Hilário, M.; Hollander, den W.Th.F.; Sidoravicius, V.; Soares dos Santos, R.; Teixeira, A.
2014-01-01
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density ¿¿(0,8). At each step the random walk performs a nearest-neighbour jump, moving to
Randomized random walk on a random walk
Lee, P.A.
1983-06-01
This paper discusses generalizations of the model introduced by Kehr and Kunter of the random walk of a particle on a one-dimensional chain which in turn has been constructed by a random walk procedure. The superimposed random walk is randomised in time according to the occurrences of a stochastic point process. The probability of finding the particle in a particular position at a certain instant is obtained explicitly in the transform domain. It is found that the asymptotic behaviour for large time of the mean-square displacement of the particle depends critically on the assumed structure of the basic random walk, giving a diffusion-like term for an asymmetric walk or a square root law if the walk is symmetric. Many results are obtained in closed form for the Poisson process case, and these agree with those given previously by Kehr and Kunter. (author)
Odagaki, Takashi; Kasuya, Keisuke
2017-09-01
Using the Monte Carlo simulation, we investigate a memory-impaired self-avoiding walk on a square lattice in which a random walker marks each of sites visited with a given probability p and makes a random walk avoiding the marked sites. Namely, p = 0 and p = 1 correspond to the simple random walk and the self-avoiding walk, respectively. When p> 0, there is a finite probability that the walker is trapped. We show that the trap time distribution can well be fitted by Stacy's Weibull distribution b(a/b){a+1}/{b}[Γ({a+1}/{b})]-1x^a\\exp(-a/bx^b)} where a and b are fitting parameters depending on p. We also find that the mean trap time diverges at p = 0 as p- α with α = 1.89. In order to produce sufficient number of long walks, we exploit the pivot algorithm and obtain the mean square displacement and its Flory exponent ν(p) as functions of p. We find that the exponent determined for 1000 step walks interpolates both limits ν(0) for the simple random walk and ν(1) for the self-avoiding walk as [ ν(p) - ν(0) ] / [ ν(1) - ν(0) ] = pβ with β = 0.388 when p ≪ 0.1 and β = 0.0822 when p ≫ 0.1. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Relation between random walks and quantum walks
Boettcher, Stefan; Falkner, Stefan; Portugal, Renato
2015-05-01
Based on studies of four specific networks, we conjecture a general relation between the walk dimensions dw of discrete-time random walks and quantum walks with the (self-inverse) Grover coin. In each case, we find that dw of the quantum walk takes on exactly half the value found for the classical random walk on the same geometry. Since walks on homogeneous lattices satisfy this relation trivially, our results for heterogeneous networks suggest that such a relation holds irrespective of whether translational invariance is maintained or not. To develop our results, we extend the renormalization-group analysis (RG) of the stochastic master equation to one with a unitary propagator. As in the classical case, the solution ρ (x ,t ) in space and time of this quantum-walk equation exhibits a scaling collapse for a variable xdw/t in the weak limit, which defines dw and illuminates fundamental aspects of the walk dynamics, e.g., its mean-square displacement. We confirm the collapse for ρ (x ,t ) in each case with extensive numerical simulation. The exact values for dw themselves demonstrate that RG is a powerful complementary approach to study the asymptotics of quantum walks that weak-limit theorems have not been able to access, such as for systems lacking translational symmetries beyond simple trees.
Transfer, loss and physical processing of water in hit-and-run collisions of planetary embryos
Burger, C.; Maindl, T. I.; Schäfer, C. M.
2018-01-01
Collisions between large, similar-sized bodies are believed to shape the final characteristics and composition of terrestrial planets. Their inventories of volatiles such as water are either delivered or at least significantly modified by such events. Besides the transition from accretion to erosion with increasing impact velocity, similar-sized collisions can also result in hit-and-run outcomes for sufficiently oblique impact angles and large enough projectile-to-target mass ratios. We study volatile transfer and loss focusing on hit-and-run encounters by means of smooth particle hydrodynamics simulations, including all main parameters: impact velocity, impact angle, mass ratio and also the total colliding mass. We find a broad range of overall water losses, up to 75% in the most energetic hit-and-run events, and confirm the much more severe consequences for the smaller body also for stripping of volatile layers. Transfer of water between projectile and target inventories is found to be mostly rather inefficient, and final water contents are dominated by pre-collision inventories reduced by impact losses, for similar pre-collision water mass fractions. Comparison with our numerical results shows that current collision outcome models are not accurate enough to reliably predict these composition changes in hit-and-run events. To also account for non-mechanical losses, we estimate the amount of collisionally vaporized water over a broad range of masses and find that these contributions are particularly important in collisions of ˜ Mars-sized bodies, with sufficiently high impact energies, but still relatively low gravity. Our results clearly indicate that the cumulative effect of several (hit-and-run) collisions can efficiently strip protoplanets of their volatile layers, especially the smaller body, as it might be common, e.g., for Earth-mass planets in systems with Super-Earths. An accurate model for stripping of volatiles that can be included in future planet
"Hit-and-Run" leaves its mark: catalyst transcription factors and chromatin modification.
Varala, Kranthi; Li, Ying; Marshall-Colón, Amy; Para, Alessia; Coruzzi, Gloria M
2015-08-01
Understanding how transcription factor (TF) binding is related to gene regulation is a moving target. We recently uncovered genome-wide evidence for a "Hit-and-Run" model of transcription. In this model, a master TF "hits" a target promoter to initiate a rapid response to a signal. As the "hit" is transient, the model invokes recruitment of partner TFs to sustain transcription over time. Following the "run", the master TF "hits" other targets to propagate the response genome-wide. As such, a TF may act as a "catalyst" to mount a broad and acute response in cells that first sense the signal, while the recruited TF partners promote long-term adaptive behavior in the whole organism. This "Hit-and-Run" model likely has broad relevance, as TF perturbation studies across eukaryotes show small overlaps between TF-regulated and TF-bound genes, implicating transient TF-target binding. Here, we explore this "Hit-and-Run" model to suggest molecular mechanisms and its biological relevance. © 2015 The Authors. Bioessays published by WILEY Periodicals, Inc.
Lawler, Gregory F.; Ferreras, José A. Trujillo
2004-01-01
The Brownian loop soup introduced in Lawler and Werner (2004) is a Poissonian realization from a sigma-finite measure on unrooted loops. This measure satisfies both conformal invariance and a restriction property. In this paper, we define a random walk loop soup and show that it converges to the Brownian loop soup. In fact, we give a strong approximation result making use of the strong approximation result of Koml\\'os, Major, and Tusn\\'ady. To make the paper self-contained, we include a proof...
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.
A hit and run approach to inducible direct reprogramming of astrocytes to neural stem cells
Maria ePoulou
2016-04-01
Full Text Available Temporal and spatial control of gene expression can be achieved using an inducible system as a fundamental tool for regulated transcription in basic, applied and eventually in clinical research. We describe a novel hit and run inducible direct reprogramming approach. In a single step, two days post-transfection, transiently transfected Sox2FLAG under the Leu3p-αIPM inducible control (iSox2 triggers the activation of endogenous Sox2, redirecting primary astrocytes into abundant distinct nestin-positive radial glia cells. This technique introduces a unique novel tool for safe, rapid and efficient reprogramming amendable to regenerative medicine.
The effect of road and environmental characteristics on pedestrian hit-and-run accidents in Ghana.
Aidoo, Eric Nimako; Amoh-Gyimah, Richard; Ackaah, Williams
2013-04-01
The number of pedestrians who have died as a result of being hit by vehicles has increased in recent years, in addition to vehicle passenger deaths. Many pedestrians who were involved in road traffic accident died as a result of the driver leaving the pedestrian who was struck unattended at the scene of the accident. This paper seeks to determine the effect of road and environmental characteristics on pedestrian hit-and-run accidents in Ghana. Using pedestrian accident data extracted from the National Road Traffic Accident Database at the Building and Road Research Institute (BRRI) of the Council for Scientific and Industrial Research (CSIR), Ghana, a binary logit model was employed in the analysis. The results from the estimated model indicate that fatal accidents, unclear weather, nighttime conditions, and straight and flat road sections without medians and junctions significantly increase the likelihood that the vehicle driver will leave the scene after hitting a pedestrian. Thus, integrating median separation and speed humps into road design and construction and installing street lights will help to curb the problem of pedestrian hit-and-run accidents in Ghana. Copyright © 2012 Elsevier Ltd. All rights reserved.
Rosenberg, D. E.; Alafifi, A.
2016-12-01
Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one
Topics in random walks in random environment
Sznitman, A.-S.
2004-01-01
Over the last twenty-five years random motions in random media have been intensively investigated and some new general methods and paradigms have by now emerged. Random walks in random environment constitute one of the canonical models of the field. However in dimension bigger than one they are still poorly understood and many of the basic issues remain to this day unresolved. The present series of lectures attempt to give an account of the progresses which have been made over the last few years, especially in the study of multi-dimensional random walks in random environment with ballistic behavior. (author)
Random walk through fractal environments
Isliker, H.; Vlahos, L.
2003-01-01
We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D F of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D F ≤2 can thus be considered as defective Levy walks. The distribution of jump increments for D F >2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D F F >2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations
Reserves Represented by Random Walks
Filipe, J A; Ferreira, M A M; Andrade, M
2012-01-01
The reserves problem is studied through models based on Random Walks. Random walks are a classical particular case in the analysis of stochastic processes. They do not appear only to study reserves evolution models. They are also used to build more complex systems and as analysis instruments, in a theoretical feature, of other kind of systems. In this work by studying the reserves, the main objective is to see and guarantee that pensions funds get sustainable. Being the use of these models considering this goal a classical approach in the study of pensions funds, this work concluded about the problematic of reserves. A concrete example is presented.
van Valkenhoef, Gert; Tervonen, Tommi; Postmus, Douwe
2014-01-01
In our previous work published in this journal, we showed how the Hit-And-Run (HAR) procedure enables efficient sampling of criteria weights from a space formed by restricting a simplex with arbitrary linear inequality constraints. In this short communication, we note that the method for generating
Thermophoresis as persistent random walk
Plyukhin, A.V.
2009-01-01
In a simple model of a continuous random walk a particle moves in one dimension with the velocity fluctuating between +v and -v. If v is associated with the thermal velocity of a Brownian particle and allowed to be position dependent, the model accounts readily for the particle's drift along the temperature gradient and recovers basic results of the conventional thermophoresis theory.
Random walk through fractal environments
Isliker, H.; Vlahos, L.
2002-01-01
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is ...
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Random walks, random fields, and disordered systems
Černý, Jiří; Kotecký, Roman
2015-01-01
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a mod...
Random walks on reductive groups
Benoist, Yves
2016-01-01
The classical theory of Random Walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
Random walks and diffusion on networks
Masuda, Naoki; Porter, Mason A.; Lambiotte, Renaud
2017-11-01
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.
Locally Perturbed Random Walks with Unbounded Jumps
Paulin, Daniel; Szász, Domokos
2010-01-01
In \\cite{SzT}, D. Sz\\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \\ge 2$. The extension of their result to finite range random walks is straightforward. Here, however, we are interested in the situation when the random walk has unbounded range. Concretely we generalize the statement of \\cite{SzT} to unbounded random walks whose jump distribution belongs to th...
Chemical Continuous Time Random Walks
Aquino, T.; Dentz, M.
