ was made possible by a trigonometric substitution method, and the transformed argument has been analyzed using residue calculus. There is a double-zero at z=0, simple-poles at z=± i, and double poles at z=± √(E0 +1)(E_0-1) i, in the Argand plane. The variance in the tangent of phase is found to be <(tan δφ)^2> = 2π(√(barn)/(barn-1) -1). An extension of this result would include effects due to amplification and saturation. The general result would include a regime of small photon numbers. Part C of program listing

  18. Phase transition in random adaptive walks on correlated fitness landscapes

    NASA Astrophysics Data System (ADS)

    Park, Su-Chan; Szendro, Ivan G.; Neidhart, Johannes; Krug, Joachim

    2015-04-01

    We study biological evolution on a random fitness landscape where correlations are introduced through a linear fitness gradient of strength c . When selection is strong and mutations rare the dynamics is a directed uphill walk that terminates at a local fitness maximum. We analytically calculate the dependence of the walk length on the genome size L . When the distribution of the random fitness component has an exponential tail, we find a phase transition of the walk length D between a phase at small c , where walks are short (D ˜lnL ) , and a phase at large c , where walks are long (D ˜L ) . For all other distributions only a single phase exists for any c >0 . The considered process is equivalent to a zero temperature Metropolis dynamics for the random energy model in an external magnetic field, thus also providing insight into the aging dynamics of spin glasses.

  19. Correlated continuous time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics

    NASA Astrophysics Data System (ADS)

    Schulz, Johannes H. P.; Chechkin, Aleksei V.; Metzler, Ralf

    2013-11-01

    Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through scale-free forms of the jump length and/or waiting time distributions by virtue of the generalized central limit theorem. Here we present a modified version of recently proposed correlated CTRW processes, where we incorporate a power-law correlated noise on the level of both jump length and waiting time dynamics. We obtain a very general stochastic model, that encompasses key features of several paradigmatic models of anomalous diffusion: discontinuous, scale-free displacements as in Lévy flights, scale-free waiting times as in subdiffusive CTRWs, and the long-range temporal correlations of fractional Brownian motion (FBM). We derive the exact solutions for the single-time probability density functions and extract the scaling behaviours. Interestingly, we find that different combinations of the model parameters lead to indistinguishable shapes of the emerging probability density functions and identical scaling laws. Our model will be useful for describing recent experimental single particle tracking data that feature a combination of CTRW and FBM properties.

  20. The RANLUX Generator:. Resonances in a Random Walk Test

    NASA Astrophysics Data System (ADS)

    Shchur, Lev N.; Butera, Paolo

    Using a recently proposed directed random walk test, we systematically investigate the popular random number generator RANLUX developed by Lüscher and implemented by James. We confirm the good quality of this generator with the recommended luxury level. At a smaller luxury level (for instance equal to 1) resonances are observed in the random walk test. We also find that the lagged Fibonacci and Subtract-with-Carry recipes exhibit similar failures in the random walk test. A revised analysis of the corresponding dynamical systems leads to the observation of resonances in the eigenvalues of Jacobi matrix.

  1. Random walks with similar transition probabilities

    NASA Astrophysics Data System (ADS)

    Schiefermayr, Klaus

    2003-04-01

    We consider random walks on the nonnegative integers with a possible absorbing state at -1. A random walk is called [alpha]-similar to a random walk if there exist constants Cij such that for the corresponding n-step transition probabilities , i,j[greater-or-equal, slanted]0, hold. We give necessary and sufficient conditions for the [alpha]-similarity of two random walks both in terms of the parameters and in terms of the corresponding spectral measures which appear in the spectral representation of the n-step transition probabilities developed by Karlin and McGregor.

  2. Random walks on generalized Koch networks

    NASA Astrophysics Data System (ADS)

    Sun, Weigang

    2013-10-01

    For deterministically growing networks, it is a theoretical challenge to determine the topological properties and dynamical processes. In this paper, we study random walks on generalized Koch networks with features that include an initial state that is a globally connected network to r nodes. In each step, every existing node produces m complete graphs. We then obtain the analytical expressions for first passage time (FPT), average return time (ART), i.e. the average of FPTs for random walks from node i to return to the starting point i for the first time, and average sending time (AST), defined as the average of FPTs from a hub node to all other nodes, excluding the hub itself with regard to network parameters m and r. For this family of Koch networks, the ART of the new emerging nodes is identical and increases with the parameters m or r. In addition, the AST of our networks grows with network size N as N ln N and also increases with parameter m. The results obtained in this paper are the generalizations of random walks for the original Koch network.

  3. Random Walks in Model Brain Tissue

    NASA Astrophysics Data System (ADS)

    Grinberg, Farida; Farrher, Ezequiel; Oros-Peusquens, Ana-Maria; Shah, N. Jon

    2011-03-01

    The propagation of water molecules in the brain and the corresponding NMR response are affected by many factors such as compartmentalization, restrictions and anisotropy imposed by the cellular microstructure. Interfacial interactions with cell membranes and exchange additionally come into play. Due to the complexity of the underlying factors, a differentiation between the various contributions to the average NMR signal in in vivo studies represents a difficult task. In this work we perform random-walk Monte Carlo simulations in well-defined model systems aiming at establishing quantitative relations between dynamics and microstructure. The results are compared with experimental data obtained for artificial anisotropic model systems.

  4. Quantum random walks and decision making.

    PubMed

    Shankar, Karthik H

    2014-01-01

    How realistic is it to adopt a quantum random walk model to account for decisions involving two choices? Here, we discuss the neural plausibility and the effect of initial state and boundary thresholds on such a model and contrast it with various features of the classical random walk model of decision making.

  5. 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

  6. 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.

  7. Random recursive trees and the elephant random walk

    NASA Astrophysics Data System (ADS)

    Kürsten, Rüdiger

    2016-03-01

    One class of random walks with infinite memory, so-called elephant random walks, are simple models describing anomalous diffusion. We present a surprising connection between these models and bond percolation on random recursive trees. We use a coupling between the two models to translate results from elephant random walks to the percolation process. We calculate, besides other quantities, exact expressions for the first and the second moment of the root cluster size and of the number of nodes in child clusters of the first generation. We further introduce another model, the skew elephant random walk, and calculate the first and second moment of this process.

  8. Random walks on simplicial complexes and harmonics†

    PubMed Central

    Steenbergen, John

    2016-01-01

    Abstract In this paper, we introduce a class of random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension d, a random walk with an absorbing state is defined which relates to the spectrum of the k‐dimensional Laplacian for 1 ≤ k ≤ d. We study an example of random walks on simplicial complexes in the context of a semi‐supervised learning problem. Specifically, we consider a label propagation algorithm on oriented edges, which applies to a generalization of the partially labelled classification problem on graphs. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 379–405, 2016

  9. Lévy random walks on multiplex networks

    PubMed Central

    Guo, Quantong; Cozzo, Emanuele; Zheng, Zhiming; Moreno, Yamir

    2016-01-01

    Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical processes that occur on top of them. Here, inspired by one specific model of random walks that seems to be ubiquitous across many scientific fields, the Lévy flight, we study a new navigation strategy on top of multiplex networks. Capitalizing on spectral graph and stochastic matrix theories, we derive analytical expressions for the mean first passage time and the average time to reach a node on these networks. Moreover, we also explore the efficiency of Lévy random walks, which we found to be very different as compared to the single layer scenario, accounting for the structure and dynamics inherent to the multiplex network. Finally, by comparing with some other important random walk processes defined on multiplex networks, we find that in some region of the parameters, a Lévy random walk is the most efficient strategy. Our results give us a deeper understanding of Lévy random walks and show the importance of considering the topological structure of multiplex networks when trying to find efficient navigation strategies. PMID:27892508

  10. Lévy random walks on multiplex networks

    NASA Astrophysics Data System (ADS)

    Guo, Quantong; Cozzo, Emanuele; Zheng, Zhiming; Moreno, Yamir

    2016-11-01

    Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical processes that occur on top of them. Here, inspired by one specific model of random walks that seems to be ubiquitous across many scientific fields, the Lévy flight, we study a new navigation strategy on top of multiplex networks. Capitalizing on spectral graph and stochastic matrix theories, we derive analytical expressions for the mean first passage time and the average time to reach a node on these networks. Moreover, we also explore the efficiency of Lévy random walks, which we found to be very different as compared to the single layer scenario, accounting for the structure and dynamics inherent to the multiplex network. Finally, by comparing with some other important random walk processes defined on multiplex networks, we find that in some region of the parameters, a Lévy random walk is the most efficient strategy. Our results give us a deeper understanding of Lévy random walks and show the importance of considering the topological structure of multiplex networks when trying to find efficient navigation strategies.

  11. Random walk with random resetting to the maximum position

    NASA Astrophysics Data System (ADS)

    Majumdar, Satya N.; Sabhapandit, Sanjib; Schehr, Grégory

    2015-11-01

    We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability r , and with probability (1 -r ) , it undergoes symmetric random walk, i.e., it hops to one of its neighboring sites, with equal probability (1 -r )/2 . For r =0 , it reduces to a standard random walk whose typical distance grows as √{n } for large n . In the presence of a nonzero resetting rate 0 dynamical phase transition, characterized by a weakly singular large deviation function. We also show that r =0 is a special "critical" point, for which the growth laws are different from the r →0 case and we calculate the exact crossover functions that interpolate between the critical (r =0 ) and the off-critical (r →0 ) behavior for finite but large n .

  12. Random walks in the history of life

    PubMed Central

    Cornette, James L.; Lieberman, Bruce S.

    2004-01-01

    The simplest null hypothesis for evolutionary time series is that the observed data follow a random walk. We examined whether aspects of Sepkoski's compilation of marine generic diversity depart from a random walk by using statistical tests from econometrics. Throughout most of the Phanerozoic, the random-walk null hypothesis is not rejected for marine diversity, accumulated origination or accumulated extinction, suggesting that either these variables were correlated with environmental variables that follow a random walk or so many mechanisms were affecting these variables, in different ways, that the resultant trends appear random. The only deviation from this pattern involves rejection of the null hypothesis for roughly the last 75 million years for the diversity and accumulated origination time series. PMID:14684835

  13. Limit Theorem and Applications of the Pauli Open Quantum Random Walk on Z

    NASA Astrophysics Data System (ADS)

    Ampadu, Clement

    2013-04-01

    Following the recent talk in the ``Workshop of Quantum Dynamics and Quantum Walks'' held at Okazaki Conference Center, Okazaki, Japan. This talk clarifies the relationship between the convergent behavior of the Pauli quantum walk on the line, and the open quantum random walk obtained from the Pauli quantum walk.

  14. Quantum random walks using quantum accelerator modes

    SciTech Connect

    Ma, Z.-Y.; Burnett, K.; D'Arcy, M. B.; Gardiner, S. A.

    2006-01-15

    We discuss the use of high-order quantum accelerator modes to achieve an atom optical realization of a biased quantum random walk. We first discuss how one can create coexistent quantum accelerator modes, and hence how momentum transfer that depends on the atoms' internal state can be achieved. When combined with microwave driving of the transition between the states, a different type of atomic beam splitter results. This permits the realization of a biased quantum random walk through quantum accelerator modes.

  15. Direct measurement of the dynamics of hole hopping in extended DNA G-tracts. An unbiased random walk.

    PubMed

    Conron, Sarah M Mickley; Thazhathveetil, Arun K; Wasielewski, Michael R; Burin, Alexander L; Lewis, Frederick D

    2010-10-20

    We report the measurement of distance- and temperature-dependent rate constants for charge separation in capped hairpins in which a stilbene hole acceptor and hole donor are separated by A(3)G(n) diblock polypurine sequences consisting of 3 adenines and 1-19 guanines. The longer diblock systems obey the simplest model for an unbiased random walk, providing a direct measurement of k(hop) = 4.3 × 10(9) s(-1) for a single reversible G-to-G hole hopping step, somewhat faster than the value of 1.2 × 10(9) s(-1) calculated for A-tract hole hopping. The temperature dependence for hopping in A(3)G(13) provides values of E(act) = 2.8 kcal/mol and A = 7 × 10(9) s(-1), consistent with a weakly activated, conformationally gated process.

  16. Walking dynamics are symmetric (enough)

    PubMed Central

    Ankaralı, M. Mert; Sefati, Shahin; Madhav, Manu S.; Long, Andrew; Bastian, Amy J.; Cowan, Noah J.

    2015-01-01

    Many biological phenomena such as locomotion, circadian cycles and breathing are rhythmic in nature and can be modelled as rhythmic dynamical systems. Dynamical systems modelling often involves neglecting certain characteristics of a physical system as a modelling convenience. For example, human locomotion is frequently treated as symmetric about the sagittal plane. In this work, we test this assumption by examining human walking dynamics around the steady state (limit-cycle). Here, we adapt statistical cross-validation in order to examine whether there are statistically significant asymmetries and, even if so, test the consequences of assuming bilateral symmetry anyway. Indeed, we identify significant asymmetries in the dynamics of human walking, but nevertheless show that ignoring these asymmetries results in a more consistent and predictive model. In general, neglecting evident characteristics of a system can be more than a modelling convenience—it can produce a better model. PMID:26236826

  17. From random walks to spin glasses

    NASA Astrophysics Data System (ADS)

    Derrida, B.

    1997-02-01

    The talk was a short review on systems which exhibit non-self-averaging effects: sums of random variables when the distribution has a long tail, mean field spin glasses, random map models and returns of a random walk to the origin. Non-self-averaging effects are identical in the case of sums of random variables and in the spin glass problem as predicted by the replica approach. Also we will see that for the random map models or for the problem of the returns of a random walk to the origin, the non-self-averaging effects coincide with the results of the replica approach when the number n of replica n = - {1}/{2} or n = -1.

  18. Quantum random-walk search algorithm

    SciTech Connect

    Shenvi, Neil; Whaley, K. Birgitta; Kempe, Julia

    2003-05-01

    Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speedup over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random-walk architecture that provides such a speedup. It will be shown that this algorithm performs an oracle search on a database of N items with O({radical}(N)) calls to the oracle, yielding a speedup similar to other quantum search algorithms. It appears that the quantum random-walk formulation has considerable flexibility, presenting interesting opportunities for development of other, possibly novel quantum algorithms.

  19. 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.

  20. Sunspot random walk and 22-year variation

    NASA Astrophysics Data System (ADS)

    Love, Jeffrey J.; Rigler, E. Joshua

    2012-05-01

    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 log-normal 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.

  1. Navigation by anomalous random walks on complex networks

    NASA Astrophysics Data System (ADS)

    Weng, Tongfeng; Zhang, Jie; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan

    2016-11-01

    Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks.

  2. Navigation by anomalous random walks on complex networks

    PubMed Central

    Weng, Tongfeng; Zhang, Jie; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan

    2016-01-01

    Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks. PMID:27876855

  3. Convergence of quantum random walks with decoherence

    SciTech Connect

    Fan Shimao; Feng Zhiyong; Yang, Wei-Shih; Xiong Sheng

    2011-10-15

    In this paper, we study the discrete-time quantum random walks on a line subject to decoherence. The convergence of the rescaled position probability distribution p(x,t) depends mainly on the spectrum of the superoperator L{sub kk}. We show that if 1 is an eigenvalue of the superoperator with multiplicity one and there is no other eigenvalue whose modulus equals 1, then P(({nu}/{radical}(t)),t) converges to a convex combination of normal distributions. In terms of position space, the rescaled probability mass function p{sub t}(x,t){identical_to}p({radical}(t)x,t), x is an element of Z/{radical}(t), converges in distribution to a continuous convex combination of normal distributions. We give a necessary and sufficient condition for a U(2) decoherent quantum walk that satisfies the eigenvalue conditions. We also give a complete description of the behavior of quantum walks whose eigenvalues do not satisfy these assumptions. Specific examples such as the Hadamard walk and walks under real and complex rotations are illustrated. For the O(2) quantum random walks, an explicit formula is provided for the scaling limit of p(x,t) and their moments. We also obtain exact critical exponents for their moments at the critical point and show universality classes with respect to these critical exponents.

  4. Quantum Random Walks with General Particle States

    NASA Astrophysics Data System (ADS)

    Belton, Alexander C. R.

    2014-06-01

    A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This unifies and extends previous work on repeated-interactions models, including that of Attal and Pautrat (Ann Henri Poincaré 7:59-104 2006) and Belton (J Lond Math Soc 81:412-434, 2010; Commun Math Phys 300:317-329, 2010). When the random-walk generator acts by ampliation and either multiplication or conjugation by a unitary operator, it is shown that the quantum stochastic cocycle which arises in the limit is driven by a unitary process.

  5. Random Walk Weakly Attracted to a Wall

    NASA Astrophysics Data System (ADS)

    de Coninck, Joël; Dunlop, François; Huillet, Thierry

    2008-10-01

    We consider a random walk X n in ℤ+, starting at X 0= x≥0, with transition probabilities {P}(X_{n+1}=Xn±1|Xn=yge1)={1over2}mp{δover4y+2δ} and X n+1=1 whenever X n =0. We prove {E}Xn˜const. n^{1-{δ over2}} as n ↗∞ when δ∈(1,2). The proof is based upon the Karlin-McGregor spectral representation, which is made explicit for this random walk.

  6. Quantum walk coherences on a dynamical percolation graph.

    PubMed

    Elster, Fabian; Barkhofen, Sonja; Nitsche, Thomas; Novotný, Jaroslav; Gábris, Aurél; Jex, Igor; Silberhorn, Christine

    2015-08-27

    Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In particular, quantum walks on percolation structures constitute an attractive platform for studying open system dynamics of random media. Here, we present an implementation of quantum walks differing from the previous experiments by achieving dynamical control of the underlying graph structure. We demonstrate the evolution of an optical time-multiplexed quantum walk over six double steps, revealing the intricate interplay between the internal and external degrees of freedom. The observation of clear non-Markovian signatures in the coin space testifies the high coherence of the implementation and the extraordinary degree of control of all system parameters. Our work is the proof-of-principle experiment of a quantum walk on a dynamical percolation graph, paving the way towards complex simulation of quantum transport in random media.

  7. Mean first return time for random walks on weighted networks

    NASA Astrophysics Data System (ADS)

    Jing, Xing-Li; Ling, Xiang; Long, Jiancheng; Shi, Qing; Hu, Mao-Bin

    2015-11-01

    Random walks on complex networks are of great importance to understand various types of phenomena in real world. In this paper, two types of biased random walks on nonassortative weighted networks are studied: edge-weight-based random walks and node-strength-based random walks, both of which are extended from the normal random walk model. Exact expressions for stationary distribution and mean first return time (MFRT) are derived and examined by simulation. The results will be helpful for understanding the influences of weights on the behavior of random walks.

  8. 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.

  9. A Random Walk on a Circular Path

    ERIC Educational Resources Information Center

    Ching, W.-K.; Lee, M. S.

    2005-01-01

    This short note introduces an interesting random walk on a circular path with cards of numbers. By using high school probability theory, it is proved that under some assumptions on the number of cards, the probability that a walker will return to a fixed position will tend to one as the length of the circular path tends to infinity.

  10. A Random Walk on a Circular Path

    ERIC Educational Resources Information Center

    Ching, W.-K.; Lee, M. S.

    2005-01-01

    This short note introduces an interesting random walk on a circular path with cards of numbers. By using high school probability theory, it is proved that under some assumptions on the number of cards, the probability that a walker will return to a fixed position will tend to one as the length of the circular path tends to infinity.

  11. 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.

  12. Charged particle dynamics in multiple colliding electromagnetic waves. Survey of random walk, Lévy flights, limit circles, attractors and structurally determinate patterns

    DOE PAGES

    Bulanov, S. V.; Esirkepov, T. Zh.; Koga, J. K.; ...

    2017-03-09

    The multiple colliding laser pulse concept formulated by Bulanovet al.(Phys. Rev. Lett., vol. 104, 2010b, 220404) is beneficial for achieving an extremely high amplitude of coherent electromagnetic field. Since the topology of electric and magnetic fields of multiple colliding laser pulses oscillating in time is far from trivial and the radiation friction effects are significant in the high field limit, the dynamics of charged particles interacting with the multiple colliding laser pulses demonstrates remarkable features corresponding to random walk trajectories, limit circles, attractors, regular patterns and Lévy flights. Lastly, under extremely high intensity conditions the nonlinear dissipation mechanism stabilizes the particle motionmore » resulting in the charged particle trajectory being located within narrow regions and in the occurrence of a new class of regular patterns made by the particle ensembles.« less

  13. Random walks in directed modular networks

    NASA Astrophysics Data System (ADS)

    Comin, Cesar H.; Viana, Mateus P.; Antiqueira, Lucas; Costa, Luciano da F.

    2014-12-01

    Because diffusion typically involves symmetric interactions, scant attention has been focused on studying asymmetric cases. However, important networked systems underlain by diffusion (e.g. cortical networks and WWW) are inherently directed. In the case of undirected diffusion, it can be shown that the steady-state probability of the random walk dynamics is fully correlated with the degree, which no longer holds for directed networks. We investigate the relationship between such probability and the inward node degree, which we call efficiency, in modular networks. Our findings show that the efficiency of a given community depends mostly on the balance between its ingoing and outgoing connections. In addition, we derive analytical expressions to show that the internal degree of the nodes does not play a crucial role in their efficiency, when considering the Erdős-Rényi and Barabási-Albert models. The results are illustrated with respect to the macaque cortical network, providing subsidies for improving transportation and communication systems.

  14. Applications of random walks: From network exploration to cellulose hydrolysis

    NASA Astrophysics Data System (ADS)

    Asztalos, Andrea

    In the first part of the thesis we investigate network exploration by random walks defined via stationary and adaptive transition probabilities on large, but finite graphs. An exact formula for the number of visited nodes and edges as function of time is presented, that is valid for arbitrary graphs and arbitrary walks defined by stationary transition probabilities (STP). We show that for STP walks site and edge exploration obey the same scaling ˜ nnu as function of time n, and therefore edge exploration on graphs with many loops is always lagging compared to site exploration. We then introduce the Edge Explorer Model, presenting a novel class of adaptive walks, that performs faithful network discovery even on dense networks. In the second part of the thesis we present a random walk-based computational model of enzymatic degradation of cellulose. The coarse-grained dynamical model accounts for the mobility and action of a single enzyme as well as for the synergy of multiple enzymes on a homogeneous cellulose surface. The quantitative description of cellulose degradation is calculated on a spatial model by including free and bound states of all enzymes with explicit reactive surface terms (e.g., hydrogen bond reformation) and corresponding reaction rates. The dynamical evolution of the system is based on physical interactions between enzymes and cellulose. We show how the model provides insight into enzyme loading and coverage for the degradation process.

  15. Random walk centrality in interconnected multilayer networks

    NASA Astrophysics Data System (ADS)

    Solé-Ribalta, Albert; De Domenico, Manlio; Gómez, Sergio; Arenas, Alex

    2016-06-01

    Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in many fields, from economics to biology and from urban planning to social sciences, to identify the most (or the less) influent nodes in a network using centrality measures. However, defining the centrality of actors in interconnected complex networks is not trivial. In this paper, we rely on the tensorial formalism recently proposed to characterize and investigate this kind of complex topologies, and extend two well known random walk centrality measures, the random walk betweenness and closeness centrality, to interconnected multilayer networks. For each of the measures we provide analytical expressions that completely agree with numerically results.

  16. An invariance property of diffusive random walks

    NASA Astrophysics Data System (ADS)

    Blanco, S.; Fournier, R.

    2003-01-01

    Starting from a simple animal-biology example, a general, somewhat counter-intuitive property of diffusion random walks is presented. It is shown that for any (non-homogeneous) purely diffusing system, under any isotropic uniform incidence, the average length of trajectories through the system (the average length of the random walk trajectories from entry point to first exit point) is independent of the characteristics of the diffusion process and therefore depends only on the geometry of the system. This exact invariance property may be seen as a generalization to diffusion of the well-known mean-chord-length property (Case K. M. and Zweifel P. F., Linear Transport Theory (Addison-Wesley) 1967), leading to broad physics and biology applications.

  17. Simulation of pedigree genotypes by random walks.

    PubMed Central

    Lange, K; Matthysse, S

    1989-01-01

    A random walk method, based on the Metropolis algorithm, is developed for simulating the distribution of trait and linkage marker genotypes in pedigrees where trait phenotypes are already known. The method complements techniques suggested by Ploughman and Boehnke and by Ott that are based on sequential sampling of genotypes within a pedigree. These methods are useful for estimating the power of linkage analysis before complete study of a pedigree is undertaken. We apply the random walk technique to a partially penetrant disease, schizophrenia, and to a recessive disease, ataxia-telangiectasia. In the first case we show that accessory phenotypes with higher penetrance than that of schizophrenia itself may be crucial for effective linkage analysis, and in the second case we show that impressionistic selection of informative pedigrees may be misleading. PMID:2589323

  18. 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.

  19. Relaxed random walk model coupled with ecological niche modeling unravel the dispersal dynamics of a Neotropical savanna tree species in the deeper Quaternary.

    PubMed

    Collevatti, Rosane G; Terribile, Levi C; Rabelo, Suelen G; Lima-Ribeiro, Matheus S

    2015-01-01

    Understanding the dispersal routes of Neotropical savanna tree species is an essential step to unravel the effects of past climate change on genetic patterns, species distribution and population demography. Here we reconstruct the demographic history and dispersal dynamics of the Neotropical savanna tree species Tabebuia aurea to understand the effects of Quaternary climate change on its current spatial patterns of genetic diversity. We sampled 285 individuals from 21 populations throughout Brazilian savannas and sequenced all individuals for three chloroplast intergenic spacers and ITS nrDNA. We analyzed data using a multi-model inference framework by coupling the relaxed random walk model (RRW), ecological niche modeling (ENM) and statistical phylogeography. The most recent common ancestor of T. aurea lineages dated from ~4.0 ± 2.5 Ma. T. aurea lineages cyclically dispersed from the West toward the Central-West Brazil, and from the Southeast toward the East and Northeast Brazil, following the paleodistribution dynamics shown by the ENMs through the last glacial cycle. A historical refugium through time may have allowed dispersal of lineages among populations of Central Brazil, overlapping with population expansion during interglacial periods and the diversification of new lineages. Range and population expansion through the Quaternary were, respectively, the most frequent prediction from ENMs and the most likely demographic scenario from coalescent simulations. Consistent phylogeographic patterns among multiple modeling inferences indicate a promising approach, allowing us to understand how cyclical climate changes through the Quaternary drove complex population dynamics and the current patterns of species distribution and genetic diversity.

  20. An Analysis of Random-Walk Cuckoo Hashing

    NASA Astrophysics Data System (ADS)

    Frieze, Alan; Melsted, Páll; Mitzenmacher, Michael

    In this paper, we provide a polylogarithmic bound that holds with high probability on the insertion time for cuckoo hashing under the random-walk insertion method. Cuckoo hashing provides a useful methodology for building practical, high-performance hash tables. The essential idea of cuckoo hashing is to combine the power of schemes that allow multiple hash locations for an item with the power to dynamically change the location of an item among its possible locations. Previous work on the case where the number of choices is larger than two has required a breadth-first search analysis, which is both inefficient in practice and currently has only a polynomial high probability upper bound on the insertion time. Here we significantly advance the state of the art by proving a polylogarithmic bound on the more efficient random-walk method, where items repeatedly kick out random blocking items until a free location for an item is found.

  1. Correlated continuous time random walk with time averaged waiting time

    NASA Astrophysics Data System (ADS)

    Lv, Longjin; Ren, Fu-Yao; Wang, Jun; Xiao, Jianbin

    2015-03-01

    In this paper, we study the dynamics of a correlated continuous time random walk with time averaged waiting time. The mean square displacement (MSD) shows this process is subdiffusive and generalized Einstein relation holds. We also get the asymptotic behavior of the probability density function (PDF) of this process is stretched Gaussian. At last, by computing the time averaged MSD, we find ergodicity breaking occurs in this process.

  2. Fragment formation in biased random walks

    NASA Astrophysics Data System (ADS)

    Ramola, Kabir

    2008-10-01

    We analyse a biased random walk on a 1D lattice with unequal step lengths. Such a walk was recently shown to undergo a phase transition from a state containing a single connected cluster of visited sites to one with several clusters of visited sites (fragments) separated by unvisited sites at a critical probability pc (Anteneodo and Morgado 2007 Phys. Rev. Lett. 99 180602). The behaviour of ρ(l), the probability of formation of fragments of length l, is analysed. An exact expression for the generating function of ρ(l) at the critical point is derived. We prove that the asymptotic behaviour is of the form \\rho (l) \\simeq 3/[l(\\log \\ l)^2] .

  3. 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.

  4. Effects of various types of molecular dynamics on 1D and 2D (2)H NMR studied by random walk simulations

    PubMed

    Vogel; Rossler

    2000-11-01

    By carrying out random walk simulations we systematically study the effects of various types of complex molecular dynamics on (2)H NMR experiments in solids. More precisely, we calculate one-dimensional (1D) (2)H NMR spectra and the results of two dimensional (2D) (2)H NMR experiments in time domain, taking into account isotropic as well as highly restricted motions which involve rotational jumps about different finite angles. Although the dynamical models are chosen to mimic the primary and secondary relaxation in supercooled liquids and glasses, we do not intend to describe experimental results quantitatively but rather to show general effects appearing for complex reorientations. We carefully investigate whether 2D (2)H NMR in time domain, which was originally designed to measure correlation times of ultraslow motions (tau >/= 1 ms), can be used to obtain shorter tau, too. It is demonstrated that an extension of the time window to tau >/= 10 &mgr;s is possible when dealing with exponential relaxation, but that it will fail if there is a distribution of correlation times G(lgtau). Vice versa, we show that 1D (2)H NMR spectra, usually recorded to look at dynamics with tau in the microsecond regime, are also applicable for studying ultraslow motions provided that the loss of correlation is achieved step by step. Therefore, it is useful to carry out 1D and 2D NMR experiments simultaneously in order to reveal the mechanism of complex molecular motions. In addition, we demonstrate that highly restricted dynamics can be clearly observed in 1D spectra and in 2D NMR in time domain if long solid-echo delays and large evolution times are applied, respectively. Finally, unexpected observations are described which appear in the latter experiment when considering very broad distributions G(lgtau). Because of these effects, time scale and geometry of a considered motion cannot be extracted from a straightforward analysis of experimental results. Copyright 2000 Academic Press.

  5. Scalable networks for discrete quantum random walks

    SciTech Connect

    Fujiwara, S.; Osaki, H.; Buluta, I.M.; Hasegawa, S.

    2005-09-15

    Recently, quantum random walks (QRWs) have been thoroughly studied in order to develop new quantum algorithms. In this paper we propose scalable quantum networks for discrete QRWs on circles, lines, and also in higher dimensions. In our method the information about the position of the walker is stored in a quantum register and the network consists of only one-qubit rotation and (controlled){sup n}-NOT gates, therefore it is purely computational and independent of the physical implementation. As an example, we describe the experimental realization in an ion-trap system.

  6. 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.

  7. 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.

  8. Molecular motors: thermodynamics and the random walk.

    PubMed Central

    Thomas, N.; Imafuku, Y.; Tawada, K.

    2001-01-01

    The biochemical cycle of a molecular motor provides the essential link between its thermodynamics and kinetics. The thermodynamics of the cycle determine the motor's ability to perform mechanical work, whilst the kinetics of the cycle govern its stochastic behaviour. We concentrate here on tightly coupled, processive molecular motors, such as kinesin and myosin V, which hydrolyse one molecule of ATP per forward step. Thermodynamics require that, when such a motor pulls against a constant load f, the ratio of the forward and backward products of the rate constants for its cycle is exp [-(DeltaG + u(0)f)/kT], where -DeltaG is the free energy available from ATP hydrolysis and u(0) is the motor's step size. A hypothetical one-state motor can therefore act as a chemically driven ratchet executing a biased random walk. Treating this random walk as a diffusion problem, we calculate the forward velocity v and the diffusion coefficient D and we find that its randomness parameter r is determined solely by thermodynamics. However, real molecular motors pass through several states at each attachment site. They satisfy a modified diffusion equation that follows directly from the rate equations for the biochemical cycle and their effective diffusion coefficient is reduced to D-v(2)tau, where tau is the time-constant for the motor to reach the steady state. Hence, the randomness of multistate motors is reduced compared with the one-state case and can be used for determining tau. Our analysis therefore demonstrates the intimate relationship between the biochemical cycle, the force-velocity relation and the random motion of molecular motors. PMID:11600075

  9. Relaxed random walk model coupled with ecological niche modeling unravel the dispersal dynamics of a Neotropical savanna tree species in the deeper Quaternary

    PubMed Central

    Collevatti, Rosane G.; Terribile, Levi C.; Rabelo, Suelen G.; Lima-Ribeiro, Matheus S.

    2015-01-01

    Understanding the dispersal routes of Neotropical savanna tree species is an essential step to unravel the effects of past climate change on genetic patterns, species distribution and population demography. Here we reconstruct the demographic history and dispersal dynamics of the Neotropical savanna tree species Tabebuia aurea to understand the effects of Quaternary climate change on its current spatial patterns of genetic diversity. We sampled 285 individuals from 21 populations throughout Brazilian savannas and sequenced all individuals for three chloroplast intergenic spacers and ITS nrDNA. We analyzed data using a multi-model inference framework by coupling the relaxed random walk model (RRW), ecological niche modeling (ENM) and statistical phylogeography. The most recent common ancestor of T. aurea lineages dated from ~4.0 ± 2.5 Ma. T. aurea lineages cyclically dispersed from the West toward the Central-West Brazil, and from the Southeast toward the East and Northeast Brazil, following the paleodistribution dynamics shown by the ENMs through the last glacial cycle. A historical refugium through time may have allowed dispersal of lineages among populations of Central Brazil, overlapping with population expansion during interglacial periods and the diversification of new lineages. Range and population expansion through the Quaternary were, respectively, the most frequent prediction from ENMs and the most likely demographic scenario from coalescent simulations. Consistent phylogeographic patterns among multiple modeling inferences indicate a promising approach, allowing us to understand how cyclical climate changes through the Quaternary drove complex population dynamics and the current patterns of species distribution and genetic diversity. PMID:26379681

  10. Random walk with chaotically driven bias

    NASA Astrophysics Data System (ADS)

    Kim, Song-Ju; Naruse, Makoto; Aono, Masashi; Hori, Hirokazu; Akimoto, Takuma

    2016-12-01

    We investigate two types of random walks with a fluctuating probability (bias) in which the random walker jumps to the right. One is a ‘time-quenched framework’ using bias time series such as periodic, quasi-periodic, and chaotic time series (chaotically driven bias). The other is a ‘time-annealed framework’ using the fluctuating bias generated by a stochastic process, which is not quenched in time. We show that the diffusive properties in the time-quenched framework can be characterised by the ensemble average of the time-averaged variance (ETVAR), whereas the ensemble average of the time-averaged mean square displacement (ETMSD) fails to capture the diffusion, even when the total bias is zero. We demonstrate that the ETVAR increases linearly with time, and the diffusion coefficient can be estimated by the time average of the local diffusion coefficient. In the time-annealed framework, we analytically and numerically show normal diffusion and superdiffusion, similar to the Lévy walk. Our findings will lead to new developments in information and communication technologies, such as efficient energy transfer for information propagation and quick solution searching.

  11. Random walk with chaotically driven bias.

    PubMed

    Kim, Song-Ju; Naruse, Makoto; Aono, Masashi; Hori, Hirokazu; Akimoto, Takuma

    2016-12-08

    We investigate two types of random walks with a fluctuating probability (bias) in which the random walker jumps to the right. One is a 'time-quenched framework' using bias time series such as periodic, quasi-periodic, and chaotic time series (chaotically driven bias). The other is a 'time-annealed framework' using the fluctuating bias generated by a stochastic process, which is not quenched in time. We show that the diffusive properties in the time-quenched framework can be characterised by the ensemble average of the time-averaged variance (ETVAR), whereas the ensemble average of the time-averaged mean square displacement (ETMSD) fails to capture the diffusion, even when the total bias is zero. We demonstrate that the ETVAR increases linearly with time, and the diffusion coefficient can be estimated by the time average of the local diffusion coefficient. In the time-annealed framework, we analytically and numerically show normal diffusion and superdiffusion, similar to the Lévy walk. Our findings will lead to new developments in information and communication technologies, such as efficient energy transfer for information propagation and quick solution searching.

  12. Random walk with chaotically driven bias

    PubMed Central

    Kim, Song-Ju; Naruse, Makoto; Aono, Masashi; Hori, Hirokazu; Akimoto, Takuma

    2016-01-01

    We investigate two types of random walks with a fluctuating probability (bias) in which the random walker jumps to the right. One is a ‘time-quenched framework’ using bias time series such as periodic, quasi-periodic, and chaotic time series (chaotically driven bias). The other is a ‘time-annealed framework’ using the fluctuating bias generated by a stochastic process, which is not quenched in time. We show that the diffusive properties in the time-quenched framework can be characterised by the ensemble average of the time-averaged variance (ETVAR), whereas the ensemble average of the time-averaged mean square displacement (ETMSD) fails to capture the diffusion, even when the total bias is zero. We demonstrate that the ETVAR increases linearly with time, and the diffusion coefficient can be estimated by the time average of the local diffusion coefficient. In the time-annealed framework, we analytically and numerically show normal diffusion and superdiffusion, similar to the Lévy walk. Our findings will lead to new developments in information and communication technologies, such as efficient energy transfer for information propagation and quick solution searching. PMID:27929091

  13. Excursion set theory for correlated random walks

    NASA Astrophysics Data System (ADS)

    Farahi, Arya; Benson, Andrew J.

    2013-08-01

    We present a new method to compute the first crossing distribution in excursion set theory for the case of correlated random walks. We use a combination of the path integral formalism of Maggiore & Riotto, and the integral equation solution of Zhang & Hui and Benson et al. to find a numerically and convenient algorithm to derive the first crossing distribution. We apply this methodology to the specific case of a Gaussian random density field filtered with a Gaussian smoothing function. By comparing our solutions to results from Monte Carlo calculations of the first crossing distribution we demonstrate that approximately it is in good agreement with exact solution for certain barriers, and at large masses. Our approach is quite general, and can be adapted to other smoothing functions and barrier function and also to non-Gaussian density fields.

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

    PubMed

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

    2017-06-21

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

  15. 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…

  16. 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…

  17. The random walk of a low-Reynolds-number swimmer

    NASA Astrophysics Data System (ADS)

    Rafaï, Salima; Garcia, Michaël; Berti, Stefano; Peyla, Philippe

    2010-11-01

    Swimming at a micrometer scale demands particular strategies. Indeed when inertia is negligible as compared to viscous forces (i.e. Reynolds number Re is lower than unity), hydrodynamics equations are reversible in time. To achieve propulsion a low Reynolds number, swimmers must then deform in a way that is not invariant under time reversal. Here we investigate the dispersal properties of self propelled organisms by means of microscopy and cell tracking. Our system of interest is the microalga Chlamydomonas Reinhardtii, a motile single celled green alga about 10 micrometers in diameter that swims with two flagellae. In the case of dilute suspensions, we show that tracked trajectories are well modelled by a correlated random walk. This process is based on short time correlations in the direction of movement called persistence. At longer times, correlations are lost and a standard random walk caracterizes the trajectories. Moreover, high speed imaging enables us to show how speed fluctuations at very short times affect the statistical description of the dynamics. Finally we show how drag forces modify the characteristics of this particular random walk.

  18. Emergence of randomness and arrow of time in quantum walks

    SciTech Connect

    Shikano, Yutaka; Chisaki, Kota; Konno, Norio; Segawa, Etsuo

    2010-06-15

    Quantum walks are powerful tools not only for constructing the quantum speedup algorithms but also for describing specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various setups. We apply the concept of the quantum walk to the problems in quantum foundations. We show that randomness and the arrow of time in the quantum walk gradually emerge by periodic projective measurements from the mathematically obtained limit distribution under the time-scale transformation.

  19. Random walk with priorities in communicationlike networks

    NASA Astrophysics Data System (ADS)

    Bastas, Nikolaos; Maragakis, Michalis; Argyrakis, Panos; ben-Avraham, Daniel; Havlin, Shlomo; Carmi, Shai

    2013-08-01

    We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.77.020103 77, 020103(R) (2008)]; here we provide additional results. We solve analytically the diffusion coefficients of the two species in lattices for a number of protocols. In networks, we find that the probability of a B particle to be free decreases exponentially with the node degree. In scale-free networks, this leads to localization of the B's at the hubs and arrest of their motion. To remedy this, we investigate several strategies to avoid trapping of the B's, including moving an A instead of the hindered B, allowing a trapped B to hop with a small probability, biased walk toward non-hub nodes, and limiting the capacity of nodes. We obtain analytic results for lattices and networks, and we discuss the advantages and shortcomings of the possible strategies.

  20. Background Extraction Using Random Walk Image Fusion.

    PubMed

    Hua, Kai-Lung; Wang, Hong-Cyuan; Yeh, Chih-Hsiang; Cheng, Wen-Huang; Lai, Yu-Chi

    2016-12-23

    It is important to extract a clear background for computer vision and augmented reality. Generally, background extraction assumes the existence of a clean background shot through the input sequence, but realistically, situations may violate this assumption such as highway traffic videos. Therefore, our probabilistic model-based method formulates fusion of candidate background patches of the input sequence as a random walk problem and seeks a globally optimal solution based on their temporal and spatial relationship. Furthermore, we also design two quality measures to consider spatial and temporal coherence and contrast distinctness among pixels as background selection basis. A static background should have high temporal coherence among frames, and thus, we improve our fusion precision with a temporal contrast filter and an optical-flow-based motionless patch extractor. Experiments demonstrate that our algorithm can successfully extract artifact-free background images with low computational cost while comparing to state-of-the-art algorithms.

  1. Lazy random walks for superpixel segmentation.

    PubMed

    Shen, Jianbing; Du, Yunfan; Wang, Wenguan; Li, Xuelong

    2014-04-01

    We present a novel image superpixel segmentation approach using the proposed lazy random walk (LRW) algorithm in this paper. Our method begins with initializing the seed positions and runs the LRW algorithm on the input image to obtain the probabilities of each pixel. Then, the boundaries of initial superpixels are obtained according to the probabilities and the commute time. The initial superpixels are iteratively optimized by the new energy function, which is defined on the commute time and the texture measurement. Our LRW algorithm with self-loops has the merits of segmenting the weak boundaries and complicated texture regions very well by the new global probability maps and the commute time strategy. The performance of superpixel is improved by relocating the center positions of superpixels and dividing the large superpixels into small ones with the proposed optimization algorithm. The experimental results have demonstrated that our method achieves better performance than previous superpixel approaches.

  2. Discriminative parameter estimation for random walks segmentation.

    PubMed

    Baudin, Pierre-Yves; Goodman, Danny; Kumrnar, Puneet; Azzabou, Noura; Carlier, Pierre G; Paragios, Nikos; Kumar, M Pawan

    2013-01-01

    The Random Walks (RW) algorithm is one of the most efficient and easy-to-use probabilistic segmentation methods. By combining contrast terms with prior terms, it provides accurate segmentations of medical images in a fully automated manner. However, one of the main drawbacks of using the RW algorithm is that its parameters have to be hand-tuned. we propose a novel discriminative learning framework that estimates the parameters using a training dataset. The main challenge we face is that the training samples are not fully supervised. Specifically, they provide a hard segmentation of the images, instead of a probabilistic segmentation. We overcome this challenge by treating the optimal probabilistic segmentation that is compatible with the given hard segmentation as a latent variable. This allows us to employ the latent support vector machine formulation for parameter estimation. We show that our approach significantly outperforms the baseline methods on a challenging dataset consisting of real clinical 3D MRI volumes of skeletal muscles.