2017-12-01
Traditional methods for modeling solute transport through heterogeneous media employ Eulerian schemes to solve for solute concentration. More recently, Lagrangian methods have removed the need for spatial discretization through the use of Monte Carlo implementations of Langevin equations for solute particle motions. While there have been recent advances in modeling chemically reactive transport with recourse to Lagrangian methods, these remain less developed than their Eulerian counterparts, and many open problems such as efficient convergence and reconstruction of the concentration field remain. We explore a different avenue and consider the question: In heterogeneous chemically reactive systems, is it possible to describe the evolution of macroscopic reactant concentrations without explicitly resolving the spatial transport? Traditional Kinetic Monte Carlo methods, such as the Gillespie algorithm, model chemical reactions as random walks in particle number space, without the introduction of spatial coordinates. The inter-reaction times are exponentially distributed under the assumption that the system is well mixed. In real systems, transport limitations lead to incomplete mixing and decreased reaction efficiency. We introduce an arbitrary inter-reaction time distribution, which may account for the impact of incomplete mixing. This process defines an inhomogeneous continuous time random walk in particle number space, from which we derive a generalized chemical Master equation and formulate a generalized Gillespie algorithm. We then determine the modified chemical rate laws for different inter-reaction time distributions. We trace Michaelis-Menten-type kinetics back to finite-mean delay times, and predict time-nonlocal macroscopic reaction kinetics as a consequence of broadly distributed delays. Non-Markovian kinetics exhibit weak ergodicity breaking and show key features of reactions under local non-equilibrium.
Random Walks with Anti-Correlated Steps
Wagner, Dirk; Noga, John
2005-01-01
We conjecture the expected value of random walks with anti-correlated steps to be exactly 1. We support this conjecture with 2 plausibility arguments and experimental data. The experimental analysis includes the computation of the expected values of random walks for steps up to 22. The result shows the expected value asymptotically converging to 1.
Brownian Optimal Stopping and Random Walks
Lamberton, D.
2002-01-01
One way to compute the value function of an optimal stopping problem along Brownian paths consists of approximating Brownian motion by a random walk. We derive error estimates for this type of approximation under various assumptions on the distribution of the approximating random walk
A comparison of random walks in dependent random environments
Scheinhardt, Willem R.W.; Kroese, Dirk
We provide exact computations for the drift of random walks in dependent random environments, including $k$-dependent and moving average environments. We show how the drift can be characterized and evaluated using Perron–Frobenius theory. Comparing random walks in various dependent environments, we
Elements of random walk and diffusion processes
Ibe, Oliver C
2013-01-01
Presents an important and unique introduction to random walk theory Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic
Iterated random walks with shape prior
Pujadas, Esmeralda Ruiz; Kjer, Hans Martin; Piella, Gemma
2016-01-01
the parametric probability density function. Then, random walks is performed iteratively aligning the prior with the current segmentation in every iteration. We tested the proposed approach with natural and medical images and compared it with the latest techniques with random walks and shape priors......We propose a new framework for image segmentation using random walks where a distance shape prior is combined with a region term. The shape prior is weighted by a confidence map to reduce the influence of the prior in high gradient areas and the region term is computed with k-means to estimate....... The experiments suggest that this method gives promising results for medical and natural images....
The random walk model of intrafraction movement
Ballhausen, H; Reiner, M; Kantz, S; Belka, C; Söhn, M
2013-01-01
The purpose of this paper is to understand intrafraction movement as a stochastic process driven by random external forces. The hypothetically proposed three-dimensional random walk model has significant impact on optimal PTV margins and offers a quantitatively correct explanation of experimental findings. Properties of the random walk are calculated from first principles, in particular fraction-average population density distributions for displacements along the principal axes. When substituted into the established optimal margin recipes these fraction-average distributions yield safety margins about 30% smaller as compared to the suggested values from end-of-fraction Gaussian fits. Stylized facts of a random walk are identified in clinical data, such as the increase of the standard deviation of displacements with the square root of time. Least squares errors in the comparison to experimental results are reduced by about 50% when accounting for non-Gaussian corrections from the random walk model. (paper)
The random walk model of intrafraction movement.
Ballhausen, H; Reiner, M; Kantz, S; Belka, C; Söhn, M
2013-04-07
The purpose of this paper is to understand intrafraction movement as a stochastic process driven by random external forces. The hypothetically proposed three-dimensional random walk model has significant impact on optimal PTV margins and offers a quantitatively correct explanation of experimental findings. Properties of the random walk are calculated from first principles, in particular fraction-average population density distributions for displacements along the principal axes. When substituted into the established optimal margin recipes these fraction-average distributions yield safety margins about 30% smaller as compared to the suggested values from end-of-fraction gaussian fits. Stylized facts of a random walk are identified in clinical data, such as the increase of the standard deviation of displacements with the square root of time. Least squares errors in the comparison to experimental results are reduced by about 50% when accounting for non-gaussian corrections from the random walk model.
Quantum random walks using quantum accelerator modes
Ma, Z.-Y.; Burnett, K.; D'Arcy, M. B.; Gardiner, S. A.
2006-01-01
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
Simulation of random walks in field theory
Rensburg, E.J.J. van
1988-01-01
The numerical simulation of random walks is considered using the Monte Carlo method previously proposed. The algorithm is tested and then generalised to generate Edwards random walks. The renormalised masses of the Edwards model are calculated and the results are compared with those obtained from a simple perturbation theory calculation for small values of the bare coupling constant. The efficiency of this algorithm is discussed and compared with an alternative approach. (author)
Many random walks are faster than one
Alon, N.; Avin, Ch.; Koucký, Michal; Kozma, G.; Lotker, Z.; Tuttle, M.R.
2011-01-01
Roč. 20, č. 4 (2011), s. 481-502 ISSN 0963-5483 R&D Projects: GA ČR GP201/07/P276; GA ČR GA201/05/0124 Institutional research plan: CEZ:AV0Z10190503 Keywords : multiple random walks * parallel random walks Subject RIV: BA - General Mathematics Impact factor: 0.778, year: 2011 http://journals.cambridge.org/ action /displayAbstract?fromPage=online&aid=8280727
Tempered stable laws as random walk limits
Chakrabarty, Arijit; Meerschaert, Mark M.
2010-01-01
Stable laws can be tempered by modifying the L\\'evy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk models that converge to a tempered stable law under a triangular array scheme. Since tempered stable laws and processes are useful in statistical physics, these random walk models can provide a basic physical model for the underlying physical phenomena.
Pedestrian Walking Behavior Revealed through a Random Walk Model
Hui Xiong
2012-01-01
Full Text Available This paper applies method of continuous-time random walks for pedestrian flow simulation. In the model, pedestrians can walk forward or backward and turn left or right if there is no block. Velocities of pedestrian flow moving forward or diffusing are dominated by coefficients. The waiting time preceding each jump is assumed to follow an exponential distribution. To solve the model, a second-order two-dimensional partial differential equation, a high-order compact scheme with the alternating direction implicit method, is employed. In the numerical experiments, the walking domain of the first one is two-dimensional with two entrances and one exit, and that of the second one is two-dimensional with one entrance and one exit. The flows in both scenarios are one way. Numerical results show that the model can be used for pedestrian flow simulation.
Random walk of passive tracers among randomly moving obstacles
Gori, Matteo; Donato, Irene; Floriani, Elena; Nardecchia, Ilaria; Pettini, Marco
2016-01-01
Background: This study is mainly motivated by the need of understanding how the diffusion behaviour 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. Method: By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random en...
Random walks and polygons in tight confinement
Diao, Y; Ernst, C; Ziegler, U
2014-01-01
We discuss the effect of confinement on the topology and geometry of tightly confined random walks and polygons. Here the walks and polygons are confined in a sphere of radius R ≥ 1/2 and the polygons are equilateral with n edges of unit length. We illustrate numerically that for a fixed length of random polygons the knotting probability increases to one as the radius decreases to 1/2. We also demonstrate that for random polygons (walks) the curvature increases to πn (π(n – 1)) as the radius approaches 1/2 and that the torsion decreases to ≈ πn/3 (≈ π(n – 1)/3). In addition we show the effect of length and confinement on the average crossing number of a random polygon
Scaling Argument of Anisotropic Random Walk
Xu Bingzhen; Jin Guojun; Wang Feifeng
2005-01-01
In this paper, we analytically discuss the scaling properties of the average square end-to-end distance (R 2 ) for anisotropic random walk in D-dimensional space (D≥2), and the returning probability P n (r 0 ) for the walker into a certain neighborhood of the origin. We will not only give the calculating formula for (R 2 ) and P n (r 0 ), but also point out that if there is a symmetric axis for the distribution of the probability density of a single step displacement, we always obtain (R p erpendicular n 2 )∼n, where perpendicular refers to the projections of the displacement perpendicular to each symmetric axes of the walk; in D-dimensional space with D symmetric axes perpendicular to each other, we always have (R n 2 )∼n and the random walk will be like a purely random motion; if the number of inter-perpendicular symmetric axis is smaller than the dimensions of the space, we must have (R n 2 )∼n 2 for very large n and the walk will be like a ballistic motion. It is worth while to point out that unlike the isotropic random walk in one and two dimensions, which is certain to return into the neighborhood of the origin, generally there is only a nonzero probability for the anisotropic random walker in two dimensions to return to the neighborhood.
Coupled continuous time-random walks in quenched random environment
Magdziarz, M.; Szczotka, W.
2018-02-01
We introduce a coupled continuous-time random walk with coupling which is characteristic for Lévy walks. Additionally we assume that the walker moves in a quenched random environment, i.e. the site disorder at each lattice point is fixed in time. We analyze the scaling limit of such a random walk. We show that for large times the behaviour of the analyzed process is exactly the same as in the case of uncoupled quenched trap model for Lévy flights.
Mesoscopic description of random walks on combs
Méndez, Vicenç; Iomin, Alexander; Campos, Daniel; Horsthemke, Werner
2015-12-01
Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic method to obtain their transport properties. The random walk along the branches may be biased, and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone. We analyze the overall diffusion properties along the backbone and find normal diffusion, anomalous diffusion, and stochastic localization (diffusion failure), respectively, depending on the characteristics of the continuous time random walk along the branches, and compare our analytical results with stochastic simulations.
Random walks of oriented particles on fractals
Haber, René; Prehl, Janett; Hoffmann, Karl Heinz; Herrmann, Heiko
2014-01-01
Random walks of point particles on fractals exhibit subdiffusive behavior, where the anomalous diffusion exponent is smaller than one, and the corresponding random walk dimension is larger than two. This is due to the limited space available in fractal structures. Here, we endow the particles with an orientation and analyze their dynamics on fractal structures. In particular, we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation, which are modeled using an appropriate move class. These interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure. A surprising finding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features. (paper)
Quantum random-walk search algorithm
Shenvi, Neil; Whaley, K. Birgitta; Kempe, Julia
2003-01-01
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(√(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
Path probabilities of continuous time random walks
Eule, Stephan; Friedrich, Rudolf
2014-01-01
Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman–Kac formulae. (paper)
Random walk with memory enhancement and decay
Tan, Zhi-Jie; Zou, Xian-Wu; Huang, Sheng-You; Zhang, Wei; Jin, Zhun-Zhi
2002-04-01
A model of random walk with memory enhancement and decay was presented on the basis of the characteristics of the biological intelligent walks. In this model, the movement of the walker is determined by the difference between the remaining information at the jumping-out site and jumping-in site. The amount of the memory information si(t) at a site i is enhanced with the increment of visiting times to that site, and decays with time t by the rate e-βt, where β is the memory decay exponent. When β=0, there exists a transition from Brownian motion (BM) to the compact growth of walking trajectory with the density of information energy u increasing. But for β>0, this transition does not appear and the walk with memory enhancement and decay can be considered as the BM of the mass center of the cluster composed of remembered sites in the late stage.
Random walk centrality for temporal networks
Rocha, Luis E C; Masuda, Naoki
2014-01-01
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. (paper)
Random walk centrality for temporal networks
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.
Random walk term weighting for information retrieval
Blanco, R.; Lioma, Christina
2007-01-01
We present a way of estimating term weights for Information Retrieval (IR), using term co-occurrence as a measure of dependency between terms.We use the random walk graph-based ranking algorithm on a graph that encodes terms and co-occurrence dependencies in text, from which we derive term weights...