  3. Homogeneous Superpixels from Markov Random Walks

    NASA Astrophysics Data System (ADS)

    Perbet, Frank; Stenger, Björn; Maki, Atsuto

    This paper presents a novel algorithm to generate homogeneous superpixels from Markov random walks. We exploit Markov clustering (MCL) as the methodology, a generic graph clustering method based on stochastic flow circulation. In particular, we introduce a graph pruning strategy called compact pruning in order to capture intrinsic local image structure. The resulting superpixels are homogeneous, i.e. uniform in size and compact in shape. The original MCL algorithm does not scale well to a graph of an image due to the square computation of the Markov matrix which is necessary for circulating the flow. The proposed pruning scheme has the advantages of faster computation, smaller memory footprint, and straightforward parallel implementation. Through comparisons with other recent techniques, we show that the proposed algorithm achieves state-of-the-art performance.

  4. Essential energy space random walks to accelerate molecular dynamics simulations: Convergence improvements via an adaptive-length self-healing strategy

    NASA Astrophysics Data System (ADS)

    Zheng, Lianqing; Yang, Wei

    2008-07-01

    Recently, accelerated molecular dynamics (AMD) technique was generalized to realize essential energy space random walks so that further sampling enhancement and effective localized enhanced sampling could be achieved. This method is especially meaningful when essential coordinates of the target events are not priori known; moreover, the energy space metadynamics method was also introduced so that biasing free energy functions can be robustly generated. Despite the promising features of this method, due to the nonequilibrium nature of the metadynamics recursion, it is challenging to rigorously use the data obtained at the recursion stage to perform equilibrium analysis, such as free energy surface mapping; therefore, a large amount of data ought to be wasted. To resolve such problem so as to further improve simulation convergence, as promised in our original paper, we are reporting an alternate approach: the adaptive-length self-healing (ALSH) strategy for AMD simulations; this development is based on a recent self-healing umbrella sampling method. Here, the unit simulation length for each self-healing recursion is increasingly updated based on the Wang-Landau flattening judgment. When the unit simulation length for each update is long enough, all the following unit simulations naturally run into the equilibrium regime. Thereafter, these unit simulations can serve for the dual purposes of recursion and equilibrium analysis. As demonstrated in our model studies, by applying ALSH, both fast recursion and short nonequilibrium data waste can be compromised. As a result, combining all the data obtained from all the unit simulations that are in the equilibrium regime via the weighted histogram analysis method, efficient convergence can be robustly ensured, especially for the purpose of free energy surface mapping.

  5. FRACTAL DIMENSION RESULTS FOR CONTINUOUS TIME RANDOM WALKS

    PubMed Central

    Meerschaert, Mark M.; Nane, Erkan; Xiao, Yimin

    2013-01-01

    Continuous time random walks impose random waiting times between particle jumps. This paper computes the fractal dimensions of their process limits, which represent particle traces in anomalous diffusion. PMID:23482421

  6. Tests of the random walk hypothesis for financial data

    NASA Astrophysics Data System (ADS)

    Nakamura, Tomomichi; Small, Michael

    2007-04-01

    We propose a method from the viewpoint of deterministic dynamical systems to investigate whether observed data follow a random walk (RW) and apply the method to several financial data. Our method is based on the previously proposed small-shuffle surrogate method. Hence, our method does not depend on the specific data distribution, although previously proposed methods depend on properties of the data distribution. The data we use are stock market (Standard & Poor's 500 in US market and Nikkei225 in Japanese market), exchange rate (British Pound/US dollar and Japanese Yen/US dollar), and commodity market (gold price and crude oil price). We found that these financial data are RW whose first differences are independently distributed random variables or time-varying random variables.

  7. Quantum walk coherences on a dynamical percolation graph

    PubMed Central

    Elster, Fabian; Barkhofen, Sonja; Nitsche, Thomas; Novotný, Jaroslav; Gábris, Aurél; Jex, Igor; Silberhorn, Christine

    2015-01-01

    Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In particular, quantum walks on percolation structures constitute an attractive platform for studying open system dynamics of random media. Here, we present an implementation of quantum walks differing from the previous experiments by achieving dynamical control of the underlying graph structure. We demonstrate the evolution of an optical time-multiplexed quantum walk over six double steps, revealing the intricate interplay between the internal and external degrees of freedom. The observation of clear non-Markovian signatures in the coin space testifies the high coherence of the implementation and the extraordinary degree of control of all system parameters. Our work is the proof-of-principle experiment of a quantum walk on a dynamical percolation graph, paving the way towards complex simulation of quantum transport in random media. PMID:26311434

  8. Random walks on activity-driven networks with attractiveness

    NASA Astrophysics Data System (ADS)

    Alessandretti, Laura; Sun, Kaiyuan; Baronchelli, Andrea; Perra, Nicola

    2017-05-01

    Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously distributed. Here, we present a time-varying network model where each node and the dynamical formation of ties are characterized by these two features. We study how these properties affect random-walk processes unfolding on the network when the time scales describing the process and the network evolution are comparable. We derive analytical solutions for the stationary state and the mean first-passage time of the process, and we study cases informed by empirical observations of social networks. Our work shows that previously disregarded properties of real social systems, such as heterogeneous distributions of activity and attractiveness as well as the correlations between them, substantially affect the dynamical process unfolding on the network.

  9. Phenomenological picture of fluctuations in branching random walks.

    PubMed

    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/sqrt[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.

  10. 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.

  11. Zero Range Process and Multi-Dimensional Random Walks

    NASA Astrophysics Data System (ADS)

    Bogoliubov, Nicolay M.; Malyshev, Cyril

    2017-07-01

    The special limit of the totally asymmetric zero range process of the low-dimensional non-equilibrium statistical mechanics described by the non-Hermitian Hamiltonian is considered. The calculation of the conditional probabilities of the model are based on the algebraic Bethe ansatz approach. We demonstrate that the conditional probabilities may be considered as the generating functions of the random multi-dimensional lattice walks bounded by a hyperplane. This type of walks we call the walks over the multi-dimensional simplicial lattices. The answers for the conditional probability and for the number of random walks in the multi-dimensional simplicial lattice are expressed through the symmetric functions.

  12. Effects of reciprocity on random walks in weighted networks.

    PubMed

    Zhang, Zhongzhi; Li, Huan; Sheng, Yibin

    2014-12-12

    It has been recently reported that the reciprocity of real-life weighted networks is very pronounced, however its impact on dynamical processes is poorly understood. In this paper, we study random walks in a scale-free directed weighted network with a trap at the central hub node, where the weight of each directed edge is dominated by a parameter controlling the extent of network reciprocity. We derive two expressions for the mean first passage time (MFPT) to the trap, by using two different techniques, the results of which agree well with each other. We also analytically determine all the eigenvalues as well as their multiplicities for the fundamental matrix of the dynamical process, and show that the largest eigenvalue has an identical dominant scaling as that of the MFPT.We find that the weight parameter has a substantial effect on the MFPT, which behaves as a power-law function of the system size with the power exponent dependent on the parameter, signaling the crucial role of reciprocity in random walks occurring in weighted networks.

  13. Effects of reciprocity on random walks in weighted networks

    PubMed Central

    Zhang, Zhongzhi; Li, Huan; Sheng, Yibin

    2014-01-01

    It has been recently reported that the reciprocity of real-life weighted networks is very pronounced, however its impact on dynamical processes is poorly understood. In this paper, we study random walks in a scale-free directed weighted network with a trap at the central hub node, where the weight of each directed edge is dominated by a parameter controlling the extent of network reciprocity. We derive two expressions for the mean first passage time (MFPT) to the trap, by using two different techniques, the results of which agree well with each other. We also analytically determine all the eigenvalues as well as their multiplicities for the fundamental matrix of the dynamical process, and show that the largest eigenvalue has an identical dominant scaling as that of the MFPT.We find that the weight parameter has a substantial effect on the MFPT, which behaves as a power-law function of the system size with the power exponent dependent on the parameter, signaling the crucial role of reciprocity in random walks occurring in weighted networks. PMID:25500907

  14. Random walks on real metro systems

    NASA Astrophysics Data System (ADS)

    Zhu, Yueying; Zhao, Longfeng; Li, Wei; Wang, Qiuping A.; Cai, Xu

    2016-04-01

    In this paper, we investigate the random walks on metro systems in 28 cities from worldwide via the Laplacian spectrum to realize the trapping process on real systems. The average trapping time is a primary description to response the trapping process. Firstly, we calculate the mean trapping time to each target station and to each entire system, respectively. Moreover, we also compare the average trapping time with the strength (the weighted degree) and average shortest path length for each station, separately. It is noted that the average trapping time has a close inverse relation with the station’s strength but rough positive correlation with the average shortest path length. And we also catch the information that the mean trapping time to each metro system approximately positively correlates with the system’s size. Finally, the trapping process on weighted and unweighted metro systems is compared to each other for better understanding the influence of weights on trapping process on metro networks. Numerical results show that the weights have no significant impact on the trapping performance on metro networks.

  15. ISWI remodels nucleosomes through a random walk.

    PubMed

    Al-Ani, Gada; Malik, Shuja Shafi; Eastlund, Allen; Briggs, Koan; Fischer, Christopher J

    2014-07-15

    The chromatin remodeler ISWI is capable of repositioning clusters of nucleosomes to create well-ordered arrays or moving single nucleosomes from the center of DNA fragments toward the ends without disrupting their integrity. Using standard electrophoresis assays, we have monitored the ISWI-catalyzed repositioning of different nucleosome samples each containing a different length of DNA symmetrically flanking the initially centrally positioned histone octamer. We find that ISWI moves the histone octamer between distinct and thermodynamically stable positions on the DNA according to a random walk mechanism. Through the application of a spectrophotometric assay for nucleosome repositioning, we further characterized the repositioning activity of ISWI using short nucleosome substrates and were able to determine the macroscopic rate of nucleosome repositioning by ISWI. Additionally, quantitative analysis of repositioning experiments performed at various ISWI concentrations revealed that a monomeric ISWI is sufficient to obtain the observed repositioning activity as the presence of a second ISWI bound had no effect on the rate of nucleosome repositioning. We also found that ATP hydrolysis is poorly coupled to nucleosome repositioning, suggesting that DNA translocation by ISWI is not energetically rate-limiting for the repositioning reaction. This is the first calculation of a microscopic ATPase coupling efficiency for nucleosome repositioning and also further supports our conclusion that a second bound ISWI does not contribute to the repositioning reaction.

  16. ISWI Remodels Nucleosomes through a Random Walk

    PubMed Central

    2015-01-01

    The chromatin remodeler ISWI is capable of repositioning clusters of nucleosomes to create well-ordered arrays or moving single nucleosomes from the center of DNA fragments toward the ends without disrupting their integrity. Using standard electrophoresis assays, we have monitored the ISWI-catalyzed repositioning of different nucleosome samples each containing a different length of DNA symmetrically flanking the initially centrally positioned histone octamer. We find that ISWI moves the histone octamer between distinct and thermodynamically stable positions on the DNA according to a random walk mechanism. Through the application of a spectrophotometric assay for nucleosome repositioning, we further characterized the repositioning activity of ISWI using short nucleosome substrates and were able to determine the macroscopic rate of nucleosome repositioning by ISWI. Additionally, quantitative analysis of repositioning experiments performed at various ISWI concentrations revealed that a monomeric ISWI is sufficient to obtain the observed repositioning activity as the presence of a second ISWI bound had no effect on the rate of nucleosome repositioning. We also found that ATP hydrolysis is poorly coupled to nucleosome repositioning, suggesting that DNA translocation by ISWI is not energetically rate-limiting for the repositioning reaction. This is the first calculation of a microscopic ATPase coupling efficiency for nucleosome repositioning and also further supports our conclusion that a second bound ISWI does not contribute to the repositioning reaction. PMID:24898619

  17. Random-walk model of homologous recombination

    NASA Astrophysics Data System (ADS)

    Fujitani, Youhei; Kobayashi, Ichizo

    1995-12-01

    Interaction between two homologous (i.e., identical or nearly identical) DNA sequences leads to their homologous recombination in the cell. We present the following stochastic model to explain the dependence of the frequency of homologous recombination on the length of the homologous region. The branch point connecting the two DNAs in a reaction intermediate follows the random-walk process along the homology (N base-pairs). If the branch point reaches either of the homology ends, it bounds back to the homologous region at a probability of γ (reflection coefficient) and is destroyed at a probability of 1-γ. When γ is small, the frequency of homologous recombination is found to be proportional to N3 for smaller N and a linear function of N for larger N. The exponent of the nonlinear dependence for smaller N decreases from three as γ increases. When γ=1, only the linear dependence is left. These theoretical results can explain many experimental data in various systems. (c) 1995 The American Physical Society

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

    PubMed

    Hausdorff, J M; Ashkenazy, Y; Peng, C K; Ivanov, P C; Stanley, H E; Goldberger, A L

    2001-12-15

    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.

  19. 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.

  20. Scaling random walks on arbitrary sets

    NASA Astrophysics Data System (ADS)

    Harris, Simon C.; Williams, David; Sibson, Robin

    1999-01-01

    Let I be a countably infinite set of points in [open face R] which we can write as I={ui: i[set membership][open face Z]}, with uirandom-walk, when repeatedly rescaled suitably in space and time, looks more and more like a Brownian motion. In this paper we explore the convergence properties of the Markov chain Y on the set I under suitable space-time scalings. Later, we consider some cases when the set I consists of the points of a renewal process and the jump rates assigned to each state in I are perhaps also randomly chosen.This work sprang from a question asked by one of us (Sibson) about ‘driftless nearest-neighbour’ Markov chains on countable subsets I of [open face R]d, work of Sibson [7] and of Christ, Friedberg and Lee [2] having identified examples of such chains in terms of the Dirichlet tessellation associated with I. Amongst methods which can be brought to bear on this d-dimensional problem is the theory of Dirichlet forms. There are potential problems in doing this because we wish I to be random (for example, a realization of a Poisson point process), we do not wish to impose artificial boundedness conditions which would clearly make things work for certain deterministic sets I. In the 1-dimensional case discussed here and in the following paper by Harris, much simpler techniques (where we embed the Markov chain in a Brownian motion using local time) work very effectively; and it is these, rather than the theory of Dirichlet forms, that we use.

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

    SciTech Connect

    Chacón-Cortes, L. F. Zúñiga-Galindo, W. A.

    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 number 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.

  2. Biased random walks on Kleinberg's spatial networks

    NASA Astrophysics Data System (ADS)

    Pan, Gui-Jun; Niu, Rui-Wu

    2016-12-01

    We investigate the problem of the particle or message that travels as a biased random walk toward a target node in Kleinberg's spatial network which is built from a d-dimensional (d = 2) regular lattice improved by adding long-range shortcuts with probability P(rij) ∼rij-α, where rij is the lattice distance between sites i and j, and α is a variable exponent. Bias is represented as a probability p of the packet to travel at every hop toward the node which has the smallest Manhattan distance to the target node. We study the mean first passage time (MFPT) for different exponent α and the scaling of the MFPT with the size of the network L. We find that there exists a threshold probability pth ≈ 0.5, for p ≥pth the optimal transportation condition is obtained with an optimal transport exponent αop = d, while for 0 < p pth, and increases with L less than a power law and get close to logarithmical law for 0 < p

  3. 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.

  4. 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.

  5. Record statistics of financial time series and geometric random walks.

    PubMed

    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.

  6. The melting phenomenon in random-walk model of DNA

    SciTech Connect

    Hayrapetyan, G. N.; Mamasakhlisov, E. Sh.; Papoyan, Vl. V.; Poghosyan, S. S.

    2012-10-15

    The melting phenomenon in a double-stranded homopolypeptide is considered. The relative distance between the corresponding monomers of two polymer chains is modeled by the two-dimensional random walk on the square lattice. Returns of the random walk to the origin describe the formation of hydrogen bonds between complementary units. To take into account the two competing interactions of monomers inside the chains, we obtain a completely denatured state at finite temperature T{sub c}.

  7. Simple model of a random walk with arbitrarily long memory

    NASA Astrophysics Data System (ADS)

    Berrones, Arturo; Larralde, Hernán

    2001-03-01

    We present a generalization of the persistent random-walk model in which the step at time n depends on the state of the step at time n-T, for arbitrary T. This gives rise to arbitrarily long memory effects, yet by an appropriate transformation the model is tractable by essentially the same techniques applicable to the usual persistent random-walk problem. We apply our results to the specific case of delayed ``step'' persistence, and analyze its asymptotic statistical properties.

  8. Numerical and Analytic Studies of Random-Walk Models.

    NASA Astrophysics Data System (ADS)

    Li, Bin

    We begin by recapitulating the universality approach to problems associated with critical systems, and discussing the role that random-walk models play in the study of phase transitions and critical phenomena. As our first numerical simulation project, we perform high-precision Monte Carlo calculations for the exponents of the intersection probability of pairs and triplets of ordinary random walks in 2 dimensions, in order to test the conformal-invariance theory predictions. Our numerical results strongly support the theory. Our second numerical project aims to test the hyperscaling relation dnu = 2 Delta_4-gamma for self-avoiding walks in 2 and 3 dimensions. We apply the pivot method to generate pairs of self-avoiding walks, and then for each pair, using the Karp-Luby algorithm, perform an inner -loop Monte Carlo calculation of the number of different translates of one walk that makes at least one intersection with the other. Applying a least-squares fit to estimate the exponents, we have obtained strong numerical evidence that the hyperscaling relation is true in 3 dimensions. Our great amount of data for walks of unprecedented length(up to 80000 steps), yield a updated value for the end-to-end distance and radius of gyration exponent nu = 0.588 +/- 0.001 (95% confidence limit), which comes out in good agreement with the renormalization -group prediction. In an analytic study of random-walk models, we introduce multi-colored random-walk models and generalize the Symanzik and B.F.S. random-walk representations to the multi-colored case. We prove that the zero-component lambdavarphi^2psi^2 theory can be represented by a two-color mutually -repelling random-walk model, and it becomes the mutually -avoiding walk model in the limit lambda to infty. However, our main concern and major break-through lies in the study of the two-point correlation function for the lambda varphi^2psi^2 theory with N > 0 components. By representing it as a two-color random-walk expansion

  9. Random walks for spike-timing-dependent plasticity

    NASA Astrophysics Data System (ADS)

    Williams, Alan; Leen, Todd K.; Roberts, Patrick D.

    2004-08-01

    Random walk methods are used to calculate the moments of negative image equilibrium distributions in synaptic weight dynamics governed by spike-timing-dependent plasticity. The neural architecture of the model is based on the electrosensory lateral line lobe of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish’s own electric discharge to optimize detection of sensory electric fields. Of particular behavioral importance to the fish is the variance of the equilibrium postsynaptic potential in the presence of noise, which is determined by the variance of the equilibrium weight distribution. Recurrence relations are derived for the moments of the equilibrium weight distribution, for arbitrary postsynaptic potential functions and arbitrary learning rules. For the case of homogeneous network parameters, explicit closed form solutions are developed for the covariances of the synaptic weight and postsynaptic potential distributions.

  10. Subdiffusion in time-averaged, confined random walks

    NASA Astrophysics Data System (ADS)

    Neusius, Thomas; Sokolov, Igor M.; Smith, Jeremy C.

    2009-07-01

    Certain techniques characterizing diffusive processes, such as single-particle tracking or molecular dynamics simulation, provide time averages rather than ensemble averages. Whereas the ensemble-averaged mean-squared displacement (MSD) of an unbounded continuous time random walk (CTRW) with a broad distribution of waiting times exhibits subdiffusion, the time-averaged MSD, δ2¯ , does not. We demonstrate that, in contrast to the unbounded CTRW, in which δ2¯ is linear in the lag time Δ , the time-averaged MSD of the CTRW of a walker confined to a finite volume is sublinear in Δ , i.e., for long lag times δ2¯˜Δ1-α . The present results permit the application of CTRW to interpret time-averaged experimental quantities.

  11. Superstatistical analysis and modelling of heterogeneous random walks.

    PubMed

    Metzner, Claus; Mark, Christoph; Steinwachs, Julian; Lautscham, Lena; Stadler, Franz; Fabry, Ben

    2015-06-25

    Stochastic time series are ubiquitous in nature. In particular, random walks with time-varying statistical properties are found in many scientific disciplines. Here we present a superstatistical approach to analyse and model such heterogeneous random walks. The time-dependent statistical parameters can be extracted from measured random walk trajectories with a Bayesian method of sequential inference. The distributions and correlations of these parameters reveal subtle features of the random process that are not captured by conventional measures, such as the mean-squared displacement or the step width distribution. We apply our new approach to migration trajectories of tumour cells in two and three dimensions, and demonstrate the superior ability of the superstatistical method to discriminate cell migration strategies in different environments. Finally, we show how the resulting insights can be used to design simple and meaningful models of the underlying random processes.

  12. Superstatistical analysis and modelling of heterogeneous random walks

    NASA Astrophysics Data System (ADS)

    Metzner, Claus; Mark, Christoph; Steinwachs, Julian; Lautscham, Lena; Stadler, Franz; Fabry, Ben

    2015-06-01

    Stochastic time series are ubiquitous in nature. In particular, random walks with time-varying statistical properties are found in many scientific disciplines. Here we present a superstatistical approach to analyse and model such heterogeneous random walks. The time-dependent statistical parameters can be extracted from measured random walk trajectories with a Bayesian method of sequential inference. The distributions and correlations of these parameters reveal subtle features of the random process that are not captured by conventional measures, such as the mean-squared displacement or the step width distribution. We apply our new approach to migration trajectories of tumour cells in two and three dimensions, and demonstrate the superior ability of the superstatistical method to discriminate cell migration strategies in different environments. Finally, we show how the resulting insights can be used to design simple and meaningful models of the underlying random processes.

  13. Superstatistical analysis and modelling of heterogeneous random walks

    PubMed Central

    Metzner, Claus; Mark, Christoph; Steinwachs, Julian; Lautscham, Lena; Stadler, Franz; Fabry, Ben

    2015-01-01

    Stochastic time series are ubiquitous in nature. In particular, random walks with time-varying statistical properties are found in many scientific disciplines. Here we present a superstatistical approach to analyse and model such heterogeneous random walks. The time-dependent statistical parameters can be extracted from measured random walk trajectories with a Bayesian method of sequential inference. The distributions and correlations of these parameters reveal subtle features of the random process that are not captured by conventional measures, such as the mean-squared displacement or the step width distribution. We apply our new approach to migration trajectories of tumour cells in two and three dimensions, and demonstrate the superior ability of the superstatistical method to discriminate cell migration strategies in different environments. Finally, we show how the resulting insights can be used to design simple and meaningful models of the underlying random processes. PMID:26108639

  14. Random walk after the big bang

    SciTech Connect

    Mijic, M. )

    1990-10-15

    The dynamics of inflation is that of a relaxation random process. We examine boundary conditions for this process and give a simple proof for the existence of eternal inflation that takes into account the field dependence of the effective cosmological constant and the finite duration of the inflationary phase. Next, natural initial conditions are formulated that lead to a specific interpretation of the wave function in quantum cosmology. We demonstrate that the Hartle-Hawking wave function describes the equilibrium regime for the stochastic process (with the correct quantum-field-theory limit), but only if the cosmological constant is sufficiently large or if it decays sufficiently slowly. We show in which sense inflation is certain even with the Hartle-Hawking wave function, and propose a new framework for the tunneling'' wave function. On the basis of boundary conditions, we argue that the dynamics of the stochastic phase and, hence, the main features of the present Universe, are independent of the physics above the Planck scale.

  15. 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

  16. 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.

  17. 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

  18. Quantum random walks do not need a coin toss

    SciTech Connect

    Patel, Apoorva; Raghunathan, K.S.; Rungta, Pranaw

    2005-03-01

    Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete quantum random walks, studied in the literature, have nonetheless used both superposition and a quantum coin toss instruction. This is not necessary, and a discrete quantum random walk without a quantum coin toss instruction is defined and analyzed here. Our construction eliminates quantum entanglement between the coin and the position degrees of freedom from the algorithm, and the results match those obtained with a quantum coin toss instruction.

  19. Current-reinforced random walks for constructing transport networks

    PubMed Central

    Ma, Qi; Johansson, Anders; Tero, Atsushi; Nakagaki, Toshiyuki; Sumpter, David J. T.

    2013-01-01

    Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by ‘walking’ particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the self-reinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed. PMID:23269849

  20. Dynamical and thermodynamical control of Open Quantum Walks

    NASA Astrophysics Data System (ADS)

    Petruccione, Francesco; Sinayskiy, Ilya

    2014-03-01

    Over the last few years dynamical properties and limit distributions of Open Quantum Walks (OQWs), quantum walks driven by dissipation, have been intensely studied [S. Attal et. al. J. Stat. Phys. 147, Issue 4, 832 (2012)]. For some particular cases of OQWs central limit theorems have been proven [S. Attal, N. Guillotin, C. Sabot, ``Central Limit Theorems for Open Quantum Random Walks,'' to appear in Annales Henri Poincaré]. However, only recently the connection between the rich dynamical behavior of OQWs and the corresponding microscopic system-environment models has been established. The microscopic derivation of an OQW as a reduced system dynamics on a 2-nodes graph [I. Sinayskiy, F. Petruccione, Open Syst. Inf. Dyn. 20, 1340007 (2013)] and its generalization to arbitrary graphs allow to explain the dependance of the dynamical behavior of the OQW on the temperature and coupling to the environment. For thermal environments we observe Gaussian behaviour, whereas at zero temperature population trapping and ``soliton''-like behaviour are possible. Physical realizations of OQWs in quantum optical setups will be also presented. This work is based on research supported by the South African Research Chair Initiative of the Department of Science and Technology and National Research Foundation.

  1. Torque-stiffness-controlled dynamic walking with central pattern generators.

    PubMed

    Huang, Yan; Vanderborght, Bram; Van Ham, Ronald; Wang, Qining

    2014-12-01

    Walking behavior is modulated by controlling joint torques in most existing passivity-based bipeds. Controlled Passive Walking with adaptable stiffness exhibits controllable natural motions and energy efficient gaits. In this paper, we propose torque-stiffness-controlled dynamic bipedal walking, which extends the concept of Controlled Passive Walking by introducing structured control parameters and a bio-inspired control method with central pattern generators. The proposed walking paradigm is beneficial in clarifying the respective effects of the external actuation and the internal natural dynamics. We present a seven-link biped model to validate the presented walking. Effects of joint torque and joint stiffness on gait selection, walking performance and walking pattern transitions are studied in simulations. The work in this paper develops a new solution of motion control of bipedal robots with adaptable stiffness and provides insights of efficient and sophisticated walking gaits of humans.

  2. Some physical consequences of a random walk in velocity space

    NASA Astrophysics Data System (ADS)

    Herzenberg, Caroline

    2012-03-01

    A simple conceptual model of stochastic behavior based on a random walk process in velocity space is examined. For objects moving at non-relativistic velocities, this leads under asymmetric directional probabilities to acceleration processes that resemble the behavior of objects subject to Newton's second law. For three dimensional space, inverse square law acceleration emerges for sufficiently separated objects. In modeling classical behavior, such non-relativistic random walks would appear to be limited to objects of sufficiently large mass. Objects with smaller mass exhibit more rapid diffusion and less localization, and a relativistic random walk would seem to be required for objects having masses smaller than a threshold mass value. Results suggest that the threshold mass value must be similar in magnitude to the Planck mass, which leads to behavior somewhat comparable to that characterizing an intrinsic quantum classical transition in the microgram mass range.

  3. Random Walks and Branching Processes in Correlated Gaussian Environment

    NASA Astrophysics Data System (ADS)

    Aurzada, Frank; Devulder, Alexis; Guillotin-Plantard, Nadine; Pène, Françoise

    2017-01-01

    We study persistence probabilities for random walks in correlated Gaussian random environment investigated by Oshanin et al. (Phys Rev Lett, 110:100602, 2013). From the persistence results, we can deduce properties of critical branching processes with offspring sizes geometrically distributed with correlated random parameters. More precisely, we obtain estimates on the tail distribution of its total population size, of its maximum population, and of its extinction time.

  4. Feature Learning Based Random Walk for Liver Segmentation

    PubMed Central

    Zheng, Yongchang; Ai, Danni; Zhang, Pan; Gao, Yefei; Xia, Likun; Du, Shunda; Sang, Xinting; Yang, Jian

    2016-01-01

    Liver segmentation is a significant processing technique for computer-assisted diagnosis. This method has attracted considerable attention and achieved effective result. However, liver segmentation using computed tomography (CT) images remains a challenging task because of the low contrast between the liver and adjacent organs. This paper proposes a feature-learning-based random walk method for liver segmentation using CT images. Four texture features were extracted and then classified to determine the classification probability corresponding to the test images. Seed points on the original test image were automatically selected and further used in the random walk (RW) algorithm to achieve comparable results to previous segmentation methods. PMID:27846217

  5. Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator

    NASA Astrophysics Data System (ADS)

    Vieira, Rafael; Amorim, Edgard P. M.; Rigolin, Gustavo

    2013-11-01

    We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value asymptotically in the number of steps, outperforming the entanglement attained by using ordered QRW. The disorder is modeled by introducing an extra random aspect to QRW, a classical coin that randomly dictates which quantum coin drives the system’s time evolution. We also show that maximal entanglement is achieved independently of the initial state of the walker, study the number of steps the system must move to be within a small fixed neighborhood of its asymptotic limit, and propose two experiments where these ideas can be tested.

  6. Ranking Competitors Using Degree-Neutralized Random Walks

    PubMed Central

    Shin, Seungkyu; Ahnert, Sebastian E.; Park, Juyong

    2014-01-01

    Competition is ubiquitous in many complex biological, social, and technological systems, playing an integral role in the evolutionary dynamics of the systems. It is often useful to determine the dominance hierarchy or the rankings of the components of the system that compete for survival and success based on the outcomes of the competitions between them. Here we propose a ranking method based on the random walk on the network representing the competitors as nodes and competitions as directed edges with asymmetric weights. We use the edge weights and node degrees to define the gradient on each edge that guides the random walker towards the weaker (or the stronger) node, which enables us to interpret the steady-state occupancy as the measure of the node's weakness (or strength) that is free of unwarranted degree-induced bias. We apply our method to two real-world competition networks and explore the issues of ranking stabilization and prediction accuracy, finding that our method outperforms other methods including the baseline win–loss differential method in sparse networks. PMID:25517977

  7. Random walk of a swimmer in a low-Reynolds-number medium

    NASA Astrophysics Data System (ADS)

    Garcia, Michaël; Berti, Stefano; Peyla, Philippe; Rafaï, Salima

    2011-03-01

    Swimming at a micrometer scale demands particular strategies. When inertia is negligible compared to viscous forces, hydrodynamics equations are reversible in time. To achieve propulsion, microswimmers must therefore deform in a way that is not invariant under time reversal. Here, we investigate dispersal properties of the microalga Chlamydomonas reinhardtii by means of microscopy and cell tracking. We show that tracked trajectories are well modeled by a correlated random walk. This process is based on short time correlations in the direction of movement called persistence. At longer times, correlation is lost and a standard random walk characterizes the trajectories. Moreover, high-speed imaging enables us to show how the back-and-forth motion of flagella at very short times affects the statistical description of the dynamics. Finally, we show how drag forces modify the characteristics of this particular random walk.

  8. 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).

  9. Random walk of a swimmer in a low-Reynolds-number medium.

    PubMed

    Garcia, Michaël; Berti, Stefano; Peyla, Philippe; Rafaï, Salima

    2011-03-01

    Swimming at a micrometer scale demands particular strategies. When inertia is negligible compared to viscous forces, hydrodynamics equations are reversible in time. To achieve propulsion, microswimmers must therefore deform in a way that is not invariant under time reversal. Here, we investigate dispersal properties of the microalga Chlamydomonas reinhardtii by means of microscopy and cell tracking. We show that tracked trajectories are well modeled by a correlated random walk. This process is based on short time correlations in the direction of movement called persistence. At longer times, correlation is lost and a standard random walk characterizes the trajectories. Moreover, high-speed imaging enables us to show how the back-and-forth motion of flagella at very short times affects the statistical description of the dynamics. Finally, we show how drag forces modify the characteristics of this particular random walk.

  10. Inference of random walk models to describe leukocyte migration

    NASA Astrophysics Data System (ADS)

    Jones, Phoebe J. M.; Sim, Aaron; Taylor, Harriet B.; Bugeon, Laurence; Dallman, Magaret J.; Pereira, Bernard; Stumpf, Michael P. H.; Liepe, Juliane

    2015-12-01

    While the majority of cells in an organism are static and remain relatively immobile in their tissue, migrating cells occur commonly during developmental processes and are crucial for a functioning immune response. The mode of migration has been described in terms of various types of random walks. To understand the details of the migratory behaviour we rely on mathematical models and their calibration to experimental data. Here we propose an approximate Bayesian inference scheme to calibrate a class of random walk models characterized by a specific, parametric particle re-orientation mechanism to observed trajectory data. We elaborate the concept of transition matrices (TMs) to detect random walk patterns and determine a statistic to quantify these TM to make them applicable for inference schemes. We apply the developed pipeline to in vivo trajectory data of macrophages and neutrophils, extracted from zebrafish that had undergone tail transection. We find that macrophage and neutrophils exhibit very distinct biased persistent random walk patterns, where the strengths of the persistence and bias are spatio-temporally regulated. Furthermore, the movement of macrophages is far less persistent than that of neutrophils in response to wounding.

  11. Protein localization prediction using random walks on graphs

    PubMed Central

    2013-01-01

    Background Understanding the localization of proteins in cells is vital to characterizing their functions and possible interactions. As a result, identifying the (sub)cellular compartment within which a protein is located becomes an important problem in protein classification. This classification issue thus involves predicting labels in a dataset with a limited number of labeled data points available. By utilizing a graph representation of protein data, random walk techniques have performed well in sequence classification and functional prediction; however, this method has not yet been applied to protein localization. Accordingly, we propose a novel classifier in the site prediction of proteins based on random walks on a graph. Results We propose a graph theory model for predicting protein localization using data generated in yeast and gram-negative (Gneg) bacteria. We tested the performance of our classifier on the two datasets, optimizing the model training parameters by varying the laziness values and the number of steps taken during the random walk. Using 10-fold cross-validation, we achieved an accuracy of above 61% for yeast data and about 93% for gram-negative bacteria. Conclusions This study presents a new classifier derived from the random walk technique and applies this classifier to investigate the cellular localization of proteins. The prediction accuracy and additional validation demonstrate an improvement over previous methods, such as support vector machine (SVM)-based classifiers. PMID:23815126

  12. Adaptive importance sampling of random walks on continuous state spaces

    SciTech Connect

    Baggerly, K.; Cox, D.; Picard, R.

    1998-11-01

    The authors consider adaptive importance sampling for a random walk with scoring in a general state space. Conditions under which exponential convergence occurs to the zero-variance solution are reviewed. These results generalize previous work for finite, discrete state spaces in Kollman (1993) and in Kollman, Baggerly, Cox, and Picard (1996). This paper is intended for nonstatisticians and includes considerable explanatory material.

  13. Amnestically Induced Persistence in Random Walks

    NASA Astrophysics Data System (ADS)

    Cressoni, J. C.; da Silva, Marco Antonio Alves; Viswanathan, G. M.

    2007-02-01

    We study how the Hurst exponent α depends on the fraction f of the total time t remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walker’s position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimer’s disease and other dementias.

  14. Amnestically induced persistence in random walks.

    PubMed

    Cressoni, J C; da Silva, Marco Antonio Alves; Viswanathan, G M

    2007-02-16

    We study how the Hurst exponent alpha depends on the fraction f of the total time t remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walker's position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimer's disease and other dementias.

  15. Vibration driven random walk in a Chladni experiment

    NASA Astrophysics Data System (ADS)

    Grabec, Igor

    2017-01-01

    Drifting of sand particles bouncing on a vibrating membrane of a Chladni experiment is characterized statistically. Records of trajectories reveal that bounces are circularly distributed and random. The mean length of their horizontal displacement is approximately proportional to the vibration amplitude above the critical level and amounts about one fourth of the corresponding bounce height. For the description of horizontal drifting of particles a model of vibration driven random walk is proposed that yields a good agreement between experimental and numerically simulated data.

  16. Random walks models with intermediate fractional diffusion asymptotics

    NASA Astrophysics Data System (ADS)

    Saichev, Alexander I.; Utkin, Sergei G.

    2004-05-01

    Random walk process was investigated with PDF of random time intervals similar to fractional exponential law on small times and to regular exponential law on long times. Generalized fractional Kolmogorov-Feller equation was derived for such kind of process. Asymptotics of its PDF in the long time limit and for intermediate times were found. They obey standard diffusion law or fractional diffusion law respectively. Exact solutions of mentioned equations were numerically calculated, demonstrating crossover of fractional diffusion law into the linear one.

  17. Homogeneous Open Quantum Random Walks on a Lattice

    NASA Astrophysics Data System (ADS)

    Carbone, Raffaella; Pautrat, Yan

    2015-09-01

    We study open quantum random walks (OQRWs) for which the underlying graph is a lattice, and the generators of the walk are homogeneous in space. Using the results recently obtained in Carbone and Pautrat (Ann Henri Poincaré, 2015), we study the quantum trajectory associated with the OQRW, which is described by a position process and a state process. We obtain a central limit theorem and a large deviation principle for the position process. We study in detail the case of homogeneous OQRWs on the lattice , with internal space.

  18. Quantization of Random Walks: Search Algorithms and Hitting Time

    NASA Astrophysics Data System (ADS)

    Santha, Miklos

    Many classical search problems can be cast in the following abstract framework: Given a finite set X and a subset M ⊆ X of marked elements, detect if M is empty or not, or find an element in M if there is any. When M is not empty, a naive approach to the finding problem is to repeatedly pick a uniformly random element of X until a marked element is sampled. A more sophisticated approach might use a Markov chain, that is a random walk on the state space X in order to generate the samples. In that case the resources spent for previous steps are often reused to generate the next sample. Random walks also model spatial search in physical regions where the possible moves are expressed by the edges of some specific graph. The hitting time of a Markov chain is the number of steps necessary to reach a marked element, starting from the stationary distribution of the chain.

  19. Sub-Markov Random Walk for Image Segmentation.

    PubMed

    Dong, Xingping; Shen, Jianbing; Shao, Ling; Van Gool, Luc

    2016-02-01

    A novel sub-Markov random walk (subRW) algorithm with label prior is proposed for seeded image segmentation, which can be interpreted as a traditional random walker on a graph with added auxiliary nodes. Under this explanation, we unify the proposed subRW and other popular random walk (RW) algorithms. This unifying view will make it possible for transferring intrinsic findings between different RW algorithms, and offer new ideas for designing novel RW algorithms by adding or changing auxiliary nodes. To verify the second benefit, we design a new subRW algorithm with label prior to solve the segmentation problem of objects with thin and elongated parts. The experimental results on both synthetic and natural images with twigs demonstrate that the proposed subRW method outperforms previous RW algorithms for seeded image segmentation.

  20. An effective Hamiltonian approach to quantum random walk

    NASA Astrophysics Data System (ADS)

    Sarkar, Debajyoti; Paul, Niladri; Bhattacharya, Kaushik; Ghosh, Tarun Kanti

    2017-03-01

    In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, Sci. Rep. 3, 2829 (18)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.

  1. Demonstration of one-dimensional quantum random walks using orbital angular momentum of photons

    SciTech Connect

    Zhang, Pei; Ren, Xi-Feng; Zou, Xu-Bo; Liu, Bi-Heng; Huang, Yun-Feng; Guo, Guang-Can

    2007-05-15

    Quantum random walks have attracted special interest because they could lead to new quantum algorithms. Photons can carry orbital angular momentum (OAM) thereby offering a practical realization of a high-dimensional quantum information carrier. By employing OAM of photons, we experimentally realized the one-dimensional discrete-time quantum random walk. Three steps of a one-dimensional quantum random walk were implemented in our protocol showing the obvious difference between quantum and classical random walks.

  2. The effects of sensory loss and walking speed on the orbital dynamic stability of human walking.

    PubMed

    Dingwell, Jonathan B; Kang, Hyun Gu; Marin, Laura C

    2007-01-01

    Peripheral sensory feedback is believed to contribute significantly to maintaining walking stability. Patients with diabetic peripheral neuropathy have a greatly increased risk of falling. Previously, we demonstrated that slower walking speeds in neuropathic patients lead to improved local dynamic stability. However, all subjects exhibited significant local instability during walking, even though no subject fell or stumbled during testing. The present study was conducted to determine if and how significant changes in peripheral sensation and walking speed affect orbital stability during walking. Trunk and lower extremity kinematics were examined from two prior experiments that compared patients with significant neuropathy to healthy controls and walking at multiple different speeds in young healthy subjects. Maximum Floquet multipliers were computed for each time series to quantify the orbital stability of these movements. All subjects exhibited orbitally stable walking kinematics, even though these same kinematics were previously shown to be locally unstable. Differences in orbital stability between neuropathic and control subjects were small and, with the exception of knee joint movements (p=0.001), not statistically significant (0.380p0.946). Differences in knee orbital stability were not mediated by differences in walking speed. This was supported by our finding that although orbital stability improved slightly with slower walking speeds, the correlations between walking speed and orbital stability were generally weak (r(2)16.7%). Thus, neuropathic patients do not gain improved orbital stability as a result of slowing down and do not experience any loss of orbital stability because of their sensory deficits.

  3. Solving Schroedinger's equation using random walks

    NASA Astrophysics Data System (ADS)

    Aspuru-Guzik, Alan

    Exact and almost exact solutions for energies and properties of atoms and molecules can be obtained by quantum Monte Carlo (QMC) methods. This thesis is composed of different contributions to various QMC methodologies, as well as applications to electronic excitations of biological systems. We propose a wave function optimization functional that is robust regarding the presence of outliers. Our work, and subsequent applications by others, has shown the convergence properties and robustness of the absolute deviation (AD) functional as compared to the variance functional (VF). We apply the method to atoms from the second row of the periodic table, as well as third-row transition metal atoms, including an all-electron calculation of Sc. In all cases, the AD functional converges faster than the VF. Soft effective core potentials (ECPs) with no divergence at the origin are constructed and validated for second- an third-row atoms of the periodic table. The ECPs we developed have been used by others in several successful studies. As an application of the DMC approach to biochemical problems, we studied the electronic excitations of free-base porphyrin and obtained results in excellent agreement with experiment. These findings validate the use of the DMC approach for these kinds of systems. A study of the role of spheroidene in the photo-protection mechanism of Rhodobacter sphaeroides is described. At the time of writing, calculations for the estimation of excitation energies for the bacteriochlorophyll and spheroidene molecules as well as storage of the random walkers for future prediction of the excitation energy transfer rate are being performed. To date, the calculations mentioned above are the largest all-electron studies on molecules. For the computation of these systems, a sparse linear-scaling DMC algorithm was developed. This algorithm provides a speedup of at least a factor of ten over previously published methods. The method is validated on systems up to 390

  4. [Some exact results for random walk models with applications].

    PubMed

    Schwarz, W

    1989-01-01

    This article presents a random walk model that can be analyzed without recourse to Wald's (1947) approximation, which neglects the excess over the absorbing barriers. Hence, the model yields exact predictions for the absorption probabilities and all mean conditional absorption times. We derive these predictions in some detail and fit them to the extensive data of an identification experiment published by Green et al. (1983). The fit of the model seems satisfactory. The relationship of the model to existing classes of random walk models (SPRT and SSR; see Luce, 1986) is discussed; for certain combinations of its parameters, the model belongs either to the SPRT or to the SSR class, or to both. We stress the theoretical significance of the knowledge of exact results for the evaluation of Wald's approximation and general properties of the several models proposed derived from this approximation.

  5. The random walk of tracers through river catchments

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Atreyee

    2012-08-01

    River catchments play critical roles in regional economies and in the global economy. In addition, rivers carry large volumes of nutrients, pollutants, and several other forms of tracers into the ocean. An intricate system of pathways and channels, both on the surface and in the subsurface of catchments, allows rivers to carry large volumes of tracers. However, scientists do not yet fully understand how pollutants and other tracers travel through the intricate web of channels in the catchment areas of rivers. In a new study, Cvetkovic et al show that the travel path of tracers through channels can be modeled as a random walk, which is mathematically similar to the path an animal would trace when foraging. Previous studies have applied the random walk approach to understand the behavior of fluids flowing through aquifers and soils but not to model the transport mechanism of tracers that travel passively with water flowing through catchments.