Random walks in Euclidean space
Varjú, Péter Pál
2012-01-01
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove a local limit theorem under a suitable moment condition and a necessary non-degeneracy condition. Under stronger hypothesis, we prove a limit theorem on a wide range of scales: between e^(-cl^(1/4)) and l^(1/2), where l is the number of steps.
RANDOM WALK HYPOTHESIS IN FINANCIAL MARKETS
Nicolae-Marius JULA
2017-05-01
Full Text Available Random walk hypothesis states that the stock market prices do not follow a predictable trajectory, but are simply random. If you are trying to predict a random set of data, one should test for randomness, because, despite the power and complexity of the used models, the results cannot be trustworthy. There are several methods for testing these hypotheses and the use of computational power provided by the R environment makes the work of the researcher easier and with a cost-effective approach. The increasing power of computing and the continuous development of econometric tests should give the potential investors new tools in selecting commodities and investing in efficient markets.
Random walk of passive tracers among randomly moving obstacles.
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.
Curvature of random walks and random polygons in confinement
Diao, Y; Ernst, C; Montemayor, A; Ziegler, U
2013-01-01
The purpose of this paper is to study the curvature of equilateral random walks and polygons that are confined in a sphere. Curvature is one of several basic geometric properties that can be used to describe random walks and polygons. We show that confinement affects curvature quite strongly, and in the limit case where the confinement diameter equals the edge length the unconfined expected curvature value doubles from π/2 to π. To study curvature a simple model of an equilateral random walk in spherical confinement in dimensions 2 and 3 is introduced. For this simple model we derive explicit integral expressions for the expected value of the total curvature in both dimensions. These expressions are functions that depend only on the radius R of the confinement sphere. We then show that the values obtained by numeric integration of these expressions agrees with numerical average curvature estimates obtained from simulations of random walks. Finally, we compare the confinement effect on curvature of random walks with random polygons. (paper)
Random walk and the heat equation
Lawler, Gregory F
2010-01-01
The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation by considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equation and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. The first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For exa...
A comparison of random walks in dependent random environments
Scheinhardt, Willem R.W.; Kroese, Dirk
2015-01-01
Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the actual evaluation of various characteristics of such processes has received relatively little attention. This paper develops new methodology for the exact computation of the drift in such
He, Lu; De Groot, Anne S; Bailey-Kellogg, Chris
2015-11-27
Different types of bacteria face different pressures from the immune system, with those that persist ("hit-and-stay") potentially having to adapt more in order to escape than those prone to short-lived infection ("hit-and-run"), and with commensal bacteria potentially different from both due to additional physical mechanisms for avoiding immune detection. The Janus Immunogenicity Score (JIS) was recently developed to assess the likelihood of T cell recognition of an antigen, using an analysis that considers both binding of a peptide within the antigen by major histocompatability complex (MHC) and recognition of the peptide:MHC complex by cognate T cell receptor (TCR). This score was shown to be predictive of T effector vs. T regulatory or null responses in experimental data, as well as to distinguish viruses representative of the hit-and-stay vs. hit-and-run phenotypes. Here, JIS-based analyses were conducted in order to characterize the extent to which the pressure to avoid T cell recognition is manifested in genomic differences among representative hit-and-run, hit-and-stay, and commensal bacteria. Overall, extracellular proteins were found to have different JIS profiles from cytoplasmic ones. Contrasting the bacterial groups, extracellular proteins were shown to be quite different across the groups, much more so than intracellular proteins. The differences were evident even at the level of corresponding peptides in homologous protein pairs from hit-and-run and hit-and-stay bacteria. The multi-level analysis of patterns of immunogenicity across different groups of bacteria provides a new way to approach questions of bacterial immune camouflage or escape, as well as to approach the selection and optimization of candidates for vaccine design. Copyright © 2015 Elsevier Ltd. All rights reserved.
Dilemma Produced by Infinity of a Random Walk
Li Jing-Hui
2015-01-01
We report a dilemma produced by the infinity of a random walk moving along a two-dimensional space sidestep. For this random walk, our investigation shows that using a different model can lead to a different diffusion coefficient of the random walk, which is produced by the infinity of the random walk. The result obtained by us in the present work can serve as a warning to us when we build the models to investigate the corresponding scientific problems. (paper)
Malicet, Dominique
2017-12-01
In this paper, we study random walks {g_n=f_{n-1}\\ldots f_0} on the group Homeo ( S 1) of the homeomorphisms of the circle, where the homeomorphisms f k are chosen randomly, independently, with respect to a same probability measure {ν}. We prove that under the only condition that there is no probability measure invariant by {ν}-almost every homeomorphism, the random walk almost surely contracts small intervals. It generalizes what has been known on this subject until now, since various conditions on {ν} were imposed in order to get the phenomenon of contractions. Moreover, we obtain the surprising fact that the rate of contraction is exponential, even in the lack of assumptions of smoothness on the f k 's. We deduce various dynamical consequences on the random walk ( g n ): finiteness of ergodic stationary measures, distribution of the trajectories, asymptotic law of the evaluations, etc. The proof of the main result is based on a modification of the Ávila-Viana's invariance principle, working for continuous cocycles on a space fibred in circles.
Quantum random walks and their convergence to Evans–Hudson ...
Quantum dynamical semigroup; Evans–Hudson flow; quantum random walk. 1. Introduction. The aim of this article is to investigate convergence of random walks on von Neumann algebra to Evans–Hudson flows. Here the random walks and Evans–Hudson flows are gene- ralizations of classical Markov chains and Markov ...
Dynamic random walks theory and applications
Guillotin-Plantard, Nadine
2006-01-01
The aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer science, mathematical physics and finance. Each chapter contains didactical material as well as more advanced technical sections. Few appendices will help refreshing memories (if necessary!).· New probabilistic model, new results in probability theory· Original applications in computer science· Applications in mathematical physics· Applications in finance
Weak limits for quantum random walks
Grimmett, Geoffrey; Janson, Svante; Scudo, Petra F.
2004-01-01
We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With X n denoting position at time n, we show that X n /n converges weakly as n→∞ to a certain distribution which is absolutely continuous and of bounded support. The proof is rigorous and makes use of Fourier transform methods. This approach simplifies and extends certain preceding derivations valid in one dimension that make use of combinatorial and path integral methods
A Random Walk Picture of Basketball
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.
Random walks on generalized Koch networks
Sun, Weigang
2013-01-01
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. (paper)
Random walk to a nonergodic equilibrium concept
Bel, G.; Barkai, E.
2006-01-01
Random walk models, such as the trap model, continuous time random walks, and comb models, exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this paper a nonergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. We show that when conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics. In the ergodic phase the distribution function of the occupation times approaches a δ function centered on the value predicted based on standard Boltzmann-Gibbs statistics. The relation of our work to single-molecule experiments is briefly discussed.
Spin, statistics, and geometry of random walks
Jaroszewicz, T.; Kurzepa, P.S.
1991-01-01
The authors develop and unify two complementary descriptions of propagation of spinning particles: the directed random walk representation and the spin factor approach. Working in an arbitrary number of dimensions D, they first represent the Dirac propagator in terms of a directed random walk. They then derive the general and explicit form of the gauge connection describing parallel transport of spin and investigate the resulting quantum-mechanical problem of a particle moving on a sphere in the field of a nonabelian SO(D-1) monopole. This construction, generalizing Polyakov's results, enables them to prove the equivalence of the random walk and path-integral (spin factor) representation. As an alternative, they construct and discuss various Wess-Zumino-Witten forms of the spin factor. They clarify the role played by the coupling between the particle's spin and translational degrees of freedom in establishing the geometrical properties of particle's paths in spacetime. To this end, they carefully define and evaluate Hausdorff dimensions of bosonic and fermionic sample paths, in the covariant as well as nonrelativistic formulations. Finally, as an application of the developed formalism, they give an intuitive spacetime interpretation of chiral anomalies in terms of the geometry of fermion trajectories
Randomness at the root of things 1: Random walks
Ogborn, Jon; Collins, Simon; Brown, Mick
2003-09-01
This is the first of a pair of articles about randomness in physics. In this article, we use some variations on the idea of a `random walk' to consider first the path of a particle in Brownian motion, and then the random variation to be expected in radioactive decay. The arguments are set in the context of the general importance of randomness both in physics and in everyday life. We think that the ideas could usefully form part of students' A-level work on random decay and quantum phenomena, as well as being good for their general education. In the second article we offer a novel and simple approach to Poisson sequences.
Efficient search by optimized intermittent random walks
Oshanin, Gleb; Lindenberg, Katja; Wio, Horacio S; Burlatsky, Sergei
2009-01-01
We study the kinetics for the search of an immobile target by randomly moving searchers that detect it only upon encounter. The searchers perform intermittent random walks on a one-dimensional lattice. Each searcher can step on a nearest neighbor site with probability α or go off lattice with probability 1 - α to move in a random direction until it lands back on the lattice at a fixed distance L away from the departure point. Considering α and L as optimization parameters, we seek to enhance the chances of successful detection by minimizing the probability P N that the target remains undetected up to the maximal search time N. We show that even in this simple model, a number of very efficient search strategies can lead to a decrease of P N by orders of magnitude upon appropriate choices of α and L. We demonstrate that, in general, such optimal intermittent strategies are much more efficient than Brownian searches and are as efficient as search algorithms based on random walks with heavy-tailed Cauchy jump-length distributions. In addition, such intermittent strategies appear to be more advantageous than Levy-based ones in that they lead to more thorough exploration of visited regions in space and thus lend themselves to parallelization of the search processes.
A random walk model to evaluate autism
Moura, T. R. S.; Fulco, U. L.; Albuquerque, E. L.
2018-02-01
A common test administered during neurological examination in children is the analysis of their social communication and interaction across multiple contexts, including repetitive patterns of behavior. Poor performance may be associated with neurological conditions characterized by impairments in executive function, such as the so-called pervasive developmental disorders (PDDs), a particular condition of the autism spectrum disorders (ASDs). Inspired in these diagnosis tools, mainly those related to repetitive movements and behaviors, we studied here how the diffusion regimes of two discrete-time random walkers, mimicking the lack of social interaction and restricted interests developed for children with PDDs, are affected. Our model, which is based on the so-called elephant random walk (ERW) approach, consider that one of the random walker can learn and imitate the microscopic behavior of the other with probability f (1 - f otherwise). The diffusion regimes, measured by the Hurst exponent (H), is then obtained, whose changes may indicate a different degree of autism.
Quantum chemistry by random walk: Higher accuracy
Anderson, J.B.
1980-01-01
The random walk method of solving the Schroedinger equation is extended to allow the calculation of eigenvalues of atomic and molecular systems with higher accuracy. The combination of direct calculation of the difference delta between a true wave function psi and a trial wave function psi/sub o/ with importance sampling greatly reduces systematic and statistical error. The method is illustrated with calculations for ground-state hydrogen and helium atoms using trial wave functions from variational calculations. The energies obtained are 20 to 100 times more accurate than those of the corresponding variational calculations
Generating random walks and polygons with stiffness in confinement
Diao, Y; Ernst, C; Saarinen, S; Ziegler, U
2015-01-01
The purpose of this paper is to explore ways to generate random walks and polygons in confinement with a bias toward stiffness. Here the stiffness refers to the curvature angle between two consecutive edges along the random walk or polygon. The stiffer the walk (polygon), the smaller this angle on average. Thus random walks and polygons with an elevated stiffness have lower than expected curvatures. The authors introduced and studied several generation algorithms with a stiffness parameter s>0 that regulates the expected curvature angle at a given vertex in which the random walks and polygons are generated one edge at a time using conditional probability density functions. Our generating algorithms also allow the generation of unconfined random walks and polygons with any desired mean curvature angle. In the case of random walks and polygons confined in a sphere of fixed radius, we observe that, as expected, stiff random walks or polygons are more likely to be close to the confinement boundary. The methods developed here require that the random walks and random polygons be rooted at the center of the confinement sphere. (paper)
Heterogeneous continuous-time random walks
Grebenkov, Denis S.; Tupikina, Liubov
2018-01-01
We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.
Understanding deterministic diffusion by correlated random walks
Klages, R.; Korabel, N.
2002-01-01
Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control parameter. Here we propose a systematic scheme of how to approximate deterministic diffusion coefficients of this kind in terms of correlated random walks. We apply this approach to two simple examples which are a one-dimensional map on the line and the periodic Lorentz gas. Starting from suitable Green-Kubo formulae we evaluate hierarchies of approximations for their parameter-dependent diffusion coefficients. These approximations converge exactly yielding a straightforward interpretation of the structure of these irregular diffusion coefficients in terms of dynamical correlations. (author)
Asymptotic Properties of Multistate Random Walks. I. Theory
Roerdink, J.B.T.M.; Shuler, K.E.
1985-01-01
A calculation is presented of the long-time behavior of various random walk properties (moments, probability of return to the origin, expected number of distinct sites visited) for multistate random walks on periodic lattices. In particular, we consider inhomogeneous periodic lattices, consisting of
How edge-reinforced random walk arises naturally
Rolles, S.W.W.
2003-01-01
We give a characterization of a modified edge-reinforced random walk in terms of certain partially exchangeable sequences. In particular, we obtain a characterization of an edge-reinforced random walk (introduced by Coppersmith and Diaconis) on a 2-edge-connected graph. Modifying the notion of
Girold, Sébastien; Rousseau, Jérome; Le Gal, Magalie; Coudeyre, Emmanuel; Le Henaff, Jacqueline
2017-07-01
With Nordic walking, or walking with poles, one can travel a greater distance and at a higher rate than with walking without poles, but whether the activity is beneficial for patients with cardiovascular disease is unknown. This randomized controlled trial was undertaken to determine whether Nordic walking was more effective than walking without poles on walk distance to support rehabilitation training for patients with acute coronary syndrome (ACS) and peripheral arterial occlusive disease (PAOD). Patients were recruited in a private specialized rehabilitation centre for cardiovascular diseases. The entire protocol, including patient recruitment, took place over 2 months, from September to October 2013. We divided patients into 2 groups: Nordic Walking Group (NWG, n=21) and Walking Group without poles (WG, n=21). All patients followed the same program over 4 weeks, except for the walk performed with or without poles. The main outcome was walk distance on the 6-min walk test. Secondary outcomes were maximum heart rate during exercise and walk distance and power output on a treadmill stress test. We included 42 patients (35 men; mean age 57.2±11 years and BMI 26.5±4.5kg/m 2 ). At the end of the training period, both groups showed improved walk distance on the 6-min walk test and treatment stress test as well as power on the treadmill stress test (PNordic walking training appeared more efficient than training without poles for increasing walk distance on the 6-min walk test for patients with ACS and PAOD. Copyright © 2017. Published by Elsevier Masson SAS.
Random walk in dynamically disordered chains: Poisson white noise disorder
Hernandez-Garcia, E.; Pesquera, L.; Rodriguez, M.A.; San Miguel, M.
1989-01-01
Exact solutions are given for a variety of models of random walks in a chain with time-dependent disorder. Dynamic disorder is modeled by white Poisson noise. Models with site-independent (global) and site-dependent (local) disorder are considered. Results are described in terms of an affective random walk in a nondisordered medium. In the cases of global disorder the effective random walk contains multistep transitions, so that the continuous limit is not a diffusion process. In the cases of local disorder the effective process is equivalent to usual random walk in the absence of disorder but with slower diffusion. Difficulties associated with the continuous-limit representation of random walk in a disordered chain are discussed. In particular, the authors consider explicit cases in which taking the continuous limit and averaging over disorder sources do not commute
Velocity and Dispersion for a Two-Dimensional Random Walk
Li Jinghui
2009-01-01
In the paper, we consider the transport of a two-dimensional random walk. The velocity and the dispersion of this two-dimensional random walk are derived. It mainly show that: (i) by controlling the values of the transition rates, the direction of the random walk can be reversed; (ii) for some suitably selected transition rates, our two-dimensional random walk can be efficient in comparison with the one-dimensional random walk. Our work is motivated in part by the challenge to explain the unidirectional transport of motor proteins. When the motor proteins move at the turn points of their tracks (i.e., the cytoskeleton filaments and the DNA molecular tubes), some of our results in this paper can be used to deal with the problem. (general)
Efficient sampling of complex network with modified random walk strategies
Xie, Yunya; Chang, Shuhua; Zhang, Zhipeng; Zhang, Mi; Yang, Lei
2018-02-01
We present two novel random walk strategies, choosing seed node (CSN) random walk and no-retracing (NR) random walk. Different from the classical random walk sampling, the CSN and NR strategies focus on the influences of the seed node choice and path overlap, respectively. Three random walk samplings are applied in the Erdös-Rényi (ER), Barabási-Albert (BA), Watts-Strogatz (WS), and the weighted USAir networks, respectively. Then, the major properties of sampled subnets, such as sampling efficiency, degree distributions, average degree and average clustering coefficient, are studied. The similar conclusions can be reached with these three random walk strategies. Firstly, the networks with small scales and simple structures are conducive to the sampling. Secondly, the average degree and the average clustering coefficient of the sampled subnet tend to the corresponding values of original networks with limited steps. And thirdly, all the degree distributions of the subnets are slightly biased to the high degree side. However, the NR strategy performs better for the average clustering coefficient of the subnet. In the real weighted USAir networks, some obvious characters like the larger clustering coefficient and the fluctuation of degree distribution are reproduced well by these random walk strategies.
Continuous-time quantum random walks require discrete space
Manouchehri, K; Wang, J B
2007-01-01
Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks
Continuous-time quantum random walks require discrete space
Manouchehri, K.; Wang, J. B.
2007-11-01
Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks.
An effective Hamiltonian approach to quantum random walk
2017-02-09
Feb 9, 2017 ... Abstract. 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 Hamil- tonians are generators of time translations. Then an attempt has been made to ...
Variational data assimilation using targetted random walks
Cotter, S. L.
2011-02-15
The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis. In either of these scenarios, it can be important to assess uncertainties in the assimilated state. Ideally, it is desirable to have complete information concerning the Bayesian posterior distribution for unknown state given data. We show that complete computational probing of this posterior distribution is now within the reach in the offline situation. We introduce a Markov chain-Monte Carlo (MCMC) method which enables us to directly sample from the Bayesian posterior distribution on the unknown functions of interest given observations. Since we are aware that these methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however, more sophisticated MCMC methods are available which exploit derivative information. For simplicity of exposition, we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number flow in a two-dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces. © 2011 John Wiley & Sons, Ltd.
Analytic results for asymmetric random walk with exponential transition probabilities
Gutkowicz-Krusin, D.; Procaccia, I.; Ross, J.
1978-01-01
We present here exact analytic results for a random walk on a one-dimensional lattice with asymmetric, exponentially distributed jump probabilities. We derive the generating functions of such a walk for a perfect lattice and for a lattice with absorbing boundaries. We obtain solutions for some interesting moment properties, such as mean first passage time, drift velocity, dispersion, and branching ratio for absorption. The symmetric exponential walk is solved as a special case. The scaling of the mean first passage time with the size of the system for the exponentially distributed walk is determined by the symmetry and is independent of the range
Record statistics of financial time series and geometric random walks.
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.
A scaling law for random walks on networks
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.
The Random-Walk Hypothesis on the Indian Stock Market
Ankita Mishra; Vinod Mishra; Russell Smyth
2014-01-01
This study tests the random walk hypothesis for the Indian stock market. Using 19 years of monthly data on six indices from the National Stock Exchange (NSE) and the Bombay Stock Exchange (BSE), this study applies three different unit root tests with two structural breaks to analyse the random walk hypothesis. We find that unit root tests that allow for two structural breaks alone are not able to reject the unit root null; however, a recently developed unit root test that simultaneously accou...
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 Bobath walking training in moderately affected stroke patients was better than Bobath walking training alone with respect to the improvement of walking velocity and capacity. The treatment approach is recommended in patients meeting the inclusion criteria. A multicentre trial should follow to strengthen the evidence.
Convergence of a random walk method for the Burgers equation
Roberts, S.
1985-10-01
In this paper we consider a random walk algorithm for the solution of Burgers' equation. The algorithm uses the method of fractional steps. The non-linear advection term of the equation is solved by advecting ''fluid'' particles in a velocity field induced by the particles. The diffusion term of the equation is approximated by adding an appropriate random perturbation to the positions of the particles. Though the algorithm is inefficient as a method for solving Burgers' equation, it does model a similar method, the random vortex method, which has been used extensively to solve the incompressible Navier-Stokes equations. The purpose of this paper is to demonstrate the strong convergence of our random walk method and so provide a model for the proof of convergence for more complex random walk algorithms; for instance, the random vortex method without boundaries
Roerdink, J.B.T.M.; Shuler, K.E.
1985-01-01
The previously developed formalism for the calculation of asymptotic properties of multistate random walks is used to study random walks on several inhomogeneous periodic lattices, where the periodically repeated unit cell contains a number of inequivalent sites, as well as on lattices with a random
Random walks in the quarter-plane: invariant measures and performance bounds
Chen, Y.
2015-01-01
This monograph focuses on random walks in the quarter-plane. Such random walks are frequently used to model queueing systems and the invariant measure of a random walk is of major importance in studying the performance of these systems. In special cases the invariant measure of a random walk can be
Adaptive random walks on the class of Web graphs
Tadić, B.
2001-09-01
We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [B. Tadić, Physica A 293, 273 (2001)], and are characterized by a pair of power-law distributions of out- and in-degree for each value of the parameter β, which measures the degree of rewiring in the graph. The walker adapts its move strategy according to locally available information both on out-degree of the visited node and in-degree of target node. A standard random walk, on the other hand, uses the out-degree only. We compute the distribution of connected subgraphs visited by an ensemble of walkers, the average access time and survival probability of the walks. We discuss these properties of the walk dynamics relative to the changes in the global graph structure when the control parameter β is varied. For β≥ 3, corresponding to the world-wide Web, the access time of the walk to a given level of hierarchy on the graph is much shorter compared to the standard random walk on the same graph. By reducing the amount of rewiring towards rigidity limit β↦βc≲ 0.1, corresponding to the range of naturally occurring biochemical networks, the survival probability of adaptive and standard random walk become increasingly similar. The adaptive random walk can be used as an efficient message-passing algorithm on this class of graphs for large degree of rewiring.
Search for Directed Networks by Different Random Walk Strategies
Zhu, Zi-Qi; Jin, Xiao-Ling; Huang, Zhi-Long
2012-03-01
A comparative study is carried out on the efficiency of five different random walk strategies searching on directed networks constructed based on several typical complex networks. Due to the difference in search efficiency of the strategies rooted in network clustering, the clustering coefficient in a random walker's eye on directed networks is defined and computed to be half of the corresponding undirected networks. The search processes are performed on the directed networks based on Erdös—Rényi model, Watts—Strogatz model, Barabási—Albert model and clustered scale-free network model. It is found that self-avoiding random walk strategy is the best search strategy for such directed networks. Compared to unrestricted random walk strategy, path-iteration-avoiding random walks can also make the search process much more efficient. However, no-triangle-loop and no-quadrangle-loop random walks do not improve the search efficiency as expected, which is different from those on undirected networks since the clustering coefficient of directed networks are smaller than that of undirected networks.
A New Random Walk for Replica Detection in WSNs
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
A New Random Walk for Replica Detection in WSNs.