  6. Random Walk on the High-Dimensional IIC

    NASA Astrophysics Data System (ADS)

    Heydenreich, Markus; van der Hofstad, Remco; Hulshof, Tim

    2014-07-01

    We study the asymptotic behavior of the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by Kumagai and Misumi (J Theor Probab 21:910-935, 2008). We do this by getting bounds on the effective resistance between the origin and the boundary of these Euclidean balls. We show that the geometric properties of long-range percolation clusters are significantly different from those of finite-range clusters. We also study the behavior of random walk on the backbone of the IIC and we prove that the Alexander-Orbach conjecture holds for the incipient infinite cluster in high dimensions, both for long-range percolation and for finite-range percolation.

  7. Aggregation is the key to succeed in random walks.

    PubMed

    Hernandez-Suarez, Carlos M

    2016-09-01

    In a random walk (RW) in Z an individual starts at 0 and moves at discrete unitary steps to the right or left with respective probabilities p and 1-p. Assuming p > 1/2 and finite a, a > 1, the probability that state a will be reached before -a is Q(a, p) where Q(a, p) > p. Here we introduce the cooperative random walk (CRW) involving two individuals that move independently according to a RW each but dedicate a fraction of time θ to approach the other one unit. This simple strategy seems to be effective in increasing the expected number of individuals arriving to a first. We conjecture that this is a possible underlying mechanism for efficient animal migration under noisy conditions. Copyright © 2016 Elsevier Inc. All rights reserved.

  8. Universal properties of branching random walks in confined geometries

    NASA Astrophysics Data System (ADS)

    de Mulatier, C.; Mazzolo, A.; Zoia, A.

    2014-08-01

    Characterizing the occupation statistics of random walks through confined geometries amounts to assessing the distribution of the travelled length ℓ and the number of collisions n performed by the stochastic process in a given region, for which remarkably simple Cauchy-like formulas were established in the case of branching Pearson random walks with exponentially distributed jumps. In this letter, we derive two key results: first, we show that such formulas strikingly carry over to the much broader class of branching processes with arbitrary jumps, and have thus a universal character; second, we obtain a stronger version of these formulas relating the travelled length density and the collision density at any point of the phase space. Our results are key to such technological issues as the analysis of radiation flow for nuclear reactor design and medical diagnosis and apply more broadly to physical and biological systems with diffusion, reproduction and death.

  9. Reheating-volume measure for random-walk inflation

    SciTech Connect

    Winitzki, Sergei

    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 the 'youngness paradox', the RV cutoff yields unbiased results that are distinct from previously proposed measures.

  10. A random walk in physical biology

    NASA Astrophysics Data System (ADS)

    Peterson, Eric Lee

    proteins such as the MscL mechanosensitive channel. The findings of the analytical studies were confirmed by a Monte Carlo Markov Chain simulation using the fully two-dimensional potentials between two model proteins in a membrane.Living systems present us with beautiful and intricate structures, from the helices and sheets of a folded protein to the dynamic morphology of cellular organelles and the self-organization of proteins in a biomembrane and a synergy of theoretical and it in silico approaches should enable us to build and refine models of in vivo biological data.

  11. A Random Walk Phenomenon under an Interesting Stopping Rule

    ERIC Educational Resources Information Center

    Chakraborty, S.

    2007-01-01

    In the simple one-dimensional random walk setup, a path is described as follows. Toss a coin. If the result is head, score +1 and move one step forward; otherwise score -1 and move one step backward. One is interested to know the position after a given number of steps. In this paper, once again a coin-tossing experiment is carried out. But this…

  12. A Random Walk Phenomenon under an Interesting Stopping Rule

    ERIC Educational Resources Information Center

    Chakraborty, S.

    2007-01-01

    In the simple one-dimensional random walk setup, a path is described as follows. Toss a coin. If the result is head, score +1 and move one step forward; otherwise score -1 and move one step backward. One is interested to know the position after a given number of steps. In this paper, once again a coin-tossing experiment is carried out. But this…

  13. Random walk of microswimmers: puller and pusher cases

    NASA Astrophysics Data System (ADS)

    Rafai, Salima; Peyla, Philippe; Dyfcom Team

    2014-11-01

    Swimming at a micrometer scale demands particular strategies. Indeed when inertia is negligible as compared to viscous forces (i.e. Reynolds number Re is lower than unity), hydrodynamics equations are reversible in time. To achieve propulsion a low Reynolds number, swimmers must then deform in a way that is not invariant under time reversal. Here we investigate the dispersal properties of self propelled organisms by means of microscopy and cell tracking. Our systems of interest are, on the one hand, the microalga Chlamydomonas Reinhardtii, a puller-type swimmer and on the other hand, Lingulodinium polyedrum, a pusher. Both are quasi-spherical single celled alga. In the case of dilute suspensions, we show that tracked trajectories are well modelled by a correlated random walk. This process is based on short time correlations in the direction of movement called persistence. At longer times, correlations are lost and a standard random walk characterizes the trajectories. Finally we show how drag forces modify the characteristics of this particular random walk.

  14. Random Walks in Social Networks and their Applications: A Survey

    NASA Astrophysics Data System (ADS)

    Sarkar, Purnamrita; Moore, Andrew W.

    A wide variety of interesting real world applications, e.g. friend suggestion in social networks, keyword search in databases, web-spam detection etc. can be framed as ranking entities in a graph. In order to obtain ranking we need a graph-theoretic measure of similarity. Ideally this should capture the information hidden in the graph structure. For example, two entities are similar, if there are lots of short paths between them. Random walks have proven to be a simple, yet powerful mathematical tool for extracting information from the ensemble of paths between entities in a graph. Since real world graphs are enormous and complex, ranking using random walks is still an active area of research. The research in this area spans from new applications to novel algorithms and mathematical analysis, bringing together ideas from different branches of statistics, mathematics and computer science. In this book chapter, we describe different random walk based proximity measures, their applications, and existing algorithms for computing them.

  15. Ant-inspired density estimation via random walks.

    PubMed

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

    2017-09-19

    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.

  16. Theory of continuum random walks and application to chemotaxis

    NASA Astrophysics Data System (ADS)

    Schnitzer, Mark J.

    1993-10-01

    We formulate the general theory of random walks in continuum, essential for treating a collision rate which depends smoothly upon direction of motion. We also consider a smooth probability distribution of correlations between the directions of motion before and after collisions, as well as orientational Brownian motion between collisions. These features lead to an effective Smoluchowski equation. Such random walks involving an infinite number of distinct directions of motion cannot be treated on a lattice, which permits only a finite number of directions of motion, nor by Langevin methods, which make no reference to individual collisions. The effective Smoluchowski equation enables a description of the biased random walk of the bacterium Escherichia coli during chemotaxis, its search for food. The chemotactic responses of cells which perform temporal comparisons of the concentration of a chemical attractant are predicted to be strongly positive, whereas those of cells which measure averages of the ambient attractant concentration are predicted to be negative. The former prediction explains the observed behavior of wild-type (naturally occurring) cells; however, the latter behavior has yet to be observed, even in cells defective in adaption.

  17. Correlated Random Walks with a Finite Memory Range

    NASA Astrophysics Data System (ADS)

    Bidaux, Roger; Boccara, Nino

    We study a family of correlated one-dimensional random walks with a finite memory range M. These walks are extensions of the Taylor's walk as investigated by Goldstein, which has a memory range equal to one. At each step, with a probability p, the random walker moves either to the right or to the left with equal probabilities, or with a probability q=1-p performs a move, which is a stochastic Boolean function of the M previous steps. We first derive the most general form of this stochastic Boolean function, and study some typical cases which ensure that the average value of the walker's location after n steps is zero for all values of n. In each case, using a matrix technique, we provide a general method for constructing the generating function of the probability distribution of Rn; we also establish directly an exact analytic expression for the step-step correlations and the variance < R2n > of the walk. From the expression of < R2n >, which is not straightforward to derive from the probability distribution, we show that, for n approaching infinity, the variance of any of these walks behaves as n, provided p>0. Moreover, in many cases, for a very small fixed value of p, the variance exhibits a crossover phenomenon as n increases from a not too large value. The crossover takes place for values of n around 1/p. This feature may mimic the existence of a nontrivial Hurst exponent, and induce a misleading analysis of numerical data issued from mathematical or natural sciences experiments.

  18. Asymptotic behaviour of random walks with correlated temporal structure

    PubMed Central

    Magdziarz, Marcin; Szczotka, Władysław; Żebrowski, Piotr

    2013-01-01

    We introduce a continuous-time random walk process with correlated temporal structure. The dependence between consecutive waiting times is generated by weighted sums of independent random variables combined with a reflecting boundary condition. The weights are determined by the memory kernel, which belongs to the broad class of regularly varying functions. We derive the corresponding diffusion limit and prove its subdiffusive character. Analysing the set of corresponding coupled Langevin equations, we verify the speed of relaxation, Einstein relations, equilibrium distributions, ageing and ergodicity breaking. PMID:24204190

  19. Subdiffusivity of a Random Walk Among a Poisson System of Moving Traps on {Z}

    NASA Astrophysics Data System (ADS)

    Athreya, Siva; Drewitz, Alexander; Sun, Rongfeng

    2017-03-01

    We consider a random walk among a Poisson system of moving traps on {Z}. In earlier work (Drewitz et al. Springer Proc. Math. 11, 119-158 2012), the quenched and annealed survival probabilities of this random walk have been investigated. Here we study the path of the random walk conditioned on survival up to time t in the annealed case and show that it is subdiffusive. As a by-product, we obtain an upper bound on the number of so-called thin points of a one-dimensional random walk, as well as a bound on the total volume of the holes in the random walk's range.

  20. Social Aggregation in Pea Aphids: Experiment and Random Walk Modeling

    PubMed Central

    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. PMID:24376691

  1. 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.

  2. Accurate multiple network alignment through context-sensitive random walk

    PubMed Central

    2015-01-01

    Background Comparative network analysis can provide an effective means of analyzing large-scale biological networks and gaining novel insights into their structure and organization. Global network alignment aims to predict the best overall mapping between a given set of biological networks, thereby identifying important similarities as well as differences among the networks. It has been shown that network alignment methods can be used to detect pathways or network modules that are conserved across different networks. Until now, a number of network alignment algorithms have been proposed based on different formulations and approaches, many of them focusing on pairwise alignment. Results In this work, we propose a novel multiple network alignment algorithm based on a context-sensitive random walk model. The random walker employed in the proposed algorithm switches between two different modes, namely, an individual walk on a single network and a simultaneous walk on two networks. The switching decision is made in a context-sensitive manner by examining the current neighborhood, which is effective for quantitatively estimating the degree of correspondence between nodes that belong to different networks, in a manner that sensibly integrates node similarity and topological similarity. The resulting node correspondence scores are then used to predict the maximum expected accuracy (MEA) alignment of the given networks. Conclusions Performance evaluation based on synthetic networks as well as real protein-protein interaction networks shows that the proposed algorithm can construct more accurate multiple network alignments compared to other leading methods. PMID:25707987

  3. Noisy vestibular stimulation improves dynamic walking stability in bilateral vestibulopathy.

    PubMed

    Wuehr, Max; Nusser, Eva; Decker, Julian; Krafczyk, Siegbert; Straube, Andreas; Brandt, Thomas; Jahn, Klaus; Schniepp, Roman

    2016-06-07

    To examine the effects of imperceptible levels of white noise galvanic vestibular stimulation (nGVS) on dynamic walking stability in patients with bilateral vestibulopathy (BVP). Walking performance of 13 patients with confirmed BVP (mean age 50.1 ± 5.5 years) at slow, preferred, and fast speeds was examined during walking with zero-amplitude nGVS (sham trial) and nonzero-amplitude nGVS set to 80% of the individual cutaneous threshold for GVS (nGVS trial). Eight standard gait measures were analyzed: stride time, stride length, base of support, double support time percentage as well as the bilateral phase coordination index, and the coefficient of variation (CV) of stride time, stride length, and base of support. Compared to the sham trial, nGVS improved stride time CV by 26.0% ± 8.4% (p < 0.041), stride length CV by 26.0% ± 7.7% (p < 0.029), base of support CV by 27.8% ± 2.9% (p < 0.037), and phase coordination index by 8.4% ± 8.8% (p < 0.013). The nGVS effects on walking performance were correlated with subjective ratings of walking balance (ρ = 0.79, p < 0.001). Effect of nGVS on walking stability was most pronounced during slow walking. In patients with BVP, nGVS is effective in improving impaired gait performance, predominantly during slower walking speeds. It primarily targets the variability and bilateral coordination characteristics of the walking pattern, which are linked to dynamic walking stability. nGVS might present an effective treatment option to immediately improve walking performance and reduce the incidence of falls in patients with BVP. This study provides Class IV evidence that in patients with BVP, an imperceptible level of nGVS improves dynamic walking stability. © 2016 American Academy of Neurology.

  4. Evidence for the effectiveness of walking training on walking and self-care after stroke: a systematic review and meta-analysis of randomized controlled trials.

    PubMed

    Peurala, Sinikka H; Karttunen, Auli H; Sjögren, Tuulikki; Paltamaa, Jaana; Heinonen, Ari

    2014-05-01

    To examine the effect of randomized controlled trials of walking training on walking and self-care in patients with stroke. MEDLINE, CINAHL, Embase, PEDro, OTSeeker, Central, and manual search to the end of August 2012. English, Finnish, Swedish, or German language walking training randomized controlled trials for patients over 18 years of age with stroke. The meta-analyses included 38 randomized controlled trials from 44 reports. There was high evidence that in the subacute stage of stroke, specific walking training resulted in improved walking speed and distance compared with traditional walking training of the same intensity. In the chronic stage, walking training resulted in increased walking speed and walking distance compared with no/placebo treatment, and increased walking speed compared with overall physio-therapy. On average, 24 training sessions for 7 weeks were needed. Walking training improves walking capacity and, to some extent, self-care in different stages of stroke, but the training frequency should be fairly high.

  5. Random walks in weighted networks with a perfect trap: an application of Laplacian spectra.

    PubMed

    Lin, Yuan; Zhang, Zhongzhi

    2013-06-01

    Trapping processes constitute a primary problem of random walks, which characterize various other dynamical processes taking place on networks. Most previous works focused on the case of binary networks, while there is much less related research about weighted networks. In this paper, we propose a general framework for the trapping problem on a weighted network with a perfect trap fixed at an arbitrary node. By utilizing the spectral graph theory, we provide an exact formula for mean first-passage time (MFPT) from one node to another, based on which we deduce an explicit expression for average trapping time (ATT) in terms of the eigenvalues and eigenvectors of the Laplacian matrix associated with the weighted graph, where ATT is the average of MFPTs to the trap over all source nodes. We then further derive a sharp lower bound for the ATT in terms of only the local information of the trap node, which can be obtained in some graphs. Moreover, we deduce the ATT when the trap is distributed uniformly in the whole network. Our results show that network weights play a significant role in the trapping process. To apply our framework, we use the obtained formulas to study random walks on two specific networks: trapping in weighted uncorrelated networks with a deep trap, the weights of which are characterized by a parameter, and Lévy random walks in a connected binary network with a trap distributed uniformly, which can be looked on as random walks on a weighted network. For weighted uncorrelated networks we show that the ATT to any target node depends on the weight parameter, that is, the ATT to any node can change drastically by modifying the parameter, a phenomenon that is in contrast to that for trapping in binary networks. For Lévy random walks in any connected network, by using their equivalence to random walks on a weighted complete network, we obtain the optimal exponent characterizing Lévy random walks, which have the minimal average of ATTs taken over all

  6. History dependent quantum random walks as quantum lattice gas automata

    SciTech Connect

    Shakeel, Asif E-mail: dmeyer@math.ucsd.edu Love, Peter J. E-mail: dmeyer@math.ucsd.edu; Meyer, David A. E-mail: dmeyer@math.ucsd.edu

    2014-12-15

    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 history information arise naturally as geometrical degrees of freedom on the lattice.

  7. Conditioned random walks and interaction-driven condensation

    NASA Astrophysics Data System (ADS)

    Szavits-Nossan, Juraj; Evans, Martin R.; Majumdar, Satya N.

    2017-01-01

    We consider a discrete-time continuous-space random walk under the constraints that the number of returns to the origin (local time) and the total area under the walk are fixed. We first compute the joint probability of an excursion having area a and returning to the origin for the first time after time τ. We then show how condensation occurs when the total area constraint is increased: an excursion containing a finite fraction of the area emerges. Finally we show how the phenomena generalises previously studied cases of condensation induced by several constraints and how it is related to interaction-driven condensation which allows us to explain the phenomenon in the framework of large deviation theory.

  8. Infrared dynamics of minimal walking technicolor

    SciTech Connect

    Del Debbio, Luigi; Lucini, Biagio; Patella, Agostino; Pica, Claudio; Rago, Antonio

    2010-07-01

    We study the gauge sector of minimal walking technicolor, which is an SU(2) gauge theory with n{sub f}=2 flavors of Wilson fermions in the adjoint representation. Numerical simulations are performed on lattices N{sub t}xN{sub s}{sup 3}, with N{sub s} ranging from 8 to 16 and N{sub t}=2N{sub s}, at fixed {beta}=2.25, and varying the fermion bare mass m{sub 0}, so that our numerical results cover the full range of fermion masses from the quenched region to the chiral limit. We present results for the string tension and the glueball spectrum. A comparison of mesonic and gluonic observables leads to the conclusion that the infrared dynamics is given by an SU(2) pure Yang-Mills theory with a typical energy scale for the spectrum sliding to zero with the fermion mass. The typical mesonic mass scale is proportional to and much larger than this gluonic scale. Our findings are compatible with a scenario in which the massless theory is conformal in the infrared. An analysis of the scaling of the string tension with the fermion mass toward the massless limit allows us to extract the chiral condensate anomalous dimension {gamma}{sub *}, which is found to be {gamma}{sub *}=0.22{+-}0.06.

  9. Clustered continuous-time random walks: diffusion and relaxation consequences

    PubMed Central

    Weron, Karina; Stanislavsky, Aleksander; Jurlewicz, Agnieszka; Meerschaert, Mark M.; Scheffler, Hans-Peter

    2012-01-01

    We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies. PMID:22792038

  10. Bicycling and Walking are Associated with Different Cortical Oscillatory Dynamics.

    PubMed

    Storzer, Lena; Butz, Markus; Hirschmann, Jan; Abbasi, Omid; Gratkowski, Maciej; Saupe, Dietmar; Schnitzler, Alfons; Dalal, Sarang S

    2016-01-01

    Although bicycling and walking involve similar complex coordinated movements, surprisingly Parkinson's patients with freezing of gait typically remain able to bicycle despite severe difficulties in walking. This observation suggests functional differences in the motor networks subserving bicycling and walking. However, a direct comparison of brain activity related to bicycling and walking has never been performed, neither in healthy participants nor in patients. Such a comparison could potentially help elucidating the cortical involvement in motor control and the mechanisms through which bicycling ability may be preserved in patients with freezing of gait. The aim of this study was to contrast the cortical oscillatory dynamics involved in bicycling and walking in healthy participants. To this end, EEG and EMG data of 14 healthy participants were analyzed, who cycled on a stationary bicycle at a slow cadence of 40 revolutions per minute (rpm) and walked at 40 strides per minute (spm), respectively. Relative to walking, bicycling was associated with a stronger power decrease in the high beta band (23-35 Hz) during movement initiation and execution, followed by a stronger beta power increase after movement termination. Walking, on the other hand, was characterized by a stronger and persisting alpha power (8-12 Hz) decrease. Both bicycling and walking exhibited movement cycle-dependent power modulation in the 24-40 Hz range that was correlated with EMG activity. This modulation was significantly stronger in walking. The present findings reveal differential cortical oscillatory dynamics in motor control for two types of complex coordinated motor behavior, i.e., bicycling and walking. Bicycling was associated with a stronger sustained cortical activation as indicated by the stronger high beta power decrease during movement execution and less cortical motor control within the movement cycle. We speculate this to be due to the more continuous nature of bicycling demanding

  11. Bicycling and Walking are Associated with Different Cortical Oscillatory Dynamics

    PubMed Central

    Storzer, Lena; Butz, Markus; Hirschmann, Jan; Abbasi, Omid; Gratkowski, Maciej; Saupe, Dietmar; Schnitzler, Alfons; Dalal, Sarang S.

    2016-01-01

    Although bicycling and walking involve similar complex coordinated movements, surprisingly Parkinson’s patients with freezing of gait typically remain able to bicycle despite severe difficulties in walking. This observation suggests functional differences in the motor networks subserving bicycling and walking. However, a direct comparison of brain activity related to bicycling and walking has never been performed, neither in healthy participants nor in patients. Such a comparison could potentially help elucidating the cortical involvement in motor control and the mechanisms through which bicycling ability may be preserved in patients with freezing of gait. The aim of this study was to contrast the cortical oscillatory dynamics involved in bicycling and walking in healthy participants. To this end, EEG and EMG data of 14 healthy participants were analyzed, who cycled on a stationary bicycle at a slow cadence of 40 revolutions per minute (rpm) and walked at 40 strides per minute (spm), respectively. Relative to walking, bicycling was associated with a stronger power decrease in the high beta band (23–35 Hz) during movement initiation and execution, followed by a stronger beta power increase after movement termination. Walking, on the other hand, was characterized by a stronger and persisting alpha power (8–12 Hz) decrease. Both bicycling and walking exhibited movement cycle-dependent power modulation in the 24–40 Hz range that was correlated with EMG activity. This modulation was significantly stronger in walking. The present findings reveal differential cortical oscillatory dynamics in motor control for two types of complex coordinated motor behavior, i.e., bicycling and walking. Bicycling was associated with a stronger sustained cortical activation as indicated by the stronger high beta power decrease during movement execution and less cortical motor control within the movement cycle. We speculate this to be due to the more continuous nature of bicycling

  12. General mapping between random walks and thermal vibrations in elastic networks: fractal networks as a case study.

    PubMed

    Reuveni, Shlomi; Granek, Rony; Klafter, Joseph

    2010-10-01

    We present an approach to mapping between random walks and vibrational dynamics on general networks. Random walk occupation probabilities, first passage time distributions and passage probabilities between nodes are expressed in terms of thermal vibrational correlation functions. Recurrence is demonstrated equivalent to the Landau-Peierls instability. Fractal networks are analyzed as a case study. In particular, we show that the spectral dimension governs whether or not the first passage time distribution is well represented by its mean. We discuss relevance to universal features arising in protein vibrational dynamics.

  13. Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking

    PubMed Central

    2011-01-01

    Background Motorized treadmills are widely used in research or in clinical therapy. Small kinematics, kinetics and energetics changes induced by Treadmill Walking (TW) as compared to Overground Walking (OW) have been reported in literature. The purpose of the present study was to characterize the differences between OW and TW in terms of stride-to-stride variability. Classical (Standard Deviation, SD) and non-linear (fractal dynamics, local dynamic stability) methods were used. In addition, the correlations between the different variability indexes were analyzed. Methods Twenty healthy subjects performed 10 min TW and OW in a random sequence. A triaxial accelerometer recorded trunk accelerations. Kinematic variability was computed as the average SD (MeanSD) of acceleration patterns among standardized strides. Fractal dynamics (scaling exponent α) was assessed by Detrended Fluctuation Analysis (DFA) of stride intervals. Short-term and long-term dynamic stability were estimated by computing the maximal Lyapunov exponents of acceleration signals. Results TW did not modify kinematic gait variability as compared to OW (multivariate T2, p = 0.87). Conversely, TW significantly modified fractal dynamics (t-test, p = 0.01), and both short and long term local dynamic stability (T2 p = 0.0002). No relationship was observed between variability indexes with the exception of significant negative correlation between MeanSD and dynamic stability in TW (3 × 6 canonical correlation, r = 0.94). Conclusions Treadmill induced a less correlated pattern in the stride intervals and increased gait stability, but did not modify kinematic variability in healthy subjects. This could be due to changes in perceptual information induced by treadmill walking that would affect locomotor control of the gait and hence specifically alter non-linear dependencies among consecutive strides. Consequently, the type of walking (i.e. treadmill or overground) is important to consider in each protocol

  14. Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking.

    PubMed

    Terrier, Philippe; Dériaz, Olivier

    2011-02-24

    Motorized treadmills are widely used in research or in clinical therapy. Small kinematics, kinetics and energetics changes induced by Treadmill Walking (TW) as compared to Overground Walking (OW) have been reported in literature. The purpose of the present study was to characterize the differences between OW and TW in terms of stride-to-stride variability. Classical (Standard Deviation, SD) and non-linear (fractal dynamics, local dynamic stability) methods were used. In addition, the correlations between the different variability indexes were analyzed. Twenty healthy subjects performed 10 min TW and OW in a random sequence. A triaxial accelerometer recorded trunk accelerations. Kinematic variability was computed as the average SD (MeanSD) of acceleration patterns among standardized strides. Fractal dynamics (scaling exponent α) was assessed by Detrended Fluctuation Analysis (DFA) of stride intervals. Short-term and long-term dynamic stability were estimated by computing the maximal Lyapunov exponents of acceleration signals. TW did not modify kinematic gait variability as compared to OW (multivariate T(2), p=0.87). Conversely, TW significantly modified fractal dynamics (t-test, p=0.01), and both short and long term local dynamic stability (T(2) p=0.0002). No relationship was observed between variability indexes with the exception of significant negative correlation between MeanSD and dynamic stability in TW (3 × 6 canonical correlation, r=0.94). Treadmill induced a less correlated pattern in the stride intervals and increased gait stability, but did not modify kinematic variability in healthy subjects. This could be due to changes in perceptual information induced by treadmill walking that would affect locomotor control of the gait and hence specifically alter non-linear dependencies among consecutive strides. Consequently, the type of walking (i.e. treadmill or overground) is important to consider in each protocol design. © 2011 Terrier and Dériaz; licensee

  15. Walking changes the dynamics of cognitive estimates of time intervals.

    PubMed

    Kiefer, Adam W; Riley, Michael A; Shockley, Kevin; Villard, Sebastien; Van Orden, Guy C

    2009-10-01

    Cognitive performance exhibits patterns of trial-to-trial variation that can be described as 1/f or pink noise, as do repeated measures of locomotor performance. Although cognitive and locomotor performances are known to interact when performed concurrently, it is not known whether concurrent performance affects the tasks' pink noise dynamical structure. In this study, participants performed a cognitive task (repeatedly producing a temporal interval) and a motor task (walking on a treadmill) in single- and dual-task conditions. In single-task conditions both tasks exhibited pink noise structure. For concurrent performance the dynamical structure of the cognitive task changed reliably in the direction of white (random) noise. The dynamical structure of locomotion remained pink noise. The change in cognitive dynamics occurred despite no reliable changes in mean or standard deviation measures for either task. The results suggest a functional reorganization of cognitive dynamics supporting successful task performance in dual-task conditions. PsycINFO Database Record (c) 2009 APA, all rights reserved.

  16. MFPT calculation for random walks in inhomogeneous networks

    NASA Astrophysics Data System (ADS)

    Wijesundera, Isuri; Halgamuge, Malka N.; Nirmalathas, Ampalavanapillai; Nanayakkara, Thrishantha

    2016-11-01

    Knowing the expected arrival time at a particular state, also known as the mean first passage time (MFPT), often plays an important role for a large class of random walkers in their respective state-spaces. Contrasting to ideal conditions required by recent advancements on MFPT estimations, many naturally occurring random walkers encounter inhomogeneity of transport characteristics in the networks they walk on. This paper presents a heuristic method to divide an inhomogeneous network into homogeneous network primitives (NPs) optimized using particle swarm optimizer, and to use a 'hop-wise' MFPT calculation method. This methodology's potential is demonstrated through simulated random walks and with a case study using the dataset of past cyclone tracks over the North Atlantic Ocean. Parallel processing was used to increase calculation efficiency. The predictions using the proposed method are compared to real data averages and predictions assuming homogeneous transport properties. The results show that breaking the problem into NPs reduces the average error from 18.8% to 5.4% with respect to the homogeneous network assumption.

  17. First Passage Time for Random Walks in Heterogeneous Networks

    NASA Astrophysics Data System (ADS)

    Hwang, S.; Lee, D.-S.; Kahng, B.

    2012-08-01

    The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous networks, is not yet fully understood. Here, we study, both analytically and numerically, the scaling behavior of the FPT distribution to a given target node, averaged over all starting nodes. We find that random walks arrive quickly at a local hub, and therefore, the FPT distribution shows a crossover with respect to time from fast decay behavior (induced from the attractive effect to the hub) to slow decay behavior (caused by the exploring of the entire system). Moreover, the mean FPT is independent of the degree of the target node in the case of compact exploration. These theoretical results justify the necessity of using a random jump protocol (empirically used in search engines) and provide guidelines for designing an effective network to make information quickly accessible.

  18. Characteristic times of biased random walks on complex networks

    NASA Astrophysics Data System (ADS)

    Bonaventura, Moreno; Nicosia, Vincenzo; Latora, Vito

    2014-01-01

    We consider degree-biased random walkers whose probability to move from a node to one of its neighbors of degree k is proportional to kα, where α is a tuning parameter. We study both numerically and analytically three types of characteristic times, namely (i) the time the walker needs to come back to the starting node, (ii) the time it takes to visit a given node for the first time, and (iii) the time it takes to visit all the nodes of the network. We consider a large data set of real-world networks and we show that the value of α which minimizes the three characteristic times differs from the value αmin=-1 analytically found for uncorrelated networks in the mean-field approximation. In addition to this, we found that assortative networks have preferentially a value of αmin in the range [-1,-0.5], while disassortative networks have αmin in the range [-0.5,0]. We derive an analytical relation between the degree correlation exponent ν and the optimal bias value αmin, which works well for real-world assortative networks. When only local information is available, degree-biased random walks can guarantee smaller characteristic times than the classical unbiased random walks by means of an appropriate tuning of the motion bias.

  19. Continuous-time random walks that alter environmental transport properties.

    PubMed

    Angstmann, C; Henry, B I

    2011-12-01

    We consider continuous-time random walks (CTRWs) in which the walkers have a finite probability to alter the waiting-time and/or step-length transport properties of their environment, resulting in possibly transient anomalous diffusion. We refer to these CTRWs as transmogrifying continuous-time random walks (TCTRWs) to emphasize that they change the form of the transport properties of their environment, and in a possibly strange way. The particular case in which the CTRW waiting-time density has a finite probability to be permanently altered at a given site, following a visitation by a walker, is considered in detail. Master equations for the probability density function of transmogrifying random walkers are derived, and results are compared with Monte Carlo simulations. An interesting finding is that TCTRWs can generate transient subdiffusion or transient superdiffusion without invoking truncated or tempered power law densities for either the waiting times or the step lengths. The transient subdiffusion or transient superdiffusion arises in TCTRWs with Gaussian step-length densities and exponential waiting-time densities when the altered average waiting time is greater than or less than, respectively, the original average waiting time.

  20. Cauchy's formulas for random walks in bounded domains

    NASA Astrophysics Data System (ADS)

    Mazzolo, Alain; de Mulatier, Clélia; Zoia, Andrea

    2014-08-01

    Cauchy's formula was originally established for random straight paths crossing a body B subset {R}n and basically relates the average chord length through B to the ratio between the volume and the surface of the body itself. The original statement was later extended in the context of transport theory so as to cover the stochastic paths of Pearson random walks with exponentially distributed flight lengths traversing a bounded domain. Some heuristic arguments suggest that Cauchy's formula may also hold true for Pearson random walks with arbitrarily distributed flight lengths. For such a broad class of stochastic processes, we rigorously derive a generalized Cauchy's formula for the average length travelled by the walkers in the body, and show that this quantity depends indeed only on the ratio between the volume and the surface, provided that some constraints are imposed on the entrance step of the walker in B. Similar results are also obtained for the average number of collisions performed by the walker in B.

  1. Cauchy's formulas for random walks in bounded domains

    SciTech Connect

    Mazzolo, Alain Zoia, Andrea

    2014-08-01

    Cauchy's formula was originally established for random straight paths crossing a body B⊂R{sup n} and basically relates the average chord length through B to the ratio between the volume and the surface of the body itself. The original statement was later extended in the context of transport theory so as to cover the stochastic paths of Pearson random walks with exponentially distributed flight lengths traversing a bounded domain. Some heuristic arguments suggest that Cauchy's formula may also hold true for Pearson random walks with arbitrarily distributed flight lengths. For such a broad class of stochastic processes, we rigorously derive a generalized Cauchy's formula for the average length traveled by the walkers in the body, and show that this quantity depends indeed only on the ratio between the volume and the surface, provided that some constraints are imposed on the entrance step of the walker in B. Similar results are also obtained for the average number of collisions performed by the walker in B.

  2. Characteristic times of biased random walks on complex networks.

    PubMed

    Bonaventura, Moreno; Nicosia, Vincenzo; Latora, Vito

    2014-01-01

    We consider degree-biased random walkers whose probability to move from a node to one of its neighbors of degree k is proportional to k(α), where α is a tuning parameter. We study both numerically and analytically three types of characteristic times, namely (i) the time the walker needs to come back to the starting node, (ii) the time it takes to visit a given node for the first time, and (iii) the time it takes to visit all the nodes of the network. We consider a large data set of real-world networks and we show that the value of α which minimizes the three characteristic times differs from the value α(min)=-1 analytically found for uncorrelated networks in the mean-field approximation. In addition to this, we found that assortative networks have preferentially a value of α(min) in the range [-1,-0.5], while disassortative networks have α(min) in the range [-0.5,0]. We derive an analytical relation between the degree correlation exponent ν and the optimal bias value α(min), which works well for real-world assortative networks. When only local information is available, degree-biased random walks can guarantee smaller characteristic times than the classical unbiased random walks by means of an appropriate tuning of the motion bias.

  3. How fast does a random walk cover a torus?

    NASA Astrophysics Data System (ADS)

    Grassberger, Peter

    2017-07-01

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

  4. A random walk to stochastic diffusion through spreadsheet analysis

    NASA Astrophysics Data System (ADS)

    Brazzle, Bob

    2013-11-01

    This paper describes a random walk simulation using a number cube and a lattice of concentric rings of tiled hexagons. At the basic level, it gives beginning students a concrete connection to the concept of stochastic diffusion and related physical quantities. A simple algorithm is presented that can be used to set up spreadsheet files to calculate these simulated quantities and even to "discover" the diffusion equation. Lattices with different geometries in two and three dimensions are also presented. This type of simulation provides fertile ground for independent investigations by all levels of undergraduate students.

  5. Non-equilibrium Phase Transitions: Activated Random Walks at Criticality

    NASA Astrophysics Data System (ADS)

    Cabezas, M.; Rolla, L. T.; Sidoravicius, V.

    2014-06-01

    In this paper we present rigorous results on the critical behavior of the Activated Random Walk model. We conjecture that on a general class of graphs, including , and under general initial conditions, the system at the critical point does not reach an absorbing state. We prove this for the case where the sleep rate is infinite. Moreover, for the one-dimensional asymmetric system, we identify the scaling limit of the flow through the origin at criticality. The case remains largely open, with the exception of the one-dimensional totally-asymmetric case, for which it is known that there is no fixation at criticality.

  6. TOPICAL REVIEW: The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics

    NASA Astrophysics Data System (ADS)

    Metzler, Ralf; Klafter, Joseph

    2004-08-01

    Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes. A large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker-Planck equation (Metzler R and Klafter J 2000a, Phys. Rep. 339 1-77). It therefore appears timely to put these new works in a cohesive perspective. In this review we cover both the theoretical modelling of sub- and superdiffusive processes, placing emphasis on superdiffusion, and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function. We also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems.

  7. Steady state and mean recurrence time for random walks on stochastic temporal networks

    NASA Astrophysics Data System (ADS)

    Speidel, Leo; Lambiotte, Renaud; Aihara, Kazuyuki; Masuda, Naoki

    2015-01-01

    Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of random walks on temporal networks. Here we theoretically study two types of event-driven random walks on a stochastic temporal network model that produces arbitrary distributions of interevent times. In the so-called active random walk, the interevent time is reinitialized on all links upon each movement of the walker. In the so-called passive random walk, the interevent time is reinitialized only on the link that has been used the last time, and it is a type of correlated random walk. We find that the steady state is always the uniform density for the passive random walk. In contrast, for the active random walk, it increases or decreases with the node's degree depending on the distribution of interevent times. The mean recurrence time of a node is inversely proportional to the degree for both active and passive random walks. Furthermore, the mean recurrence time does or does not depend on the distribution of interevent times for the active and passive random walks, respectively.

  8. Random and directed walk-based top-(k) queries in wireless sensor networks.

    PubMed

    Fu, Jun-Song; Liu, Yun

    2015-05-26

    In wireless sensor networks, filter-based top-  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-  query approach called RWTQ and a directed walk-based top-  query approach called DWTQ are proposed. At the beginning of a top-  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.

  9. 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.

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

    PubMed

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

    2017-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

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

  12. Joint clustering of protein interaction networks through Markov random walk

    PubMed Central

    2014-01-01

    Biological networks obtained by high-throughput profiling or human curation are typically noisy. For functional module identification, single network clustering algorithms may not yield accurate and robust results. In order to borrow information across multiple sources to alleviate such problems due to data quality, we propose a new joint network clustering algorithm ASModel in this paper. We construct an integrated network to combine network topological information based on protein-protein interaction (PPI) datasets and homological information introduced by constituent similarity between proteins across networks. A novel random walk strategy on the integrated network is developed for joint network clustering and an optimization problem is formulated by searching for low conductance sets defined on the derived transition matrix of the random walk, which fuses both topology and homology information. The optimization problem of joint clustering is solved by a derived spectral clustering algorithm. Network clustering using several state-of-the-art algorithms has been implemented to both PPI networks within the same species (two yeast PPI networks and two human PPI networks) and those from different species (a yeast PPI network and a human PPI network). Experimental results demonstrate that ASModel outperforms the existing single network clustering algorithms as well as another recent joint clustering algorithm in terms of complex prediction and Gene Ontology (GO) enrichment analysis. PMID:24565376

  13. Cochlea segmentation using iterated random walks with shape prior

    NASA Astrophysics Data System (ADS)

    Ruiz Pujadas, Esmeralda; Kjer, Hans Martin; Vera, Sergio; Ceresa, Mario; González Ballester, Miguel Ángel

    2016-03-01

    Cochlear implants can restore hearing to deaf or partially deaf patients. In order to plan the intervention, a model from high resolution µCT images is to be built from accurate cochlea segmentations and then, adapted to a patient-specific model. Thus, a precise segmentation is required to build such a model. We propose a new framework for segmentation of µCT cochlear images using random walks where a region term is combined with a distance shape prior weighted by a confidence map to adjust its influence according to the strength of the image contour. Then, the region term can take advantage of the high contrast between the background and foreground and the distance prior guides the segmentation to the exterior of the cochlea as well as to less contrasted regions inside the cochlea. Finally, a refinement is performed preserving the topology using a topological method and an error control map to prevent boundary leakage. We tested the proposed approach with 10 datasets and compared it with the latest techniques with random walks and priors. The experiments suggest that this method gives promising results for cochlea segmentation.

  14. Radio variability and random walk noise properties of four blazars

    SciTech Connect

    Park, Jong-Ho; Trippe, Sascha E-mail: trippe@astro.snu.ac.kr

    2014-04-10

    We present the results of a time series analysis of the long-term radio light curves of four blazars: 3C 279, 3C 345, 3C 446, and BL Lacertae. We exploit the database of the University of Michigan Radio Astronomy Observatory monitoring program which provides densely sampled light curves spanning 32 years in time in three frequency bands located at 4.8, 8, and 14.5 GHz. Our sources show mostly flat or inverted (spectral indices –0.5 ≲ α ≲ 0) spectra, in agreement with optically thick emission. All light curves show strong variability on all timescales. Analyzing the time lags between the light curves from different frequency bands, we find that we can distinguish high-peaking flares and low-peaking flares in accordance with the classification of Valtaoja et al. The periodograms (temporal power spectra) of the observed light curves are consistent with random-walk power-law noise without any indication of (quasi-)periodic variability. The fact that all four sources studied are in agreement with being random-walk noise emitters at radio wavelengths suggests that such behavior is a general property of blazars.

  15. Combinatorial approximation algorithms for MAXCUT using random walks.

    SciTech Connect

    Seshadhri, Comandur; Kale, Satyen

    2010-11-01

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

  16. Ergodic transitions in continuous-time random walks

    NASA Astrophysics Data System (ADS)

    Saa, Alberto; Venegeroles, Roberto

    2010-09-01

    We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent results presented in the literature. For the case where sojourn times are identically distributed independent random variables, our results shed some light on the recently proposed transitions between ergodic and weakly nonergodic regimes. On the other hand, for the case of nonidentical trapping time densities over the lattice points, the distribution of time-averaged observables reveals that such systems are typically nonergodic, in agreement with some recent experimental evidences on the statistics of blinking quantum dots. Some explicit examples are considered in detail. Our results are independent of the lattice topology and dimensionality.

  17. Statistics of largest loops in a random walk

    NASA Astrophysics Data System (ADS)

    Ertas, Deniz; Kantor, Yacov

    1997-01-01

    We report further findings on the size distribution of the largest neutral segments in a sequence of N randomly charged monomers [D. Ertaş and Y. Kantor, Phys. Rev. E 53, 846 (1996)]. Upon mapping to one-dimensional random walks (RW's), this corresponds to finding the probability distribution for the size L of the largest segment that returns to its starting position in an N-step RW. We focus primarily on the large N, l=L/N<<1 limit, which exhibits an essential singularity. We establish analytical upper and lower bounds on the probability distribution, and numerically probe the distribution down to l~0.04 (corresponding to probabilities as low as 10-15) using a recursive Monte Carlo algorithm. We also investigate the possibility of singularities at l=1/k for integer k.

  18. The linear Ising model and its analytic continuation, random walk

    NASA Astrophysics Data System (ADS)

    Lavenda, B. H.

    2004-02-01

    A generalization of Gauss's principle is used to derive the error laws corresponding to Types II and VII distributions in Pearson's classification scheme. Student's r-p.d.f. (Type II) governs the distribution of the internal energy of a uniform, linear chain, Ising model, while the analytic continuation of the uniform exchange energy converts it into a Student t-density (Type VII) for the position of a random walk in a single spatial dimension. Higher-dimensional spaces, corresponding to larger degrees of freedom and generalizations to multidimensional Student r- and t-densities, are obtained by considering independent and identically random variables, having rotationally invariant densities, whose entropies are additive and generating functions are multiplicative.

  19. Some Minorants and Majorants of Random Walks and Levy Processes

    NASA Astrophysics Data System (ADS)

    Abramson, Joshua Simon

    This thesis consists of four chapters, all relating to some sort of minorant or majorant of random walks or Levy processes. In Chapter 1 we provide an overview of recent work on descriptions and properties of the convex minorant of random walks and Levy processes as detailed in Chapter 2, [72] and [73]. This work rejuvenated the field of minorants, and led to the work in all the subsequent chapters. The results surveyed include point process descriptions of the convex minorant of random walks and Levy processes on a fixed finite interval, up to an independent exponential time, and in the infinite horizon case. These descriptions follow from the invariance of these processes under an adequate path transformation. In the case of Brownian motion, we note how further special properties of this process, including time-inversion, imply a sequential description for the convex minorant of the Brownian meander. This chapter is based on [3], which was co-written with Jim Pitman, Nathan Ross and Geronimo Uribe Bravo. Chapter 1 serves as a long introduction to Chapter 2, in which we offer a unified approach to the theory of concave majorants of random walks. The reasons for the switch from convex minorants to concave majorants are discussed in Section 1.1, but the results are all equivalent. This unified theory is arrived at by providing a path transformation for a walk of finite length that leaves the law of the walk unchanged whilst providing complete information about the concave majorant - the path transformation is different from the one discussed in Chapter 1, but this is necessary to deal with a more general case than the standard one as done in Section 2.6. The path transformation of Chapter 1, which is discussed in detail in Section 2.8, is more relevant to the limiting results for Levy processes that are of interest in Chapter 1. Our results lead to a description of a walk of random geometric length as a Poisson point process of excursions away from its concave

  20. Asymptotic normality in a two-dimensional random walk model for cell motility

    SciTech Connect

    Stadje, W.