Aalsalem, Mohammed Y; Khan, Wazir Zada; Saad, N M; Hossain, Md Shohrab; Atiquzzaman, Mohammed; Khan, Muhammad Khurram
2016-01-01
Wireless Sensor Networks (WSNs) are vulnerable to Node Replication attacks or Clone attacks. Among all the existing clone detection protocols in WSNs, RAWL shows the most promising results by employing Simple Random Walk (SRW). More recently, RAND outperforms RAWL by incorporating Network Division with SRW. Both RAND and RAWL have used SRW for random selection of witness nodes which is problematic because of frequently revisiting the previously passed nodes that leads to longer delays, high expenditures of energy with lower probability that witness nodes intersect. To circumvent this problem, we propose to employ a new kind of constrained random walk, namely Single Stage Memory Random Walk and present a distributed technique called SSRWND (Single Stage Memory Random Walk with Network Division). In SSRWND, single stage memory random walk is combined with network division aiming to decrease the communication and memory costs while keeping the detection probability higher. Through intensive simulations it is verified that SSRWND guarantees higher witness node security with moderate communication and memory overheads. SSRWND is expedient for security oriented application fields of WSNs like military and medical.
First steps in random walks from tools to applications
Klafter, J
2011-01-01
The name ""random walk"" for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of ""Nature"". The same year, a similar problem was formulated by Albert Einstein in one of his Annus Mirabilis works. Even earlier such a problem was posed by Louis Bachelier in his thesis devoted to the theory of financial speculations in 1900. Nowadays the theory of random walks has proved useful in physics andchemistry (diffusion, reactions, mixing in flows), economics, biology (from animal spread to motion of subcel
Maximal Increments of Local Time of a Random Walk
Jain, Naresh C.; Pruitt, William E.
1987-01-01
Let $(S_j)$ be a lattice random walk, i.e., $S_j = X_1 + \\cdots + X_j$, where $X_1, X_2,\\ldots$ are independent random variables with values in $\\mathbb{Z}$ and common nondegenerate distribution $F$. Let $\\{t_n\\}$ be a nondecreasing sequence of positive integers, $t_n \\leq n$, and $L^\\ast_n = \\max_{0\\leq j\\leq n-t_n}(L_{j+t_n} - L_j)$, where $L_n = \\sum^n_{j=1}1_{\\{0\\}}(S_j)$, the number of times zero is visited by the random walk by time $n$. Assuming that the random walk is recurrent and sa...
Decoherence in optimized quantum random-walk search algorithm
Zhang Yu-Chao; Bao Wan-Su; Wang Xiang; Fu Xiang-Qun
2015-01-01
This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative. (paper)
A random walk down Main Street
David Matthew Levinson
2016-08-01
Full Text Available US suburbs have often been characterized by their relatively low walk accessibility compared to more urban environments, and US urban environments have been char- acterized by low walk accessibility compared to cities in other countries. Lower overall density in the suburbs implies that activities, if spread out, would have a greater distance between them. But why should activities be spread out instead of developed contiguously? This brief research note builds a positive model for the emergence of contiguous development along “Main Street” to illustrate the trade-offs that result in the built environment we observe. It then suggests some policy interventions to place a “thumb on the scale” to choose which parcels will develop in which sequence to achieve socially preferred outcomes.
The use of random walk in field theory
Brydges, D.
1984-01-01
Ferromagnetic spin systems and gauge theories where the gauge group is topologically a sphere, e.g. Z 2 , U(1) and SU(2) are related to the theory of random walk and random surfaces respectively. I survey some applications of this theme to the phi 4 field theories. (orig.)
A generalized model via random walks for information filtering
Ren, Zhuo-Ming; Kong, Yixiu; Shang, Ming-Sheng; Zhang, Yi-Cheng
2016-01-01
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. - Highlights: • We propose a generalized recommendation model employing the random walk dynamics. • The proposed model with single and hybrid of degree information is analyzed. • A strategy with the hybrid degree information improves precision of recommendation.
A generalized model via random walks for information filtering
Ren, Zhuo-Ming, E-mail: zhuomingren@gmail.com [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland); Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, ChongQing, 400714 (China); Kong, Yixiu [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland); Shang, Ming-Sheng, E-mail: msshang@cigit.ac.cn [Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, ChongQing, 400714 (China); Zhang, Yi-Cheng [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland)
2016-08-06
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. - Highlights: • We propose a generalized recommendation model employing the random walk dynamics. • The proposed model with single and hybrid of degree information is analyzed. • A strategy with the hybrid degree information improves precision of recommendation.
Dynamical correlations for vicious random walk with a wall
Nagao, Taro
2003-01-01
A one-dimensional system of nonintersecting Brownian particles is constructed as the diffusion scaling limit of Fisher's vicious random walk model. N Brownian particles start from the origin at time t=0 and undergo mutually avoiding motion until a finite time t=T. Dynamical correlation functions among the walkers are exactly evaluated in the case with a wall at the origin. Taking an asymptotic limit N→∞, we observe discontinuous transitions in the dynamical correlations. It is further shown that the vicious walk model with a wall is equivalent to a parametric random matrix model describing the crossover between the Bogoliubov-deGennes universality classes
Application of continuous-time random walk to statistical arbitrage
Sergey Osmekhin
2015-01-01
Full Text Available An analytical statistical arbitrage strategy is proposed, where the distribution of the spread is modelled as a continuous-time random walk. Optimal boundaries, computed as a function of the mean and variance of the firstpassage time ofthe spread,maximises an objective function. The predictability of the trading strategy is analysed and contrasted for two forms of continuous-time random walk processes. We found that the waiting-time distribution has a significant impact on the prediction of the expected profit for intraday trading
Navigation by anomalous random walks on complex networks.
Weng, Tongfeng; Zhang, Jie; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan
2016-11-23
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.
Navigation by anomalous random walks on complex networks
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.
Directed self-avoiding walks in random media
Santra, S. B.; Seitz, W. A.; Klein, D. J.
2001-01-01
Two types of directed self-avoiding walks (SAW's), namely, three-choice directed SAW and outwardly directed SAW, have been studied on infinite percolation clusters on the square lattice in two dimensions. The walks on the percolation clusters are generated via a Monte Carlo technique. The longitudinal extension R N and the transverse fluctuation W N have been measured as a function of the number of steps N. Slight swelling is observed in the longitudinal direction on the random lattices. A crossover from shrinking to swelling of the transverse fluctuations is found at a certain length N c of the walks. The exponents related to the transverse fluctuations are seen to be unchanged in the random media even as the percolation threshold is reached. The scaling function form of the extensions are verified
Metastability of Reversible Random Walks in Potential Fields
Landim, C.; Misturini, R.; Tsunoda, K.
2015-09-01
Let be an open and bounded subset of , and let be a twice continuously differentiable function. Denote by the discretization of , , and denote by the continuous-time, nearest-neighbor, random walk on which jumps from to at rate . We examine in this article the metastable behavior of among the wells of the potential F.
Adaptive importance sampling of random walks on continuous state spaces
Baggerly, K.; Cox, D.; Picard, R.
1998-01-01
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
Random-walk diffusion and drying of porous materials
Mehrafarin, M.; Faghihi, M.
2001-12-01
Based on random-walk diffusion, a microscopic model for drying is proposed to explain the characteristic features of the drying-rate curve of porous materials. The constant drying-rate period is considered as a normal diffusion process. The transition to the falling-rate regime is attributed to the fractal nature of porous materials which results in crossover to anomalous diffusion.
Random walk loop soups and conformal loop ensembles
van de Brug, T.; Camia, F.; Lis, M.
2016-01-01
The random walk loop soup is a Poissonian ensemble of lattice loops; it has been extensively studied because of its connections to the discrete Gaussian free field, but was originally introduced by Lawler and Trujillo Ferreras as a discrete version of the Brownian loop soup of Lawler and Werner, a
The Dickey-Fuller test for exponential random walks
Davies, P.L.; Krämer, W.
2003-01-01
A common test in econometrics is the Dickey–Fuller test, which is based on the test statistic . We investigate the behavior of the test statistic if the data yt are given by an exponential random walk exp(Zt) where Zt = Zt-1 + [sigma][epsilon]t and the [epsilon]t are independent and identically
Simulating intrafraction prostate motion with a random walk model
Tobias Pommer, PhD
2017-07-01
Conclusions: Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during delivery of radiation therapy.
Numerical solution of field theories using random walks
Barnes, T.; Daniell, G.J.
1985-01-01
We show how random walks in function space can be employed to evaluate field theoretic vacuum expectation values numerically. Specific applications which we study are the two-point function, mass gap, magnetization and classical solutions. This technique offers the promise of faster calculations using less computer memory than current methods. (orig.)
Averaging in SU(2) open quantum random walk
Ampadu Clement
2014-01-01
We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT
Averaging in SU(2) open quantum random walk
Clement, Ampadu
2014-03-01
We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.
Statistical shape model with random walks for inner ear segmentation
Pujadas, Esmeralda Ruiz; Kjer, Hans Martin; Piella, Gemma
2016-01-01
is required. We propose a new framework for segmentation of micro-CT cochlear images using random walks combined with a statistical shape model (SSM). The SSM allows us to constrain the less contrasted areas and ensures valid inner ear shape outputs. Additionally, a topology preservation method is proposed...
Stability of reaction fronts in random walk simulations
Nagy, Noemi; Izsak, F.
A model of propagating reaction fronts is given for simple autocatalytic reactions and the stability of the propagating reaction fronts are studied in several numerical experiments. The corresponding random walk simulations - extending of a recent algorithm - make possible the simultaneous treatment
Random walks of a quantum particle on a circle
Fjeldsoe, N.; Midtdal, J.; Ravndal, F.
1987-07-01
When the quantum planar rotor is put on a lattice, its dynamics can be approximated by random walks on a circle. This allows for fast and accurate Monto Carlo simulations to determine the topological charge of different configurations of the system and thereby the Θ-dependency of the lowest energy levels
Magnetic field line random walk in non-axisymmetric turbulence
Tautz, R.C.; Lerche, I.
2011-01-01
Including a random component of a magnetic field parallel to an ambient field introduces a mean perpendicular motion to the average field line. This effect is normally not discussed because one customarily chooses at the outset to ignore such a field component in discussing random walk and diffusion of field lines. A discussion of the basic effect is given, indicating that any random magnetic field with a non-zero helicity will lead to such a non-zero perpendicular mean motion. Several exact analytic illustrations are given of the effect as well as a simple numerical illustration. -- Highlights: → For magnetic field line random walk all magnetic field components are important. → Non-vanishing magnetic helicity leads to mean perpendicular motion. → Analytically exact stream functions illustrate that the novel transverse effect exists.
Renewal theory for perturbed random walks and similar processes
Iksanov, Alexander
2016-01-01
This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration. Being of major importance in modern probability theory, both theoretical and applied, these objects have been used to model various phenomena in the natural sciences as well as in insurance and finance. The book also presents the many significant results and efficient techniques and methods that have been worked out in the last decade. The first chapter is devoted to perturbed random walks and discusses their asymptotic behavior and various functionals pertaining to them, including supremum and first-passage time. The second chapter examines perpetuities, presenting results on continuity of their distributions and the existence of moments, as well as weak convergence of divergent perpetuities. Focusing on random processes with immigration, the third chapter investigates the existence of moments, describes long-time behavior and discusses limit theorems, both with and without scaling. Chapters fou...
Amnestically Induced Persistence in Random Walks
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.
Return probabilities for the reflected random walk on N_0
Essifi, R.; Peigné, M.
2015-01-01
Let \\((Y_n)\\) be a sequence of i.i.d. \\(\\mathbb{Z }\\)-valued random variables with law \\(\\mu \\). The reflected random walk \\((X_n)\\) is defined recursively by \\(X_0=x \\in \\mathbb{N }_0, X_{n+1}=\\vert X_n+Y_{n+1}\\vert \\). Under mild hypotheses on the law \\(\\mu \\), it is proved that, for any \\( y \\in
On reflexivity of random walks in a random environment on a metric space
Rozikov, U.A.
2002-11-01
In this paper, we consider random walks in random environments on a countable metric space when jumps of the walks of the fractions are finite. The transfer probabilities of the random walk from x is an element of G (where G is the considering metric space) are defined by vector p(x) is an element of R k , k>1, where {p(x), x is an element of G} is the set of independent and indentically distributed random vectors. For the random walk, a sufficient condition of nonreflexivity is obtained. Examples for metric spaces Z d free groups and free product of finite numbers cyclic groups of the second order and some other metric spaces are considered. (author)
Random walk of the baryon number
Kazaryan, A.M.; Khlebnikov, S.Y.; Shaposhnikov, M.E.
1989-01-01
A new approach is suggested for the anomalous nonconservation of baryon number in the electroweak theory at high temperatures. Arguments are presented in support of the idea that the baryon-number changing reactions may be viewed as random Markov processes. Making use of the general theory of Markov processes, the Fokker--Planck equation for the baryon-number distribution density is obtained and kinetic coefficients are calculated
Random Walks and Diffusions on Graphs and Databases An Introduction
Blanchard, Philippe
2011-01-01
Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.
Random walks, critical phenomena, and triviality in quantum field theory
Fernandez, R.; Froehlich, J.; Sokal, A.D.
1992-01-01
The subject of this book is equilibrium statistical mechanics - in particular the theory of critical phenomena - and quantum field theory. A general review of the theory of critical phenomena in spin systems, field theories, and random-walk and random-surface models is presented. Among the more technical topics treated in this book, the central theme is the use of random-walk representations as a tool to derive correlation inequalities. The consequences of these inequalities for critical-exponent theory and the triviality question in quantum field theory are expounded in detail. The book contains some previously unpublished results. It addresses both the researcher and the graduate student in modern statistical mechanics and quantum field theory. (orig.)
Winning quick and dirty: the greedy random walk
Ben-Naim, E; Redner, S
2004-01-01
As a strategy to complete games quickly, we investigate one-dimensional random walks where the step length increases deterministically upon each return to the origin. When the step length after the kth return equals k, the displacement of the walk x grows linearly in time. Asymptotically, the probability distribution of displacements is a purely exponentially decaying function of |x|/t. The probability E(t, L) for the walk to escape a bounded domain of size L at time t decays algebraically in the long-time limit, E(t, L) ∼ L/t 2 . Consequently, the mean escape time (t) ∼ Lln L, while (t n ) ∼ L 2n-1 for n > 1. Corresponding results are derived when the step length after the kth return scales as k α for α > 0
Spherically symmetric random walks. II. Dimensionally dependent critical behavior
Bender, C.M.; Boettcher, S.; Meisinger, P.N.
1996-01-01
A recently developed model of random walks on a D-dimensional hyperspherical lattice, where D is not restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state distributions of random walkers are obtained for all dimensions D approx-gt 0 by solving a discrete eigenvalue problem. These distributions exhibit dimensionally dependent critical behavior as a function of the birth rate. This remarkably simple model exhibits a second-order phase transition with a universal, nontrivial critical exponent for all dimensions D approx-gt 0. copyright 1996 The American Physical Society
Reheating-volume measure for random-walk inflation
Winitzki, Sergei
2008-01-01
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.
Biasing the random walk of a molecular motor
Astumian, R Dean [Department of Physics, University of Maine, Orono, ME 04469-5709 (United States)
2005-11-30
Biomolecular motors are often described in mechanical terms, with analogy to cars, turbines, judo throws, levers, etc. It is important to remember however that because of their small size, and because of the aqueous environment in which molecular motors move, viscous drag and thermal noise dominate the inertial forces that drive macroscopic machines. The sequence of motions-conformational changes-by which a motor protein moves can best be described as a random walk, with transitions from one state to another occurring by thermal activation over energy barriers. In this paper I will address the question of how this random walk is biased by a non-equilibrium chemical reaction (ATP hydrolysis) so that the motor molecule moves preferentially (with almost unit certainty) in one direction, even when an external force is applied to drive it in the opposite direction. I will also discuss how these 'soft matter' motors can achieve thermodynamic efficiencies of nearly 100%.
Biasing the random walk of a molecular motor
Astumian, R Dean
2005-01-01
Biomolecular motors are often described in mechanical terms, with analogy to cars, turbines, judo throws, levers, etc. It is important to remember however that because of their small size, and because of the aqueous environment in which molecular motors move, viscous drag and thermal noise dominate the inertial forces that drive macroscopic machines. The sequence of motions-conformational changes-by which a motor protein moves can best be described as a random walk, with transitions from one state to another occurring by thermal activation over energy barriers. In this paper I will address the question of how this random walk is biased by a non-equilibrium chemical reaction (ATP hydrolysis) so that the motor molecule moves preferentially (with almost unit certainty) in one direction, even when an external force is applied to drive it in the opposite direction. I will also discuss how these 'soft matter' motors can achieve thermodynamic efficiencies of nearly 100%
A generalized model via random walks for information filtering
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.
Limit distributions of random walks on stochastic matrices
condition that μm(P) > 0 for some positive integer m (as opposed to just 1, instead of m, considered in [1]), where μm is the ...... Limit distributions of random walks. 611. PROPOSITION 3.2. Let f be as introduced before Proposition 3.1. The probability distribution λ is the image of π by the map b ↦→ f (b). In other words, λ = ∑.
Random walks on semaphore codes and delay de Bruijn semigroups
Rhodes, John; Schilling, Anne; Silva, Pedro V.
2015-01-01
© 2016 World Scientific Publishing Company. We develop a new approach to random walks on de Bruijn graphs over the alphabet A through right congruences on A k , defined using the natural right action of A + . A major role is played by special right congruences, which correspond to semaphore codes and allow an easier computation of the hitting time. We show how right congruences can be approximated by special right congruences.
Autocatalytic polymerization generates persistent random walk of crawling cells.
Sambeth, R; Baumgaertner, A
2001-05-28
The autocatalytic polymerization kinetics of the cytoskeletal actin network provides the basic mechanism for a persistent random walk of a crawling cell. It is shown that network remodeling by branching processes near the cell membrane is essential for the bimodal spatial stability of the network which induces a spontaneous breaking of isotropic cell motion. Details of the phenomena are analyzed using a simple polymerization model studied by analytical and simulation methods.
Simulating intrafraction prostate motion with a random walk model.
Pommer, Tobias; Oh, Jung Hun; Munck Af Rosenschöld, Per; Deasy, Joseph O
2017-01-01
Prostate motion during radiation therapy (ie, intrafraction motion) can cause unwanted loss of radiation dose to the prostate and increased dose to the surrounding organs at risk. A compact but general statistical description of this motion could be useful for simulation of radiation therapy delivery or margin calculations. We investigated whether prostate motion could be modeled with a random walk model. Prostate motion recorded during 548 radiation therapy fractions in 17 patients was analyzed and used for input in a random walk prostate motion model. The recorded motion was categorized on the basis of whether any transient excursions (ie, rapid prostate motion in the anterior and superior direction followed by a return) occurred in the trace and transient motion. This was separately modeled as a large step in the anterior/superior direction followed by a returning large step. Random walk simulations were conducted with and without added artificial transient motion using either motion data from all observed traces or only traces without transient excursions as model input, respectively. A general estimate of motion was derived with reasonable agreement between simulated and observed traces, especially during the first 5 minutes of the excursion-free simulations. Simulated and observed diffusion coefficients agreed within 0.03, 0.2 and 0.3 mm 2 /min in the left/right, superior/inferior, and anterior/posterior directions, respectively. A rapid increase in variance at the start of observed traces was difficult to reproduce and seemed to represent the patient's need to adjust before treatment. This could be estimated somewhat using artificial transient motion. Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during
From elongated spanning trees to vicious random walks
Gorsky, A.; Nechaev, S.; Poghosyan, V. S.; Priezzhev, V. B.
2012-01-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of the paths are grouped in a fashion a $k$--leg watermelon. For large distance $r$ between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as $r^{-\
First-passage exponents of multiple random walks
Ben-Naim, E; Krapivsky, P L
2010-01-01
We investigate first-passage statistics of an ensemble of N noninteracting random walks on a line. Starting from a configuration in which all particles are located in the positive half-line, we study S n (t), the probability that the nth rightmost particle remains in the positive half-line up to time t. This quantity decays algebraically, S n (t)∼t -β n , in the long-time limit. Interestingly, there is a family of nontrivial first-passage exponents, β 1 2 N-1 ; the only exception is the two-particle case where β 1 = 1/3. In the N → ∞ limit, however, the exponents attain a scaling form, β n (N) → β(z) with z=(n-N/2)/√N. We also demonstrate that the smallest exponent decays exponentially with N. We deduce these results from first-passage kinetics of a random walk in an N-dimensional cone and confirm them using numerical simulations. Additionally, we investigate the family of exponents that characterizes leadership statistics of multiple random walks and find that in this case, the cone provides an excellent approximation.
A random walk rule for phase I clinical trials.
Durham, S D; Flournoy, N; Rosenberger, W F
1997-06-01
We describe a family of random walk rules for the sequential allocation of dose levels to patients in a dose-response study, or phase I clinical trial. Patients are sequentially assigned the next higher, same, or next lower dose level according to some probability distribution, which may be determined by ethical considerations as well as the patient's response. It is shown that one can choose these probabilities in order to center dose level assignments unimodally around any target quantile of interest. Estimation of the quantile is discussed; the maximum likelihood estimator and its variance are derived under a two-parameter logistic distribution, and the maximum likelihood estimator is compared with other nonparametric estimators. Random walk rules have clear advantages: they are simple to implement, and finite and asymptotic distribution theory is completely worked out. For a specific random walk rule, we compute finite and asymptotic properties and give examples of its use in planning studies. Having the finite distribution theory available and tractable obviates the need for elaborate simulation studies to analyze the properties of the design. The small sample properties of our rule, as determined by exact theory, compare favorably to those of the continual reassessment method, determined by simulation.
Random walk theory and exchange rate dynamics in transition economies
Gradojević Nikola
2010-01-01
Full Text Available This paper investigates the validity of the random walk theory in the Euro-Serbian dinar exchange rate market. We apply Andrew Lo and Archie MacKinlay's (1988 conventional variance ratio test and Jonathan Wright's (2000 non-parametric ranks and signs based variance ratio tests to the daily Euro/Serbian dinar exchange rate returns using the data from January 2005 - December 2008. Both types of variance ratio tests overwhelmingly reject the random walk hypothesis over the data span. To assess the robustness of our findings, we examine the forecasting performance of a non-linear, nonparametric model in the spirit of Francis Diebold and James Nason (1990 and find that it is able to significantly improve upon the random walk model, thus confirming the existence of foreign exchange market imperfections in a small transition economy such as Serbia. In the last part of the paper, we conduct a comparative study on how our results relate to those of other transition economies in the region.
Ant-inspired density estimation via random walks.
Musco, Cameron; Su, Hsin-Hao; Lynch, Nancy A
2017-10-03
Many ant species use distributed population density estimation in applications ranging from quorum sensing, to task allocation, to appraisal of enemy colony strength. It has been shown that ants estimate local population density by tracking encounter rates: The higher the density, the more often the ants bump into each other. We study distributed density estimation from a theoretical perspective. We prove that a group of anonymous agents randomly walking on a grid are able to estimate their density within a small multiplicative error in few steps by measuring their rates of encounter with other agents. Despite dependencies inherent in the fact that nearby agents may collide repeatedly (and, worse, cannot recognize when this happens), our bound nearly matches what would be required to estimate density by independently sampling grid locations. From a biological perspective, our work helps shed light on how ants and other social insects can obtain relatively accurate density estimates via encounter rates. From a technical perspective, our analysis provides tools for understanding complex dependencies in the collision probabilities of multiple random walks. We bound the strength of these dependencies using local mixing properties of the underlying graph. Our results extend beyond the grid to more general graphs, and we discuss applications to size estimation for social networks, density estimation for robot swarms, and random walk-based sampling for sensor networks.