    1988-05-01

    We prove the asymptotic normality of a two-dimensional random walk describing the locomotion of cells on planar surfaces and calculate the asymptotic covariance matrix. The trajectories of the walk are random broken lines covered with constant speed, where the time intervals between turns as well as the turn angles are random and stochastically independent.

  1. 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.

  2. Influence of Neuromuscular Noise and Walking Speed on Fall Risk and Dynamic Stability in a 3D Dynamic Walking Model

    PubMed Central

    Roos, Paulien E.; Dingwell, Jonathan B.

    2013-01-01

    Older adults and those with increased fall risk tend to walk slower. They may do this voluntarily to reduce their fall risk. However, both slower and faster walking speeds can predict increased risk of different types of falls. The mechanisms that contribute to fall risk across speeds are not well known. Faster walking requires greater forward propulsion, generated by larger muscle forces. However, greater muscle activation induces increased signal-dependent neuromuscular noise. These speed-related increases in neuromuscular noise may contribute to the increased fall risk observed at faster walking speeds. Using a 3D dynamic walking model, we systematically varied walking speed without and with physiologically-appropriate neuromuscular noise. We quantified how actual fall risk changed with gait speed, how neuromuscular noise affected speed-related changes in fall risk, and how well orbital and local dynamic stability measures predicted changes in fall risk across speeds. When we included physiologically-appropriate noise to the ‘push-off’ force in our model, fall risk increased with increasing walking speed. Changes in kinematic variability, orbital, and local dynamic stability did not predict these speed-related changes in fall risk. Thus, the increased neuromuscular variability that results from increased signal-dependent noise that is necessitated by the greater muscular force requirements of faster walking may contribute to the increased fall risk observed at faster walking speeds. The lower fall risk observed at slower speeds supports experimental evidence that slowing down can be an effective strategy to reduce fall risk. This may help explain the slower walking speeds observed in older adults and others. PMID:23659911

  3. Influence of neuromuscular noise and walking speed on fall risk and dynamic stability in a 3D dynamic walking model.

    PubMed

    Roos, Paulien E; Dingwell, Jonathan B

    2013-06-21

    Older adults and those with increased fall risk tend to walk slower. They may do this voluntarily to reduce their fall risk. However, both slower and faster walking speeds can predict increased risk of different types of falls. The mechanisms that contribute to fall risk across speeds are not well known. Faster walking requires greater forward propulsion, generated by larger muscle forces. However, greater muscle activation induces increased signal-dependent neuromuscular noise. These speed-related increases in neuromuscular noise may contribute to the increased fall risk observed at faster walking speeds. Using a 3D dynamic walking model, we systematically varied walking speed without and with physiologically-appropriate neuromuscular noise. We quantified how actual fall risk changed with gait speed, how neuromuscular noise affected speed-related changes in fall risk, and how well orbital and local dynamic stability measures predicted changes in fall risk across speeds. When we included physiologically-appropriate noise to the 'push-off' force in our model, fall risk increased with increasing walking speed. Changes in kinematic variability, orbital, and local dynamic stability did not predict these speed-related changes in fall risk. Thus, the increased neuromuscular variability that results from increased signal-dependent noise that is necessitated by the greater muscular force requirements of faster walking may contribute to the increased fall risk observed at faster walking speeds. The lower fall risk observed at slower speeds supports experimental evidence that slowing down can be an effective strategy to reduce fall risk. This may help explain the slower walking speeds observed in older adults and others. Copyright © 2013 Elsevier Ltd. All rights reserved.

  4. Scaling analysis of random walks with persistence lengths: Application to self-avoiding walks

    NASA Astrophysics Data System (ADS)

    Granzotti, C. R. F.; Martinez, A. S.; da Silva, M. A. A.

    2016-05-01

    We develop an approach for performing scaling analysis of N -step random walks (RWs). The mean square end-to-end distance, , is written in terms of inner persistence lengths (IPLs), which we define by the ensemble averages of dot products between the walker's position and displacement vectors, at the j th step. For RW models statistically invariant under orthogonal transformations, we analytically introduce a relation between and the persistence length, λN, which is defined as the mean end-to-end vector projection in the first step direction. For self-avoiding walks (SAWs) on 2D and 3D lattices we introduce a series expansion for λN, and by Monte Carlo simulations we find that λ∞ is equal to a constant; the scaling corrections for λN can be second- and higher-order corrections to scaling for . Building SAWs with typically 100 steps, we estimate the exponents ν0 and Δ1 from the IPL behavior as function of j . The obtained results are in excellent agreement with those in the literature. This shows that only an ensemble of paths with the same length is sufficient for determining the scaling behavior of , being that the whole information needed is contained in the inner part of the paths.

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

    NASA Astrophysics Data System (ADS)

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

    2017-09-01

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

  6. Energy efficient walking with central pattern generators: from passive dynamic walking to biologically inspired control.

    PubMed

    Verdaasdonk, B W; Koopman, H F J M; van der Helm, F C T

    2009-07-01

    Like human walking, passive dynamic walking-i.e. walking down a slope with no actuation except gravity-is energy efficient by exploiting the natural dynamics. In the animal world, neural oscillators termed central pattern generators (CPGs) provide the basic rhythm for muscular activity in locomotion. We present a CPG model, which automatically tunes into the resonance frequency of the passive dynamics of a bipedal walker, i.e. the CPG model exhibits resonance tuning behavior. Each leg is coupled to its own CPG, controlling the hip moment of force. Resonance tuning above the endogenous frequency of the CPG-i.e. the CPG's eigenfrequency-is achieved by feedback of both limb angles to their corresponding CPG, while integration of the limb angles provides resonance tuning at and below the endogenous frequency of the CPG. Feedback of the angular velocity of both limbs to their corresponding CPG compensates for the time delay in the loop coupling each limb to its CPG. The resonance tuning behavior of the CPG model allows the gait velocity to be controlled by a single parameter, while retaining the energy efficiency of passive dynamic walking.

  7. A Branching Random Walk Seen from the Tip

    NASA Astrophysics Data System (ADS)

    Brunet, Éric; Derrida, Bernard

    2011-05-01

    We show that all the time-dependent statistical properties of the rightmost points of a branching Brownian motion can be extracted from the traveling wave solutions of the Fisher-KPP equation. The distribution of all the distances between the rightmost points has a long time limit which can be understood as the delay of the Fisher-KPP traveling waves when the initial condition is modified. The limiting measure exhibits the surprising property of superposability: the statistical properties of the distances between the rightmost points of the union of two realizations of the branching Brownian motion shifted by arbitrary amounts are the same as those of a single realization. We discuss the extension of our results to more general branching random walks.

  8. Maps of random walks on complex networks reveal community structure.

    PubMed

    Rosvall, Martin; Bergstrom, Carl T

    2008-01-29

    To comprehend the multipartite organization of large-scale biological and social systems, we introduce an information theoretic approach that reveals community structure in weighted and directed networks. We use the probability flow of random walks on a network as a proxy for information flows in the real system and decompose the network into modules by compressing a description of the probability flow. The result is a map that both simplifies and highlights the regularities in the structure and their relationships. We illustrate the method by making a map of scientific communication as captured in the citation patterns of >6,000 journals. We discover a multicentric organization with fields that vary dramatically in size and degree of integration into the network of science. Along the backbone of the network-including physics, chemistry, molecular biology, and medicine-information flows bidirectionally, but the map reveals a directional pattern of citation from the applied fields to the basic sciences.

  9. First-passage properties of bursty random walks

    NASA Astrophysics Data System (ADS)

    Volovik, D.; Redner, S.

    2010-06-01

    We investigate the first-passage properties of bursty random walks on a finite one-dimensional interval of length L, in which unit-length steps to the left occur with probability close to one, while steps of length b to the right—'bursts'—occur with small probability. This stochastic process provides a crude description of the early stages of virus spread in an organism after exposure. The interesting regime arises when b/L\\lesssim 1 , where the conditional exit time to reach L, corresponding to an infected state, has a non-monotonic dependence on initial position. Both the exit probability and the infection time exhibit complex dependencies on the initial condition due to the interplay between the burst length and interval length.

  10. Information filtering via biased random walk on coupled social network.

    PubMed

    Nie, Da-Cheng; Zhang, Zi-Ke; Dong, Qiang; Sun, Chongjing; Fu, Yan

    2014-01-01

    The recommender systems have advanced a great deal in the past two decades. However, most researchers focus their attentions on mining the similarities among users or objects in recommender systems and overlook the social influence which plays an important role in users' purchase process. In this paper, we design a biased random walk algorithm on coupled social networks which gives recommendation results based on both social interests and users' preference. Numerical analyses on two real data sets, Epinions and Friendfeed, demonstrate the improvement of recommendation performance by taking social interests into account, and experimental results show that our algorithm can alleviate the user cold-start problem more effectively compared with the mass diffusion and user-based collaborative filtering methods.

  11. Maxima of two random walks: Universal statistics of lead changes

    SciTech Connect

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

    2016-04-18

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

  12. Spectral coarse graining for random walks in bipartite networks.

    PubMed

    Wang, Yang; Zeng, An; Di, Zengru; Fan, Ying

    2013-03-01

    Many real-world networks display a natural bipartite structure, yet analyzing and visualizing large bipartite networks is one of the open challenges in complex network research. A practical approach to this problem would be to reduce the complexity of the bipartite system while at the same time preserve its functionality. However, we find that existing coarse graining methods for monopartite networks usually fail for bipartite networks. In this paper, we use spectral analysis to design a coarse graining scheme specific for bipartite networks, which keeps their random walk properties unchanged. Numerical analysis on both artificial and real-world networks indicates that our coarse graining can better preserve most of the relevant spectral properties of the network. We validate our coarse graining method by directly comparing the mean first passage time of the walker in the original network and the reduced one.

  13. Knots and Random Walks in Vibrated Granular Chains

    NASA Astrophysics Data System (ADS)

    Ben-Naim, Eli

    2002-03-01

    We study experimentally and theoretically statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard-core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with theoretical values. E. Ben-Naim, Z. A. Daya, P. Vorobieff, and R. E. Ecke, Phys. Rev. Lett. 86, 1414 (2001).

  14. Information Filtering via Biased Random Walk on Coupled Social Network

    PubMed Central

    Dong, Qiang; Fu, Yan

    2014-01-01

    The recommender systems have advanced a great deal in the past two decades. However, most researchers focus their attentions on mining the similarities among users or objects in recommender systems and overlook the social influence which plays an important role in users' purchase process. In this paper, we design a biased random walk algorithm on coupled social networks which gives recommendation results based on both social interests and users' preference. Numerical analyses on two real data sets, Epinions and Friendfeed, demonstrate the improvement of recommendation performance by taking social interests into account, and experimental results show that our algorithm can alleviate the user cold-start problem more effectively compared with the mass diffusion and user-based collaborative filtering methods. PMID:25147867

  15. Phase diffusion and random walk interpretation of electromagnetic scattering.

    PubMed

    Bahcivan, Hasan; Hysell, David L; Kelley, Michael C

    2003-08-01

    The relaxation behavior of phase observables for different particle diffusion models is found to establish a ground for radioscience interpretations of coherent backscatter spectra. The characteristic function for a random walk process at twice the incident radiation wave number is associated with the complex amplitude of the scattered field from a medium containing refractive index fluctuations. The phase relaxation function can be connected to the evolution of the characteristic function and may describe the average regression of the scattered field from a spontaneous fluctuation undergoing turbulent mixing. This connection holds when we assume that the stochastic description of particle movements based on a diffusion model is valid. The phase relaxation function, when identified as the generalized susceptibility function of the fluctuation dissipation theorem, is related to the spectral density of the scattered field from steady-state fluctuations.

  16. Maxima of two random walks: Universal statistics of lead changes

    SciTech Connect

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

    2016-04-18

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

  17. Composition of many spins, random walks and statistics

    NASA Astrophysics Data System (ADS)

    Polychronakos, Alexios P.; Sfetsos, Konstantinos

    2016-12-01

    The multiplicities of the decomposition of the product of an arbitrary number n of spin s states into irreducible SU (2) representations are computed. Two complementary methods are presented, one based on random walks in representation space and another based on the partition function of the system in the presence of a magnetic field. The large-n scaling limit of these multiplicities is derived, including nonperturbative corrections, and related to semiclassical features of the system. A physical application of these results to ferromagnetism is explicitly worked out. Generalizations involving several types of spins, as well as spin distributions, are also presented. The corresponding problem for (anti-)symmetric composition of spins is also considered and shown to obey remarkable duality and bosonization relations and exhibit novel large-n scaling properties.

  18. Correlated continuous time random walk and option pricing

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  19. DCPT: A dual-continua random walk particle tracker fortransport

    SciTech Connect

    Pan, L.; Liu, H.H.; Cushey, M.; Bodvarsson, G.S.

    2000-04-11

    Accurate and efficient simulation of chemical transport processes in the unsaturated zone of Yucca Mountain is important to evaluate the performance of the potential repository. The scale of the unsaturated zone model domain for Yucca Mountain (50 km{sup 2} area with a 600 meter depth to the water table) requires a large gridblock approach to efficiently analyze complex flow & transport processes. The conventional schemes based on finite element or finite difference methods perform well for dispersion-dominated transport, but are subject to considerable numerical dilution/dispersion for advection-dominated transport, especially when a large gridblock size is used. Numerical dispersion is an artificial, grid-dependent chemical spreading, especially for otherwise steep concentration fronts. One effective scheme to deal with numerical dispersion is the random walk particle method (RWPM). While significant progress has been made in developing RWPM algorithms and codes for single continuum systems, a random walk particle tracker, which can handle chemical transport in dual-continua (fractured porous media) associated with irregular grid systems, is still absent (to our knowledge) in the public domain. This is largely due to the lacking of rigorous schemes to deal with particle transfer between the continua, and efficient schemes to track particles in irregular grid systems. The main objectives of this study are (1) to develop approaches to extend RWPM from a single continuum to a dual-continua system; (2) to develop an efficient algorithm for tracking particles in 3D irregular grids; and (3) to integrate these approaches into an efficient and user-friendly software, DCPT, for simulating chemical transport in fractured porous media.

  20. Dynamics of Human Walking at Steady Speeds

    NASA Astrophysics Data System (ADS)

    Kokshenev, Valery B.

    2004-11-01

    Biped locomotion is discussed through a Lagrangian formulation for velocity-dependent, body driving forces. An analysis of level walking in humans is given through the known experimental data on the ground-reaction force and the external work without recourse to inverted-pendulum modeling. At a certain speed, rectilinear motion of the center of mass with its backward rotation along a shortened hypocycloid is ensured by double-frequency nonlinear oscillations, whose energy cost is 1% of the external work. With increasing speed, a peculiarity and an instability of the trajectory indicate, respectively, a slow-to-normal gait crossover and the maximal fast walking speed. Key words: integrative biology, biped locomotion, human gaits, muscles.

  1. Scaling properties of random walks on small-world networks.

    PubMed

    Almaas, E; Kulkarni, R V; Stroud, D

    2003-11-01

    Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These properties include the average number of distinct sites visited by the random walker, the mean-square displacement of the walker, and the distribution of first-return times. The scaling form has three characteristic time regimes. At short times, the walker does not see the small-world shortcuts and effectively probes an ordinary Euclidean network in d dimensions. At intermediate times, the properties of the walker shows scaling behavior characteristic of an infinite small-world network. Finally, at long times, the finite size of the network becomes important, and many of the properties of the walker saturate. We propose general analytical forms for the scaling properties in all three regimes, and show that these analytical forms are consistent with our numerical simulations.

  2. 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.

  3. Treadmill Training Improves Overground Walking Economy in Parkinson’s Disease: A Randomized, Controlled Pilot Study

    PubMed Central

    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. PMID:25309510

  4. 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

  5. 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.

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

    NASA Astrophysics Data System (ADS)

    Iomin, A.

    2015-10-01

    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.

  7. Continuous time random walk with linear force applied to hydrated proteins

    NASA Astrophysics Data System (ADS)

    Fa, Kwok Sau

    2013-08-01

    An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations. Analytical expressions for transition probability density, mean square displacement, and intermediate scattering function are presented. The mean square displacement and intermediate scattering function can fit well the simulation data of the temperature-dependent translational dynamics of nitrogen atoms of elastin for a wide range of temperatures and various scattering vectors. Moreover, the numerical results are also compared with those of a fractional diffusion equation.

  8. Continuous time random walk with linear force applied to hydrated proteins.

    PubMed

    Fa, Kwok Sau

    2013-08-14

    An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations. Analytical expressions for transition probability density, mean square displacement, and intermediate scattering function are presented. The mean square displacement and intermediate scattering function can fit well the simulation data of the temperature-dependent translational dynamics of nitrogen atoms of elastin for a wide range of temperatures and various scattering vectors. Moreover, the numerical results are also compared with those of a fractional diffusion equation.

  9. Continuous Time Open Quantum Random Walks and Non-Markovian Lindblad Master Equations

    NASA Astrophysics Data System (ADS)

    Pellegrini, Clément

    2014-02-01

    A new type of quantum random walks, called Open Quantum Random Walks, has been developed and studied in Attal et al. (Open quantum random walks, preprint) and (Central limit theorems for open quantum random walks, preprint). In this article we present a natural continuous time extension of these Open Quantum Random Walks. This continuous time version is obtained by taking a continuous time limit of the discrete time Open Quantum Random Walks. This approximation procedure is based on some adaptation of Repeated Quantum Interactions Theory (Attal and Pautrat in Annales Henri Poincaré Physique Théorique 7:59-104, 2006) coupled with the use of correlated projectors (Breuer in Phys Rev A 75:022103, 2007). The limit evolutions obtained this way give rise to a particular type of quantum master equations. These equations appeared originally in the non-Markovian generalization of the Lindblad theory (Breuer in Phys Rev A 75:022103, 2007). We also investigate the continuous time limits of the quantum trajectories associated with Open Quantum Random Walks. We show that the limit evolutions in this context are described by jump stochastic differential equations. Finally we present a physical example which can be described in terms of Open Quantum Random Walks and their associated continuous time limits.

  10. A Continuous Time Random Walk Description of Monodisperse, Hard-Sphere Colloids below the Ordering Transition

    NASA Astrophysics Data System (ADS)

    Lechman, Jeremy; Pierce, Flint

    2012-02-01

    Diffusive transport is a ubiquitous process that is typically understood in terms of a classical random walk of non-interacting particles. Here we present the results for a model of hard-sphere colloids in a Newtonian incompressible solvent at various volume fractions below the ordering transition (˜50%). We numerically simulate the colloidal systems via Fast Lubrication Dynamics -- a Brownian Dynamics approach with corrected mean-field hydrodynamic interactions. Colloid-colloid interactions are also included so that we effectively solve a system of interacting Langevin equations. The results of the simulations are analyzed in terms of the diffusion coefficient as a function of time with the early and late time diffusion coefficients comparing well with experimental results. An interpretation of the full time dependent behavior of the diffusion coefficient and mean-squared displacement is given in terms of a continuous time random walk. Therefore, the deterministic, continuum diffusion equation which arises from the discrete, interacting random walkers is presented. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

  11. Optimization-based Dynamic Human Walking Prediction

    DTIC Science & Technology

    2007-01-01

    9(1), 1997, p 10-17. 3. Chevallereau, C. and Aousin, Y. Optimal reference trajectories for walking and running of a biped robot. Robotica , v 19...28, 2001, Arlington, Virginia. 13. Mu, XP. and Wu, Q. Synthesis of a complete sagittal gait cycle for a five-link biped robot. Robotica , v 21...gait cycles of a biped robot. Robotica , v 21(2), 2003, p 199-210. 16. Sardain, P. and Bessonnet, G. Forces acting on a biped robot. Center of

  12. Convex hulls of random walks: Large-deviation properties

    NASA Astrophysics Data System (ADS)

    Claussen, Gunnar; Hartmann, Alexander K.; Majumdar, Satya N.

    2015-05-01

    We study the convex hull of the set of points visited by a two-dimensional random walker of T discrete time steps. Two natural observables that characterize the convex hull in two dimensions are its perimeter L and area A . While the mean perimeter and the mean area have been studied before, analytically and numerically, and exact results are known for large T (Brownian motion limit), little is known about the full distributions P (A ) and P (L ) . In this paper we provide numerical results for these distributions. We use a sophisticated large-deviation approach that allows us to study the distributions over a larger range of the support, where the probabilities P (A ) and P (L ) are as small as 10-300. We analyze (open) random walks as well as (closed) Brownian bridges on the two-dimensional discrete grid as well as in the two-dimensional plane. The resulting distributions exhibit, for large T , a universal scaling behavior (independent of the details of the jump distributions) as a function of A /T and L /√{T } , respectively. We are also able to obtain the rate function, describing rare events at the tails of these distributions, via a numerical extrapolation scheme and find a linear and square dependence as a function of the rescaled perimeter and the rescaled area, respectively.

  13. Convex hulls of random walks: Large-deviation properties.

    PubMed

    Claussen, Gunnar; Hartmann, Alexander K; Majumdar, Satya N

    2015-05-01

    We study the convex hull of the set of points visited by a two-dimensional random walker of T discrete time steps. Two natural observables that characterize the convex hull in two dimensions are its perimeter L and area A. While the mean perimeter 〈L〉 and the mean area 〈A〉 have been studied before, analytically and numerically, and exact results are known for large T (Brownian motion limit), little is known about the full distributions P(A) and P(L). In this paper we provide numerical results for these distributions. We use a sophisticated large-deviation approach that allows us to study the distributions over a larger range of the support, where the probabilities P(A) and P(L) are as small as 10(-300). We analyze (open) random walks as well as (closed) Brownian bridges on the two-dimensional discrete grid as well as in the two-dimensional plane. The resulting distributions exhibit, for large T, a universal scaling behavior (independent of the details of the jump distributions) as a function of A/T and L/√[T], respectively. We are also able to obtain the rate function, describing rare events at the tails of these distributions, via a numerical extrapolation scheme and find a linear and square dependence as a function of the rescaled perimeter and the rescaled area, respectively.

  14. Intracellular transport of insulin granules is a subordinated random walk

    PubMed Central

    Tabei, S. M. Ali; Burov, Stanislav; Kim, Hee Y.; Kuznetsov, Andrey; Huynh, Toan; Jureller, Justin; Philipson, Louis H.; Dinner, Aaron R.; Scherer, Norbert F.

    2013-01-01

    We quantitatively analyzed particle tracking data on insulin granules expressing fluorescent fusion proteins in MIN6 cells to better understand the motions contributing to intracellular transport and, more generally, the means for characterizing systems far from equilibrium. Care was taken to ensure that the statistics reflected intrinsic features of the individual granules rather than details of the measurement and overall cell state. We find anomalous diffusion. Interpreting such data conventionally requires assuming that a process is either ergodic with particles working against fluctuating obstacles (fractional Brownian motion) or nonergodic with a broad distribution of dwell times for traps (continuous-time random walk). However, we find that statistical tests based on these two models give conflicting results. We resolve this issue by introducing a subordinated scheme in which particles in cages with random dwell times undergo correlated motions owing to interactions with a fluctuating environment. We relate this picture to the underlying microtubule structure by imaging in the presence of vinblastine. Our results provide a simple physical picture for how diverse pools of insulin granules and, in turn, biphasic secretion could arise. PMID:23479621

  15. Effects of perturbation magnitude on dynamic stability when walking in destabilizing environments.

    PubMed

    Sinitksi, Emily H; Terry, Kevin; Wilken, Jason M; Dingwell, Jonathan B

    2012-08-09

    External perturbations applied to the walking surface or visual field can challenge an individual's ability to maintain stability during walking. Accurately quantifying and predicting changes in stability during walking will further our understanding of how individuals respond to challenges encountered during daily life and guide the development of assessments and rehabilitation interventions for individuals at increased risk of falling. This study is the first to determine how orbital and local dynamic stability metrics, including maximum Floquet multipliers and local divergence exponents, change in response to continuous mediolateral visual and surface perturbations of different amplitudes. Eleven healthy individuals walked in a fully immersive virtual environment. Participants completed two 3-min walking trials each under the following nine conditions: no perturbations, surface perturbations at each of 3 amplitudes, and visual perturbations at each of 5 amplitudes. All perturbations were applied as continuous pseudo-random oscillations. During both surface and visual perturbations, individuals were significantly more orbitally and locally unstable compared to un-perturbed walking. As walking surface perturbation amplitudes increased, individuals were more orbitally (but not locally) unstable. As visual perturbation amplitudes increased, individuals were more locally (but not orbitally) unstable between lower and higher amplitudes. Overall, these dynamic stability metrics were much less sensitive to changes in perturbation amplitudes than to differences between un-perturbed and perturbed walking, or to differences between mechanical and visual perturbations. This suggests that the type of perturbation(s) applied has a far greater impact than the magnitude of those perturbations in determining the response that will be elicited. Copyright © 2012 Elsevier Ltd. All rights reserved.

  16. A Randomized Trial of Two Forms of Therapeutic Activity to Improve Walking: Effect on the Energy Cost of Walking

    PubMed Central

    Perera, Subashan; Brach, Jennifer S.; Cham, Rakie; Rosano, Caterina; Studenski, Stephanie A.

    2009-01-01

    Background Therapeutic activities to improve mobility often include walking practice and exercises to improve deficits in endurance, strength, and balance. Because walking may also be energy inefficient in people with decreased mobility, another approach is to reduce energy cost by improving timing and coordination (TC) of movement. Methods This pilot randomized trial of older adults with slow and variable gait offered two types of therapeutic activity over 12 weeks. One addressed Walking, Endurance, Balance, and Strength (WEBS) and the other focused on TC. Outcomes were energy cost of walking and measures of mobility. Results Of 50 participants (mean age, 77.2 ± 5.5 years, 65% women), 47 completed the study. Baseline gait speed was 0.85 ± 0.13 m/s and energy cost of walking was 0.30 ± 0.10 mL/kg/m, nearly twice normal. Both interventions increased gait speed (TC by 0.21 m/s and WEBS by 0.14 m/s, p < .001). TC reduced the energy cost of walking 0.10 ± 0.03 mL/kg/m more than WEBS (p < .001) and reduced the modified Gait Abnormalities Rating Scale 1.5 ± 0.6 more points than WEBS (p < .05). TC had a 9.8 ± 3.5 points greater gain than WEBS in self-reported confidence in walking (p < .01). Conclusions In older adults with slow and variable gait, activity focused on TC reduced the energy cost of walking and improved confidence in walking more than WEBS while generating at least equivalent gains in mobility. To optimize mobility, future larger studies should assess various combinations of TC and WEBS over longer periods of time. PMID:19643842

  17. Kardar-Parisi-Zhang Equation and Large Deviations for Random Walks in Weak Random Environments

    NASA Astrophysics Data System (ADS)

    Corwin, Ivan; Gu, Yu

    2017-01-01

    We consider the transition probabilities for random walks in 1+1 dimensional space-time random environments (RWRE). For critically tuned weak disorder we prove a sharp large deviation result: after appropriate rescaling, the transition probabilities for the RWRE evaluated in the large deviation regime, converge to the solution to the stochastic heat equation (SHE) with multiplicative noise (the logarithm of which is the KPZ equation). We apply this to the exactly solvable Beta RWRE and additionally present a formal derivation of the convergence of certain moment formulas for that model to those for the SHE.

  18. Random walk approach for dispersive transport in pipe networks

    NASA Astrophysics Data System (ADS)

    Sämann, Robert; Graf, Thomas; Neuweiler, Insa

    2016-04-01

    Keywords: particle transport, random walk, pipe, network, HYSTEM-EXTAN, OpenGeoSys After heavy pluvial events in urban areas the available drainage system may be undersized at peak flows (Fuchs, 2013). Consequently, rainwater in the pipe network is likely to spill out through manholes. The presence of hazardous contaminants in the pipe drainage system represents a potential risk to humans especially when the contaminated drainage water reaches the land surface. Real-time forecasting of contaminants in the drainage system needs a quick calculation. Numerical models to predict the fate of contaminants are usually based on finite volume methods. Those are not applicable here because of their volume averaging elements. Thus, a more efficient method is preferable, which is independent from spatial discretization. In the present study, a particle-based method is chosen to calculate transport paths and spatial distribution of contaminants within a pipe network. A random walk method for particles in turbulent flow in partially filled pipes has been developed. Different approaches for in-pipe-mixing and node-mixing with respect to the geometry in a drainage network are shown. A comparison of dispersive behavior and calculation time is given to find the fastest model. The HYSTEM-EXTRAN (itwh, 2002) model is used to provide hydrodynamic conditions in the pipe network according to surface runoff scenarios in order to real-time predict contaminant transport in an urban pipe network system. The newly developed particle-based model will later be coupled to the subsurface flow model OpenGeoSys (Kolditz et al., 2012). References: Fuchs, L. (2013). Gefährdungsanalyse zur Überflutungsvorsorge kommunaler Entwässerungssysteme. Sanierung und Anpassung von Entwässerungssystemen-Alternde Infrastruktur und Klimawandel, Österreichischer Wasser-und Abfallwirtschaftsverband, Wien, ISBN, 978-3. itwh (2002). Modellbeschreibung, Institut für technisch-wissenschaftliche Hydrologie Gmb

  19. Static standing and dynamic walking of a practical biped robot

    SciTech Connect

    Zheng, Yuan F.; Rao, M.

    1987-01-01

    The study of static standing and dynamic walking of a practical biped robot is presented in this research report. A systematic method for describing the kinematic behavior of a biped robot is first developed. The development is based on the well-known Denavit-Hartenburg convention. As a result, the method is basically the same as the one used for robot manipulators, except for some considerations given to the unique functions and structure of a biped robot. The static standing of a biped robot is then studied. It is argued that static standing capability is very important if a biped robot is to be employed in an industrial environment. In order to measure the performance of the biped in static standing in terms of its stability, two parameters, stable margin and stable index, are introduced. Based on these parameters, optimal stability of the biped robot with one-foot and two-foot standing cases are discussed. For dynamic walking, a mathematical treatment is first described. Conclusion is reached that by proper positioning of the landing, stable dynamic walking can be realized. A practical biped robot is introduced in the final part of the report. Experimental results of static standing and dynamic walking of the biped robot are presented, to verify the theoretical results. 28 refs., 9 figs., 1 tab.

  20. Anomalous transport in turbulent plasmas and continuous time random walks

    SciTech Connect

    Balescu, R.

    1995-05-01

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

  1. IS QUASAR OPTICAL VARIABILITY A DAMPED RANDOM WALK?

    SciTech Connect

    Zu Ying; Kochanek, C. S.; Kozlowski, Szymon; Udalski, Andrzej

    2013-03-10

    The damped random walk (DRW) model is increasingly used to model the variability in quasar optical light curves, but it is still uncertain whether the DRW model provides an adequate description of quasar optical variability across all timescales. Using a sample of OGLE quasar light curves, we consider four modifications to the DRW model by introducing additional parameters into the covariance function to search for deviations from the DRW model on both short and long timescales. We find good agreement with the DRW model on timescales that are well sampled by the data (from a month to a few years), possibly with some intrinsic scatter in the additional parameters, but this conclusion depends on the statistical test employed and is sensitive to whether the estimates of the photometric errors are correct to within {approx}10%. On very short timescales (below a few months), we see some evidence of the existence of a cutoff below which the correlation is stronger than the DRW model, echoing the recent finding of Mushotzky et al. using quasar light curves from Kepler. On very long timescales (>a few years), the light curves do not constrain models well, but are consistent with the DRW model.

  2. Electron avalanche structure determined by random walk theory

    NASA Technical Reports Server (NTRS)

    Englert, G. W.

    1973-01-01

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

  3. Learning Markov Random Walks for robust subspace clustering and estimation.

    PubMed

    Liu, Risheng; Lin, Zhouchen; Su, Zhixun

    2014-11-01

    Markov Random Walks (MRW) has proven to be an effective way to understand spectral clustering and embedding. However, due to less global structural measure, conventional MRW (e.g., the Gaussian kernel MRW) cannot be applied to handle data points drawn from a mixture of subspaces. In this paper, we introduce a regularized MRW learning model, using a low-rank penalty to constrain the global subspace structure, for subspace clustering and estimation. In our framework, both the local pairwise similarity and the global subspace structure can be learnt from the transition probabilities of MRW. We prove that under some suitable conditions, our proposed local/global criteria can exactly capture the multiple subspace structure and learn a low-dimensional embedding for the data, in which giving the true segmentation of subspaces. To improve robustness in real situations, we also propose an extension of the MRW learning model based on integrating transition matrix learning and error correction in a unified framework. Experimental results on both synthetic data and real applications demonstrate that our proposed MRW learning model and its robust extension outperform the state-of-the-art subspace clustering methods.

  4. Stochastic calculus for uncoupled continuous-time random walks

    NASA Astrophysics Data System (ADS)

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

    2009-06-01

    The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingale transform theorem, if the CTRW is a martingale, the Itō integral is a martingale too. It is shown how the definition of the stochastic integrals can be used to easily compute them by Monte Carlo simulation. The relations between a CTRW, its quadratic variation, its Stratonovich integral, and its Itō integral are highlighted by numerical calculations when the jumps in space of the CTRW have a symmetric Lévy α -stable distribution and its waiting times have a one-parameter Mittag-Leffler distribution. Remarkably, these distributions have fat tails and an unbounded quadratic variation. In the diffusive limit of vanishing scale parameters, the probability density of this kind of CTRW satisfies the space-time fractional diffusion equation (FDE) or more in general the fractional Fokker-Planck equation, which generalizes the standard diffusion equation, solved by the probability density of the Wiener process, and thus provides a phenomenologic model of anomalous diffusion. We also provide an analytic expression for the quadratic variation of the stochastic process described by the FDE and check it by Monte Carlo.

  5. Peer-to-Peer Topology Formation Using Random Walk

    NASA Astrophysics Data System (ADS)

    Kwong, Kin-Wah; Tsang, Danny H. K.

    Peer-to-Peer (P2P) systems such as live video streaming and content sharing are usually composed of a huge number of users with heterogeneous capacities. As a result, designing a distributed algorithm to form such a giant-scale topology in a heterogeneous environment is a challenging question because, on the one hand, the algorithm should exploit the heterogeneity of users' capacities to achieve load-balancing and, on the other hand, the overhead of the algorithm should be kept as low as possible. To meet such requirements, we introduce a very simple protocol for building heterogeneous unstructured P2P networks. The basic idea behind our protocol is to exploit a simple, distributed nature of random walk sampling to assist the peers in selecting their suitable neighbors in terms of capacity and connectivity to achieve load-balancing. To gain more insights into our proposed protocol, we also develop a detailed analysis to investigate our protocol under any heterogeneous P2P environment. The analytical results are validated by the simulations. The ultimate goal of this chapter is to stimulate further research to explore the fundamental issues in heterogeneous P2P networks.

  6. Stochastic calculus for uncoupled continuous-time random walks.

    PubMed

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

    2009-06-01

    The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingale transform theorem, if the CTRW is a martingale, the Itō integral is a martingale too. It is shown how the definition of the stochastic integrals can be used to easily compute them by Monte Carlo simulation. The relations between a CTRW, its quadratic variation, its Stratonovich integral, and its Itō integral are highlighted by numerical calculations when the jumps in space of the CTRW have a symmetric Lévy alpha -stable distribution and its waiting times have a one-parameter Mittag-Leffler distribution. Remarkably, these distributions have fat tails and an unbounded quadratic variation. In the diffusive limit of vanishing scale parameters, the probability density of this kind of CTRW satisfies the space-time fractional diffusion equation (FDE) or more in general the fractional Fokker-Planck equation, which generalizes the standard diffusion equation, solved by the probability density of the Wiener process, and thus provides a phenomenologic model of anomalous diffusion. We also provide an analytic expression for the quadratic variation of the stochastic process described by the FDE and check it by Monte Carlo.

  7. Maxima of two random walks: Universal statistics of lead changes

    DOE PAGES

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

    2016-04-18

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

  8. Random walk models of worker sorting in ant colonies.

    PubMed

    Sendova-Franks, Ana B; Van Lent, Jan

    2002-07-21

    Sorting can be an important mechanism for the transfer of information from one level of biological organization to another. Here we study the algorithm underlying worker sorting in Leptothorax ant colonies. Worker sorting is related to task allocation and therefore to the adaptive advantages associated with an efficient system for the division of labour in ant colonies. We considered four spatially explicit individual-based models founded on two-dimensional correlated random walk. Our aim was to establish whether sorting at the level of the worker population could occur with minimal assumptions about the behavioural algorithm of individual workers. The behaviour of an individual worker in the models could be summarized by the rule "move if you can, turn always". We assume that the turning angle of a worker is individually specific and negatively dependent on the magnitude of an internal parameter micro which could be regarded as a measure of individual experience or task specialization. All four models attained a level of worker sortedness that was compatible with results from experiments onLeptothorax ant colonies. We found that the presence of a sorting pivot, such as the nest wall or an attraction force towards the centre of the worker population, was crucial for sorting. We make a distinction between such pivots and templates and discuss the biological implications of their difference.

  9. Random Walks and Effective Optical Depth in Relativistic Flow

    NASA Astrophysics Data System (ADS)

    Shibata, Sanshiro; Tominaga, Nozomu; Tanaka, Masaomi

    2014-05-01

    We investigate the random walk process in relativistic flow. In the relativistic flow, photon propagation is concentrated in the direction of the flow velocity due to the relativistic beaming effect. We show that in the pure scattering case, the number of scatterings is proportional to the size parameter ξ ≡ L/l 0 if the flow velocity β ≡ v/c satisfies β/Γ Gt ξ-1, while it is proportional to ξ2 if β/Γ Lt ξ-1, where L and l 0 are the size of the system in the observer frame and the mean free path in the comoving frame, respectively. We also examine the photon propagation in the scattering and absorptive medium. We find that if the optical depth for absorption τa is considerably smaller than the optical depth for scattering τs (τa/τs Lt 1) and the flow velocity satisfies \\beta \\gg \\sqrt{2\\tau _a/\\tau _s}, then the effective optical depth is approximated by τ* ~= τa(1 + β)/β. Furthermore, we perform Monte Carlo simulations of radiative transfer and compare the results with the analytic expression for the number of scatterings. The analytic expression is consistent with the results of the numerical simulations. The expression derived in this study can be used to estimate the photon production site in relativistic phenomena, e.g., gamma-ray burst and active galactic nuclei.

  10. The linking number and the writhe of uniform random walks and polygons in confined spaces

    NASA Astrophysics Data System (ADS)

    Panagiotou, E.; Millett, K. C.; Lambropoulou, S.

    2010-01-01

    Random walks and polygons are used to model polymers. In this paper we consider the extension of the writhe, self-linking number and linking number to open chains. We then study the average writhe, self-linking and linking number of random walks and polygons over the space of configurations as a function of their length. We show that the mean squared linking number, the mean squared writhe and the mean squared self-linking number of oriented uniform random walks or polygons of length n, in a convex confined space, are of the form O(n2). Moreover, for a fixed simple closed curve in a convex confined space, we prove that the mean absolute value of the linking number between this curve and a uniform random walk or polygon of n edges is of the form O(\\sqrt{n}) . Our numerical studies confirm those results. They also indicate that the mean absolute linking number between any two oriented uniform random walks or polygons, of n edges each, is of the form O(n). Equilateral random walks and polygons are used to model polymers in θ-conditions. We use numerical simulations to investigate how the self-linking and linking number of equilateral random walks scale with their length.

  11. Glassy behavior and jamming of a random walk process for sequentially satisfying a constraint satisfaction formula

    NASA Astrophysics Data System (ADS)

    Zhou, Haijun

    2010-02-01

    Random K-satisfiability (K-SAT) is a model system for studying typical-case complexity of combinatorial optimization. Recent theoretical and simulation work revealed that the solution space of a random K-SAT formula has very rich structures, including the emergence of solution communities within single solution clusters. In this paper we investigate the influence of the solution space landscape to a simple stochastic local search process SEQSAT, which satisfies a K-SAT formula in a sequential manner. Before satisfying each newly added clause, SEQSAT walk randomly by single-spin flips in a solution cluster of the old subformula. This search process is efficient when the constraint density α of the satisfied subformula is less than certain value αcm; however it slows down considerably as α> αcm and finally reaches a jammed state at α≈αj. The glassy dynamical behavior of SEQSAT for α≥αcm probably is due to the entropic trapping of various communities in the solution cluster of the satisfied subformula. For random 3-SAT, the jamming transition point αj is larger than the solution space clustering transition point αd, and its value can be predicted by a long-range frustration mean-field theory. For random K-SAT with K ≥ 4, however, our simulation results indicate that αj = αd. The relevance of this work for understanding the dynamic properties of glassy systems is also discussed.

  12. Dynamic Margins of Stability During Human Walking in Destabilizing Environments☆

    PubMed Central

    McAndrew Young, Patricia M.; Wilken, Jason M.; Dingwell, Jonathan B.

    2012-01-01

    Understanding how humans maintain stability when walking, particularly when exposed to perturbations, is key to preventing falls. Here, we quantified how imposing continuous, pseudorandom anterior-posterior (AP) and mediolateral (ML) oscillations affected the control of dynamic walking stability. Twelve subjects completed five 3-minute walking trials in the Computer Assisted Rehabilitation ENvironment (CAREN) system under each of 5 conditions: no perturbation (NOP), AP platform (APP) or visual (APV) or ML platform (MLP) or visual (MLV) oscillations. We computed AP and ML margins of stability (MOS) for each trial. Mean MOSml were consistently slightly larger than NOP during all perturbation conditions (p ≤ 0.038). Mean MOSap for the APP, MLP and MLV oscillations were significantly smaller than during NOP (p < 0.0005). Variability of both MOSap and MOSml was significantly greater during the MLP and MLV oscillations than during NOP (p < 0.0005). We also directly quantified how the MOS on any given step affected the MOS on the following step using first-return plots. There were significant changes in step-to-step MOSml dynamics between experimental conditions (p < 0.0005). These changes suggested that subjects may have been trying to control foot placement, and consequently stability, during the perturbation conditions. Quantifying step-to-step changes in margins of dynamic stability may be more useful than mean MOS in assessing how individuals control walking stability. PMID:22326059

  13. Dynamic margins of stability during human walking in destabilizing environments.

    PubMed

    McAndrew Young, Patricia M; Wilken, Jason M; Dingwell, Jonathan B

    2012-04-05

    Understanding how humans maintain stability when walking, particularly when exposed to perturbations, is key to preventing falls. Here, we quantified how imposing continuous, pseudorandom anterior-posterior (AP) and mediolateral (ML) oscillations affected the control of dynamic walking stability. Twelve subjects completed five 3-minute walking trials in the Computer Assisted Rehabilitation ENvironment (CAREN) system under each of 5 conditions: no perturbation (NOP), AP platform (APP) or visual (APV) or ML platform (MLP) or visual (MLV) oscillations. We computed AP and ML margins of stability (MOS) for each trial. Mean MOS(ml) were consistently slightly larger during all perturbation conditions than during NOP (p≤0.038). Mean MOS(ap) for the APP, MLP and MLV oscillations were significantly smaller than during NOP (p<0.0005). Variability of both MOS(ap) and MOS(ml) was significantly greater during the MLP and MLV oscillations than during NOP (p<0.0005). We also directly quantified how the MOS on any given step affected the MOS on the following step using first-return plots. There were significant changes in step-to-step MOS(ml) dynamics between experimental conditions (p<0.0005). These changes suggested that subjects may have been trying to control foot placement, and consequently stability, during the perturbation conditions. Quantifying step-to-step changes in margins of dynamic stability may be more useful than mean MOS in assessing how individuals control walking stability. Copyright © 2012 Elsevier Ltd. All rights reserved.

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

    NASA Astrophysics Data System (ADS)

    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.

  15. 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.

  16. 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

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

    PubMed

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

    2014-09-01

    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). 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. 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. 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. 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.

  18. Dynamic instability during post-stroke hemiparetic walking.

    PubMed

    Kao, Pei-Chun; Dingwell, Jonathan B; Higginson, Jill S; Binder-Macleod, Stuart

    2014-07-01

    Falls and fall-related injuries cause extremely costly and potentially fatal health problems in people post-stroke. However, there is no global indicator of walking instability for detecting which individuals will have increased risk of falls. The purposes of this study were to directly quantify walking stability in stroke survivors and neurologically intact controls and to determine which stability measures would reveal the changes in walking stability following stroke. This study thus provided an initial step to establish objective measures for identifying potential fallers. Nine post-stroke individuals and nine controls walked on a treadmill at four different speeds. We computed short-term local divergence exponent (LDE) and maximum Floquet multiplier (maxFM) of the trunk motion, average and variability of dynamic margins of stability (MOS) and step spatiotemporal measures. Post-stroke individuals demonstrated larger short-term LDE (p = 0.002) and maxFM (p = 0.041) in the mediolateral (ML) direction compared to the controls but remained orbitally stable (maxFM < 1). In addition, post-stroke individuals walked with greater average step width (p = 0.003) but similar average ML MOS (p = 0.154) compared to the controls. Post-stroke individuals also exhibited greater variability in all MOS and step measures (all p < 0.005). Our findings indicate that post-stroke individuals walked with greater local and orbital instability and gait variability than neurologically intact controls. The results suggest that short-term LDE of ML trunk motion and the variability of MOS and step spatiotemporal measures detect the changes in walking stability associated with stroke. These stability measures may have the potential for identifying those post-stroke individuals at increased risk of falls. Copyright © 2014 Elsevier B.V. All rights reserved.

  19. Effective-medium approximation for lattice random walks with long-range jumps

    NASA Astrophysics Data System (ADS)

    Thiel, Felix; Sokolov, Igor M.

    2016-07-01

    We consider the random walk on a lattice with random transition rates and arbitrarily long-range jumps. We employ Bruggeman's effective-medium approximation (EMA) to find the disorder-averaged (coarse-grained) dynamics. The EMA procedure replaces the disordered system with a cleverly guessed reference system in a self-consistent manner. We give necessary conditions on the reference system and discuss possible physical mechanisms of anomalous diffusion. In the case of a power-law scaling between transition rates and distance, lattice variants of Lévy-flights emerge as the effective medium, and the problem is solved analytically, bearing the effective anomalous diffusivity. Finally, we discuss several example distributions and demonstrate very good agreement with numerical simulations.

  20. 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

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

    SciTech Connect

    Rudinger, Kenneth; Gamble, John King; Bach, Eric; Friesen, Mark; Joynt, Robert; Coppersmith, S. N.

    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 erences 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.

  2. A Straightforward Random Walk Model for Fast Push-Pull Tracer Test Evaluation.

    PubMed

    Klotzsch, Stephan; Binder, Martin; Händel, Falk

    2017-01-01

    In this article, we present a straightforward random walk model for fast evaluation of push-pull tracer tests. By developing an adaptive algorithm, we overcome the problem of manually defining how many particles have to be used to simulate the transport problem. Beside this, we validate the random walk model by evaluating a push-pull tracer test with drift phase and confirm the results with MT3DMS. The random walk model took less than 1% of computational time of MT3DMS, thus allowing a remarkable faster evaluation of push-pull tracer tests. © 2016, National Ground Water Association.

  3. Dynamic perception of dynamic affordances: walking on a ship at sea.

    PubMed

    Walter, Hannah; Wagman, Jeffrey B; Stergiou, Nick; Erkmen, Nurtekin; Stoffregen, Thomas A

    2017-02-01

    Motion of the surface of the sea (waves, and swell) causes oscillatory motion of ships at sea. Generally, ships are longer than they are wide. One consequence of this structural difference is that oscillatory ship motion typically will be greater in roll (i.e., the ship rolling from side to side) than in pitch (i.e., the bow and stern rising and falling). For persons on ships at sea, affordances for walking on the open deck should be differentially influenced by ship motion in roll and pitch. Specifically, the minimum width of a walkable path should be greater when walking along the ship's short, or athwart axis than when walking along its long, or fore-aft axis. On a ship at sea, we evaluated the effects of walking in different directions (fore-aft vs. athwart) on actual walking performance. We did this by laying out narrow paths on the deck and asking participants (experienced maritime crewmembers) to walk as far as they could while remaining within the lateral path boundaries. As predicted, participants walked farther along the athwart path than along the fore-aft path. Before actual walking, we evaluated participants' judgments of their walking ability in the fore-aft and athwart directions. These judgments mirrored the observed differences in walking performance, and the accuracy of judgments did not differ between the two directions. We conclude that experienced maritime crewmembers were sensitive to affordances for walking in which the relevant properties of the environment were exclusively dynamic.

  4. Dynamic structure of locomotor behavior in walking fruit flies

    PubMed Central

    Katsov, Alexander Y; Freifeld, Limor; Horowitz, Mark; Kuehn, Seppe; Clandinin, Thomas R

    2017-01-01

    The function of the brain is unlikely to be understood without an accurate description of its output, yet the nature of movement elements and their organization remains an open problem. Here, movement elements are identified from dynamics of walking in flies, using unbiased criteria. On one time scale, dynamics of walking are consistent over hundreds of milliseconds, allowing elementary features to be defined. Over longer periods, walking is well described by a stochastic process composed of these elementary features, and a generative model of this process reproduces individual behavior sequences accurately over seconds or longer. Within elementary features, velocities diverge, suggesting that dynamical stability of movement elements is a weak behavioral constraint. Rather, long-term instability can be limited by the finite memory between these elementary features. This structure suggests how complex dynamics may arise in biological systems from elements whose combination need not be tuned for dynamic stability. DOI: http://dx.doi.org/10.7554/eLife.26410.001 PMID:28742018

  5. Note: Network random walk model of two-state protein folding: Test of the theory

    NASA Astrophysics Data System (ADS)

    Berezhkovskii, Alexander M.; Murphy, Ronan D.; Buchete, Nicolae-Viorel

    2013-01-01

    We study two-state protein folding in the framework of a toy model of protein dynamics. This model has an important advantage: it allows for an analytical solution for the sum of folding and unfolding rate constants [A. M. Berezhkovskii, F. Tofoleanu, and N.-V. Buchete, J. Chem. Theory Comput. 7, 2370 (2011), 10.1021/ct200281d] and hence for the reactive flux at equilibrium. We use the model to test the Kramers-type formula for the reactive flux, which was derived assuming that the protein dynamics is described by a Markov random walk on a network of complex connectivity [A. Berezhkovskii, G. Hummer, and A. Szabo, J. Chem. Phys. 130, 205102 (2009), 10.1063/1.3139063]. It is shown that the Kramers-type formula leads to the same result for the reactive flux as the sum of the rate constants.

  6. Exact and approximate graph matching using random walks.

    PubMed

    Gori, Marco; Maggini, Marco; Sarti, Lorenzo

    2005-07-01

    In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection.

  7. RANDOM WALKS AND EFFECTIVE OPTICAL DEPTH IN RELATIVISTIC FLOW

    SciTech Connect

    Shibata, Sanshiro; Tominaga, Nozomu; Tanaka, Masaomi

    2014-05-20

    We investigate the random walk process in relativistic flow. In the relativistic flow, photon propagation is concentrated in the direction of the flow velocity due to the relativistic beaming effect. We show that in the pure scattering case, the number of scatterings is proportional to the size parameter ξ ≡ L/l {sub 0} if the flow velocity β ≡ v/c satisfies β/Γ >> ξ{sup –1}, while it is proportional to ξ{sup 2} if β/Γ << ξ{sup –1}, where L and l {sub 0} are the size of the system in the observer frame and the mean free path in the comoving frame, respectively. We also examine the photon propagation in the scattering and absorptive medium. We find that if the optical depth for absorption τ{sub a} is considerably smaller than the optical depth for scattering τ{sub s} (τ{sub a}/τ{sub s} << 1) and the flow velocity satisfies β≫√(2τ{sub a}/τ{sub s}), then the effective optical depth is approximated by τ{sub *} ≅ τ{sub a}(1 + β)/β. Furthermore, we perform Monte Carlo simulations of radiative transfer and compare the results with the analytic expression for the number of scatterings. The analytic expression is consistent with the results of the numerical simulations. The expression derived in this study can be used to estimate the photon production site in relativistic phenomena, e.g., gamma-ray burst and active galactic nuclei.

  8. A reflexive neural network for dynamic biped walking control.

    PubMed

    Geng, Tao; Porr, Bernd; Wörgötter, Florentin

    2006-05-01

    Biped walking remains a difficult problem, and robot models can greatly facilitate our understanding of the underlying biomechanical principles as well as their neuronal control. The goal of this study is to specifically demonstrate that stable biped walking can be achieved by combining the physical properties of the walking robot with a small, reflex-based neuronal network governed mainly by local sensor signals. Building on earlier work (Taga, 1995; Cruse, Kindermann, Schumm, Dean, & Schmitz, 1998), this study shows that human-like gaits emerge without specific position or trajectory control and that the walker is able to compensate small disturbances through its own dynamical properties. The reflexive controller used here has the following characteristics, which are different from earlier approaches: (1) Control is mainly local. Hence, it uses only two signals (anterior extreme angle and ground contact), which operate at the interjoint level. All other signals operate only at single joints. (2) Neither position control nor trajectory tracking control is used. Instead, the approximate nature of the local reflexes on each joint allows the robot mechanics itself (e.g., its passive dynamics) to contribute substantially to the overall gait trajectory computation. (3) The motor control scheme used in the local reflexes of our robot is more straightforward and has more biological plausibility than that of other robots, because the outputs of the motor neurons in our reflexive controller are directly driving the motors of the joints rather than working as references for position or velocity control. As a consequence, the neural controller and the robot mechanics are closely coupled as a neuromechanical system, and this study emphasizes that dynamically stable biped walking gaits emerge from the coupling between neural computation and physical computation. This is demonstrated by different walking experiments using a real robot as well as by a Poincaré map analysis

  9. 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

  10. Generalized essential energy space random walks to more effectively accelerate solute sampling in aqueous environment.

    PubMed

    Lv, Chao; Zheng, Lianqing; Yang, Wei

    2012-01-28

    Molecular dynamics sampling can be enhanced via the promoting of potential energy fluctuations, for instance, based on a Hamiltonian modified with the addition of a potential-energy-dependent biasing term. To overcome the diffusion sampling issue, which reveals the fact that enlargement of event-irrelevant energy fluctuations may abolish sampling efficiency, the essential energy space random walk (EESRW) approach was proposed earlier. To more effectively accelerate the sampling of solute conformations in aqueous environment, in the current work, we generalized the EESRW method to a two-dimension-EESRW (2D-EESRW) strategy. Specifically, the essential internal energy component of a focused region and the essential interaction energy component between the focused region and the environmental region are employed to define the two-dimensional essential energy space. This proposal is motivated by the general observation that in different conformational events, the two essential energy components have distinctive interplays. Model studies on the alanine dipeptide and the aspartate-arginine peptide demonstrate sampling improvement over the original one-dimension-EESRW strategy; with the same biasing level, the present generalization allows more effective acceleration of the sampling of conformational transitions in aqueous solution. The 2D-EESRW generalization is readily extended to higher dimension schemes and employed in more advanced enhanced-sampling schemes, such as the recent orthogonal space random walk method. © 2012 American Institute of Physics

  11. A Random Walk in the Park: An Individual-Based Null Model for Behavioral Thermoregulation.

    PubMed

    Vickers, Mathew; Schwarzkopf, Lin

    2016-04-01

    Behavioral thermoregulators leverage environmental temperature to control their body temperature. Habitat thermal quality therefore dictates the difficulty and necessity of precise thermoregulation, and the quality of behavioral thermoregulation in turn impacts organism fitness via the thermal dependence of performance. Comparing the body temperature of a thermoregulator with a null (non-thermoregulating) model allows us to estimate habitat thermal quality and the effect of behavioral thermoregulation on body temperature. We define a null model for behavioral thermoregulation that is a random walk in a temporally and spatially explicit thermal landscape. Predicted body temperature is also integrated through time, so recent body temperature history, environmental temperature, and movement influence current body temperature; there is no particular reliance on an organism's equilibrium temperature. We develop a metric called thermal benefit that equates body temperature to thermally dependent performance as a proxy for fitness. We measure thermal quality of two distinct tropical habitats as a temporally dynamic distribution that is an ergodic property of many random walks, and we compare it with the thermal benefit of real lizards in both habitats. Our simple model focuses on transient body temperature; as such, using it we observe such subtleties as shifts in the thermoregulatory effort and investment of lizards throughout the day, from thermoregulators to thermoconformers.

  12. Identify the diversity of mesoscopic structures in networks: A mixed random walk approach

    NASA Astrophysics Data System (ADS)

    Ma, Yifang; Jiang, Xin; Li, Meng; Shen, Xin; Guo, Quantong; Lei, Yanjun; Zheng, Zhiming

    2013-10-01

    Community or cluster structure, which can provide insight into the natural partitions and inner connections of a network, is a key feature in studying the mesoscopic structure of complex systems. Although numerous methods for community detection have been proposed ever since, there is still a lack of understanding on how to quantify the diversity of pre-divided community structures, or rank the roles of communities in participating in specific dynamic processes. Inspired by the Law of Mass Action in chemical kinetics, we introduce here the community random walk energy (CRWE), which reflects a potential based on the diffusion phase of a mixed random walk process taking place on the network, to identify the configuration of community structures. The difference of CRWE allows us to distinguish the intrinsic topological diversity between individual communities, on condition that all the communities are pre-arranged in the network. We illustrate our method by performing numerical simulations on constructive community networks and a real social network with distinct community structures. As an application, we apply our method to characterize the diversity of human genome communities, which provides a possible use of our method in inferring the genetic similarity between human populations.

  13. 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.

  14. 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.

  15. Quantum walk and potential application

    NASA Astrophysics Data System (ADS)

    Wang, J. B.; Douglas, B. L.

    2010-06-01

    Quantum walk represents a generalised version of the well-known classical random walk. Regardless of their apparent connection, the dynamics of quantum walk is often non-intuitive and far deviate from its classical counterpart. However, despite such potentially superior efficiency in quantum walks, it has yet to be applied to problems of practical importance. In this paper, we will give a brief introduction to quantum walks and discuss potential applications.

  16. Position-space renormalization-group approach to the resistance of random walks

    NASA Astrophysics Data System (ADS)

    Sahimi, Muhammad; Jerauld, Gary R.; Scriven, L. E.; Davis, H. Ted

    1984-06-01

    We consider a Pólya random walk, i.e., an unbiased, nearest-neighbor walk, on a d-dimensional hypercubic lattice and study the scaling behavior of the mean end-to-end resistance of the walk as a function of the number of steps in the walk. The resistance of the walk is generated by assigning a constant conductance to each step of the walk. This problem was recently proposed by Banavar, Harris, and Koplik, and may be useful for understanding the physics of disordered systems. We develop a position-space renormalization-group approach, a generalization of the one developed for percolation conductivity, and study the problem and a modification of it proposed here in one, two, and three dimensions. Our results are in good agreement with the numerical estimates of Banavar et al.

  17. 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.

  18. Relationship between flux and concentration gradient of diffusive particles with the usage of random walk model

    NASA Astrophysics Data System (ADS)

    Ovchinnikov, M. N.

    2017-09-01

    The fundamental solutions of the diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences between fundamental solutions, flows and concentration gradients were studied. The new modified non-local diffusion equation of the telegrapher type with correction function is suggested. It contains only microparameters of the random walk problem.

  19. Optically Resolving the Dynamic Walking of a Plasmonic Walker Couple.

    PubMed

    Urban, Maximilian J; Zhou, Chao; Duan, Xiaoyang; Liu, Na

    2015-12-09

    Deterministic placement and dynamic manipulation of individual plasmonic nanoparticles with nanoscale precision feature an important step toward active nanoplasmonic devices with prescribed levels of performance and functionalities at optical frequencies. In this Letter, we demonstrate a plasmonic walker couple system, in which two gold nanorod walkers can independently or simultaneously perform stepwise walking powered by DNA hybridization along the same DNA origami track. We utilize optical spectroscopy to resolve such dynamic walking with nanoscale steps well below the optical diffraction limit. We also show that the number of walkers and the optical response of the system can be correlated. Our studies exemplify the power of plasmonics, when integrated with DNA nanotechnology for realization of advanced artificial nanomachinery with tailored optical functionalities.

  20. The Length Scale of 3-Space Knots, Ephemeral Knots, and Slipknots in Random Walks

    NASA Astrophysics Data System (ADS)

    Millett, K. C.

    The probability that a random walk or polygon in the 3-space or in the simple cubic lattice contains a small knot, an ephemeral knot, or a slipknot goes to one as the length goes to infinity. The probability that a polygon or walk contains a ``global'' knot also goes to one as the length goes to infinity. What immerges is a highly complex picture of the length scale of knotting in polygons and walks. Here we study the average scale of knots, ephemeral knots, and slipknots in 3-space random walks, paying special attention to the probability of their occurance and to the growth of their average sizes as a function of the length of the walk.

  1. 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.

  2. Dynamic visual acuity during walking after long-duration spaceflight.

    PubMed

    Peters, Brian T; Miller, Chris A; Brady, Rachel A; Richards, Jason T; Mulavara, Ajitkumar P; Bloomberg, Jacob J

    2011-04-01

    Astronauts experience alterations in gaze control as a result of adaptive changes in eye-head coordination produced by microgravity exposure. This may lead to potential changes in postflight visual acuity during head and body motion. We gathered dynamic visual acuity (DVA) data from 14 astronauts and cosmonauts after long-duration (approximately 6 mo) stays in space. Walking was used to induce self-motion and visual acuity was determined by sequentially presenting Landolt ring optotypes on a computer display placed 4 m in front of subjects. Acuity assessments were made while seated (static condition) and walking (dynamic condition) at 6.4 km x h(-1) on a motorized treadmill. In each condition, a psychophysical threshold detection algorithm minimized the required number of optotype presentations by maximizing the amount displayed around the subject's acuity threshold. The difference between static and dynamic acuity measures provided a metric of change in the subjects' ability to maintain gaze fixation on the visual target while walking. A decrement in postflight visual acuity during walking was found. A mean dynamic acuity decrement of approximately 0.75 eye-chart lines was observed 1 d after returning from space. The population mean showed a consistent improvement in DVA performance during the first postflight week. The recovery curves for individual subjects did not necessarily follow a pattern of continuous improvement with each passing day. When adjusted for previous long-duration flight experience, the population mean showed an unexpected DVA reduction in the re-adaptation curve that is similar to recovery patterns observed in prism adaptation studies.

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

    PubMed Central

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

    2017-01-01

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

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

    PubMed

    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.

  5. 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

  6. Generalized master equation via aging continuous-time random walks.

    PubMed

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

    2003-11-01

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

  7. 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.

  8. Some recent variations on the expected number of distinct sites visited by an n-step random walk

    NASA Astrophysics Data System (ADS)

    Weiss, George H.; Dayan, Ido; Havlin, Shlomo; Kiefer, James E.; Larralde, Hernan; Stanley, H. Eugene; Trunfio, Paul

    1992-12-01

    Asymptotic forms for the expected number of distinct sites visited by an n-step random walk, being calculable for many random walks, have been used in a number of analyses of physical models. We describe three recent extensions of the problem, the first replacing the single random walker by N→∞ random walkers, the second to the study of a random walk in the presence of a trapping site, and the third to a random walk in the presence of a trapping hyperplane.

  9. International Randomized Clinical Trial, Stroke Inpatient Rehabilitation With Reinforcement of Walking Speed (SIRROWS), Improves Outcomes

    PubMed Central

    Dobkin, Bruce H.; Plummer-D’Amato, Prudence; Elashoff, Robert; Lee, Jihey; Group, the SIRROWS

    2014-01-01

    Background Feedback about performance may optimize motor relearning after stroke. Objectives Develop an international collaboration to rapidly test the potential efficacy of daily verbal feedback about walking speed during inpatient rehabilitation after stroke, using a protocol that requires no research funds. Methods This phase 2, single-blinded, multicenter trial randomized inpatients to either feedback about self-selected fast walking speed (daily reinforcement of speed, DRS) immediately after a single, daily 10-m walk or to no reinforcement of speed (NRS) after the walk, performed within the context of routine physical therapy. The primary outcome was velocity for a 15.2-m (50-foot) timed walk at discharge. Secondary outcomes were walking distance in 3 minutes, length of stay (LOS), and level of independence (Functional Ambulation Classification, FAC). Results Within 18 months, 179 participants were randomized. The groups were balanced for age, gender, time from onset of stroke to entry, initial velocity, and level of walking-related disability. The walking speed at discharge for DRS (0.91 m/s) was greater (P = .01) than that for NRS (0.72 m/s). No difference was found for LOS. LOS for both DRS and NRS was significantly shorter, however, for those who had mean walking speeds >0.4 m/s at entry. The DRS group did not have a higher proportion of FAC independent walkers (P = .1) and did not walk longer distances (P = .09). Conclusions An Internet-based collaboration of 18 centers found that feedback about performance once a day produced gains in walking speed large enough to permit unlimited, slow community ambulation at discharge from inpatient rehabilitation. PMID:20164411

  10. 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.

  11. Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

    NASA Astrophysics Data System (ADS)

    Ni, Xiao-Hui; Jiang, Zhi-Qiang; Zhou, Wei-Xing

    2009-10-01

    The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.

  12. Social influencing and associated random walk models: Asymptotic consensus times on the complete graph

    NASA Astrophysics Data System (ADS)

    Zhang, W.; Lim, C.; Sreenivasan, S.; Xie, J.; Szymanski, B. K.; Korniss, G.

    2011-06-01

    We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of individual-based models on finite complete graphs, we introduce a coarse-graining approach (lumping microscopic variables into macrostates) to analyze the ordering dynamics in an associated random-walk framework. Within this framework, yielding a linear system, we derive general equations for the expected consensus time and the expected time spent in each macro-state. Further, we present the asymptotic solutions of the 2-word naming game and separately discuss its behavior under the influence of an external field and with the introduction of committed agents.

  13. Effectiveness of backward walking training on walking ability in children with hemiparetic cerebral palsy: a randomized controlled trial.

    PubMed

    Abdel-Aziem, Amr A; El-Basatiny, Heba My

    2017-06-01

    To compare the effects of backward walking training and forward walking training on spatiotemporal gait parameters, and gross motor function measures in children with cerebral palsy. Randomized controlled clinical trial. Physical therapy clinics. A total of 30 children with hemiparetic cerebral palsy of both sexes (10 to 14 years of age, classified as I or II by gross motor function classification system) participated in this study. They were randomly assigned into two equal groups. Both groups received a conventional physical therapy program for 12 successive weeks (three sessions per week). The experimental group additionally received (25 min) backward walking training. The control group additionally received (25 min) forward walking training. Baseline, posttreatment, and follow-up assessment for spatiotemporal gait parameters and gross motor functions were evaluated by using three dimensional gait analysis system and gross motor function measures. There was a significant improvement in step length, walking velocity, cadence, stance phase, and swing phase percentage and gross motor function measures (Dimensions D and E) of the experimental group (0.55 ±0.16, 0.53 ±0.19, 121.73 ±2.89, 54.73 ±1.67, 44.40 ±1.40, 90.20 ±6.44, 82.47 ±12.82), respectively, than the control group (0.39 ±0.13, 0.46 ±0.20, 125.80 ±2.96, 50.27 ±1.62, 49.47 ±1.55, 82.47 ±7.05, 80.47 ±12.61), respectively, ( p < 0.05). The significant improvement of all measured outcomes of the experimental group was maintained at 1 month follow-up assessment ( p < 0.05). In addition to a conventional physical therapy program, backward walking training is more effective than forward walking training on spatiotemporal gait parameters, and gross motor function measures in children with hemiparetic cerebral palsy.

  14. Generalized Pareto for Pattern-Oriented Random Walk Modelling of Organisms’ Movements

    PubMed Central

    Bertrand, Sophie; Joo, Rocío; Fablet, Ronan

    2015-01-01

    How organisms move and disperse is crucial to understand how population dynamics relates to the spatial heterogeneity of the environment. Random walk (RW) models are typical tools to describe movement patterns. Whether Lévy or alternative RW better describes forager movements is keenly debated. We get around this issue using the Generalized Pareto Distribution (GPD). GPD includes as specific cases Normal, exponential and power law distributions, which underlie Brownian, Poisson-like and Lévy walks respectively. Whereas previous studies typically confronted a limited set of candidate models, GPD lets the most likely RW model emerge from the data. We illustrate the wide applicability of the method using GPS-tracked seabird foraging movements and fishing vessel movements tracked by Vessel Monitoring System (VMS), both collected in the Peruvian pelagic ecosystem. The two parameters from the fitted GPD, a scale and a shape parameter, provide a synoptic characterization of the observed movement in terms of characteristic scale and diffusive property. They reveal and quantify the variability, among species and individuals, of the spatial strategies selected by predators foraging on a common prey field. The GPD parameters constitute relevant metrics for (1) providing a synthetic and pattern–oriented description of movement, (2) using top predators as ecosystem indicators and (3) studying the variability of spatial behaviour among species or among individuals with different personalities. PMID:26172045

  15. Generalized Pareto for Pattern-Oriented Random Walk Modelling of Organisms' Movements.

    PubMed

    Bertrand, Sophie; Joo, Rocío; Fablet, Ronan

    2015-01-01

    How organisms move and disperse is crucial to understand how population dynamics relates to the spatial heterogeneity of the environment. Random walk (RW) models are typical tools to describe movement patterns. Whether Lévy or alternative RW better describes forager movements is keenly debated. We get around this issue using the Generalized Pareto Distribution (GPD). GPD includes as specific cases Normal, exponential and power law distributions, which underlie Brownian, Poisson-like and Lévy walks respectively. Whereas previous studies typically confronted a limited set of candidate models, GPD lets the most likely RW model emerge from the data. We illustrate the wide applicability of the method using GPS-tracked seabird foraging movements and fishing vessel movements tracked by Vessel Monitoring System (VMS), both collected in the Peruvian pelagic ecosystem. The two parameters from the fitted GPD, a scale and a shape parameter, provide a synoptic characterization of the observed movement in terms of characteristic scale and diffusive property. They reveal and quantify the variability, among species and individuals, of the spatial strategies selected by predators foraging on a common prey field. The GPD parameters constitute relevant metrics for (1) providing a synthetic and pattern-oriented description of movement, (2) using top predators as ecosystem indicators and (3) studying the variability of spatial behaviour among species or among individuals with different personalities.

  16. 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

  17. A stochastic simulation framework for the prediction of strategic noise mapping and occupational noise exposure using the random walk approach.

    PubMed

    Han, Lim Ming; Haron, Zaiton; Yahya, Khairulzan; 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.

  18. Effects on Balance and Walking with the CoDuSe Balance Exercise Program in People with Multiple Sclerosis: A Multicenter Randomized Controlled Trial

    PubMed Central

    von Koch, Lena

    2016-01-01

    Background. Balance and walking impairments are frequent in people with multiple sclerosis (MS). Objective. The aim was to investigate the effects of a group-based balance exercise program targeting core stability, dual tasking, and sensory strategies (CoDuSe) on balance, postural sway, walking, perceived walking limitations, and balance confidence. Design. A single-blinded randomized multicenter trial. No intervention was given to controls. Participants. People with MS able to walk 100 meters but unable to maintain tandem stance ≥30 seconds. Eighty-seven participants were randomized to intervention or control. Intervention. The 60-minute CoDuSe group program, twice weekly for seven weeks, supervised by physical therapists. Measurements. Primary outcome was dynamic balance (Berg Balance Scale (BBS)). Secondary outcomes were postural sway, walking (Timed-Up and Go test; Functional Gait Assessment (FGA)), MS Walking Scale, and Activities-specific Balance Confidence (ABC) Scale. Assessments were performed before and after (week 8) the intervention. Results. 73 participants fulfilled the study. There were significant differences between the intervention and the control groups in change in the BBS and in the secondary measures: postural sway with eyes open, FGA, MS Walking Scale, and ABC scale in favor of the intervention. Conclusions. The seven-week CoDuSe program improved dynamic balance more than no intervention. PMID:28042485

  19. The expected number of distinct sites visited by N biased random walks in one dimension

    NASA Astrophysics Data System (ADS)

    Larralde, Hernan; Weiss, George H.; Eugene Stanley, H.

    1994-09-01

    We calculate the asymptotic form of the expected number of distinct sites visited by N random walkers moving independently in one dimension. It is shown that to lowest order and at long times, the leading term in the asymptotic result is that found for the random walk of a single biased particle, which implies that the bias is strong enough a factor to dominate the many-body effects in that regime. The lowest order correction term contains the many-body contribution. This is essentially the result for the unbiased random walk.

  20. Central limit theorem and related results for the elephant random walk

    NASA Astrophysics Data System (ADS)

    Coletti, Cristian F.; Gava, Renato; Schütz, Gunter M.

    2017-05-01

    We study the so-called elephant random walk (ERW) which is a non-Markovian discrete-time random walk on ℤ with unbounded memory which exhibits a phase transition from a diffusive to superdiffusive behavior. We prove a law of large numbers and a central limit theorem. Remarkably the central limit theorem applies not only to the diffusive regime but also to the phase transition point which is superdiffusive. Inside the superdiffusive regime, the ERW converges to a non-degenerate random variable which is not normal. We also obtain explicit expressions for the correlations of increments of the ERW.

  1. 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...

  2. Walking improves sleep in individuals with cancer: a meta-analysis of randomized, controlled trials.

    PubMed

    Chiu, Hsiao-Yean; Huang, Hui-Chuan; Chen, Pin-Yuan; Hou, Wen-Hsuan; Tsai, Pei-Shan

    2015-03-01

    To evaluate the effectiveness of walking exercise on sleep in people with cancer.
 Databases searched included China Knowledge Resource Integrated Database, CINAHL®, Cochrane Central Register of Controlled Trials, EMBASE, PsycINFO®, PubMed, Wanfang Data, and Web of Science. 
 Nine randomized, controlled trials involving 599 patients were included. Most of the studies used moderate-intensity walking exercise. Overall, walking exercise significantly improved sleep in people with cancer (Hedges' g = –0.52). Moderator analyses showed that walking exercise alone and walking exercise combined with other forms of interventions yielded comparable effects on sleep improvement, and that the effect size did not differ among participants who were at different stages of cancer. The effect sizes for studies involving individuals with breast cancer and for studies including individuals with other types of cancer were similar.
 Moderate-intensity walking exercise is effective in improving sleep in individuals with cancer. 
 The authors' findings support the inclusion of walking exercise into the multimodal approaches to managing sleep in people with cancer. Healthcare providers must convey the benefits of walking exercise to individuals with cancer who are suffering from sleep problems. 


  3. Random-walk analysis of displacement statistics of particles in concentrated suspensions of hard spheres

    NASA Astrophysics Data System (ADS)

    van Megen, W.

    2006-01-01

    Mean-squared displacements (MSDs) of colloidal fluids of hard spheres are analyzed in terms of a random walk, an analysis which assumes that the process of structural relaxation among the particles can be described in terms of thermally driven memoryless encounters. For the colloidal fluid in thermodynamic equilibrium the magnitude of the stretching of the MSD is able to be reconciled by a bias in the walk. This description fails for the under-cooled colloidal fluid.

  4. A random walk-based method for segmentation of intravascular ultrasound images

    NASA Astrophysics Data System (ADS)

    Yan, Jiayong; Liu, Hong; Cui, Yaoyao

    2014-04-01

    Intravascular ultrasound (IVUS) is an important imaging technique that is used to study vascular wall architecture for diagnosis and assessment of the vascular diseases. Segmentation of lumen and media-adventitia boundaries from IVUS images is a basic and necessary step for quantitative assessment of the vascular walls. Due to ultrasound speckles, artifacts and individual differences, automated segmentation of IVUS images represents a challenging task. In this paper, a random walk based method is proposed for fully automated segmentation of IVUS images. Robust and accurate determination of the seed points for different regions is the key to successful use of the random walk algorithm in segmentation of IVUS images and is the focus of our work. The presented method mainly comprises five steps: firstly, the seed points inside the lumen and outside the adventitia are roughly estimated with intensity information, respectively; secondly, the seed points outside the adventitia are refined, and those of the media are determined through the results of applying random walk to the IVUS image with the roughly estimated seed points; thirdly, the media-adventitia boundary is detected by using random walk with the seed points obtained in the second step and the image gradient; fourthly, the seed points for media and lumen are refined; finally, the lumen boundary is extracted by using random walk again with the seed points obtained in the fourth step and the image gradient. The tests of the proposed algorithm on the in vivo dataset demonstrate the effectiveness of the presented IVUS image segmentation approach.

  5. 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.

  6. Dynamic performance of slender suspension footbridges under eccentric walking dynamic loads

    NASA Astrophysics Data System (ADS)

    Huang, Ming-Hui; Thambiratnam, David P.; Perera, Nimal J.

    2007-06-01

    This paper treats the vibration of slender suspension footbridges caused by eccentrically distributed walking dynamic loads. A suspension footbridge model with reverse profiled cables in both the vertical and horizontal planes was used in this conceptual study, while SAP2000 package is adopted in the numerical analysis. The dynamic behaviour of slender footbridges under walking dynamic loads is simulated by resonant vibration caused by synchronous excitations. It is found that slender suspension footbridges with shallow cable profiles often have coupled vibration modes such as coupled lateral-torsional or coupled torsional-lateral modes. When these coupled vibration modes are excited by walking pedestrians, excessive lateral vibration can be induced. Results also show that the effects of the reverse profiled cables on the dynamic performance in different vibration modes are complex. Reverse profiled cables in the horizontal plane can significantly suppress the lateral vibration in coupled lateral-torsional modes, but slightly increase the lateral vibration in coupled torsional-lateral modes.

  7. 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

  8. Novel pseudo-random number generator based on quantum random walks

    PubMed Central

    Yang, Yu-Guang; Zhao, Qian-Qian

    2016-01-01

    In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation. PMID:26842402

  9. Novel pseudo-random number generator based on quantum random walks.

    PubMed

    Yang, Yu-Guang; Zhao, Qian-Qian

    2016-02-04

    In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.

  10. Novel pseudo-random number generator based on quantum random walks

    NASA Astrophysics Data System (ADS)

    Yang, Yu-Guang; Zhao, Qian-Qian

    2016-02-01

    In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.

  11. Apparent randomness in quantum dynamics

    NASA Astrophysics Data System (ADS)

    Cerdeira, Hilda A.; Huberman, B. A.

    1987-08-01

    We show how bounded quantum systems in the presence of time-periodic fields can mimic random behavior in spite of their almost periodic character. We calculate the distribution of values taken by observables in the course of time, and demonstrate how they become asymptotically Gaussian in the large-N limit but with constant variance and a posteriori, δ-correlated noise. Thus, unlike a priori processes, the quantum dynamics of bounded systems remains nondiffusive while appearing to be random.

  12. Formation mechanism of a basin of attraction for passive dynamic walking induced by intrinsic hyperbolicity

    NASA Astrophysics Data System (ADS)

    Obayashi, Ippei; Aoi, Shinya; Tsuchiya, Kazuo; Kokubu, Hiroshi

    2016-06-01

    Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the difficulty in producing stable passive dynamic walking. The underlying mechanism that produces these geometric characteristics was not known. In this paper, we consider this from the viewpoint of dynamical systems theory, and we use the simplest walking model to clarify the mechanism that forms the basin of attraction for passive dynamic walking. We show that the intrinsic saddle-type hyperbolicity of the upright equilibrium point in the governing dynamics plays an important role in the geometrical characteristics of the basin of attraction; this contributes to our understanding of the stability mechanism of bipedal walking.

  13. Imitation of Dynamic Walking With BSN for Humanoid Robot.

    PubMed

    Teachasrisaksakul, Krittameth; Zhang, Zhi-Qiang; Yang, Guang-Zhong; Lo, Benny

    2015-05-01

    Humanoid robots have been used in a wide range of applications including entertainment, healthcare, and assistive living. In these applications, the robots are expected to perform a range of natural body motions, which can be either preprogrammed or learnt from human demonstration. This paper proposes a strategy for imitating dynamic walking gait for a humanoid robot by formulating the problem as an optimization process. The human motion data are recorded with an inertial sensor-based motion tracking system (Biomotion+). Joint angle trajectories are obtained from the transformation of the estimated posture. Key locomotion frames corresponding to gait events are chosen from the trajectories. Due to differences in joint structures of the human and robot, the joint angles at these frames need to be optimized to satisfy the physical constraints of the robot while preserving robot stability. Interpolation among the optimized angles is needed to generate continuous angle trajectories. The method is validated using a NAO humanoid robot, with results demonstrating the effectiveness of the proposed strategy for dynamic walking.

  14. Passive Dynamics Explain Quadrupedal Walking, Trotting, and Tölting

    PubMed Central

    Gan, Zhenyu; Wiestner, Thomas; Weishaupt, Michael A.; Waldern, Nina M.; David Remy, C.

    2016-01-01

    This paper presents a simplistic passive dynamic model that is able to create realistic quadrupedal walking, tölting, and trotting motions. The model is inspired by the bipedal spring loaded inverted pendulum (SLIP) model and consists of a distributed mass on four massless legs. Each of the legs is either in ground contact, retracted for swing, or is ready for touch down with a predefined angle of attack. Different gaits, that is, periodic motions differing in interlimb coordination patterns, are generated by choosing different initial model states. Contact patterns and ground reaction forces (GRFs) evolve solely from these initial conditions. By identifying appropriate system parameters in an optimization framework, the model is able to closely match experimentally recorded vertical GRFs of walking and trotting of Warmblood horses, and of tölting of Icelandic horses. In a detailed study, we investigated the sensitivity of the obtained solutions with respect to all states and parameters and quantified the improvement in fitting GRF by including an additional head and neck segment. Our work suggests that quadrupedal gaits are merely different dynamic modes of the same structural system and that we can interpret different gaits as different nonlinear elastic oscillations that propel an animal forward. PMID:27222653

  15. Randomized Controlled Theory-Based, E-Mail-Mediated Walking Intervention.

    PubMed

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

    2017-02-01

    The purpose of this study was to evaluate the ability of two concurrent randomized controlled interventions based on social cognitive theory to increase walking. A second purpose was to compare the efficacy of the intervention between two distinct groups: dog owners and non-dog owners. Adult dog owners ( n = 40) and non-dog owners ( n = 65) were randomized into control or intervention groups. Intervention groups received bi-weekly emails for first 4 weeks and then weekly email for the next 8 weeks targeting self-efficacy, social support, goal setting, and benefits/barriers to walking. Dog owner messages focused on dog walking while non-dog owners received general walking messages. Control groups received a 1-time email reviewing current physical activity guidelines. At 6 months, both intervention groups reported greater increases in walking and maintained these increases at 12 months. The greatest increases were seen in the dog owner intervention group. In conclusion, dog owners accumulated more walking, which may be attributed to the dog-owner relationship.

  16. 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.

  17. Random walks on finite lattices with multiple traps: Application to particle-cluster aggregation

    NASA Astrophysics Data System (ADS)

    Evans, J. W.; Nord, R. S.

    1985-11-01

    For random walks on finite lattices with multiple (completely adsorbing) traps, one is interested in the mean walk length until trapping and in the probability of capture for the various traps (either for a walk with a specific starting site, or for an average over all nontrap sites). We develop the formulation of Montroll to enable determination of the large-lattice-size asymptotic behavior of these quantities. (Only the case of a single trap has been analyzed in detail previously.) Explicit results are given for the case of symmetric nearest-neighbor random walks on two-dimensional (2D) square and triangular lattices. Procedures for exact calculation of walk lengths on a finite lattice with a single trap are extended to the multiple-trap case to determine all the above quantities. We examine convergence to asymptotic behavior as the lattice size increases. Connection with Witten-Sander irreversible particle-cluster aggregation is made by noting that this process corresponds to designating all sites adjacent to the cluster as traps. Thus capture probabilities for different traps determine the proportions of the various shaped clusters formed. (Reciprocals of) associated average walk lengths relate to rates for various irreversible aggregation processes involving a gas of walkers and clusters. Results are also presented for some of these quantities.

  18. A multiple step random walk Monte Carlo method for heat conduction involving distributed heat sources

    NASA Astrophysics Data System (ADS)

    Naraghi, M. H. N.; Chung, B. T. F.

    1982-06-01

    A multiple step fixed random walk Monte Carlo method for solving heat conduction in solids with distributed internal heat sources is developed. In this method, the probability that a walker reaches a point a few steps away is calculated analytically and is stored in the computer. Instead of moving to the immediate neighboring point the walker is allowed to jump several steps further. The present multiple step random walk technique can be applied to both conventional Monte Carlo and the Exodus methods. Numerical results indicate that the present method compares well with finite difference solutions while the computation speed is much faster than that of single step Exodus and conventional Monte Carlo methods.

  19. 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.

  20. Local time of Lévy random walks: A path integral approach

    NASA Astrophysics Data System (ADS)

    Zatloukal, Václav

    2017-05-01

    The local time of a stochastic process quantifies the amount of time that sample trajectories x (τ ) spend in the vicinity of an arbitrary point x . For a generic Hamiltonian, we employ the phase-space path-integral representation of random walk transition probabilities in order to quantify the properties of the local time. For time-independent systems, the resolvent of the Hamiltonian operator proves to be a central tool for this purpose. In particular, we focus on the local times of Lévy random walks (Lévy flights), which correspond to fractional diffusion equations.

  1. Revisiting random walks in fractal media: on the occurrence of time discrete scale invariance.

    PubMed

    Bab, M A; Fabricius, G; Albano, Ezequiel V

    2008-01-28

    This paper addresses the kinetic behavior of random walks in fractal media. We perform extensive numerical simulations of both single and annihilating random walkers on several Sierpinski carpets, in order to study the time behavior of three observables: the average number of distinct sites visited by a single walker, the mean-square displacement from the origin, and the density of annihilating random walkers. We found that the time behavior of those observables is given by a power law modulated by soft logarithmic-periodic oscillations. We conjecture that logarithmic-periodic oscillations are a manifestation of a time domain discrete scale iNvariance (DSI) that occurs as a consequence of the spatial DSI of the substrate. Our conjecture implies that the logarithmic periods of oscillations in space and time domains are linked by a dynamic exponent z, through z=log(tau)/log(b(1)), where tau and b(1) are the fundamental scaling ratios of the DSI symmetry in the time and space domains, respectively. We use this relationship in order to compute z for different observables and fractals. Furthermore, we check the values obtained with independent measurements provided by the power-law behavior of the mean-square displacement with time [R(2)(t) proportional variant t(2/z)]. The very good agreement obtained between both computations of the z exponent gives strong support to the idea of an intimate interplay between spatial and time symmetry properties that we expect will have a quite general scope. We expect that the application of the outlined concepts in the field of dynamic processes in fractal media will stimulate further research.

  2. Random time averaged diffusivities for Lévy walks

    NASA Astrophysics Data System (ADS)

    Froemberg, D.; Barkai, E.

    2013-07-01

    We investigate a Lévy walk alternating between velocities ±v0 with opposite sign. The sojourn time probability distribution at large times is a power law lacking its mean or second moment. The first case corresponds to a ballistic regime where the ensemble averaged mean squared displacement (MSD) at large times is ⟨x2⟩ ∝ t2, the latter to enhanced diffusion with ⟨x2⟩ ∝ tν, 1 < ν < 2. The correlation function and the time averaged MSD are calculated. In the ballistic case, the deviations of the time averaged MSD from a purely ballistic behavior are shown to be distributed according to a Mittag-Leffler density function. In the enhanced diffusion regime, the fluctuations of the time averages MSD vanish at large times, yet very slowly. In both cases we quantify the discrepancy between the time averaged and ensemble averaged MSDs.