On the pertinence to Physics of random walks induced by random dynamical systems: a survey
Petritis, Dimitri
2016-01-01
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 (( S_a)_a , ( p_a)_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 p_a (x) , the transformation S_a and evolve to S_a (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. (paper)
Social aggregation in pea aphids: experiment and random walk modeling.
Christa Nilsen
Full Text Available 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.
A Novel Algorithm of Quantum Random Walk in Server Traffic Control and Task Scheduling
Dong Yumin
2014-01-01
Full Text Available A quantum random walk optimization model and algorithm in network cluster server traffic control and task scheduling is proposed. In order to solve the problem of server load balancing, we research and discuss the distribution theory of energy field in quantum mechanics and apply it to data clustering. We introduce the method of random walk and illuminate what the quantum random walk is. Here, we mainly research the standard model of one-dimensional quantum random walk. For the data clustering problem of high dimensional space, we can decompose one m-dimensional quantum random walk into m one-dimensional quantum random walk. In the end of the paper, we compare the quantum random walk optimization method with GA (genetic algorithm, ACO (ant colony optimization, and SAA (simulated annealing algorithm. In the same time, we prove its validity and rationality by the experiment of analog and simulation.
History dependent quantum random walks as quantum lattice gas automata
Shakeel, Asif, E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu; Love, Peter J., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu [Department of Physics, Haverford College, Haverford, Pennsylvania 19041 (United States); Meyer, David A., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu [Department of Mathematics, University of California/San Diego, La Jolla, California 92093-0112 (United States)
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.
Conditioned random walks and interaction-driven condensation
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. (paper)
Karpatkin, Herb; Cohen, Evan T; Rzetelny, Adam; Parrott, J Scott; Breismeister, Breanne; Hartman, Ryan; Luu, Ronald; Napolione, Danielle
2015-07-01
Fatigue is a common, disabling symptom experienced by persons with multiple sclerosis (MS). Evidence shows that intermittent exercise is associated in improved performance and negligible fatigue. The purpose of this study was to examine whether subjects with MS walk greater distances with less fatigue under intermittent (INT) or continuous (CONT) walking condition. Twenty-seven subjects with MS (median Extended Disability Severity Scale 3.5, interquartile range 1.6) walked in the CONT (ie, 6 uninterrupted minutes) and INT (ie, three 2-minute walking bouts) conditions in a randomized crossover. Distance was measured for the entire 6-minute walking period and each 2-minute increment. Fatigue was measured as the difference in a visual analog scale of fatigue (ΔVAS-F) immediately preceding and following each trial. Participants walked greater distances in the INT condition compared to the CONT condition (P = 0.005). There was a significant interaction of walking condition and time (P walked in the INT condition changed across time. ΔVAS-F was significantly lower in the INT condition than in the CONT condition (P = 0.036). Subjects with MS walked farther, and with less fatigue, when walking intermittently rather than continuously. Persons with MS may be able to tolerate a greater dose of walking training if the walking bouts are intermittent. Further study to determine the benefits of a walking exercise program using intermittent walking is recommended.Video Abstract available for additional insights from the authors (Supplemental Digital Content 1, http://links.lww.com/JNPT/A103).
Intermittent random walks: transport regimes and implications on search strategies
Gomez Portillo, Ignacio; Campos, Daniel; Méndez, Vicenç
2011-01-01
We construct a transport model for particles that alternate rests of random duration and flights with random velocities. The model provides a balance equation for the mesoscopic particle density obtained from the continuous-time random walk framework. By assuming power laws for the distributions of waiting times and flight durations (for any velocity distribution with finite moments) we have found that the model can yield all the transport regimes ranging from subdiffusion to ballistic depending on the values of the characteristic exponents of the distributions. In addition, if the exponents satisfy a simple relationship it is shown how the competition between the tails of the distributions gives rise to a diffusive transport. Finally, we explore how the details of this intermittent transport process affect the success probability in an optimal search problem where an individual searcher looks for a target distributed (heterogeneously) in space. All the results are conveniently checked with numerical simulations
Why the null matters: statistical tests, random walks and evolution.
Sheets, H D; Mitchell, C E
2001-01-01
A number of statistical tests have been developed to determine what type of dynamics underlie observed changes in morphology in evolutionary time series, based on the pattern of change within the time series. The theory of the 'scaled maximum', the 'log-rate-interval' (LRI) method, and the Hurst exponent all operate on the same principle of comparing the maximum change, or rate of change, in the observed dataset to the maximum change expected of a random walk. Less change in a dataset than expected of a random walk has been interpreted as indicating stabilizing selection, while more change implies directional selection. The 'runs test' in contrast, operates on the sequencing of steps, rather than on excursion. Applications of these tests to computer generated, simulated time series of known dynamical form and various levels of additive noise indicate that there is a fundamental asymmetry in the rate of type II errors of the tests based on excursion: they are all highly sensitive to noise in models of directional selection that result in a linear trend within a time series, but are largely noise immune in the case of a simple model of stabilizing selection. Additionally, the LRI method has a lower sensitivity than originally claimed, due to the large range of LRI rates produced by random walks. Examination of the published results of these tests show that they have seldom produced a conclusion that an observed evolutionary time series was due to directional selection, a result which needs closer examination in light of the asymmetric response of these tests.
Discrete random walk models for space-time fractional diffusion
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-01-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order α is part of (0,2] and skewness θ (moduleθ≤{α,2-α}), and the first-order time derivative with a Caputo derivative of order β is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation
Random walk on a population of random walkers
Agliari, E; Burioni, R; Cassi, D; Neri, F M
2008-01-01
We consider a population of N labelled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label X(t) of the walker carrying the excitation at time t can be viewed as a stochastic process, where the transition probabilities are a stochastic process themselves. Upon mapping onto two simpler processes, the quantities characterizing X(t) can be calculated in the limit of long times and low walkers density. The results are compared with numerical simulations. Several different topologies for the substrate underlying diffusion are considered
How fast does a random walk cover a torus?
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.
Knots and Random Walks in Vibrated Granular Chains
Ben-Naim, E.; Daya, Z. A.; Vorobieff, P.; Ecke, R. E.
2001-01-01
We study experimentally 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
Correlation effects in a discrete quantum random walk
Stang, J B; Rezakhani, A T; Sanders, B C
2009-01-01
We introduce memory-dependent discrete-time quantum random walk models by adding uncorrelated memory terms and also by modifying the Hamiltonian of the walker to include couplings with memory-keeping agents. We next study numerically the correlation effects in these models. We also propose a correlation exponent as a relevant and promising tool for investigation of correlation or memory (hence non-Markovian) effects. Our analysis can easily be applied to more realistic models in which different regimes may emerge because of competition between different underlying physical mechanisms
Time-delayed fronts from biased random walks
Fort, Joaquim; Pujol, Toni
2007-01-01
We generalize a previous model of time-delayed reaction-diffusion fronts (Fort and Mendez 1999 Phys. Rev. Lett. 82 867) to allow for a bias in the microscopic random walk of particles or individuals. We also present a second model which takes the time order of events (diffusion and reproduction) into account. As an example, we apply them to the human invasion front across the USA in the 19th century. The corrections relative to the previous model are substantial. Our results are relevant to physical and biological systems with anisotropic fronts, including particle diffusion in disordered lattices, population invasions, the spread of epidemics, etc
Universality in random-walk models with birth and death
Bender, C.M.; Boettcher, S.; Meisinger, P.N.
1995-01-01
Models of random walks are considered in which walkers are born at one site and die at all other sites. Steady-state distributions of walkers exhibit dimensionally dependent critical behavior as a function of the birth rate. Exact analytical results for a hyperspherical lattice yield a second-order phase transition with a nontrivial critical exponent for all positive dimensions D≠2, 4. Numerical studies of hypercubic and fractal lattices indicate that these exact results are universal. This work elucidates the adsorption transition of polymers at curved interfaces. copyright 1995 The American Physical Society
Random-walk simulation of selected aspects of dissipative collisions
Toeke, J.; Gobbi, A.; Matulewicz, T.
1984-11-01
Internuclear thermal equilibrium effects and shell structure effects in dissipative collisions are studied numerically within the framework of the model of stochastic exchanges by applying the random-walk technique. Effective blocking of the drift through the mass flux induced by the temperature difference, while leaving the variances of the mass distributions unaltered is found possible, provided an internuclear potential barrier is present. Presence of the shell structure is found to lead to characteristic correlations between the consecutive exchanges. Experimental evidence for the predicted effects is discussed. (orig.)
Record statistics of a strongly correlated time series: random walks and Lévy flights
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.
Continuous time quantum random walks in free space
Eichelkraut, Toni; Vetter, Christian; Perez-Leija, Armando; Christodoulides, Demetrios; Szameit, Alexander
2014-05-01
We show theoretically and experimentally that two-dimensional continuous time coherent random walks are possible in free space, that is, in the absence of any external potential, by properly tailoring the associated initial wave function. These effects are experimentally demonstrated using classical paraxial light. Evidently, the usage of classical beams to explore the dynamics of point-like quantum particles is possible since both phenomena are mathematically equivalent. This in turn makes our approach suitable for the realization of random walks using different quantum particles, including electrons and photons. To study the spatial evolution of a wavefunction theoretically, we consider the one-dimensional paraxial wave equation (i∂z +1/2 ∂x2) Ψ = 0 . Starting with the initially localized wavefunction Ψ (x , 0) = exp [ -x2 / 2σ2 ] J0 (αx) , one can show that the evolution of such Gaussian-apodized Bessel envelopes within a region of validity resembles the probability pattern of a quantum walker traversing a uniform lattice. In order to generate the desired input-field in our experimental setting we shape the amplitude and phase of a collimated light beam originating from a classical HeNe-Laser (633 nm) utilizing a spatial light modulator.
The Random Walk Model Based on Bipartite Network
Zhang Man-Dun
2016-01-01
Full Text Available With the continuing development of the electronic commerce and growth of network information, there is a growing possibility for citizens to be confused by the information. Though the traditional technology of information retrieval have the ability to relieve the overload of information in some extent, it can not offer a targeted personality service based on user’s interests and activities. In this context, the recommendation algorithm arose. In this paper, on the basis of conventional recommendation, we studied the scheme of random walk based on bipartite network and the application of it. We put forward a similarity measurement based on implicit feedback. In this method, a uneven character vector is imported(the weight of item in the system. We put forward a improved random walk pattern which make use of partial or incomplete neighbor information to create recommendation information. In the end, there is an experiment in the real data set, the recommendation accuracy and practicality are improved. We promise the reality of the result of the experiment
Do MENA stock market returns follow a random walk process?
Salim Lahmiri
2013-01-01
Full Text Available In this research, three variance ratio tests: the standard variance ratio test, the wild bootstrap multiple variance ratio test, and the non-parametric rank scores test are adopted to test the random walk hypothesis (RWH of stock markets in Middle East and North Africa (MENA region using most recent data from January 2010 to September 2012. The empirical results obtained by all three econometric tests show that the RWH is strongly rejected for Kuwait, Tunisia, and Morocco. However, the standard variance ratio test and the wild bootstrap multiple variance ratio test reject the null hypothesis of random walk in Jordan and KSA, while non-parametric rank scores test do not. We may conclude that Jordan and KSA stock market are weak efficient. In sum, the empirical results suggest that return series in Kuwait, Tunisia, and Morocco are predictable. In other words, predictable patterns that can be exploited in these markets still exit. Therefore, investors may make profits in such less efficient markets.
A Random Walk Approach to Query Informative Constraints for Clustering.