  3. Space-time hole filling with random walks in view extrapolation for 3D video.

    PubMed

    Choi, Sunghwan; Ham, Bumsub; Sohn, Kwanghoon

    2013-06-01

    In this paper, a space-time hole filling approach is presented to deal with a disocclusion when a view is synthesized for the 3D video. The problem becomes even more complicated when the view is extrapolated from a single view, since the hole is large and has no stereo depth cues. Although many techniques have been developed to address this problem, most of them focus only on view interpolation. We propose a space-time joint filling method for color and depth videos in view extrapolation. For proper texture and depth to be sampled in the following hole filling process, the background of a scene is automatically segmented by the random walker segmentation in conjunction with the hole formation process. Then, the patch candidate selection process is formulated as a labeling problem, which can be solved with random walks. The patch candidates that best describe the hole region are dynamically selected in the space-time domain, and the hole is filled with the optimal patch for ensuring both spatial and temporal coherence. The experimental results show that the proposed method is superior to state-of-the-art methods and provides both spatially and temporally consistent results with significantly reduced flicker artifacts.

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

    PubMed

    Hausdorff, J M; Peng, C K; Ladin, Z; Wei, J Y; Goldberger, A L

    1995-01-01

    Complex fluctuations 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 successfully accounts for the experimentally observed long-range correlations.

  5. 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.

  6. 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.

  7. Repetitive mass practice or focused precise practice for retraining walking after incomplete spinal cord injury? A pilot randomized clinical trial.

    PubMed

    Yang, Jaynie F; Musselman, Kristin E; Livingstone, Donna; Brunton, Kelly; Hendricks, Gregory; Hill, Denise; Gorassini, Monica

    2014-05-01

    Retraining walking following spinal cord injury using visually guided tasks may be especially efficacious because it engages the motor cortex, whose input may facilitate improvements in functional walking. To contrast 2 methods of retraining, one emphasizing precise, visually guided walking over obstacles and on targets (Precision Training), the other emphasizing mass practice of walking on a treadmill (Endurance Training). A randomized, single-blind, crossover design was used. Twenty-two participants, ≥7 months postinjury, were randomly allocated to start with Precision or Endurance Training. Each phase of training was 5 times per week for 2 months, followed by a 2-month rest. of walking speed, distance, skill, confidence, and depression were obtained before training, then monthly thereafter. Both forms of training led to significant improvements in walking, with Endurance Training inducing bigger improvements in walking distance than Precision Training, especially for high-functioning walkers who had initial walking speeds >0.5 m/s. The largest improvements in walking speed and distance occurred in the first month of Endurance Training, with minimal changes in the second month of training. In contrast, improvements in walking skill occurred over both months during both types of training. Retention of over ground walking speed, distance, and skill was excellent for both types of training. Intensive walking training in the chronic phase after spinal cord injury is effective in improving over ground walking. Visually guided tasks for training individuals with chronic spinal cord injury were not superior to mass practice on a treadmill.

  8. Dynamic stability of human walking in visually and mechanically destabilizing environments.

    PubMed

    McAndrew, Patricia M; Wilken, Jason M; Dingwell, Jonathan B

    2011-02-24

    Understanding how humans remain stable during challenging locomotor activities is critical to developing effective tests to diagnose patients with increased fall risk. This study determined if different continuous low-amplitude perturbations would induce specific measureable changes in measures of dynamic stability during walking. We applied continuous pseudo-random oscillations of either the visual scene or support surface in either the anterior-posterior or mediolateral directions to subjects walking in a virtual environment with speed-matched optic flow. Floquet multipliers and short-term local divergence exponents both increased (indicating greater instability) during perturbed walking. These responses were generally much stronger for body movements occurring in the same directions as the applied perturbations. Likewise, subjects were more sensitive to both visual and mechanical perturbations applied in the mediolateral direction than to those applied in the anterior-posterior direction, consistent with previous experiments and theoretical predictions. These responses were likewise consistent with subjects' anecdotal perceptions of which perturbation conditions were most challenging. Contrary to the Floquet multipliers and short-term local divergence exponents, which both increased, long-term local divergence exponents decreased during perturbed walking. However, this was consistent with specific changes in the mean log divergence curves, which indicated that subjects' movements reached their maximum local divergence limits more quickly during perturbed walking. Overall, the Floquet multipliers were less sensitive, but reflected greater specificity in their responses to the different perturbation conditions. Conversely, the short-term local divergence exponents exhibited less specificity in their responses, but were more sensitive measures of instability in general. Copyright © 2010 Elsevier Ltd. All rights reserved.

  9. Exercise training improves walking function in an African group of stroke survivors: a randomized controlled trial.

    PubMed

    Olawale, O A; Jaja, S I; Anigbogu, C N; Appiah-Kubi, K O; Jones-Okai, D

    2011-05-01

    To evaluate the effects of treadmill walking and overground walking exercise training on recovery of walking function in an African group of stroke survivors. Prospective, randomized controlled study. Outpatient stroke rehabilitation unit in a tertiary hospital. Sixty patients with chronic stroke (≥3 months). All subjects received individual outpatient conventional physiotherapy rehabilitation for 12 weeks. In addition, subjects in Group A (n = 20) received treadmill walking exercise training (TWET) while those in Group B (n = 20) received overground walking exercise training (OWET). Those in Group C (control) (n = 20) received conventional physiotherapy rehabilitation only. Outcome measures were (i) 10-metre walk time (10MWT) test and (ii) six-minute walk distance (6MWD) test. These were evaluated at entry into the study and at the end of every four weeks. Paired t-tests were used to evaluate the significance of the difference between pre-training and post-training scores on the two measures (P < 0.05). Subjects in the TWET group recorded 22.6 ± 1.5% decrease in 10MWT and 31.0 ± 4.3% increase in 6MWD; those in the OWET group made 26.8 ± 1.3% and 45.2 ± 4.6% improvement in 10MWT and 6MWD respectively. Subjects in the control group made 2.2 ± 0.7% and 2.9 ± 0.8% improvement in the two functions. These changes were significant for the TWET and OWET groups (P < 0.05). This study indicated that treadmill and overground walking exercise training programmes, combined with conventional rehabilitation, improved walking function in an African group of adult stroke survivors. Therefore, professionals who conduct stroke rehabilitation programmes should utilize exercise training to optimize patient outcomes.

  10. On your feet: protocol for a randomized controlled trial to compare the effects of pole walking and regular walking on physical and psychosocial health in older adults.

    PubMed

    Fritschi, Juliette O; Brown, Wendy J; van Uffelen, Jannique G Z

    2014-04-17

    Physical activity is associated with better physical and mental health in older adults. Pole walking is a form of walking which may have additional health benefits in older adults, because of the addition of hand held poles, and consequent upper limb involvement. However, few studies have examined the potential additional effects of pole walking on physical and psychosocial health in older adults compared with walking. The aim of this study is to compare the effect of a pole walking program with the effects of a walking program, on physical and psychosocial wellbeing, in older adults in assisted living facilities. Sixty men and women from assisted living communities over 65 years will be recruited from senior retirement facilities and randomized into a group based, pole walking program, or walking program. The pole walking group will use the Exerstrider method of pole walking. Total duration of the programs is 12 weeks, with three sessions per week, building from 20 minute to 30 minute sessions.The primary outcome is physical function, as measured by items from the Seniors Fitness Test and hand grip strength. Secondary outcomes include, physical activity levels, sedentary behaviour, joint pain, and quality of life. All outcomes will be assessed before and after the programs, using valid and reliable measures. The study will add to the evidence base for the effects of pole walking, compared with walking, on physical and psychosocial health and physical function, in healthy older adults. This will improve understanding about the feasibility of pole walking programs and its specific benefits in this population. Australian New Zealand Clinical Trials Registry ACTRN12612001127897.

  11. An exploration of impaired walking dynamics and fatigue in Multiple Sclerosis

    PubMed Central

    2012-01-01

    Background Physical disability in multiple sclerosis (MS) is frequently characterized by impaired ambulation. Although walking tests have been successfully employed to assess walking ability in MS patients, data analytic procedures have predominantly relied on result-oriented parameters (e.g. total distance covered during a given amount of time), whereas process-oriented, dynamic walking patterns have mostly been ignored. This is striking, since healthy individuals have been observed to display a stereotypical U-shaped pattern of walking speed during timed walking, characterized by relatively high speed during the initial phase, subsequent slowing and final acceleration. Objective of the current study was to test the utility of the 6 min Walk (6MW) and the 12 min Walk (12MW) for revealing putatively abnormal temporal dynamic features of walking in MS. Methods A group of 37 MS patients was divided into subgroups with regard to their level of disability analyzed with the Expanded Disability Status Scale (EDSS; Mild MS Group, n = 20, EDSS 0 – 3.5; Moderate MS Group, n = 17, EDSS 4 – 5). Subsequently, both groups were compared to age-matched healthy controls (n = 25) on both tests with regard to result-oriented characteristics (mean walking speed), as well as dynamic features (mean decline in walking speed, degree of observed U-shape). Results Both MS groups showed a significantly lower mean walking speed than healthy controls, independent of test duration. Compared to controls, the Moderate MS Group also slowed down more rapidly throughout both tests. The same pronounced decline in walking speed was observed for the Mild MS Group in case of the 12MW. Additionally, for both MS groups an attenuated U-shaped velocity pattern was observed relative to controls in the 6MW. Patients' subjective fatigue scores were more strongly correlated with the decline in walking speed than with the common parameter of mean walking speed in the 6MW. Conclusions MS patients

  12. Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms

    PubMed Central

    Skliros, Aris; Park, Wooram; Chirikjian, Gregory S.

    2010-01-01

    This paper presents an efficient group-theoretic approach for computing the statistics of non-reversal random walks (NRRW) on lattices. These framed walks evolve on proper crystallographic space groups. In a previous paper we introduced a convolution method for computing the statistics of NRRWs in which the convolution product is defined relative to the space-group operation. Here we use the corresponding concept of the fast Fourier transform for functions on crystallographic space groups together with a non-Abelian version of the convolution theorem. We develop the theory behind this technique and present numerical results for two-dimensional and three-dimensional lattices (square, cubic and diamond). In order to verify our results, the statistics of the end-to-end distance and the probability of ring closure are calculated and compared with results obtained in the literature for the random walks for which closed-form expressions exist. PMID:21037950

  13. 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.

  14. Reliability of the walking speed and gait dynamics variables while walking on a feedback-controlled treadmill.

    PubMed

    Choi, Jin-Seung; Kang, Dong-Won; Seo, Jeong-Woo; Tack, Gye-Rae

    2015-05-01

    The purpose of this study is to identify the reliability of walking speed and gait dynamics measured with a feedback-controlled treadmill and to assess the applicability of the treadmill to gait dynamics studies. The intraclass correlation coefficient (ICC) and the standard error of measurement (SEM) for the walking speed and the mean, variability (coefficient of variance, CV), and fractal dynamics (the scaling exponent α of detrended fluctuation analysis, DFA) of the stride time and stride length were used to evaluate the within-day and between-day reliability. Fifteen subjects walked on a feedback-controlled treadmill for three trials that were each more than 10 min in length (within-day); this protocol was repeated on another day to identify the between-day reliability. The results showed that all variables were consistent for within-day and between-day reliability (ICC: 0.633-0.982, p<0.05; SEM: 0.02-0.43). The within- and between-day reliability of the walking speed and the mean, variability, and fractal dynamics for the stride time and stride length were identified. Good ICCs and low SEMs for within-day and between-day reliability were obtained for all variables. Therefore, it is concluded that it is possible to use a feedback-controlled treadmill to the study of gait dynamics.

  15. 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

  16. Kinematics and dynamics analysis of a quadruped walking robot with parallel leg mechanism

    NASA Astrophysics Data System (ADS)

    Wang, Hongbo; Sang, Lingfeng; Hu, Xing; Zhang, Dianfan; Yu, Hongnian

    2013-09-01

    It is desired to require a walking robot for the elderly and the disabled to have large capacity, high stiffness, stability, etc. However, the existing walking robots cannot achieve these requirements because of the weight-payload ratio and simple function. Therefore, Improvement of enhancing capacity and functions of the walking robot is an important research issue. According to walking requirements and combining modularization and reconfigurable ideas, a quadruped/biped reconfigurable walking robot with parallel leg mechanism is proposed. The proposed robot can be used for both a biped and a quadruped walking robot. The kinematics and performance analysis of a 3-UPU parallel mechanism which is the basic leg mechanism of a quadruped walking robot are conducted and the structural parameters are optimized. The results show that performance of the walking robot is optimal when the circumradius R, r of the upper and lower platform of leg mechanism are 161.7 mm, 57.7 mm, respectively. Based on the optimal results, the kinematics and dynamics of the quadruped walking robot in the static walking mode are derived with the application of parallel mechanism and influence coefficient theory, and the optimal coordination distribution of the dynamic load for the quadruped walking robot with over-determinate inputs is analyzed, which solves dynamic load coupling caused by the branches’ constraint of the robot in the walk process. Besides laying a theoretical foundation for development of the prototype, the kinematics and dynamics studies on the quadruped walking robot also boost the theoretical research of the quadruped walking and the practical applications of parallel mechanism.

  17. An Application of the Random Walk Model to Proper Motions of Coronal Bright Points from SDO Data

    NASA Astrophysics Data System (ADS)

    Skokić, I.; Sudar, D.; Saar, S. H.; Brajša, R.; Poljančić-Beljan, I.

    Atmospheric Imaging Assembly (AIA) images from the Solar Dynamics Observatory (SDO) were used to follow the motions of coronal bright points (CBPs) in the period 1 January - 19 May 2011 with a cadence of 10 minutes. This resulted in a data set of 80966 CBPs with measured lifetimes and mean velocities which were used in a random walk model to calculate the diffusion coefficient, D. The results show that D has a value of ≈260 km^2 s^{-1} for CBPs with lifetime below 6 hours, decreasing to ≈170 km^2 s^{-1} for lifetimes above 12 hours, with a mean value of ≈230 km^2 s^{-1}.

  18. The random walk of a drilling laser beam

    NASA Technical Reports Server (NTRS)

    Anthony, T. R.

    1980-01-01

    The disregistry of holes drilled with a pulse laser beam in 330-micron-thick single-crystal silicon-on-sapphire wafers is examined. The exit positions of the holes were displaced from the hole entrance positions on the opposing face of the wafer, and this random displacement increased with the number of laser pulses required. A model in which the bottom of the drill hole experiences small random displacements during each laser pulse is used to describe the experimental observations. It is shown that the average random displacement caused by each pulse is only a few percent of the hole diameter and can be reduced by using as few laser pulses as necessary while avoiding the cracking and spalling of the wafer that occur with a hole drilled with a single pulse.

  19. Erosion by a one-dimensional random walk

    NASA Astrophysics Data System (ADS)

    Chisholm, Rebecca H.; Hughes, Barry D.; Landman, Kerry A.

    2014-08-01

    We consider a model introduced by Baker et al. [Phys. Rev. E 88, 042113 (2013), 10.1103/PhysRevE.88.042113] of a single lattice random walker moving on a domain of allowed sites, surrounded by blocked sites. The walker enlarges the allowed domain by eroding the boundary at its random encounters with blocked boundary sites: attempts to step onto blocked sites succeed with a given probability and convert these sites to allowed sites. The model interpolates continuously between the Pólya random walker on the one-dimensional lattice and a "blind" walker who attempts freely, but always aborts, moves to blocked sites. We obtain some exact results about the walker's location and the rate of erosion.

  20. Expected number of sites visited by a constrained n-step random walk

    NASA Astrophysics Data System (ADS)

    Larralde, Hernan; Weiss, George H.

    1995-08-01

    We develop a formalism based on generating functions for calculating the expected number of sites visited by a lattice random walk constrained to visit a fixed point at the nth step. Explicit results are given in the large-n limit when the target point is not too far from the origin.

  1. Comment on ’Corrected Diffusion Approximations in Certain Random Walk Problems’.

    DTIC Science & Technology

    1984-05-01

    This paper is concerned with extensions to the nonexponential family case of two problems considered in an earlier work. The first problem is to find the...expected value of the maximum of a random walk with small, negative drift, and the second is to find the distribution of the same quantity.

  2. Energy difference space random walk to achieve fast free energy calculations.

    PubMed

    Min, Donghong; Yang, Wei

    2008-05-21

    A method is proposed to efficiently obtain free energy differences. In the present algorithm, free energy calculations proceed by the realization of an energy difference space random walk. Thereby, this algorithm can greatly improve the sampling of the regions in phase space where target states overlap.

  3. Functional equation for the crossover in the model of one-dimensional Weierstrass random walks

    NASA Astrophysics Data System (ADS)

    Rudoi, Yu. G.; Kotel'nikova, O. A.

    2016-12-01

    We consider the problem of one-dimensional symmetric diffusion in the framework of Markov random walks of the Weierstrass type using two-parameter scaling for the transition probability. We construct a solution for the characteristic Lyapunov function as a sum of regular (homogeneous) and singular (nonhomogeneous) solutions and find the conditions for the crossover from normal to anomalous diffusion.

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

    NASA Astrophysics Data System (ADS)

    Comolli, Alessandro; Hakoun, Vivien; Dentz, Marco

    2017-04-01

    Achieving the understanding of the process of solute transport in heterogeneous porous media is of crucial importance for several environmental and social purposes, ranging from aquifers contamination and remediation, to risk assessment in nuclear waste repositories. The complexity of this aim is mainly ascribable to the heterogeneity of natural media, which can be observed at all the scales of interest, from pore scale to catchment scale. In fact, the intrinsic heterogeneity of porous media is responsible for the arising of the well-known non-Fickian footprints of transport, including heavy-tailed breakthrough curves, non-Gaussian spatial density profiles and the non-linear growth of the mean squared displacement. Several studies investigated the processes through which heterogeneity impacts the transport properties, which include local modifications to the advective-dispersive motion of solutes, mass exchanges between some mobile and immobile phases (e.g. sorption/desorption reactions or diffusion into solid matrix) and spatial correlation of the flow field. In the last decades, the continuous time random walk (CTRW) model has often been used to describe solute transport in heterogenous conditions and to quantify the impact of point heterogeneity, spatial correlation and mass transfer on the average transport properties [1]. Open issues regarding this approach are the possibility to relate measurable properties of the medium to the parameters of the model, as well as its capability to provide predictive information. In a recent work [2] the authors have shed new light on understanding the relationship between Lagrangian and Eulerian dynamics as well as on their evolution from arbitrary initial conditions. On the basis of these results, we derive a CTRW model for the description of Darcy-scale transport in d-dimensional media characterized by spatially random permeability fields. The CTRW approach models particle velocities as a spatial Markov process, which is

  5. On the asymptotics of the mean sojourn time of a random walk on a semi-axis

    NASA Astrophysics Data System (ADS)

    Lotov, V. I.; Tarasenko, A. S.

    2015-06-01

    We find asymptotic expansions for the expectation of the sojourn time above an increasing level of a trajectory of a random walk with zero drift. The Cramér condition on the existence of an exponential moment is imposed on the distribution of jumps of the random walk.

  6. Exercise and self-esteem in menopausal women: a randomized controlled trial involving walking and yoga.

    PubMed

    Elavsky, Steriani; McAuley, Edward

    2007-01-01

    To examine the effects of walking and yoga on multidimensional self-esteem and roles played by self-efficacy, body composition, and physical activity (PA) in changes in esteem. Four-month randomized controlled exercise trial with three arms: walking, yoga, and control. Previously low-active middle-aged women (n=164; M age = 49.9; SD = 3.6). Structured and supervised walking program meeting three times per week for I hour and supervised yoga program meeting twice per week for 90 minutes. Body composition, fitness assessment, and battery of psychologic measures. Panel analysis within a structural equation modeling framework using Mplus 3.0. The walking and yoga interventions failed to enhance global or physical self-esteem but improved subdomain esteem relative to physical condition and strength (for walking) and body attractiveness (for both walking and yoga). Over time the effects of PA, self-efficacy, and body fat on changes in physical self-esteem and global esteem were mediated by changes in physical condition and body attractiveness subdomain esteem. Women reporting greater levels of self-efficacy and PA with lower body fat also reported greater enhancements in subdomain esteem. These results provide support for the hierarchic and multidimensional nature of self-esteem and indicate that middle-aged women may enhance certain aspects of physical self-esteem by participating in PA.

  7. Bounding the Edge Cover Time of Random Walks on Graphs

    DTIC Science & Technology

    2011-07-21

    34. The Annals of Probability, Vol 16, No. 1, pp. 189-199, 1988. [21] Niels Erik N6rlund. Vorlesungen Uber Diffcrcnzenrechnung. New York, Chelsea, 1954...16, No. 1, pp. 189-199, 1988. [21] Niels Erik N6rlund. Voriesungen Uber Differenzenrcchnung. New York, Chelsea, 1954. [22] Prasad Tetali. "Random

  8. 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.

  9. 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.

  10. Random walk of motor planning in task-irrelevant dimensions.

    PubMed

    van Beers, Robert J; Brenner, Eli; Smeets, Jeroen B J

    2013-02-01

    The movements that we make are variable. It is well established that at least a part of this variability is caused by noise in central motor planning. Here, we studied how the random effects of planning noise translate into changes in motor planning. Are the random effects independently added to a constant mean end point, or do they accumulate over movements? To distinguish between these possibilities, we examined repeated, discrete movements in various tasks in which the motor output could be decomposed into a task-relevant and a task-irrelevant component. We found in all tasks that the task-irrelevant component had a positive lag 1 autocorrelation, suggesting that the random effects of planning noise accumulate over movements. In contrast, the task-relevant component always had a lag 1 autocorrelation close to zero, which can be explained by effective trial-by-trial correction of motor planning on the basis of observed motor errors. Accumulation of the effects of planning noise is consistent with current insights into the stochastic nature of synaptic plasticity. It leads to motor exploration, which may subserve motor learning and performance optimization.

  11. Transport properties of a two-dimensional ``chiral'' persistent random walk

    NASA Astrophysics Data System (ADS)

    Larralde, H.

    1997-11-01

    The usual two-dimensional persistent random walk is generalized by introducing a clockwise (or counterclockwise) angular bias at each new step direction. This bias breaks the reflection symmetry of the problem, giving the walker a tendency to ``loop,'' and gives rise to unusual transport properties. In particular, there is a resonantlike enhancement of the diffusion constant as the parameters of the system are changed. Also, in response to an external field, the looping tendency can resist or enhance the drift along the field and gives rise to a drift transverse to the field. These results are obtained analytically, and, for completeness, compared with Monte Carlo simulations of the walk.

  12. The effect of walking speed on local dynamic stability is sensitive to calculation methods.

    PubMed

    Stenum, Jan; Bruijn, Sjoerd M; Jensen, Bente R

    2014-11-28

    Local dynamic stability has been assessed by the short-term local divergence exponent (λS), which quantifies the average rate of logarithmic divergence of infinitesimally close trajectories in state space. Both increased and decreased local dynamic stability at faster walking speeds have been reported. This might pertain to methodological differences in calculating λS. Therefore, the aim was to test if different calculation methods would induce different effects of walking speed on local dynamic stability. Ten young healthy participants walked on a treadmill at five speeds (60%, 80%, 100%, 120% and 140% of preferred walking speed) for 3min each, while upper body accelerations in three directions were sampled. From these time-series, λS was calculated by three different methods using: (a) a fixed time interval and expressed as logarithmic divergence per stride-time (λS-a), (b) a fixed number of strides and expressed as logarithmic divergence per time (λS-b) and (c) a fixed number of strides and expressed as logarithmic divergence per stride-time (λS-c). Mean preferred walking speed was 1.16±0.09m/s. There was only a minor effect of walking speed on λS-a. λS-b increased with increasing walking speed indicating decreased local dynamic stability at faster walking speeds, whereas λS-c decreased with increasing walking speed indicating increased local dynamic stability at faster walking speeds. Thus, the effect of walking speed on calculated local dynamic stability was significantly different between methods used to calculate local dynamic stability. Therefore, inferences and comparisons of studies employing λS should be made with careful consideration of the calculation method. Copyright © 2014 Elsevier Ltd. All rights reserved.

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

    PubMed

    Schulz, Johannes H P; Barkai, Eli

    2015-06-01

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

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

    NASA Astrophysics Data System (ADS)

    Gubiec, Tomasz; Kutner, Ryszard

    2010-10-01

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

  15. Heterogeneous Memorized Continuous Time Random Walks in an External Force Fields

    NASA Astrophysics Data System (ADS)

    Wang, Jun; Zhou, Ji; Lv, Long-Jin; Qiu, Wei-Yuan; Ren, Fu-Yao

    2014-09-01

    In this paper, we study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated memorized waiting times, which involves Reimann-Liouville fractional derivative or Reimann-Liouville fractional integral. We show that the mean squared displacement of the test particle which is dependent on its location of the form (El-Wakil and Zahran, Chaos Solitons Fractals, 12, 1929-1935, 2001) where is the anomalous exponent, the diffusion exponent is dependent on the model parameters. We obtain the Fokker-Planck-type dynamic equations, and their stationary solutions are of the Boltzmann-Gibbs form. These processes obey a generalized Einstein-Stokes-Smoluchowski relation and the second Einstein relation. We observe that the asymptotic behavior of waiting times and subordinations are of stretched Gaussian distributions. We also discuss the time averaged in the case of an harmonic potential, and show that the process exhibits aging and ergodicity breaking.

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

    PubMed

    Gubiec, Tomasz; Kutner, Ryszard

    2010-10-01

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

  17. Exact Solutions for Average Trapping Time of Random Walks on Weighted Scale-Free Networks

    NASA Astrophysics Data System (ADS)

    Xing, Changming; Zhang, Yigong; Ma, Jun; Yang, Lin; Guo, Lei

    In this paper, we present two deterministic weighted scale-free networks controlled by a weight parameter r(0 < r ≤ 1). One is fractal network, the other one is non-fractal network, while they have the same weight distribution when the parameter r is identical. Based on their special network structure, we study random walks on network with a trap located at a fixed node. For each network, we calculate exact solutions for average trapping time (ATT). Analyzing and comparing the obtained solutions, we find that their ATT all grow asymptotically as a power-law function of network order (number of nodes) with the exponent f(r) dependent on the weight parameter, but their exponent f(r) are obviously different, one is an increasing function of r, while the other is opposite. Collectively, all the obtained results show that the efficiency of trapping on weighted Scale-free networks has close relation to the weight distribution, but there is no stable positive or negative correlation between the weight distribution and the trapping time on different networks. We hope these results given in this paper could help us get deeper understanding about the weight distribution on the property and dynamics of scale-free networks.

  18. Dynamical continuous time random Lévy flights

    NASA Astrophysics Data System (ADS)

    Liu, Jian; Chen, Xiaosong

    2016-03-01

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

  19. Random-walk-based stochastic modeling of three-dimensional fiber systems.

    PubMed

    Altendorf, Hellen; Jeulin, Dominique

    2011-04-01

    For the simulation of fiber systems, there exist several stochastic models: systems of straight nonoverlapping fibers, systems of overlapping bending fibers, or fiber systems created by sedimentation. However, there is a lack of models providing dense, nonoverlapping fiber systems with a given random orientation distribution and a controllable level of bending. We introduce a new stochastic model in this paper that generalizes the force-biased packing approach to fibers represented as chains of balls. The starting configuration is modeled using random walks, where two parameters in the multivariate von Mises-Fisher orientation distribution control the bending. The points of the random walk are associated with a radius and the current orientation. The resulting chains of balls are interpreted as fibers. The final fiber configuration is obtained as an equilibrium between repulsion forces avoiding crossing fibers and recover forces ensuring the fiber structure. This approach provides high volume fractions up to 72.0075%.

  20. Optimization of goal-directed movements in the cerebellum: a random walk hypothesis.

    PubMed

    Kitazawa, Shigeru

    2002-08-01

    Voluntary goal-directed movements, such as arm reaching, are nearly optimized in terms of smoothness over the entire movement. Such smoothness is lost with cerebellar dysfunction, suggesting the essential role of the cerebellum in optimizing movement. However, it is still not clear how the cerebellum contributes to achieving smoothness over an entire movement. A recent study has shown that such smoothness of movement can be achieved by reducing the variance of errors at the end of the movement. Here, I hypothesize that the terminal errors conveyed by climbing fibers in the cerebellum serve to reduce not only the mean error, but also the variance of the error, through a process analogous to the random walk through movement control candidates. In the random walk, the direction of each step is randomly determined, but the size of each step is determined by the error at the end of each trial.

  1. Random walks on cubic lattices with bond disorder

    SciTech Connect

    Ernst, M.H.; van Velthoven, P.F.J.

    1986-12-01

    The authors consider diffusive systems with static disorder, such as Lorentz gases, lattice percolation, ants in a labyrinth, termite problems, random resistor networks, etc. In the case of diluted randomness the authors can apply the methods of kinetic theory to obtain systematic expansions of dc and ac transport properties in powers of the impurity concentration c. The method is applied to a hopping model on a d-dimensional cubic lattice having two types of bonds with conductivity sigma and sigma/sub 0/ = 1, with concentrations c and 1-c, respectively. For the square lattice the authors explicitly calculate the diffusion coefficient D(c,sigma) as a function of c, to O(c/sup 2/) terms included for different ratios of the bond conductivity sigma. The probability of return at long times is given by P/sub 0/(t) approx. (4..pi..D(c,sigma)t)/sup -d/2/, which is determined by the diffusion coefficient of the disordered system.

  2. Limb dominance changes in walking evolution explored by asymmetric correlations in gait dynamics

    NASA Astrophysics Data System (ADS)

    Echeverria, Juan C.; Rodriguez, Eduardo; Velasco, Alejandra; Alvarez-Ramirez, Jose

    2010-04-01

    Fluctuations in the stride interval time series of unconstrained walking are not random but seem to exhibit long-range correlations that decay as a power law (Hausdorff et al. (1995) [35]). Here, we examine whether asymmetries are present in the long-range correlations of different gait parameters (stride, swing and stance intervals) for the left and right limbs. Gait dynamics corresponding to 16 healthy subjects were obtained from the Physionet database, which contains stride, stance and swing intervals for both left and right limbs. Detrended Fluctuation Analysis (DFA) revealed the presence of asymmetric long-range correlations in all gait cycle variables investigated. A rich variety of scaling exponent dynamics was found, with the presence of synchronicity, decreased correlations and dominant correlations. The results are discussed in terms of the hypothesis that reduced strength of long-range correlations reflect both enhanced stability and adaptability.

  3. The influence of gait speed on local dynamic stability of walking

    PubMed Central

    England, Scott A.; Granata, Kevin P.

    2006-01-01

    The focus of this study was to examine the role of walking velocity in stability during normal gait. Local dynamic stability was quantified through the use of maximum finite-time Lyapunov exponents, λMax. These quantify the rate of attenuation of kinematic variability of joint angle data recorded as subjects walked on a motorized treadmill at 20%, 40%, 60%, and 80% of the Froude velocity. A monotonic trend between λMax and walking velocity was observed with smaller λMax at slower walking velocities. Smaller λMax indicates more stable walking dynamics. This trend was evident whether stride duration variability remained or was removed by time normalizing the data. This suggests that slower walking velocities lead to increases in stability. These results may reveal more detailed information on the behavior of the neuro-controller than variability-based analyses alone. PMID:16621565

  4. The influence of gait speed on local dynamic stability of walking.

    PubMed

    England, Scott A; Granata, Kevin P

    2007-02-01

    The focus of this study was to examine the role of walking velocity in stability during normal gait. Local dynamic stability was quantified through the use of maximum finite-time Lyapunov exponents, lambda(Max). These quantify the rate of attenuation of kinematic variability of joint angle data recorded as subjects walked on a motorized treadmill at 20%, 40%, 60%, and 80% of the Froude velocity. A monotonic trend between lambda(Max) and walking velocity was observed with smaller lambda(Max) at slower walking velocities. Smaller lambda(Max) indicates more stable walking dynamics. This trend was evident whether stride duration variability remained or was removed by time normalizing the data. This suggests that slower walking velocities lead to increases in stability. These results may reveal more detailed information on the behavior of the neuro-controller than variability-based analyses alone.

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

    PubMed Central

    2011-01-01

    Background Falls in older people continue to be a major public health issue in industrialized countries. Extensive research into falls prevention has identified exercise as a proven fall prevention strategy. However, despite over a decade of promoting physical activity, hospitalisation rates due to falls injuries in older people are still increasing. This could be because efforts to increase physical activity amongst older people have been unsuccessful, or the physical activity that older people engage in is insufficient and/or inappropriate. The majority of older people choose walking as their predominant form of exercise. While walking has been shown to lower the risk of many chronic diseases its role in falls prevention remains unclear. This paper outlines the methodology of a study whose aims are to determine: if a home-based walking intervention will reduce the falls rate among healthy but inactive community-dwelling older adults (65 + years) compared to no intervention (usual activity) and; whether such an intervention can improve risk factors for falls, such as balance, strength and reaction time. Methods/Design This study uses a randomised controlled trial design. A total of 484 older people exercising less than 120 minutes per week will be recruited through the community and health care referrals throughout Sydney and neighboring regions. All participants are randomised into either the self-managed walking program group or the health-education waiting list group using a block randomization scheme. Outcome measures include prospective falls and falls injuries, quality of life, and physical activity levels. A subset of participants (n = 194) will also receive physical performance assessments comprising of tests of dynamic balance, strength, reaction time and lower limb functional status. Discussion Certain types of physical activity can reduce the risk of falls. As walking is already the most popular physical activity amongst older people, if walking is

  6. Self-Avoiding Walks on the Random Lattice and the Random Hopping Model on a Cayley Tree

    NASA Astrophysics Data System (ADS)

    Kim, Yup

    Using a field theoretic method based on the replica trick, it is proved that the three-parameter renormalization group for an n-vector model with quenched randomness reduces to a two-parameter one in the limit n (--->) 0 which corresponds to self-avoiding walks (SAWs). This is also shown by the explicit calculation of the renormalization group recursion relations to second order in (epsilon). From this reduction we find that SAWs on the random lattice are in the same universality class as SAWs on the regular lattice. By analogy with the case of the n-vector model with cubic anisotropy in the limit n (--->) 1, the fixed-point structure of the n-vector model with randomness is analyzed in the SAW limit, so that a physical interpretation of the unphysical fixed point is given. Corrections of the values of critical exponents of the unphysical fixed point published previously is also given. Next we formulate an integral equation and recursion relations for the configurationally averaged one particle Green's function of the random hopping model on a Cayley tree of coordination number ((sigma) + 1). This formalism is tested by applying it successfully to the nonrandom model. Using this scheme for 1 << (sigma) < (INFIN) we calculate the density of states of this model with a Gaussian distribution of hopping matrix elements in the range of energy E('2) > E(,c)('2), where E(,c) is a critical energy described below. The singularity in the Green's function which occurs at energy E(,1)('(0)) for (sigma) = (INFIN) is shifted to complex energy E(,1) (on the unphysical sheet of energy E) for small (sigma)('-1). This calculation shows that the density of states is smooth function of energy E around the critical energy E(,c) = Re E(,1) in accord with Wegner's theorem. In this formulation the density of states has no sharp phase transition on the real axis of E because E(,1) has developed an imaginary part. Using the Lifschitz argument, we calculate the density of states near the

  7. 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

  8. A directed continuous time random walk model with jump length depending on waiting time.

    PubMed

    Shi, Long; Yu, Zuguo; Mao, Zhi; Xiao, Aiguo

    2014-01-01

    In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x, t) of finding the walker at position x at time t is completely determined by the Laplace transform of the probability density function φ(t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.

  9. MODEL OF THE FIELD LINE RANDOM WALK EVOLUTION AND APPROACH TO ASYMPTOTIC DIFFUSION IN MAGNETIC TURBULENCE

    SciTech Connect

    Snodin, A. P.; Ruffolo, D.; Matthaeus, W. H. E-mail: david.ruf@mahidol.ac.th

    2013-01-01

    The turbulent random walk of magnetic field lines plays an important role in the transport of plasmas and energetic particles in a wide variety of astrophysical situations, but most theoretical work has concentrated on determination of the asymptotic field line diffusion coefficient. Here we consider the evolution with distance of the field line random walk using a general ordinary differential equation (ODE), which for most cases of interest in astrophysics describes a transition from free streaming to asymptotic diffusion. By challenging theories of asymptotic diffusion to also describe the evolution, one gains insight on how accurately they describe the random walk process. Previous theoretical work has effectively involved closure of the ODE, often by assuming Corrsin's hypothesis and a Gaussian displacement distribution. Approaches that use quasilinear theory and prescribe the mean squared displacement ({Delta}x {sup 2}) according to free streaming (random ballistic decorrelation, RBD) or asymptotic diffusion (diffusive decorrelation, DD) can match computer simulation results, but only over specific parameter ranges, with no obvious 'marker' of the range of validity. Here we make use of a unified description in which the ODE determines ({Delta}x {sup 2}) self-consistently, providing a natural transition between the assumptions of RBD and DD. We find that the minimum kurtosis of the displacement distribution provides a good indicator of whether the self-consistent ODE is applicable, i.e., inaccuracy of the self-consistent ODE is associated with non-Gaussian displacement distributions.

  10. Impact of pedometer-based walking on menopausal women's sleep quality: a randomized controlled trial.

    PubMed

    Tadayon, M; Abedi, P; Farshadbakht, F

    2016-08-01

    Objective Sleep disturbances are one of the most common psycho-physiological issues among postmenopausal women. This study was designed to evaluate the impact of walking with a pedometer on the sleep quality of postmenopausal Iranian women. Methods This randomized, controlled trial was conducted on 112 women who were randomly assigned to two groups. The women in the intervention group (n = 56) were asked to walk with a pedometer each day for 12 weeks and to increase their walking distance by 500 steps per week. A sociodemographic instrument and the Pittsburgh Sleep Quality Index were used to collect data. Sleep quality was measured at baseline, 4, 8, and 12 weeks after intervention. The control group (n = 56) did not receive any intervention. Results After 12 weeks, subjective sleep quality, sleep latency, sleep duration, habitual sleep efficiency, sleep disturbances, use of sleeping medication, and daytime dysfunction improved to a significantly greater extent in the intervention group than in the control group (p < 0.05). The total sleep quality score was significantly higher in the intervention group than in the control group (0.64 vs. 0.98, p = 0.001). Conclusion This study showed that walking with a pedometer is an easy and cost-effective way to improve the quality of sleep among postmenopausal women. Use of this method in public health centers is recommended.

  11. 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.

  12. Random walk expectancies for recent global climate, and in an enhanced Greenhouse warming

    NASA Astrophysics Data System (ADS)

    Gordon, Adrian H.; Bye, John A. T.

    1993-11-01

    We partition the United Kingdom Meteorological Office Global Temperature Series ( Tk) using an exponential decay filter into a filtered series ( T̂k) and a difference series ( T' k = T k - T̂k). For a decay time constant, τ ≈ 0.85 years, T̂k is shown to be agood approximation to a random walk generated by a cumulation of normally distributed interannual temperature transitions, and hence ' k contains the predictable temperature signal. The standard deviation of the T̂k series, σ = 0.083K, which is about 1 1/2 that of the T' k series. From this partition, it is argued that τ is the decay time costant (e-folding time) for the global temperature series, and also by the elementary theory of damped oscillations, that the global cimate system (as represented by the global temperature) can only support free oscillations of natural period less than T = 2 πτ ≈ 5 years, i.e. the QBO and ENSO signals. On assuming that σ does not vary significantly over periods up to 20,000 B.P. we find that the expected maximum excursions of the random walks are consistent with the actual inferred temperature variability. On the other hand, the projected temperature rise due to the enhanced Greenhouse effect possibly cannot be supported as a random walk by σ. This suggests that the interannual structure of the climate system would change under these conditions. This conjecture can be tested adequately only with climate models which correctly reproduced random walk behaviour. This is inhibited in published simulated temperature series from coupled models, possibly because of flux correction. An assessment of the likelihood of a change in the interannual variance, and of the ratio between its predictable and random proportions is clearly of utmost significance in the Greenhouse debate, yet it appears to have received very little discussion.

  13. Parabolic Anderson Model in a Dynamic Random Environment: Random Conductances

    NASA Astrophysics Data System (ADS)

    Erhard, D.; den Hollander, F.; Maillard, G.

    2016-06-01

    The parabolic Anderson model is defined as the partial differential equation ∂ u( x, t)/ ∂ t = κ Δ u( x, t) + ξ( x, t) u( x, t), x ∈ ℤ d , t ≥ 0, where κ ∈ [0, ∞) is the diffusion constant, Δ is the discrete Laplacian, and ξ is a dynamic random environment that drives the equation. The initial condition u( x, 0) = u 0( x), x ∈ ℤ d , is typically taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump at rate 2 d κ, split into two at rate ξ ∨ 0, and die at rate (- ξ) ∨ 0. In earlier work we looked at the Lyapunov exponents λ p(κ ) = limlimits _{tto ∞} 1/t log {E} ([u(0,t)]p)^{1/p}, quad p in {N} , qquad λ 0(κ ) = limlimits _{tto ∞} 1/2 log u(0,t). For the former we derived quantitative results on the κ-dependence for four choices of ξ : space-time white noise, independent simple random walks, the exclusion process and the voter model. For the latter we obtained qualitative results under certain space-time mixing conditions on ξ. In the present paper we investigate what happens when κΔ is replaced by Δ𝓚, where 𝓚 = {𝓚( x, y) : x, y ∈ ℤ d , x ˜ y} is a collection of random conductances between neighbouring sites replacing the constant conductances κ in the homogeneous model. We show that the associated annealed Lyapunov exponents λ p (𝓚), p ∈ ℕ, are given by the formula λ p({K} ) = {sup} {λ p(κ ) : κ in {Supp} ({K} )}, where, for a fixed realisation of 𝓚, Supp(𝓚) is the set of values taken by the 𝓚-field. We also show that for the associated quenched Lyapunov exponent λ 0(𝓚) this formula only provides a lower bound, and we conjecture that an upper bound holds when Supp(𝓚) is replaced by its convex hull. Our proof is valid for three classes of reversible ξ, and for all 𝓚

  14. Anisotropy of the monomer random walk in a polymer melt: local-order and connectivity effects

    NASA Astrophysics Data System (ADS)

    Bernini, S.; Leporini, D.

    2016-05-01

    The random walk of a bonded monomer in a polymer melt is anisotropic due to local order and bond connectivity. We investigate both effects by molecular-dynamics simulations on melts of fully-flexible linear chains ranging from dimers (M  =  2) up to entangled polymers (M  =  200). The corresponding atomic liquid is also considered a reference system. To disentangle the influence of the local geometry and the bond arrangements, and to reveal their interplay, we define suitable measures of the anisotropy emphasising either the former or the latter aspect. Connectivity anisotropy, as measured by the correlation between the initial bond orientation and the direction of the subsequent monomer displacement, shows a slight enhancement due to the local order at times shorter than the structural relaxation time. At intermediate times—when the monomer displacement is comparable to the bond length—a pronounced peak and then decays slowly as t -1/2, becoming negligible when the displacement is as large as about five bond lengths, i.e. about four monomer diameters or three Kuhn lengths. Local-geometry anisotropy, as measured by the correlation between the initial orientation of a characteristic axis of the Voronoi cell and the subsequent monomer dynamics, is affected at shorter times than the structural relaxation time by the cage shape with antagonistic disturbance by the connectivity. Differently, at longer times, the connectivity favours the persistence of the local-geometry anisotropy, which vanishes when the monomer displacement exceeds the bond length. Our results strongly suggest that the sole consideration of the local order is not enough to understand the microscopic origin of the rattling amplitude of the trapped monomer in the cage of the neighbours.

  15. Entropy, complexity, and Markov diagrams for random walk cancer models

    NASA Astrophysics Data System (ADS)

    Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

    2014-12-01

    The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

  16. Entropy, complexity, and Markov diagrams for random walk cancer models

    PubMed Central

    Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

    2014-01-01

    The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential. PMID:25523357

  17. Entropy, complexity, and Markov diagrams for random walk cancer models.

    PubMed

    Newton, Paul K; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

    2014-12-19

    The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

  18. Exercise on a treadmill or walking outdoors? A randomized controlled trial comparing effectiveness of two walking exercise programmes late after stroke.

    PubMed

    Langhammer, Birgitta; Stanghelle, Johan K

    2010-01-01

    To evaluate spatial and temporal gait characteristics and endurance late after stroke in people who had received two different walking exercises. A secondary aim was to compare the outcomes in relation to length of time exercising and number of exercise occasions between the two. A randomized controlled trial. A private rehabilitation centre. Thirty-nine people with stroke entered the study, and five dropped out. Treadmill training versus walking outdoors. Six-Minute Walk Test, a 10-metre walk test and pulse rates at rest and in activity. There were significant differences in favour of the treadmill group in Six-Minute Walk Test distance (P = 0.04), Six-Minute Walk Test speed (P = 0.03), 10-m walking speed (P = 0.03), bilateral stride length (right leg; P = 0.009, left leg; P = 0.003) and step width (P = 0.01), indicating more symmetrical use of the legs in the treadmill group (1.02-1.10 m versus 0.97-0.92 m). There were no significant differences between groups in cadence (P = 0.78). All participants complied 100% with their respective programmes. Exercise frequency did not differ between the groups but significantly less time was spent exercising on the treadmill compared with walking exercise outdoors (107 versus 316 minutes, P = 0.002). There were no differences in use of assistive aids between the groups on arrival at the clinic or at departure. The results indicate that treadmill walking improves spatial and temporal gait characteristics more effectively than walking outdoors.

  19. The effects of treadmill walking combined with obstacle-crossing on walking ability in ambulatory patients after stroke: a pilot randomized controlled trial.

    PubMed

    Jeong, Yeon-Gyu; Koo, Jung-Wan

    2016-12-01

    Treadmill walking training (TWT) provides greater amount and intensity of stepping practice than conventional walking training in patients with chronic stroke. However, there is not any conclusive evidence regarding the effects of TWT for ambulatory post-stroke patients. This study investigated the effects of treadmill walking combined with obstacle-crossing on the walking ability of ambulatory post-stroke patients. Twenty-nine subjects from a university hospital-based rehabilitation center were randomly assigned to one of the following: experimental group (15 subjects) or control group (14 subjects). All subjects underwent 30 min of active/passive exercises and 30 min of gait training in the form of treadmill walking. The subjects in the experimental group underwent simultaneous training in obstacle-crossing while walking on the treadmill for 30 min/day, 5 times/week, for 4 weeks. Main measures were the 10-m walk test (10MWT), 6-min walk test (6MWT), Berg Balance Scale (BBS), timed "Up & Go" (TUG) test, and Activities-specific Balance Confidence (ABC) scale used before and after the intervention. The changed values of the 6MWT and BBS were significantly higher in the experimental group than in the control group after adjusting for each baseline value, with large effects of 1.12 and 0.78, respectively, but not in the 10MWT, TUG, and ABC scale scores. Both groups showed a significant difference in all variables before and after the intervention. Treadmill walking combined with obstacle-crossing training may help improve the walking ability of patients with hemiplegic stroke and can possibly be used as an adjunct to routine rehabilitation therapy as a task-oriented practice based on community ambulation.

  20. Random-walk model simulation of air pollutant dispersion in atmospheric boundary layer in China.

    PubMed

    Wang, Peng; Mu, Hailin

    2011-01-01

    In this study, the land-sea breeze circulation model coupled with a random-walk model is developed by the analysis of the formation and the mechanism of the land-sea breeze. Based on the data of the land-sea circulation in Dalian, China, the model simulated the diurnal variation of pressure, flow, temperature, and turbulent kinetic energy field and also provides a basis for solving the air pollutant concentration in the land-sea breeze circulation so as to estimate the economic cost attributable to the atmospheric pollution. The air pollutant concentration in the background of land-sea circulation is also simulated by a Gaussian dispersion model, and the results revealed that the land-sea circulation model coupled with the random-walk model gives a reasonable description of air pollutant dispersion in coastal areas.

  1. Random walks in Rindler spacetime and string theory at the tip of the cigar

    NASA Astrophysics Data System (ADS)

    Mertens, Thomas G.; Verschelde, Henri; Zakharov, Valentin I.

    2014-03-01

    In this paper, we discuss Rindler space string thermodynamics from a thermal scalar point of view as an explicit example of the results obtained in [1]. We discuss the critical behavior of the string gas and interpret this as a random walk near the black hole horizon. Combining field theory arguments with the random walk path integral picture, we realize (at genus one) the picture put forward by Susskind of a long string surrounding black hole horizons. We find that thermodynamics is dominated by a long string living at stringscale distance from the horizon whose redshifted temperature is the Rindler or Hawking temperature. We provide further evidence of the recent proposal for string theory at the tip of the cigar by comparing with the flat space orbifold approach to Rindler thermodynamics. We discuss all types of closed strings (bosonic, type II and heterotic strings).

  2. A partially reflecting random walk on spheres algorithm for electrical impedance tomography

    SciTech Connect

    Maire, Sylvain; Simon, Martin

    2015-12-15

    In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute the voltage-to-current map in an embarrassingly parallel manner, which is an important issue with regard to the corresponding inverse problem. Our method uses the well-known random walk on spheres algorithm inside subdomains where the diffusion coefficient is constant and employs replacement techniques motivated by finite difference discretization to deal with both mixed boundary conditions and interface transmission conditions. We analyze the global bias and the variance of the new estimator both theoretically and experimentally. Subsequently, the variance of the new estimator is considerably reduced via a novel control variate conditional sampling technique which yields a highly efficient hybrid forward solver coupling probabilistic and deterministic algorithms.

  3. 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.

  4. 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.

  5. The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective.

    PubMed

    Kuo, Arthur D

    2007-08-01

    We examine two prevailing, yet surprisingly contradictory, theories of human walking. The six determinants of gait are kinematic features of gait proposed to minimize the energetic cost of locomotion by reducing the vertical displacement of the body center of mass (COM). The inverted pendulum analogy proposes that it is beneficial for the stance leg to behave like a pendulum, prescribing a more circular arc, rather than a horizontal path, for the COM. Recent literature presents evidence against the six determinants theory, and a simple mathematical analysis shows that a flattened COM trajectory in fact increases muscle work and force requirements. A similar analysis shows that the inverted pendulum fares better, but paradoxically predicts no work or force requirements. The paradox may be resolved through the dynamic walking approach, which refers to periodic gaits produced almost entirely by the dynamics of the limbs alone. Demonstrations include passive dynamic walking machines that descend a gentle slope, and active dynamic walking robots that walk on level ground. Dynamic walking takes advantage of the inverted pendulum mechanism, but requires mechanical work to transition from one pendular stance leg to the next. We show how the step-to-step transition is an unavoidable energetic consequence of the inverted pendulum gait, and gives rise to predictions that are experimentally testable on humans and machines. The dynamic walking approach provides a new perspective, focusing on mechanical work rather than the kinematics or forces of gait. It is helpful for explaining human gait features in a constructive rather than interpretive manner.

  6. The reliability of local dynamic stability in walking while texting and performing an arithmetical problem.

    PubMed

    Hamacher, Dennis; Hamacher, Daniel; Törpel, Alexander; Krowicki, Martin; Herold, Fabian; Schega, Lutz

    2016-02-01

    In the recent years, local dynamic stability of walking was frequently used to quantify motor control. Particularly, dual-task paradigms are used to assess a shift in gait control strategy to test walking in real life situations. Texting short messages while walking is a common motor-cognitive dual task of daily living. To able to monitor possible intervention effects on motor-cognitive dual-task performance, the test-retest reliability of the measure has to be evaluated. Since the reliability of the effects of cognitive tasks including texting while walking on local dynamic gait stability has not been assessed yet, this will be evaluated in the current study. Eleven young individuals were included. Gait data was registered twice (test-retest interval: seven days) using an inertial sensor fixed on the subjects' trunks in three conditions: normal walking, walking while texting a message and walking while reciting serials of 7. Short-term finite maximum Lyapunov Exponents were quantified to assess local dynamic stability. The test-retest reliability was calculated using intra-class correlation coefficients and Bland and Altman Plots (bias and limits of agreement). ICC values of the current study show that in normal walking and walking while texting, outcomes are comparable and indicate mostly good to excellent reliability. The reliability values were almost always the lowest in walking while reciting serials of 7. Local dynamic stability derived from kinematic data of walking while cell phone texting can be reliably collected and, in turn, be used as an outcome measure in clinical trials with repeated measures design. Copyright © 2015 Elsevier B.V. All rights reserved.

  7. 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.

  8. 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.

  9. Random Walk Models for the Spike Activity of a Single Neuron

    PubMed Central

    Gerstein, George L.; Mandelbrot, Benoit

    1964-01-01

    Quantitative methods for the study of the statistical properties of spontaneously occurring spike trains from single neurons have recently been presented. Such measurements suggest a number of descriptive mathematical models. One of these, based on a random walk towards an absorbing barrier, can describe a wide range of neuronal activity in terms of two parameters. These parameters are readily associated with known physiological mechanisms. ImagesFigure 3 PMID:14104072

  10. Solving the Hodgkin-Huxley equations by a random walk method

    SciTech Connect

    Sherman, A.S.; Peskin, C.S.

    1988-01-01

    A numerical method is describes for solving the Hodgkin-Huxley cable equations, set up as an initial boundary value problem. The method uses a gradient random walk combined with creation and destruction of the diffusing elements. It is designed to be efficient in the presence of sharp wavefronts. Details of implementation are given with particular emphasis on satisfying the boundary conditions without introducing excessive noise.

  11. Does visual augmented feedback reduce local dynamic stability while walking?

    PubMed

    Hamacher, Daniel; Hamacher, Dennis; Schega, Lutz

    2015-10-01

    Augmented feedback is frequently used in gait training to efficiently correct specific gait patterns in patients with different disorders. The patients use this external augmented feedback to align actual movements in a way that predefined gait characteristics can be achieved. Voluntary changes of gait characteristics are reported to reduce local dynamic stability (LDS) which in turn is associated with increased risk of falling. The aim of this study was to evaluate the instantaneous effect of visual feedback, provided to help patients to correct frontal plane pelvis and trunk movements, on the LDS of pelvis and trunk. Kinematic gait data was captured in ten women with gait disorders. The effect of visual feedback on LDS, quantified with the largest Lyapunov exponent, of walking was examined. We found a significant decreased LDS (e.g. pelvis: p=.009) in our subjects when they were using visual augmented feedback. Our data suggest that the use of visual augmented feedback causes less stable gait patterns indicating a reduced ability to respond to small perturbations which might increase risk of falling. Therefore, researchers or clinicians who aim to correct gait patterns through real time based external augmented feedback should consider the potential negative effect on gait stability. It should be evaluated if the possible increased fall risk provoked by visual feedback exceeds possible increases in fall risk induced by conventional gait-retraining interventions. The external validity of the study is limited because of the low sample size and inhomogeneous group characteristics. Thus, further studies including homogeneous cohorts are required.

  12. 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…

  13. 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…

  14. Local dynamic stability of lower extremity joints in lower limb amputees during slope walking.

    PubMed

    Chen, Jin-Ling; Gu, Dong-Yun

    2013-01-01

    Lower limb amputees have a higher fall risk during slope walking compared with non-amputees. However, studies on amputees' slope walking were not well addressed. The aim of this study was to identify the difference of slope walking between amputees and non-amputees. Lyapunov exponents λS was used to estimate the local dynamic stability of 7 transtibial amputees' and 7 controls' lower extremity joint kinematics during uphill and downhill walking. Compared with the controls, amputees exhibited significantly lower λS in hip (P=0.04) and ankle (P=0.01) joints of the sound limb, and hip joints (P=0.01) of the prosthetic limb during uphill walking, while they exhibited significantly lower λS in knee (P=0.02) and ankle (P=0.03) joints of the sound limb, and hip joints (P=0.03) of the prosthetic limb during downhill walking. Compared with amputees level walking, they exhibited significantly lower λS in ankle joints of the sound limb during both uphill (P=0.01) and downhill walking (P=0.01). We hypothesized that the better local dynamic stability of amputees was caused by compensation strategy during slope walking.

  15. Estimating Mean First Passage Time of Biased Random Walks with Short Relaxation Time on Complex Networks

    PubMed Central

    Lee, Zhuo Qi; Hsu, Wen-Jing; Lin, Miao

    2014-01-01

    Biased random walk has been studied extensively over the past decade especially in the transport and communication networks communities. The mean first passage time (MFPT) of a biased random walk is an important performance indicator in those domains. While the fundamental matrix approach gives precise solution to MFPT, the computation is expensive and the solution lacks interpretability. Other approaches based on the Mean Field Theory relate MFPT to the node degree alone. However, nodes with the same degree may have very different local weight distribution, which may result in vastly different MFPT. We derive an approximate bound to the MFPT of biased random walk with short relaxation time on complex network where the biases are controlled by arbitrarily assigned node weights. We show that the MFPT of a node in this general case is closely related to not only its node degree, but also its local weight distribution. The MFPTs obtained from computer simulations also agree with the new theoretical analysis. Our result enables fast estimation of MFPT, which is useful especially to differentiate between nodes that have very different local node weight distribution even though they share the same node degrees. PMID:24699325

  16. Mean first-passage time for maximal-entropy random walks in complex networks.

    PubMed

    Lin, Yuan; Zhang, Zhongzhi

    2014-06-20

    We perform an in-depth study for mean first-passage time (MFPT)--a primary quantity for random walks with numerous applications--of maximal-entropy random walks (MERW) performed in complex networks. For MERW in a general network, we derive an explicit expression of MFPT in terms of the eigenvalues and eigenvectors of the adjacency matrix associated with the network. For MERW in uncorrelated networks, we also provide a theoretical formula of MFPT at the mean-field level, based on which we further evaluate the dominant scalings of MFPT to different targets for MERW in uncorrelated scale-free networks, and compare the results with those corresponding to traditional unbiased random walks (TURW). We show that the MFPT to a hub node is much lower for MERW than for TURW. However, when the destination is a node with the least degree or a uniformly chosen node, the MFPT is higher for MERW than for TURW. Since MFPT to a uniformly chosen node measures real efficiency of search in networks, our work provides insight into general searching process in complex networks.

  17. Hierarchical random walks in trace fossils and the origin of optimal search behavior.

    PubMed

    Sims, David W; Reynolds, Andrew M; Humphries, Nicolas E; Southall, Emily J; Wearmouth, Victoria J; Metcalfe, Brett; Twitchett, Richard J

    2014-07-29

    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.

  18. Self-organized anomalous aggregation of particles performing nonlinear and non-Markovian random walks

    NASA Astrophysics Data System (ADS)

    Fedotov, Sergei; Korabel, Nickolay

    2015-12-01

    We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bimodal aggregation.

  19. 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.

  20. 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

  1. Random Walk Based Segmentation for the Prostate on 3D Transrectal Ultrasound Images.

    PubMed

    Ma, Ling; Guo, Rongrong; Tian, Zhiqiang; Venkataraman, Rajesh; Sarkar, Saradwata; Liu, Xiabi; Nieh, Peter T; Master, Viraj V; Schuster, David M; Fei, Baowei

    2016-02-27

    This paper proposes a new semi-automatic segmentation method for the prostate on 3D transrectal ultrasound images (TRUS) by combining the region and classification information. We use a random walk algorithm to express the region information efficiently and flexibly because it can avoid segmentation leakage and shrinking bias. We further use the decision tree as the classifier to distinguish the prostate from the non-prostate tissue because of its fast speed and superior performance, especially for a binary classification problem. Our segmentation algorithm is initialized with the user roughly marking the prostate and non-prostate points on the mid-gland slice which are fitted into an ellipse for obtaining more points. Based on these fitted seed points, we run the random walk algorithm to segment the prostate on the mid-gland slice. The segmented contour and the information from the decision tree classification are combined to determine the initial seed points for the other slices. The random walk algorithm is then used to segment the prostate on the adjacent slice. We propagate the process until all slices are segmented. The segmentation method was tested in 32 3D transrectal ultrasound images. Manual segmentation by a radiologist serves as the gold standard for the validation. The experimental results show that the proposed method achieved a Dice similarity coefficient of 91.37±0.05%. The segmentation method can be applied to 3D ultrasound-guided prostate biopsy and other applications.

  2. 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.

  3. Random Walk Based Segmentation for the Prostate on 3D Transrectal Ultrasound Images

    PubMed Central

    Ma, Ling; Guo, Rongrong; Tian, Zhiqiang; Venkataraman, Rajesh; Sarkar, Saradwata; Liu, Xiabi; Nieh, Peter T.; Master, Viraj V.; Schuster, David M.; Fei, Baowei

    2016-01-01

    This paper proposes a new semi-automatic segmentation method for the prostate on 3D transrectal ultrasound images (TRUS) by combining the region and classification information. We use a random walk algorithm to express the region information efficiently and flexibly because it can avoid segmentation leakage and shrinking bias. We further use the decision tree as the classifier to distinguish the prostate from the non-prostate tissue because of its fast speed and superior performance, especially for a binary classification problem. Our segmentation algorithm is initialized with the user roughly marking the prostate and non-prostate points on the mid-gland slice which are fitted into an ellipse for obtaining more points. Based on these fitted seed points, we run the random walk algorithm to segment the prostate on the mid-gland slice. The segmented contour and the information from the decision tree classification are combined to determine the initial seed points for the other slices. The random walk algorithm is then used to segment the prostate on the adjacent slice. We propagate the process until all slices are segmented. The segmentation method was tested in 32 3D transrectal ultrasound images. Manual segmentation by a radiologist serves as the gold standard for the validation. The experimental results show that the proposed method achieved a Dice similarity coefficient of 91.37±0.05%. The segmentation method can be applied to 3D ultrasound-guided prostate biopsy and other applications. PMID:27660383

  4. Random walk with long-range interaction with a barrier and its dual: Exact results

    NASA Astrophysics Data System (ADS)

    Huillet, Thierry

    2010-03-01

    We consider the random walk on , with up and down transition probabilities given the chain is in state x[set membership, variant]{1,2,...}: Here [delta]>=-1 is a real tuning parameter. We assume that this random walk is reflected at the origin. For [delta]>0, the walker is attracted to the origin. The strength of the attraction goes like for large x and so is long-ranged. For [delta]<0, the walker is repelled from the origin. This chain is irreducible and periodic; it is always recurrent, either positive or null recurrent. Using Karlin-McGregor's spectral representations in terms of orthogonal polynomials and first associated orthogonal polynomials, exact expressions are obtained for first return time probabilities to the origin (excursion length), eventual return (contact) probability, excursion height and spatial moments of the walker. All exhibit power-law decay in some range of the parameter [delta]. In the study, an important role is played by the Wall duality relation for birth and death chains with reflecting barrier. Some qualitative aspects of the dual random walk (obtained by interchanging px and qx) are therefore also included.

  5. Random walk based segmentation for the prostate on 3D transrectal ultrasound images

    NASA Astrophysics Data System (ADS)

    Ma, Ling; Guo, Rongrong; Tian, Zhiqiang; Venkataraman, Rajesh; Sarkar, Saradwata; Liu, Xiabi; Nieh, Peter T.; Master, Viraj V.; Schuster, David M.; Fei, Baowei

    2016-03-01

    This paper proposes a new semi-automatic segmentation method for the prostate on 3D transrectal ultrasound images (TRUS) by combining the region and classification information. We use a random walk algorithm to express the region information efficiently and flexibly because it can avoid segmentation leakage and shrinking bias. We further use the decision tree as the classifier to distinguish the prostate from the non-prostate tissue because of its fast speed and superior performance, especially for a binary classification problem. Our segmentation algorithm is initialized with the user roughly marking the prostate and non-prostate points on the mid-gland slice which are fitted into an ellipse for obtaining more points. Based on these fitted seed points, we run the random walk algorithm to segment the prostate on the mid-gland slice. The segmented contour and the information from the decision tree classification are combined to determine the initial seed points for the other slices. The random walk algorithm is then used to segment the prostate on the adjacent slice. We propagate the process until all slices are segmented. The segmentation method was tested in 32 3D transrectal ultrasound images. Manual segmentation by a radiologist serves as the gold standard for the validation. The experimental results show that the proposed method achieved a Dice similarity coefficient of 91.37+/-0.05%. The segmentation method can be applied to 3D ultrasound-guided prostate biopsy and other applications.

  6. Self-organized anomalous aggregation of particles performing nonlinear and non-Markovian random walks.

    PubMed

    Fedotov, Sergei; Korabel, Nickolay

    2015-12-01

    We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bimodal aggregation.

  7. The impact of dynamic balance measures on walking performance in multiple sclerosis

    PubMed Central

    Fritz, Nora E.; Marasigan, Rhul Evans R.; Calabresi, Peter A.; Newsome, Scott D.; Zackowski, Kathleen M.

    2014-01-01

    Background Static posture imbalance and gait dysfunction are common in individuals with multiple sclerosis (MS). Although the impact of strength and static balance on walking has been examined, little is known about the impact of dynamic standing balance on walking in MS. Objective To determine the impact of dynamic balance, static balance, sensation, and strength measures to walking in individuals with MS. Methods 52 individuals with MS (27 females; 26 relapsing-remitting; mean age 45.6±10.3 years; median EDSS 3.5 (range 0-7) participated in testing for dynamic and static posturography (Kistler 9281 force plate), hip flexion, hip extension, and ankle dorsiflexion strength (Microfet2 hand-held dynamometer), sensation (Vibratron II) and walk velocity (Optotrak Motion Analysis System). Mann-Whitney tests, Spearman correlation coefficients, and forward stepwise multiple regression were used to assess statistical significance. Results All measures were significantly abnormal in MS subjects when compared to age and sex-matched norms (p<0.05 for all). Static balance (eyes open, feet together [EOFT]), anterior- posterior (AP) dynamic sway, and hip extension strength were strongly correlated with fast walking velocity (AP sway r=0.68; hip extension strength r=0.73; EOFT r=-0.40). Together, AP dynamic sway (ρr=0.71, p<0.001), hip extension strength (ρr=0.54, p<0.001), and EOFT static balance (ρr=-0.41, p=0.01) explained more than 70% of the variance in fast walking velocity (p<0.001). Conclusions These data suggest that AP dynamic sway impacts walking performance in MS. A combined evaluation of dynamic balance, static balance and strength may lead to a better understanding of walking mechanisms as well as the development of strategies to improve walking. PMID:24795162

  8. Effects of smartphone texting on the visual perception and dynamic walking stability

    PubMed Central

    Lim, Jongil; Chang, Seung Ho; Lee, Jihyun; Kim, Kijeong

    2017-01-01

    Mobile phone use while walking can cause dual-task interference and increases safety risks by increasing attentional and cognitive demands. While the interference effect on cognitive function has been examined extensively, how perception of the environment and walking dynamics are affected by mobile phone use while walking is not well understood. The amount of visual information loss and its consequent impact on dynamic walking stability was examined in this study. Young adults (mean, 20.3 years) volunteered and walked on a treadmill while texting and attending to visual tasks simultaneously. Performance of visual task, field of regard loss, and margin of stability under dual-task conditions were compared with those of single-task conditions (i.e., visual task only). The results revealed that the size of visual field and visual acuity demand were varied across the visual task conditions. Approximately half of the visual cues provided during texting while walking were not perceived as compared to the visual task only condition. The field of regard loss also increased with increased dual-task cost of mobile phone use. Dynamic walking stability, however, showed no significant differences between the conditions. Taken together, the results demonstrate that the loss of situational awareness is unavoidable and occurs simultaneously with decrements in concurrent task performance. The study indicates the importance of considering the nature of attentional resources for the studies in dual-task paradigm and may provide practical information to improve the safe use of mobile phones while walking. PMID:28349033

  9. Dynamic Optimization of FES and Orthosis-Based Walking Using Simple Models.

    PubMed

    Sharma, Nitin; Mushahwar, Vivian; Stein, Richard

    2014-01-01

    Computation of an analytical control solution for functional electrical stimulation (FES) and orthosis-based walking is a daunting task due to the inherent nonlinear structure of the human muscle and walking dynamics. Furthermore, since muscle fatigue and available muscle force are major limiting issues, we explored the domains of numerical optimal control methods to address these issues. We first focused on the development of simple models to represent walking movement. These models account for walking produced via a limited number of activated muscles using FES along with a novel orthosis, and an assistive device such as a walker. Using dynamic optimization, the lower limb joint angle trajectories and control inputs were computed by minimizing the cost function comprising muscle stimulation variables and forces required to push a walker. Computer simulations for optimizations were performed across a range of step lengths to find the optimal step length (minimum cost per distance). Then, the optimal steady-state initial angular velocity (for optimal step length) was computed from a range of angular velocities of the lower-limb segments. We found considerable differences between able-bodied walking trajectories and the optimal walking trajectories for FES and orthosis-based walking. Based on this computer simulation study, we recommend that instead of arbitrary selection of stimulation profiles or gait parameters, dynamic optimization can be utilized to compute gait parameters such as step length, steady state velocity, and joint angle trajectories in future clinical implementation of FES and orthosis-based walking.

  10. Effects of smartphone texting on the visual perception and dynamic walking stability.

    PubMed

    Lim, Jongil; Chang, Seung Ho; Lee, Jihyun; Kim, Kijeong

    2017-02-01

    Mobile phone use while walking can cause dual-task interference and increases safety risks by increasing attentional and cognitive demands. While the interference effect on cognitive function has been examined extensively, how perception of the environment and walking dynamics are affected by mobile phone use while walking is not well understood. The amount of visual information loss and its consequent impact on dynamic walking stability was examined in this study. Young adults (mean, 20.3 years) volunteered and walked on a treadmill while texting and attending to visual tasks simultaneously. Performance of visual task, field of regard loss, and margin of stability under dual-task conditions were compared with those of single-task conditions (i.e., visual task only). The results revealed that the size of visual field and visual acuity demand were varied across the visual task conditions. Approximately half of the visual cues provided during texting while walking were not perceived as compared to the visual task only condition. The field of regard loss also increased with increased dual-task cost of mobile phone use. Dynamic walking stability, however, showed no significant differences between the conditions. Taken together, the results demonstrate that the loss of situational awareness is unavoidable and occurs simultaneously with decrements in concurrent task performance. The study indicates the importance of considering the nature of attentional resources for the studies in dual-task paradigm and may provide practical information to improve the safe use of mobile phones while walking.

  11. Statistics at the tip of a branching random walk and the delay of traveling waves

    NASA Astrophysics Data System (ADS)

    Brunet, É.; Derrida, B.

    2009-09-01

    We study the limiting distribution of particles at the frontier of a branching random walk. The positions of these particles can be viewed as the lowest energies of a directed polymer in a random medium in the mean-field case. We show that the average distances between these leading particles can be computed as the delay of a traveling wave evolving according to the Fisher-KPP front equation. These average distances exhibit universal behaviors, different from those of the probability cascades studied recently in the context of mean-field spin-glasses.

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

    PubMed

    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.

  13. Parrondo-like behavior in continuous-time random walks with memory

    NASA Astrophysics Data System (ADS)

    Montero, Miquel

    2011-11-01

    The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

  14. Effects of Nordic walking training on functional parameters in Parkinson's disease: a randomized controlled clinical trial.

    PubMed

    Monteiro, E P; Franzoni, L T; Cubillos, D M; de Oliveira Fagundes, A; Carvalho, A R; Oliveira, H B; Pantoja, P D; Schuch, F B; Rieder, C R; Martinez, F G; Peyré-Tartaruga, L A

    2017-03-01

    We compare the effects of Nordic walking training (NW) and Free walk (FW) on functional parameters (motor symptoms, balance) and functional mobility (Timed Up and Go at Self-selected Speed - TUGSS, and at forced speed, TUGFS; Self-selected Walking Speed, SSW; locomotor rehabilitation index, LRI) of Parkinson's disease (PD) patients. The study included 33 patients with clinical diagnosis of idiopathic PD, and staging between 1 and 4 in the Hoehn and Yahr scale (H&Y) randomized into two groups: NW (N = 16) and FW (N = 17) for 6 weeks. Baseline characteristics were compared trough a one-way ANOVA. Outcomes were analyzed using the Generalized Estimation Equations (GEE) with a Bonferroni post-hoc. Data were analyzed using SPSS v.20.0. Improvements in UPDRS III (P < 0.001), balance scores (P < 0.035), TUGSS distance (P < 0.001), TUGFS distance (P < 0.001), SSW (P < 0.001), and LRI (P < 0.001) were found for both groups. However, the NW group showed significant differences (P < 0.001) when compared to the FW group for the functional mobility. We conclude the NW improves functional parameters and walking mobility demonstrating that NW is as effective as the FW, including benefits for FW on the functional mobility of people with PD. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

  15. Determining global mean-first-passage time of random walks on Vicsek fractals using eigenvalues of Laplacian matrices.

    PubMed

    Zhang, Zhongzhi; Wu, Bin; Zhang, Hongjuan; Zhou, Shuigeng; Guan, Jihong; Wang, Zhigang

    2010-03-01

    The family of Vicsek fractals is one of the most important and frequently studied regular fractal classes, and it is of considerable interest to understand the dynamical processes on this treelike fractal family. In this paper, we investigate discrete random walks on the Vicsek fractals, with the aim to obtain the exact solutions to the global mean-first-passage time (GMFPT), defined as the average of first-passage time (FPT) between two nodes over the whole family of fractals. Based on the known connections between FPTs, effective resistance, and the eigenvalues of graph Laplacian, we determine implicitly the GMFPT of the Vicsek fractals, which is corroborated by numerical results. The obtained closed-form solution shows that the GMFPT approximately grows as a power-law function with system size (number of all nodes), with the exponent lies between 1 and 2. We then provide both the upper bound and lower bound for GMFPT of general trees, and show that the leading behavior of the upper bound is the square of system size and the dominating scaling of the lower bound varies linearly with system size. We also show that the upper bound can be achieved in linear chains and the lower bound can be reached in star graphs. This study provides a comprehensive understanding of random walks on the Vicsek fractals and general treelike networks.

  16. Stability of a Random Walk Model for Fruiting Body Aggregation in M. xanthus

    NASA Astrophysics Data System (ADS)

    McKenzie-Smith, G. C.; Schüttler, H. B.; Cotter, C.; Shimkets, L.

    2015-03-01

    Myxococcus xanthus exhibits the social starvation behavior of aggregation into a fruiting body containing myxospores able to survive harsh conditions. During fruiting body aggregation, individual bacteria follow random walk paths determined by randomly selected runtimes, turning angles, and speeds. We have simulated this behavior in terms of a continuous-time random walk (CTRW) model, re-formulated as a system of integral equations, describing the angle-resolved cell density, R(r, t, θ), at position r and cell orientation angle θ at time t, and angle-integrated ambient cell density ρ(r, t). By way of a linear stability analysis, we investigated whether a uniform cell density R0 will be unstable for a small non-uniform density perturbation δR(r, t, θ). Such instability indicates aggregate formation, whereas stability indicates absence of aggregation. We show that a broadening of CTRW distributions of the random speed and/or random runtimes strongly favors aggregation. We also show that, in the limit of slowly-varying (long-wavelength) density perturbations, the time-dependent linear density response can be approximated by a drift-diffusion model for which we calculate diffusion and drift coefficients as functions of the CTRW model parameters. Funded by the Fungal Genomics and Computational Biology REU at UGA.

  17. Equivalence between Step Selection Functions and Biased Correlated Random Walks for Statistical Inference on Animal Movement.

    PubMed

    Duchesne, Thierry; Fortin, Daniel; Rivest, Louis-Paul

    2015-01-01

    Animal movement has a fundamental impact on population and community structure and dynamics. Biased correlated random walks (BCRW) and step selection functions (SSF) are commonly used to study movements. Because no studies have contrasted the parameters and the statistical properties of their estimators for models constructed under these two Lagrangian approaches, it remains unclear whether or not they allow for similar inference. First, we used the Weak Law of Large Numbers to demonstrate that the log-likelihood function for estimating the parameters of BCRW models can be approximated by the log-likelihood of SSFs. Second, we illustrated the link between the two approaches by fitting BCRW with maximum likelihood and with SSF to simulated movement data in virtual environments and to the trajectory of bison (Bison bison L.) trails in natural landscapes. Using simulated and empirical data, we found that the parameters of a BCRW estimated directly from maximum likelihood and by fitting an SSF were remarkably similar. Movement analysis is increasingly used as a tool for understanding the influence of landscape properties on animal distribution. In the rapidly developing field of movement ecology, management and conservation biologists must decide which method they should implement to accurately assess the determinants of animal movement. We showed that BCRW and SSF can provide similar insights into the environmental features influencing animal movements. Both techniques have advantages. BCRW has already been extended to allow for multi-state modeling. Unlike BCRW, however, SSF can be estimated using most statistical packages, it can simultaneously evaluate habitat selection and movement biases, and can easily integrate a large number of movement taxes at multiple scales. SSF thus offers a simple, yet effective, statistical technique to identify movement taxis.

  18. Equivalence between Step Selection Functions and Biased Correlated Random Walks for Statistical Inference on Animal Movement

    PubMed Central

    Duchesne, Thierry; Fortin, Daniel; Rivest, Louis-Paul

    2015-01-01

    Animal movement has a fundamental impact on population and community structure and dynamics. Biased correlated random walks (BCRW) and step selection functions (SSF) are commonly used to study movements. Because no studies have contrasted the parameters and the statistical properties of their estimators for models constructed under these two Lagrangian approaches, it remains unclear whether or not they allow for similar inference. First, we used the Weak Law of Large Numbers to demonstrate that the log-likelihood function for estimating the parameters of BCRW models can be approximated by the log-likelihood of SSFs. Second, we illustrated the link between the two approaches by fitting BCRW with maximum likelihood and with SSF to simulated movement data in virtual environments and to the trajectory of bison (Bison bison L.) trails in natural landscapes. Using simulated and empirical data, we found that the parameters of a BCRW estimated directly from maximum likelihood and by fitting an SSF were remarkably similar. Movement analysis is increasingly used as a tool for understanding the influence of landscape properties on animal distribution. In the rapidly developing field of movement ecology, management and conservation biologists must decide which method they should implement to accurately assess the determinants of animal movement. We showed that BCRW and SSF can provide similar insights into the environmental features influencing animal movements. Both techniques have advantages. BCRW has already been extended to allow for multi-state modeling. Unlike BCRW, however, SSF can be estimated using most statistical packages, it can simultaneously evaluate habitat selection and movement biases, and can easily integrate a large number of movement taxes at multiple scales. SSF thus offers a simple, yet effective, statistical technique to identify movement taxis. PMID:25898019

  19. Systematic angle random walk estimation of the constant rate biased ring laser gyro.

    PubMed

    Yu, Huapeng; Wu, Wenqi; Wu, Meiping; Feng, Guohu; Hao, Ming

    2013-02-27

    An actual account of the angle random walk (ARW) coefficients of gyros in the constant rate biased rate ring laser gyro (RLG) inertial navigation system (INS) is very important in practical engineering applications. However, no reported experimental work has dealt with the issue of characterizing the ARW of the constant rate biased RLG in the INS. To avoid the need for high cost precise calibration tables and complex measuring set-ups, the objective of this study is to present a cost-effective experimental approach to characterize the ARW of the gyros in the constant rate biased RLG INS. In the system, turntable dynamics and other external noises would inevitably contaminate the measured RLG data, leading to the question of isolation of such disturbances. A practical observation model of the gyros in the constant rate biased RLG INS was discussed, and an experimental method based on the fast orthogonal search (FOS) for the practical observation model to separate ARW error from the RLG measured data was proposed. Validity of the FOS-based method was checked by estimating the ARW coefficients of the mechanically dithered RLG under stationary and turntable rotation conditions. By utilizing the FOS-based method, the average ARW coefficient of the constant rate biased RLG in the postulate system is estimated. The experimental results show that the FOS-based method can achieve high denoising ability. This method estimate the ARW coefficients of the constant rate biased RLG in the postulate system accurately. The FOS-based method does not need precise calibration table with high cost and complex measuring set-up, and Statistical results of the tests will provide us references in engineering application of the constant rate biased RLG INS.

  20. Systematic Angle Random Walk Estimation of the Constant Rate Biased Ring Laser Gyro

    PubMed Central

    Yu, Huapeng; Wu, Wenqi; Wu, Meiping; Feng, Guohu; Hao, Ming

    2013-01-01

    An actual account of the angle random walk (ARW) coefficients of gyros in the constant rate biased rate ring laser gyro (RLG) inertial navigation system (INS) is very important in practical engineering applications. However, no reported experimental work has dealt with the issue of characterizing the ARW of the constant rate biased RLG in the INS. To avoid the need for high cost precise calibration tables and complex measuring set-ups, the objective of this study is to present a cost-effective experimental approach to characterize the ARW of the gyros in the constant rate biased RLG INS. In the system, turntable dynamics and other external noises would inevitably contaminate the measured RLG data, leading to the question of isolation of such disturbances. A practical observation model of the gyros in the constant rate biased RLG INS was discussed, and an experimental method based on the fast orthogonal search (FOS) for the practical observation model to separate ARW error from the RLG measured data was proposed. Validity of the FOS-based method was checked by estimating the ARW coefficients of the mechanically dithered RLG under stationary and turntable rotation conditions. By utilizing the FOS-based method, the average ARW coefficient of the constant rate biased RLG in the postulate system is estimated. The experimental results show that the FOS-based method can achieve high denoising ability. This method estimate the ARW coefficients of the constant rate biased RLG in the postulate system accurately. The FOS-based method does not need precise calibration table with high cost and complex measuring set-up, and Statistical results of the tests will provide us references in engineering application of the constant rate biased RLG INS. PMID:23447008

  1. The importance of being atomic: Ecological invasions as random walks instead of waves.

    PubMed

    Reluga, Timothy C

    2016-12-01

    Invasions are one of the most easily identified spatial phenomena in ecology, and have inspired a rich variety of theories for ecologists' and naturalists' consideration. However, a number of arguments over the sensitivities of invasion rates to stochasticity, density-dependence, dimension, and discreteness persist in the literature. The standard mathematical approach to invasions is based on Fisher's analysis of traveling waves solutions for the spread of an advantageous allele. In this paper, we exploit an alternative theory based on Ellner's premise that species invasions are best interpreted not as waves, but as random walks, and that the discreteness of living organisms is fundamentally important. Using a density-dependent invasion model in a stationary environment with indivisible (atomic) individuals where reproduction and dispersal are stochastic and independent, we show 4 key properties of Ellner's invasions previously suggested by simulation analysis: (1) greater spatial dispersal stochasticity quickens invasions, (2) greater demographic stochasticity slows invasions, (3) negative density-dependence slows invasions, and (4) greater temporal dispersal stochasticity quickens invasions. We prove the first three results by using generating functions and stochastic-dominance methods to rank furthest-forward dispersal distributions. The fourth result is proven in the special case of atomless theory, but remains an open conjecture in atomic theory. In addition, we explain why, unlike atomless invasions, an infinitely wide atomic invasion in two-dimensions can travel faster than a finite-width invasion and a one-dimensional invasion. The paper concludes with a classification of invasion dynamics based on dispersal kernel tails.

  2. Dynamic Simulation and Analysis of Human Walking Mechanism

    NASA Astrophysics Data System (ADS)

    Azahari, Athirah; Siswanto, W. A.; Ngali, M. Z.; Salleh, S. Md.; Yusup, Eliza M.

    2017-01-01

    Behaviour such as gait or posture may affect a person with the physiological condition during daily activities. The characteristic of human gait cycle phase is one of the important parameter which used to described the human movement whether it is in normal gait or abnormal gait. This research investigates four types of crouch walking (upright, interpolated, crouched and severe) by simulation approach. The assessment are conducting by looking the parameters of hamstring muscle joint, knee joint and ankle joint. The analysis results show that based on gait analysis approach, the crouch walking have a weak pattern of walking and postures. Short hamstring and knee joint is the most influence factor contributing to the crouch walking due to excessive hip flexion that typically accompanies knee flexion.

  3. Dynamic gait stability of treadmill versus overground walking in young adults.

    PubMed

    Yang, Feng; King, George A

    2016-12-01

    Treadmill has been broadly used in laboratory and rehabilitation settings for the purpose of facilitating human locomotion analysis and gait training. The objective of this study was to determine whether dynamic gait stability differs or resembles between the two walking conditions (overground vs. treadmill) among young adults. Fifty-four healthy young adults (age: 23.9±4.7years) participated in this study. Each participant completed five trials of overground walking followed by five trials of treadmill walking at a self-selected speed while their full body kinematics were gathered by a motion capture system. The spatiotemporal gait parameters and dynamic gait stability were compared between the two walking conditions. The results revealed that participants adopted a "cautious gait" on the treadmill compared with over ground in response to the possible inherent challenges to balance imposed by treadmill walking. The cautious gait, which was achieved by walking slower with a shorter step length, less backward leaning trunk, shortened single stance phase, prolonged double stance phase, and more flatfoot landing, ensures the comparable dynamic stability between the two walking conditions. This study could provide insightful information about dynamic gait stability control during treadmill ambulation in young adults. Copyright © 2016 Elsevier Ltd. All rights reserved.

  4. An improved label propagation algorithm based on the similarity matrix using random walk

    NASA Astrophysics Data System (ADS)

    Zhang, Xian-Kun; Song, Chen; Jia, Jia; Lu, Zeng-Lei; Zhang, Qian

    2016-05-01

    Community detection based on label propagation algorithm (LPA) has attracted widespread concern because of its high efficiency. But it is difficult to guarantee the accuracy of community detection as the label spreading is random in the algorithm. In response to the problem, an improved LPA based on random walk (RWLPA) is proposed in this paper. Firstly, a matrix measuring similarity among various nodes in the network is obtained through calculation. Secondly, during the process of label propagation, when a node has more than a neighbor label with the highest frequency, not the label of a random neighbor but the label of the neighbor with the highest similarity will be chosen to update. It can avoid label propagating randomly among communities. Finally, we test LPA and the improved LPA in benchmark networks and real-world networks. The results show that the quality of communities discovered by the improved algorithm is improved compared with the traditional algorithm.

  5. Evolutionary dynamics on random structures

    SciTech Connect

    Fraser, S.M.; Reidys, C.M. |

    1997-04-01

    In this paper the authors consider the evolutionary dynamics of populations of sequences, under a process of selection at the phenotypic level of structures. They use a simple graph-theoretic representation of structures which captures well the properties of the mapping between RNA sequences and their molecular structure. Each sequence is assigned to a structure by means of a sequence-to-structure mapping. The authors make the basic assumption that every fitness landscape can be factorized through the structures. The set of all sequences that map into a particular random structure can then be modeled as a random graph in sequence space, the so-called neutral network. They analyze in detail how an evolving population searches for new structures, in particular how they switch from one neutral network to another. They verify that transitions occur directly between neutral networks, and study the effects of different population sizes and the influence of the relatedness of the structures on these transitions. In fitness landscapes where several structures exhibit high fitness, the authors then study evolutionary paths on the structural level taken by the population during its search. They present a new way of expressing structural similarities which are shown to have relevant implications for the time evolution of the population.

  6. Walking and Non–HDL-C in Adults: A Meta-Analysis of Randomized Controlled Trials

    PubMed Central

    Kelley, George A.; Kelley, Kristi S.; Tran, Zung Vu

    2007-01-01

    An elevated level of non–high-density lipoprotein cholesterol (non–HDL-C) is a major risk factor for cardiovascular disease. The purpose of this study was to use the meta-analytic approach to examine the effects of walking on non–HDL-C in adults. Twenty-two randomized controlled trials representing 30 outcomes from 948 subjects (573 exercise, 375 control) met our inclusion criteria. Across all designs and categories, random effects modeling resulted in a significantly greater decrease in the walking group when compared with the control group of approximately 4% for non–HDL-C (X̄ ± standard error of the mean, −5.6±1.8 mg/dL, 95% confidence interval, −8.8 to −2.4 mg/dL). Meta-regression showed a statistically significant association between changes in non–HDL-C and the year of publication, with greater reductions associated with more recent publication year (R2=0.23, p=0.005). The results of this meta-analytic review suggest that walking reduces non–HDL-C in adult humans. PMID:15860986

  7. 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.

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

    NASA Astrophysics Data System (ADS)

    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), 10.1103/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.

  9. Local dynamic stability of the trunk segments and lower extremity joints during backward walking.

    PubMed

    Wu, Yu; Xiao, Fei; Gu, Dong-Yun

    2015-01-01

    Backward walking has become a popular training method in physical exercise and clinical rehabilitation. For the sake of safety, it is important to keep a stable gait during backward walking. However, the gait stability during backward walking was rarely studied. This study investigated the effects of walking direction on local dynamic stability of the trunk segments (neck, torso and pelvis) and lower extremity joints (hip, knee and ankle joint). The maximum Lyapunov exponents (λ(s)) of 17 young healthy male adults were calculated while they were walking under three conditions: backward walking with preferred walking speed (BW), forward walking (FW) with the same speed determined by BW, and forward walking with normal speed (FWN). We found that compared with FW, BW showed significant higher values of λ(s) in the trunk segments in vertical (VT) direction (p<0.05). The torso segment also displayed a higher value of λ(s) in anterior-posterior (AP) direction (p<0.01); Higher values of λ(s) during BW were found in the rotation (RT) motion of hip and knee joint (p=0.036, and p=0.009, respectively), and in the abduction/adduction (AB/AD) motion of knee and ankle joint (p=0.013, and p=0.021, respectively). The significant effect of walking speed was found between FW and FWN condition in VT direction (p<0.01). These findings indicate that backward walking did impair the local dynamic stability in trunk segments and lower extremity joints. Especially, the negative effect of BW on the poor gait stability in the AP direction of torso segment, and AB/AD and RT motion of knee joint should not be neglected.

  10. Kinematic variability and local dynamic stability of upper body motions when walking at different speeds.

    PubMed

    Dingwell, Jonathan B; Marin, Laura C

    2006-01-01

    A ubiquitous characteristic of elderly and patients with gait disabilities is that they walk slower than healthy controls. Many clinicians assume these patients walk slower to improve their stability, just as healthy people slow down when walking across ice. However, walking slower also leads to greater variability, which is often assumed to imply deteriorated stability. If this were true, then slowing down would be completely antithetical to the goal of maintaining stability. This study sought to resolve this paradox by directly quantifying the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability. Eleven young healthy subjects walked on a motorized treadmill at five different speeds. Three-dimensional movements of a single marker placed over the first thoracic vertebra were recorded during continuous walking. Mean stride-to-stride standard deviations and maximum finite-time Lyapunov exponents were computed for each time series to quantify the variability and local dynamic stability, respectively, of these movements. Quadratic regression analyses of the dependent measures vs. walking speed revealed highly significant U shaped trends for all three mean standard deviations, but highly significant linear trends, with significant or nearly significant quadratic terms, for five of the six finite-time Lyapunov exponents. Subjects exhibited consistently better local dynamic stability at slower speeds for these five measures. These results support the clinically based intuition that people who are at increased risk of falling walk slower to improve their stability, even at the cost of increased variability.

  11. Unbinding of mutually avoiding random walks and two-dimensional quantum gravity

    NASA Astrophysics Data System (ADS)

    Carlon, Enrico; Baiesi, Marco

    2004-12-01

    We analyze the unbinding transition for a two-dimensional lattice polymer in which the constituent strands are mutually avoiding random walks. At low temperatures the strands are bound and form a single self-avoiding walk. We show that unbinding in this model is a strong first order transition. The entropic exponents associated with denaturated loops and end-segment distributions show sharp differences at the transition point and in the high temperature phase. Their values can be deduced from some exact arguments relying on a conformal mapping of copolymer networks into a fluctuating geometry, i.e., in the presence of quantum gravity. An excellent agreement between analytical and numerical estimates is observed for all cases analyzed.

  12. Lattice statistical theory of random walks on a fractal-like geometry.

    PubMed

    Kozak, John J; Garza-López, Roberto A; Abad, Enrique

    2014-03-01

    We have designed a two-dimensional, fractal-like lattice and explored, both numerically and analytically, the differences between random walks on this lattice and a regular, square-planar Euclidean lattice. We study the efficiency of diffusion-controlled processes for flows from external sites to a centrosymmetric reaction center and, conversely, for flows from a centrosymmetric source to boundary sites. In both cases, we find that analytic expressions derived for the mean walk length on the fractal-like lattice have an algebraic dependence on system size, whereas for regular Euclidean lattices the dependence can be transcendental. These expressions are compared with those derived in the continuum limit using classical diffusion theory. Our analysis and the numerical results quantify the extent to which one paradigmatic class of spatial inhomogeneities can compromise the efficiency of adatom diffusion on solid supports and of surface-assisted self-assembly in metal-organic materials.

  13. Humans robustly adhere to dynamic walking principles by harnessing motor abundance to control forces.

    PubMed

    Toney, Megan E; Chang, Young-Hui

    2013-12-01

    Human walking dynamics are typically framed in the context of mechanics and energetics rather than in the context of neuromuscular control. Dynamic walking principles describe one helpful theoretical approach to characterize efficient human walking mechanics over many steps. These principles do not, however, address how such walking is controlled step-by-step despite small perturbations from natural variability. Our purpose was to identify neuromechanical control strategies used to achieve consistent and robust locomotion despite natural step-to-step force variability. We used the uncontrolled manifold concept to test whether human walkers select combinations of leading and trailing leg-forces that generate equivalent net-force trajectories during step-to-step transitions. Subjects selected leading and trailing leg-force combinations that generated consistent vertical net-force during step-to-step transitions. We conclude that vertical net-force is an implicit neuromechanical goal of human walking whose trajectory is stabilized for consistent step-to-step transitions, which agrees with the principles of dynamic walking. In contrast, inter-leg-force combinations modulated anterior-posterior net-force trajectories with each step to maintain constant walking speed, indicating that a consistent anterior-posterior net-force trajectory is not an implicit goal of walking. For a more complete picture of hierarchical locomotor control, we also tested whether each individual leg-force trajectory was stabilized through the selection of leg-force equivalent joint-torque combinations. The observed consistent vertical net-force trajectory was achieved primarily through the selection of joint-torque combinations that modulated trailing leg-force during step-to-step transitions. We conclude that humans achieve robust walking by harnessing inherent motor abundance of the joints and legs to maintain consistent step-by-step walking performance.

  14. 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.

  15. An improved label propagation algorithm based on node importance and random walk for community detection

    NASA Astrophysics Data System (ADS)

    Ma, Tianren; Xia, Zhengyou

    2017-05-01

    Currently, with the rapid development of information technology, the electronic media for social communication is becoming more and more popular. Discovery of communities is a very effective way to understand the properties of complex networks. However, traditional community detection algorithms consider the structural characteristics of a social organization only, with more information about nodes and edges wasted. In the meanwhile, these algorithms do not consider each node on its merits. Label propagation algorithm (LPA) is a near linear time algorithm which aims to find the community in the network. It attracts many scholars owing to its high efficiency. In recent years, there are more improved algorithms that were put forward based on LPA. In this paper, an improved LPA based on random walk and node importance (NILPA) is proposed. Firstly, a list of node importance is obtained through calculation. The nodes in the network are sorted in descending order of importance. On the basis of random walk, a matrix is constructed to measure the similarity of nodes and it avoids the random choice in the LPA. Secondly, a new metric IAS (importance and similarity) is calculated by node importance and similarity matrix, which we can use to avoid the random selection in the original LPA and improve the algorithm stability. Finally, a test in real-world and synthetic networks is given. The result shows that this algorithm has better performance than existing methods in finding community structure.

  16. Solvable random-walk model with memory and its relations with Markovian models of anomalous diffusion

    NASA Astrophysics Data System (ADS)

    Boyer, D.; Romo-Cruz, J. C. R.

    2014-10-01

    Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random-walk model with long-range memory for which not only the mean-square displacement (MSD) but also the propagator can be obtained exactly in the asymptotic limit. The model consists of a random walker on a lattice, which, at a constant rate, stochastically relocates at a site occupied at some earlier time. This time in the past is chosen randomly according to a memory kernel, whose temporal decay can be varied via an exponent parameter. In the weakly non-Markovian regime, memory reduces the diffusion coefficient from the bare value. When the mean backward jump in time diverges, the diffusion coefficient vanishes and a transition to an anomalous subdiffusive regime occurs. Paradoxically, at the transition, the process is an anticorrelated Lévy flight. Although in the subdiffusive regime the model exhibits some features of the continuous time random walk with infinite mean waiting time, it belongs to another universality class. If memory is very long-ranged, a second transition takes place to a regime characterized by a logarithmic growth of the MSD with time. In this case the process is asymptotically Gaussian and effectively described as a scaled Brownian motion with a diffusion coefficient decaying as 1 /t .

  17. Propagators and related descriptors for non-Markovian asymmetric random walks with and without boundaries.

    PubMed

    Berezhkovskii, Alexander M; Weiss, George H

    2008-01-28

    There are many current applications of the continuous-time random walk (CTRW), particularly in describing kinetic and transport processes in different chemical and biophysical phenomena. We derive exact solutions for the Laplace transforms of the propagators for non-Markovian asymmetric one-dimensional CTRW's in an infinite space and in the presence of an absorbing boundary. The former is used to produce exact results for the Laplace transforms of the first two moments of the displacement of the random walker, the asymptotic behavior of the moments as t-->infinity, and the effective diffusion constant. We show that in the infinite space, the propagator satisfies a relation that can be interpreted as a generalized fluctuation theorem since it reduces to the conventional fluctuation theorem at large times. Based on the Laplace transform of the propagator in the presence of an absorbing boundary, we derive the Laplace transform of the survival probability of the random walker, which is then used to find the mean lifetime for terminated trajectories of the random walk.

  18. Automatic Oxygen Titration During Walking in Subjects With COPD: A Randomized Crossover Controlled Study.

    PubMed

    Lellouche, François; L'Her, Erwan; Bouchard, Pierre-Alexandre; Brouillard, Cynthia; Maltais, François

    2016-11-01

    Arterial oxygen desaturation frequently occurs in patients with COPD during daily activities at home. Oxygen flow is usually set at fixed and low rates for ambulatory patients. We evaluated an innovative closed-loop system (FreeO2) that automatically adjusts the oxygen flow to the patient's needs in subjects with COPD during walking followed by recovery time, such as during ambulatory conditions. Patients with COPD who exhibited oxygen desaturation on exertion were included in the study. Subjects performed endurance shuttle walk tests followed by 10 min of recovery. The tests were conducted in a random order and in crossover with the 3 following conditions: subjects breathing (1) air at 2 L/min, (2) oxygen at 2 L/min, or (3) FreeO2 (variable oxygen flow). SpO2, pulse rate, PETCO2 , breathing frequency, and oxygen flow were continuously recorded during the 3 conditions. The primary outcome was the percentage of time within the SpO2 target of 92-96%. Secondary outcomes included the endurance shuttle walk test time and distance. Sixteen subjects with COPD were recruited. The percentage of time with SpO2 in the target range (92-96%) was higher while using the FreeO2, and time with severe oxygen desaturation (SpO2 <88%) was lower with FreeO2 in comparison with constant-flow oxygen and air testing conditions (0.6% vs 23.9% vs 52.2%, P < .001). In comparison with air, walking distance was increased by 35% with oxygen (P = .045) and by 63% with FreeO2 (P < .001). The walking distance was increased by 17% with FreeO2 in comparison with constant oxygen, but the difference was not statistically significant (P = .22). Automatic titration of oxygen flow during walking to maintain oxygen saturation in a specified range improves oxygenation and may improve exercise tolerance during daily activity, such as walking, in patients with COPD in comparison with room air and fixed oxygen administration. (ClinicalTrials.gov registration: NCT02150434.). Copyright © 2016 by Daedalus

  19. NMR-based, molecular dynamics- and random walk molecular mechanics-supported study of conformational aspects of a carbohydrate ligand (Gal beta 1-2Gal beta 1-R) for an animal galectin in the free and in the bound state.

    PubMed

    Siebert, H C; Gilleron, M; Kaltner, H; von der Lieth, C W; Kozár, T; Bovin, N; Korchagina, E Y; Vliegenthart, J F; Gabius, H J

    1996-02-06

    The binding of a carbohydrate to a lectin may affect the conformation of the ligand. To address this question for the galectin from chicken liver, the conformation of Gal beta 1-2Gal beta 1-R was analyzed in the free and in the galectin-bound state with 2D-ROESY- and 1D- as well as 2D-transferred NOE-experiments. A computer-assisted analysis of spatial parameters of the ligand by molecular dynamics (MD) and random walk molecular mechanics (RAMM) calculations, taking different dielectric constraints from epsilon = 1 to epsilon = 80 and various force fields into account, were instrumental to define the energetic minima of the free state. NMR-derived interresidual distance constraints enabled a conformational mapping. The two overlapping interresidual distance constraints obtained from transferred-NOE experiments of the galectin-ligand complex clearly support the notion that the conformation of the disaccharide in the bound state is at least very close to its global energy minimum state in solution.

  20. 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.

  1. Dynamic stability of superior vs. inferior body segments in individuals with transtibial amputation walking in destabilizing environments.

    PubMed

    Beurskens, Rainer; Wilken, Jason M; Dingwell, Jonathan B

    2014-09-22

    Interestingly, young and highly active people with lower limb amputation appear to maintain a similar trunk and upper body stability during walking as able-bodied individuals. Understanding the mechanisms underlying how this stability is achieved after lower-leg amputation is important to improve training regimens for improving walking function in these patients. This study quantified how superior (i.e., head, trunk, and pelvis) and inferior (i.e., thigh, shank, and feet) segments of the body respond to continuous visual or mechanical perturbations during walking. Nine persons with transtibial amputation (TTA) and 12 able-bodied controls (AB) walked on a 2 m × 3 m treadmill in a Computer Assisted Rehabilitation Environment (CAREN). Subjects were perturbed by continuous pseudo-random mediolateral movements of either the treadmill platform or the visual scene. TTA maintained a similar local and orbital stability in their superior body segments as AB throughout both perturbation types. However, for their inferior body segments, TTA subjects exhibited greater dynamic instability during perturbed walking. In TTA subjects, these increases in instability were even more pronounced in their prosthetic limb compared to their intact leg. These findings demonstrate that persons with unilateral lower leg amputation maintain upper body stability in spite of increased dynamic instability in their impaired lower leg. Thus, transtibial amputation does significantly impair sensorimotor function, leading to substantially altered dynamic movements of their lower limb segments. However, otherwise relatively healthy patients with unilateral transtibial amputation appear to retain sufficient remaining sensorimotor function in their proximal and contralateral limbs to adequately compensate for their impairment.

  2. The Walking Behaviour of Pedestrian Social Groups and Its Impact on Crowd Dynamics

    PubMed Central

    Moussaïd, Mehdi; Perozo, Niriaska; Garnier, Simon; Helbing, Dirk; Theraulaz, Guy

    2010-01-01

    Human crowd motion is mainly driven by self-organized processes based on local interactions among pedestrians. While most studies of crowd behaviour consider only interactions among isolated individuals, it turns out that up to 70% of people in a crowd are actually moving in groups, such as friends, couples, or families walking together. These groups constitute medium-scale aggregated structures and their impact on crowd dynamics is still largely unknown. In this work, we analyze the motion of approximately 1500 pedestrian groups under natural condition, and show that social interactions among group members generate typical group walking patterns that influence crowd dynamics. At low density, group members tend to walk side by side, forming a line perpendicular to the walking direction. As the density increases, however, the linear walking formation is bent forward, turning it into a V-like pattern. These spatial patterns can be well described by a model based on social communication between group members. We show that the V-like walking pattern facilitates social interactions within the group, but reduces the flow because of its “non-aerodynamic” shape. Therefore, when crowd density increases, the group organization results from a trade-off between walking faster and facilitating social exchange. These insights demonstrate that crowd dynamics is not only determined by physical constraints induced by other pedestrians and the environment, but also significantly by communicative, social interactions among individuals. PMID:20383280

  3. The walking behaviour of pedestrian social groups and its impact on crowd dynamics.

    PubMed

    Moussaïd, Mehdi; Perozo, Niriaska; Garnier, Simon; Helbing, Dirk; Theraulaz, Guy

    2010-04-07

    Human crowd motion is mainly driven by self-organized processes based on local interactions among pedestrians. While most studies of crowd behaviour consider only interactions among isolated individuals, it turns out that up to 70% of people in a crowd are actually moving in groups, such as friends, couples, or families walking together. These groups constitute medium-scale aggregated structures and their impact on crowd dynamics is still largely unknown. In this work, we analyze the motion of approximately 1500 pedestrian groups under natural condition, and show that social interactions among group members generate typical group walking patterns that influence crowd dynamics. At low density, group members tend to walk side by side, forming a line perpendicular to the walking direction. As the density increases, however, the linear walking formation is bent forward, turning it into a V-like pattern. These spatial patterns can be well described by a model based on social communication between group members. We show that the V-like walking pattern facilitates social interactions within the group, but reduces the flow because of its "non-aerodynamic" shape. Therefore, when crowd density increases, the group organization results from a trade-off between walking faster and facilitating social exchange. These insights demonstrate that crowd dynamics is not only determined by physical constraints induced by other pedestrians and the environment, but also significantly by communicative, social interactions among individuals.

  4. An upper-body can improve the stability and efficiency of passive dynamic walking.

    PubMed

    Chyou, T; Liddell, G F; Paulin, M G

    2011-09-21

    The compass-gait walker proposed by McGeer can walk down a shallow slope with a self-stabilizing gait that requires no actuation or control. However, as the slope goes to zero so does the walking speed, and dynamic gait stability is only possible over a very narrow range of slopes. Gomes and Ruina have results demonstrating that by adding a torso to the compass-gait walker, it can walk passively on level-ground with a non-infinitesimal constant average speed. However, the gait involves exaggerated joint movements, and for energetic reasons horizontal passive dynamic walking cannot be stable. We show in this research that in addition to collision-free walking, adding a torso improves stability and walking speed when walking downhill. Furthermore, adding arms to the torso results in a collision-free periodic gait with natural-looking torso and limb movements. Overall, in contrast to the suggestions that active control may be needed to balance an upper-body on legs, it turns out that the upper and lower bodies can be integrated to improve the stability, efficiency and speed of a passive dynamic walker. Copyright © 2011 Elsevier Ltd. All rights reserved.

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

    PubMed

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

    2017-09-01

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

  6. Intra-fraction motion of the prostate is a random walk

    NASA Astrophysics Data System (ADS)

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

    2015-01-01

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

  7. Painlevé's paradox and dynamic jamming in simple models of passive dynamic walking

    NASA Astrophysics Data System (ADS)

    Or, Yizhar

    2014-02-01

    Painlevé's paradox occurs in the rigid-body dynamics of mechanical systems with frictional contacts at configurations where the instantaneous solution is either indeterminate or inconsistent. Dynamic jamming is a scenario where the solution starts with consistent slippage and then converges in finite time to a configuration of inconsistency, while the contact force grows unbounded. The goal of this paper is to demonstrate that these two phenomena are also relevant to the field of robotic walking, and can occur in two classical theoretical models of passive dynamic walking — the rimless wheel and the compass biped. These models typically assume sticking contact and ignore the possibility of foot slippage, an assumption which requires sufficiently large ground friction. Nevertheless, even for large friction, a perturbation that involves foot slippage can be kinematically enforced due to external forces, vibrations, or loose gravel on the surface. In this work, the rimless wheel and compass biped models are revisited, and it is shown that the periodic solutions under sticking contact can suffer from both Painlevé's paradox and dynamic jamming when given a perturbation of foot slippage. Thus, avoidance of these phenomena and analysis of orbital stability with respect to perturbations that include slippage are of crucial importance for robotic legged locomotion.

  8. 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.

  9. Random Walks with Preferential Relocations to Places Visited in the Past and their Application to Biology

    NASA Astrophysics Data System (ADS)

    Boyer, Denis; Solis-Salas, Citlali

    2014-06-01

    Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where a random walker intermittently revisits previously visited sites according to a reinforced rule. The emergence of frequently visited locations generates very slow diffusion, logarithmic in time, whereas the walker probability density tends to a Gaussian. This scaling form does not emerge from the central limit theorem but from an unusual balance between random and long-range memory steps. In single trajectories, occupation patterns are heterogeneous and have a scale-free structure. The model exhibits good agreement with data of free-ranging capuchin monkeys.

  10. Monotonic continuous-time random walks with drift and stochastic reset events

    NASA Astrophysics Data System (ADS)

    Montero, Miquel; Villarroel, Javier

    2013-01-01

    In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

  11. Self-avoiding walks on random networks of resistors and diodes

    NASA Astrophysics Data System (ADS)

    Marković, D.; Milošević, S.; Stanley, H. E.

    1987-07-01

    We study the self-avoiding walks (SAW) on a square lattice whose various degrees of randomness encompasses many different random networks, including the incipient clusters of the directed, mixed and isotropic bond percolation. We apply the position-space renormalization group (PSRG) method and demonstrate that within the framework of this method one is bound to find that the critical exponent v of the mean end-to-end distance of SAW on various two-dimensional random networks should be equal to the critical exponent of SAW on the ordinary square lattice. A detailed analysis of this finding, and similar findings of other authors, lead us to conclude that a debatable opposite finding, which has been predicted on the basis of different approaches, could be attained after a substantial refinement of the method applied.

  12. Statistics of Persistent Events in the Binomial Random Walk: Will the Drunken Sailor Hit the Sober Man?

    NASA Astrophysics Data System (ADS)

    Bauer, M.; Godrèche, C.; Luck, J. M.

    1999-09-01

    The statistics of persistent events, recently introduced in the context of phase ordering dynamics, is investigated in the case of the one-dimensional lattice random walk in discrete time. We determine the survival probability of the random walker in the presence of an obstacle moving ballistically with velocity v, i.e., the probability that the random walker remains up to time n on the left of the obstacle. Three regimes are to be considered for the long-time behavior of this probability, according to the sign of the difference between v and the drift velocity V¯ of the random walker. In one of these regimes ( v> V¯), the survival probability has a nontrivial limit at long times which is discontinuous at all rational values of v. An algebraic approach allows us to compute these discontinuities as well as several related quantities. The mathematical structure underlying the solvability of this model combines elementary number theory, algebraic functions, and algebraic curves defined over the rationals.

  13. Noise-Enhanced Vestibular Input Improves Dynamic Walking Stability in Healthy Subjects.

    PubMed

    Wuehr, M; Nusser, E; Krafczyk, S; Straube, A; Brandt, T; Jahn, K; Schniepp, R

    2016-01-01

    White noise galvanic vestibular stimulation (GVS) is thought to enhance the sensitivity of vestibular organs. To examine the effects of noise-enhanced vestibular input on the walking performance in healthy subjects walking with eyes closed. Walking performance of 17 healthy subjects (mean age 28.8 ± 1.7 years) at slow, preferred, and fast speeds was examined during three different conditions: (1) walking with eyes open (EO) as baseline condition, (2) walking with eyes closed and sham noisy GVS (EC), and (3) walking with eyes closed and non-zero amplitude noisy GVS set to 80% of the individual sensory threshold for GVS (EC-GVS). Ten gait parameters were examined: stride time, stride length, base of support, swing time percentage, double support time percentage as well as gait asymmetry, bilateral phase coordination and the coefficient of variation (CV) of stride time, stride length and base of support. Noisy GVS improved stride time CV by 36% (p < 0.034), stride length CV by 31% (p < 0.037), base of support CV by 14% (p < 0.009), and bilateral phase coordination by 23% (p < 0.034). The ameliorating effects of noisy GVS on locomotion function were primarily observable during slow walking speeds. Noise-enhanced vestibular input is effective in improving locomotion function and is accompanied by a subjectively felt improvement of walking balance. It predominantly targets the variability and bilateral coordination characteristics of the walking pattern, which are critically linked to dynamic walking stability. Noisy GVS might present an effective treatment option to improve walking performance in patients with bilateral vestibular dysfunction. Copyright © 2015 Elsevier Inc. All rights reserved.

  14. Continuous time random walks for non-local radial solute transport

    NASA Astrophysics Data System (ADS)

    Dentz, Marco; Kang, Peter K.; Le Borgne, Tanguy

    2015-08-01

    This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile-immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection-dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer

  15. 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

  16. Generalized Hammersley Process and Phase Transition for Activated Random Walk Models

    NASA Astrophysics Data System (ADS)

    Rolla, Leonardo T.

    2008-12-01

    * ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to passive, then stopping to jump. When particles of both types occupy the same site, they all become active. This model exhibits phase transition in the sense that for low initial densities the system locally fixates and for high densities it keeps active. Though extensively studied in the physics literature, the matter of giving a mathematical proof of such phase transition remained as an open problem for several years. In this work we identify some variables that are sufficient to characterize fixation and at the same time are stochastically monotone in the model's parameters. We employ an explicit graphical representation in order to obtain the monotonicity. With this method we prove that there is a unique phase transition for the one-dimensional finite-range random walk. Joint with V. Sidoravicius. * BROKEN LINE PROCESS * We introduce the broken line process and derive some of its properties. Its discrete version is presented first and a natural generalization to the continuum is then proposed and studied. The broken lines are related to the Young diagram and the Hammersley process and are useful for computing last passage percolation values and finding maximal oriented paths. For a class of passage time distributions there is a family of boundary conditions that make the process stationary and reversible. One application is a simple proof of the explicit law of large numbers for last passage percolation with exponential and geometric distributions. Joint with V. Sidoravicius, D. Surgailis, and M. E. Vares.

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

    SciTech Connect

    Snodin, A. P.; Ruffolo, D.; Oughton, S.; Servidio, S.; Matthaeus, W. H.

    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 function 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.

  18. Self organization of social hierarchy and clusters in a challenging society with free random walks

    NASA Astrophysics Data System (ADS)

    Fujie, Ryo; Odagaki, Takashi

    2010-04-01

    Emergence of social hierarchy and clusters in a challenging equal-right society is studied on the basis of the agent-based model, where warlike individuals who have own power or wealth perform random walks in a random order on a lattice and when meeting others the individuals challenge the strongest among the neighbors. We assume that the winning probability depends on the difference in their wealth and after the fight the winner gets and the loser loses a unit of the wealth. We show that hierarchy is self organized when the population exceeds a critical value and the transition from egalitarian state to hierarchical state occurs in two steps. The first transition is continuous to the society with widespread winning-probability. At the second transition the variance of the winning fraction decrease discontinuously, which was not observed in previous studies. The second hierarchical society consists of a small number of extreme winners and many individuals in the middle class and losers. We also show that when the relaxation parameter for the wealth is large, the first transition disappears. In the second hierarchical society, a giant cluster of individuals is formed with a layered structure in the power order and some people stray around it. The structure of the cluster and the distribution of wealth are quite different from the results of the previous challenging model [M. Tsujiguchi and T. Odagaki, Physica A 375 (2007) 317] which adopts the preassigned order for random walk.

  19. Multiple random walks on complex networks: A harmonic law predicts search time.

    PubMed

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

    2017-05-01

    We investigate multiple random walks traversing independently and concurrently on complex networks and introduce the concept of mean first parallel passage time (MFPPT) to quantify their search efficiency. The mean first parallel passage time represents the expected time required to find a given target by one or some of the multiple walkers. We develop a general theory that allows us to calculate the MFPPT analytically. Interestingly, we find that the global MFPPT follows a harmonic law with respect to the global mean first passage times of the associated walkers. Remarkably, when the properties of multiple walkers are identical, the global MFPPT decays in a power law manner with an exponent of unity, irrespective of network structure. These findings are confirmed by numerical and theoretical results on various synthetic and real networks. The harmonic law reveals a universal principle governing multiple random walks on networks that uncovers the contribution and role of the combined walkers in a target search. Our paradigm is also applicable to a broad range of random search processes.

  20. Random walk model of subdiffusion in a system with a thin membrane.

    PubMed

    Kosztołowicz, Tadeusz

    2015-02-01

    We consider in this paper subdiffusion in a system with a thin membrane. The subdiffusion parameters are the same in both parts of the system separated by the membrane. Using the random walk model with discrete time and space variables the probabilities (Green's functions) P(x,t) describing a particle's random walk are found. The membrane, which can be asymmetrical, is characterized by the two probabilities of stopping a random walker by the membrane when it tries to pass through the membrane in both opposite directions. Green's functions are transformed to the system in which the variables are continuous, and then the membrane permeability coefficients are given by special formulas which involve the probabilities mentioned above. From the obtained Green's functions, we derive boundary conditions at the membrane. One of the conditions demands the continuity of a flux at the membrane, but the other one is rather unexpected and contains the Riemann-Liouville fractional time derivative P(x(N)(-),t)=λ(1)P(x(N)(+),t)+λ(2)∂(α/2)P(x(N)(+),t)/∂t(α/2), where λ(1),λ(2) depending on membrane permeability coefficients (λ(1)=1 for a symmetrical membrane), α is a subdiffusion parameter, and x(N) is the position of the membrane. This boundary condition shows that the additional "memory effect," represented by the fractional derivative, is created by the membrane. This effect is also created by the membrane for a normal diffusion case in which α=1.

  1. Multiple random walks on complex networks: A harmonic law predicts search time

    NASA Astrophysics Data System (ADS)

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

    2017-05-01

    We investigate multiple random walks traversing independently and concurrently on complex networks and introduce the concept of mean first parallel passage time (MFPPT) to quantify their search efficiency. The mean first parallel passage time represents the expected time required to find a given target by one or some of the multiple walkers. We develop a general theory that allows us to calculate the MFPPT analytically. Interestingly, we find that the global MFPPT follows a harmonic law with respect to the global mean first passage times of the associated walkers. Remarkably, when the properties of multiple walkers are identical, the global MFPPT decays in a power law manner with an exponent of unity, irrespective of network structure. These findings are confirmed by numerical and theoretical results on various synthetic and real networks. The harmonic law reveals a universal principle governing multiple random walks on networks that uncovers the contribution and role of the combined walkers in a target search. Our paradigm is also applicable to a broad range of random search processes.

  2. Comparing quantum versus Markov random walk models of judgements measured by rating scales

    PubMed Central

    Wang, Z.; Busemeyer, J. R.

    2016-01-01

    Quantum and Markov random walk models are proposed for describing how people evaluate stimuli using rating scales. To empirically test these competing models, we conducted an experiment in which participants judged the effectiveness of public health service announcements from either their own personal perspective or from the perspective of another person. The order of the self versus other judgements was manipulated, which produced significant sequential effects. The quantum and Markov models were fitted to the data using the same number of parameters, and the model comparison strongly supported the quantum over the Markov model. PMID:26621984

  3. Tracking Random Walk of Individual Domain Walls in Cylindrical Nanomagnets with Resistance Noise

    NASA Astrophysics Data System (ADS)

    Singh, Amrita; Mukhopadhyay, Soumik; Ghosh, Arindam

    2010-08-01

    The stochasticity of domain-wall (DW) motion in magnetic nanowires has been probed by measuring slow fluctuations, or noise, in electrical resistance at small magnetic fields. By controlled injection of DWs into isolated cylindrical nanowires of nickel, we have been able to track the motion of the DWs between the electrical leads by discrete steps in the resistance. Closer inspection of the time dependence of noise reveals a diffusive random walk of the DWs with a universal kinetic exponent. Our experiments outline a method with which electrical resistance is able to detect the kinetic state of the DWs inside the nanowires, which can be useful in DW-based memory designs.

  4. Experimental implementation of a quantum random-walk search algorithm using strongly dipolar coupled spins

    NASA Astrophysics Data System (ADS)

    Lu, Dawei; Zhu, Jing; Zou, Ping; Peng, Xinhua; Yu, Yihua; Zhang, Shanmin; Chen, Qun; Du, Jiangfeng

    2010-02-01

    An important quantum search algorithm based on the quantum random walk performs an oracle search on a database of N items with O(phN) calls, yielding a speedup similar to the Grover quantum search algorithm. The algorithm was implemented on a quantum information processor of three-qubit liquid-crystal nuclear magnetic resonance (NMR) in the case of finding 1 out of 4, and the diagonal elements’ tomography of all the final density matrices was completed with comprehensible one-dimensional NMR spectra. The experimental results agree well with the theoretical predictions.

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

    PubMed

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

    2005-01-01

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

  6. The exact probability distribution of a two-dimensional random walk

    NASA Astrophysics Data System (ADS)

    Stadje, W.

    1987-01-01

    A calculation is made of the exact probability distribution of the two-dimensional displacement of a particle at time t that starts at the origin, moves in straight-line paths at constant speed, and changes its direction after exponentially distributed time intervals, where the lengths of the straight-line paths and the turn angles are independent, the angles being uniformly distributed. This random walk is the simplest model for the locomotion of microorganisms on surfaces. Its weak convergence to a Wiener process is also shown.

  7. A boundary element-Random walk model of mass transport in groundwater

    USGS Publications Warehouse

    Kemblowski, M.

    1986-01-01

    A boundary element solution to the convective mass transport in groundwater is presented. This solution produces a continuous velocity field and reduces the amount of data preparation time and bookkeeping. By combining this solution and the random walk procedure, a convective-dispersive mass transport model is obtained. This model may be easily used to simulate groundwater contamination problems. The accuracy of the boundary element model has been verified by reproducing the analytical solution to a two-dimensional convective mass transport problem. The method was also used to simulate a convective-dispersive problem. ?? 1986.

  8. Slower deviations of the branching Brownian motion and of branching random walks

    NASA Astrophysics Data System (ADS)

    Derrida, Bernard; Shi, Zhan

    2017-08-01

    We have shown recently how to calculate the large deviation function of the position X\\max(t) of the rightmost particle of a branching Brownian motion at time t. This large deviation function exhibits a phase transition at a certain negative velocity. Here we extend this result to more general branching random walks and show that the probability distribution of X\\max(t) has, asymptotically in time, a prefactor characterized by a non trivial power law. Dedicated to John Cardy on the occasion of his 70th birthday.

  9. Experimental implementation of a quantum random-walk search algorithm using strongly dipolar coupled spins

    SciTech Connect

    Lu Dawei; Peng Xinhua; Du Jiangfeng; Zhu Jing; Zou Ping; Yu Yihua; Zhang Shanmin; Chen Qun

    2010-02-15

    An important quantum search algorithm based on the quantum random walk performs an oracle search on a database of N items with O({radical}(phN)) calls, yielding a speedup similar to the Grover quantum search algorithm. The algorithm was implemented on a quantum information processor of three-qubit liquid-crystal nuclear magnetic resonance (NMR) in the case of finding 1 out of 4, and the diagonal elements' tomography of all the final density matrices was completed with comprehensible one-dimensional NMR spectra. The experimental results agree well with the theoretical predictions.

  10. Trapping photons on the line: controllable dynamics of a quantum walk

    PubMed Central

    Xue, Peng; Qin, Hao; Tang, Bao

    2014-01-01

    Optical interferometers comprising birefringent-crystal beam displacers, wave plates, and phase shifters serve as stable devices for simulating quantum information processes such as heralded coined quantum walks. Quantum walks are important for quantum algorithms, universal quantum computing circuits, quantum transport in complex systems, and demonstrating intriguing nonlinear dynamical quantum phenomena. We introduce fully controllable polarization-independent phase shifters in optical pathes in order to realize site-dependent phase defects. The effectiveness of our interferometer is demonstrated through realizing single-photon quantum-walk dynamics in one dimension. By applying site-dependent phase defects, the translational symmetry of an ideal standard quantum walk is broken resulting in localization effect in a quantum walk architecture. The walk is realized for different site-dependent phase defects and coin settings, indicating the strength of localization signature depends on the level of phase due to site-dependent phase defects and coin settings and opening the way for the implementation of a quantum-walk-based algorithm. PMID:24769869

  11. Quantum walks with tuneable self-avoidance in one dimension

    NASA Astrophysics Data System (ADS)

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

    2014-04-01

    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.

  12. 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

  13. Random walk to describe diffusion phenomena in three-dimensional discontinuous media: Step-balance and fictitious-velocity corrections

    NASA Astrophysics Data System (ADS)

    Maruyama, Yutaka

    2017-09-01

    In this paper, we show that diffusion phenomena in three-dimensional discontinuous media can be described as a random walk by two simple interface-correction methods, namely step-balance and fictitious-velocity corrections, which are completely different in a physical picture but equivalent in that the continuity of the random walk at interfaces is considered. In both corrections, asymmetric interface permeability of a random walker, which comes from ensuring the continuity, causes apparent confinement of the walker in higher-diffusivity layers for benchmark tests on heat diffusion in two-phase multilayered systems. Effective thermal conductivities (walker diffusivities) computed from the trajectories are in excellent agreement with the series and parallel conduction formulas, indicating the equivalence of the two corrections and the importance of ensuring the continuity of a random walk at interfaces.

  14. Economy, Movement Dynamics, and Muscle Activity of Human Walking at Different Speeds

    PubMed Central

    Raffalt, P. C.; Guul, M. K.; Nielsen, A. N.; Puthusserypady, S.; Alkjær, T.

    2017-01-01

    The complex behaviour of human walking with respect to movement variability, economy and muscle activity is speed dependent. It is well known that a U-shaped relationship between walking speed and economy exists. However, it is an open question if the movement dynamics of joint angles and centre of mass and muscle activation strategy also exhibit a U-shaped relationship with walking speed. We investigated the dynamics of joint angle trajectories and the centre of mass accelerations at five different speeds ranging from 20 to 180% of the predicted preferred speed (based on Froude speed) in twelve healthy males. The muscle activation strategy and walking economy were also assessed. The movement dynamics was investigated using a combination of the largest Lyapunov exponent and correlation dimension. We observed an intermediate stage of the movement dynamics of the knee joint angle and the anterior-posterior and mediolateral centre of mass accelerations which coincided with the most energy-efficient walking speed. Furthermore, the dynamics of the joint angle trajectories and the muscle activation strategy was closely linked to the functional role and biomechanical constraints of the joints. PMID:28272484

  15. Continuous-time random walk models of DNA electrophoresis in a post array: part I. Evaluation of existing models.

    PubMed

    Olson, Daniel W; Ou, Jia; Tian, Mingwei; Dorfman, Kevin D

    2011-02-01

    Several continuous-time random walk (CTRW) models exist to predict the dynamics of DNA in micropost arrays, but none of them quantitatively describes the separation seen in experiments or simulations. In Part I of this series, we examine the assumptions underlying these models by observing single molecules of λ DNA during electrophoresis in a regular, hexagonal array of oxidized silicon posts. Our analysis takes advantage of a combination of single-molecule videomicroscopy and previous Brownian dynamics simulations. Using a custom-tracking program, we automatically identify DNA-post collisions and thus study a large ensemble of events. Our results show that the hold-up time and the distance between collisions for consecutive collisions are uncorrelated. The distance between collisions is a random variable, but it can be smaller than the minimum value predicted by existing models of DNA transport in post arrays. The current CTRW models correctly predict the exponential decay in the probability density of the collision hold-up times, but they fail to account for the influence of finite-sized posts on short hold-up times. The shortcomings of the existing models identified here motivate the development of a new CTRW approach, which is presented in Part II of this series.

  16. Continuous-time random-walk approach to supercooled liquids. II. Mean-square displacements in polymer melts.

    PubMed

    Helfferich, J; Ziebert, F; Frey, S; Meyer, H; Farago, J; Blumen, A; Baschnagel, J

    2014-04-01

    The continuous-time random walk (CTRW) describes the single-particle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al. [Phys. Rev. E 89, 042603 (2014)], we detect jump events of the monomers. As a function of temperature and chain length, we examine key distributions of the CTRW: the jump-length distribution (JLD), the waiting-time distribution (WTD), and the persistence-time distribution (PTD), i.e., the distribution of waiting times for the first jump. For the equilibrium (polymer) liquid under consideration, we verify that the PTD is determined by the WTD. For the mean-square displacement (MSD) of a monomer, the results for the CTRW model are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early α process and another at later times due to chain connectivity. By contrast, the analytical solution of the CTRW yields diffusive behavior for the MSD at all times. Empirically, we can account for the effect of chain connectivity in Monte Carlo simulations of the CTRW. The results of these simulations are then in good agreement with the MD data in the connectivity-dominated regime, but not in the early α regime where they systematically underestimate the MSD from the MD.

  17. The survival probability of a branching random walk in presence of an absorbing wall

    NASA Astrophysics Data System (ADS)

    Derrida, B.; Simon, D.

    2007-06-01

    A branching random walk in presence of an absorbing wall moving at a constant velocity v undergoes a phase transition as v varies. The problem can be analyzed using the properties of the Fisher-Kolmogorov-Petrovsky-Piscounov (F-KPP) equation. We find that the survival probability of the branching random walk vanishes at a critical velocity vc of the wall with an essential singularity and we characterize the divergences of the relaxation times for vvc. At v=vc the survival probability decays like a stretched exponential. Using the F-KPP equation, one can also calculate the distribution of the population size at time t conditioned by the survival of one individual at a later time T>t. Our numerical results indicate that the size of the population diverges like the exponential of (vc-v)-1/2 in the quasi-stationary regime below vc. Moreover for v>vc, our data indicate that there is no quasi-stationary regime.

  18. BRWLDA: bi-random walks for predicting lncRNA-disease associations

    PubMed Central

    Yu, Guoxian; Fu, Guangyuan; Lu, Chang; Ren, Yazhou; Wang, Jun

    2017-01-01

    Increasing efforts have been done to figure out the association between lncRNAs and complex diseases. Many computational models construct various lncRNA similarity networks, disease similarity networks, along with known lncRNA-disease associations to infer novel associations. However, most of them neglect the structural difference between lncRNAs network and diseases network, hierarchical relationships between diseases and pattern of newly discovered associations. In this study, we developed a model that performs Bi-Random Walks to predict novel LncRNA-Disease Associations (BRWLDA in short). This model utilizes multiple heterogeneous data to construct the lncRNA functional similarity network, and Disease Ontology to construct a disease network. It then constructs a directed bi-relational network based on these two networks and available lncRNAs-disease associations. Next, it applies bi-random walks on the network to predict potential associations. BRWLDA achieves reliable and better performance than other comparing methods not only on experiment verified associations, but also on the simulated experiments with masked associations. Case studies further demonstrate the feasibility of BRWLDA in identifying new lncRNA-disease associations.

  19. BRWLDA: bi-random walks for predicting lncRNA-disease associations.

    PubMed

    Yu, Guoxian; Fu, Guangyuan; Lu, Chang; Ren, Yazhou; Wang, Jun

    2017-09-01

    Increasing efforts have been done to figure out the association between lncRNAs and complex diseases. Many computational models construct various lncRNA similarity networks, disease similarity networks, along with known lncRNA-disease associations to infer novel associations. However, most of them neglect the structural difference between lncRNAs network and diseases network, hierarchical relationships between diseases and pattern of newly discovered associations. In this study, we developed a model that performs Bi-Random Walks to predict novel LncRNA-Disease Associations (BRWLDA in short). This model utilizes multiple heterogeneous data to construct the lncRNA functional similarity network, and Disease Ontology to construct a disease network. It then constructs a directed bi-relational network based on these two networks and available lncRNAs-disease associations. Next, it applies bi-random walks on the network to predict potential associations. BRWLDA achieves reliable and better performance than other comparing methods not only on experiment verified associations, but also on the simulated experiments with masked associations. Case studies further demonstrate the feasibility of BRWLDA in identifying new lncRNA-disease associations.

  20. Random walk theory of a trap-controlled hopping transport process

    PubMed Central

    Scher, H.; Wu, C. H.

    1981-01-01

    A random walk theory of hopping motion in the presence of a periodic distribution of traps is presented. The solution of the continuous-time random walk equations is exact and valid for arbitrary intersite interactions and trap concentration. The treatment is shown to be equivalent to an exact solution of the master equation for this trapping problem. These interactions can be a general function of electric field and are not restricted to nearest neighbors. In particular, with the inclusion of trap-to-trap interactions, as well as trap-to-host interactions, an exact treatment of the change from one hopping channel to another has been obtained. The trap-modulated propagator has been derived in terms of a type of Green's function that is introduced. The results are specialized to spatial moments of the propagator, from which expressions for the drift velocity and diffusion coefficient are obtained. Numerical results for the drift velocity are presented and shown to account for the change in hopping channels in recent transport measurements in mixed molecularly doped polymers. PMID:16592944