Abin, Ahmad Ali
2017-08-09
This paper presents a random walk approach to the problem of querying informative constraints for clustering. The proposed method is based on the properties of the commute time, that is the expected time taken for a random walk to travel between two nodes and return, on the adjacency graph of data. Commute time has the nice property of that, the more short paths connect two given nodes in a graph, the more similar those nodes are. Since computing the commute time takes the Laplacian eigenspectrum into account, we use this property in a recursive fashion to query informative constraints for clustering. At each recursion, the proposed method constructs the adjacency graph of data and utilizes the spectral properties of the commute time matrix to bipartition the adjacency graph. Thereafter, the proposed method benefits from the commute times distance on graph to query informative constraints between partitions. This process iterates for each partition until the stop condition becomes true. Experiments on real-world data show the efficiency of the proposed method for constraints selection.
An explicit semantic relatedness measure based on random walk
HU Sihui
2016-10-01
Full Text Available The semantic relatedness calculation of open domain knowledge network is a significant issue.In this paper,pheromone strategy is drawn from the thought of ant colony algorithm and is integrated into the random walk which is taken as the basic framework of calculating the semantic relatedness degree.The pheromone distribution is taken as a criterion of determining the tightness degree of semantic relatedness.A method of calculating semantic relatedness degree based on random walk is proposed and the exploration process of calculating the semantic relatedness degree is presented in a dominant way.The method mainly contains Path Select Model(PSM and Semantic Relatedness Computing Model(SRCM.PSM is used to simulate the path selection of ants and pheromone release.SRCM is used to calculate the semantic relatedness by utilizing the information returned by ants.The result indicates that the method could complete semantic relatedness calculation in linear complexity and extend the feasible strategy of semantic relatedness calculation.
Numerical modelling of random walk one-dimensional diffusion
Vamos, C.; Suciu, N.; Peculea, M.
1996-01-01
The evolution of a particle which moves on a discrete one-dimensional lattice, according to a random walk low, approximates better the diffusion process smaller the steps of the spatial lattice and time are. For a sufficiently large assembly of particles one can assume that their relative frequency at lattice knots approximates the distribution function of the diffusion process. This assumption has been tested by simulating on computer two analytical solutions of the diffusion equation: the Brownian motion and the steady state linear distribution. To evaluate quantitatively the similarity between the numerical and analytical solutions we have used a norm given by the absolute value of the difference of the two solutions. Also, a diffusion coefficient at any lattice knots and moment of time has been calculated, by using the numerical solution both from the diffusion equation and the particle flux given by Fick's low. The difference between diffusion coefficient of analytical solution and the spatial lattice mean coefficient of numerical solution constitutes another quantitative indication of the similarity of the two solutions. The results obtained show that the approximation depends first on the number of particles at each knot of the spatial lattice. In conclusion, the random walk is a microscopic process of the molecular dynamics type which permits simulations precision of the diffusion processes with given precision. The numerical method presented in this work may be useful both in the analysis of real experiments and for theoretical studies
Random-walk simulation of the Schrodinger equation: H+3
Anderson, J.B.
1975-01-01
A simple random-walk method for obtaining ab initio solutions of the Schrodinger equation is examined in its application to the case of the molecular ion H + 3 in the equilateral triangle configuration with side length R=1.66 bohr. The method, which is based on the similarity of the Schrodinger equation and the diffusion equation, involves the random movement of imaginary particles (psips) in electron configuration space subject to a variable chance of multiplication or disappearance. The computation requirements for high accuracy in determining energies of H + 3 are greater than those of existing LCAO--MO--SCF--CI methods. For more complex molecular systems the method may be competitive. (auth)
Random Walks in Stock Exchange Prices and the Vienna Stock Exchange
Huber, Peter
1995-01-01
This paper uses the multiple variance ratio test procedure developed by Chow and Denning (1993) to test for a random walk of stock returns on the Austrian Stock Exchange. I find that with daily data the test rejects the random walk hypothesis at all conventional significance levels for each and every title and for both indeces tested. Individual shares, however, do seem to follow a random walk when weekly returns are considered, while the hypothesis is rejected for both indices. Dieser Art...
Some Tests of Random Walk Hypothesis for Bulgarian Foreign Exchange Rates
Nikolai Gueorguiev
1993-01-01
The objective of this paper is to check if the exchange rate in newly emerged, relatively thin foreign exchange markets, follows a random walk pattern. The findings of the current study cast doubts on random walk presence in Bulgarian exchange rates against major international currencies. It turns out that the series of daily returns are stationary but correlated and therefore can be modelled better by higher-order ARIMA processes than by random walk.
Subdiffusivity of a random walk among a Poisson system of moving traps on ${\\mathbb Z}$
Athreya, Siva; Drewitz, Alexander; Sun, Rongfeng
2016-01-01
We consider a random walk among a Poisson system of moving traps on ${\\mathbb Z}$. In earlier work [DGRS12], 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 th...
The average inter-crossing number of equilateral random walks and polygons
Diao, Y; Dobay, A; Stasiak, A
2005-01-01
In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is a = 3ln2/8 ∼ 0.2599. In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance ρ apart and ρ is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of ρ. Our simulation result shows that the model in fact works very well for the entire range of ρ. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well
Complex networks: when random walk dynamics equals synchronization
Kriener, Birgit; Anand, Lishma; Timme, Marc
2012-01-01
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. (paper)
Scattering quantum random-walk search with errors
Gabris, A.; Kiss, T.; Jex, I.
2007-01-01
We analyze the realization of a quantum-walk search algorithm in a passive, linear optical network. The specific model enables us to consider the effect of realistic sources of noise and losses on the search efficiency. Photon loss uniform in all directions is shown to lead to the rescaling of search time. Deviation from directional uniformity leads to the enhancement of the search efficiency compared to uniform loss with the same average. In certain cases even increasing loss in some of the directions can improve search efficiency. We show that while we approach the classical limit of the general search algorithm by introducing random phase fluctuations, its utility for searching is lost. Using numerical methods, we found that for static phase errors the averaged search efficiency displays a damped oscillatory behavior that asymptotically tends to a nonzero value
Information filtering via biased random walk on coupled social network.
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.
A random walk in the land of precompound decay
Akkermans, J.M.
1982-09-01
Several aspects of precompound-decay (preequilibrium) reactions, relevant for the application to fusion-reactor design, are considered. Preequilibrium angular distributions are discussed in the framework of the generalized exciton model. A critical discussion of the theory is given and various refinements are suggested. A comparison is made with experimental data on 14 MeV neutron-induced reactions for a large number of nuclides covering the whole mass range. The exciton model is further generalized to the description of multiparticle emission. Preequilibrium effects in multiple emission are investigated. Computational aspects of preequilibrium theory are examined whereby the exact solution for the mean exciton-state lifetimes is derived in closed form. A random-walk model of precompound decay is developed. The dynamics of the nuclear relaxation process and the fluctuations originating from its stochastic nature are studied in detail. Uncertainty calculations are presented for the exciton-state lifetimes and the emission cross-sections. (Auth.)
Correlated continuous time random walk and option pricing
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.
From elongated spanning trees to vicious random walks
Gorsky, A.; Nechaev, S.; Poghosyan, V. S.; Priezzhev, V. B.
2013-05-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of k paths (k is odd) along branches of trees or, equivalently, k loop-erased random walks. Starting and ending points of the paths are grouped such that they form a k-leg watermelon. For large distance r between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as r-ν log r with ν = (k2 - 1) / 2. Considering the spanning forest stretched along the meridian of this watermelon, we show that the two-dimensional k-leg loop-erased watermelon exponent ν is converting into the scaling exponent for the reunion probability (at a given point) of k (1 + 1)-dimensional vicious walkers, ν˜ =k2 / 2. At the end, we express the conjectures about the possible relation to integrable systems.
From elongated spanning trees to vicious random walks
Gorsky, A.; Nechaev, S.; Poghosyan, V.S.; Priezzhev, V.B.
2013-01-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of k paths (k is odd) along branches of trees or, equivalently, k loop-erased random walks. Starting and ending points of the paths are grouped such that they form a k-leg watermelon. For large distance r between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as r −ν logr with ν=(k 2 −1)/2. Considering the spanning forest stretched along the meridian of this watermelon, we show that the two-dimensional k-leg loop-erased watermelon exponent ν is converting into the scaling exponent for the reunion probability (at a given point) of k(1+1)-dimensional vicious walkers, ν -tilde= k 2 /2. At the end, we express the conjectures about the possible relation to integrable systems
A random walk approach to stochastic neutron transport
Mulatier, Clelia de
2015-01-01
One of the key goals of nuclear reactor physics is to determine the distribution of the neutron population within a reactor core. This population indeed fluctuates due to the stochastic nature of the interactions of the neutrons with the nuclei of the surrounding medium: scattering, emission of neutrons from fission events and capture by nuclear absorption. Due to these physical mechanisms, the stochastic process performed by neutrons is a branching random walk. For most applications, the neutron population considered is very large, and all physical observables related to its behaviour, such as the heat production due to fissions, are well characterised by their average values. Generally, these mean quantities are governed by the classical neutron transport equation, called linear Boltzmann equation. During my PhD, using tools from branching random walks and anomalous diffusion, I have tackled two aspects of neutron transport that cannot be approached by the linear Boltzmann equation. First, thanks to the Feynman-Kac backward formalism, I have characterised the phenomenon of 'neutron clustering' that has been highlighted for low-density configuration of neutrons and results from strong fluctuations in space and time of the neutron population. Then, I focused on several properties of anomalous (non-exponential) transport, that can model neutron transport in strongly heterogeneous and disordered media, such as pebble-bed reactors. One of the novel aspects of this work is that problems are treated in the presence of boundaries. Indeed, even though real systems are finite (confined geometries), most of previously existing results were obtained for infinite systems. (author) [fr
Miguel eFERNANDEZ-DEL-OLMO
2014-09-01
Full Text Available 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. 22 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 Parkinson’s disease.
Random walk generated by random permutations of {1, 2, 3, ..., n + 1}
Oshanin, G; Voituriez, R
2004-01-01
We study properties of a non-Markovian random walk X (n) l , l = 0, 1, 2, ..., n, evolving in discrete time l on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the rise-and-descent sequences characterizing random permutations π of [n + 1] = {1, 2, 3, ..., n + 1}. We determine exactly the probability of finding the end-point X n = X (n) n of the trajectory of such a permutation-generated random walk (PGRW) at site X, and show that in the limit n → ∞ it converges to a normal distribution with a smaller, compared to the conventional Polya random walk, diffusion coefficient. We formulate, as well, an auxiliary stochastic process whose distribution is identical to the distribution of the intermediate points X (n) l , l < n, which enables us to obtain the probability measure of different excursions and to define the asymptotic distribution of the number of 'turns' of the PGRW trajectories
First-passage time asymptotics over moving boundaries for random walk bridges
Sloothaak, F.; Zwart, B.; Wachtel, V.
2017-01-01
We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with
Scaling Limit of Symmetric Random Walk in High-Contrast Periodic Environment
Piatnitski, A.; Zhizhina, E.
2017-11-01
The paper deals with the asymptotic properties of a symmetric random walk in a high contrast periodic medium in Z^d, d≥1. From the existing homogenization results it follows that under diffusive scaling the limit behaviour of this random walk need not be Markovian. The goal of this work is to show that if in addition to the coordinate of the random walk in Z^d we introduce an extra variable that characterizes the position of the random walk inside the period then the limit dynamics of this two-component process is Markov. We describe the limit process and observe that the components of the limit process are coupled. We also prove the convergence in the path space for the said random walk.
Dispersal of spores following a persistent random walk.
Bicout, D J; Sache, I
2003-03-01
A model of a persistent random walk is used to describe the transport and deposition of the spore dispersal process. In this model, the spore particle flies along straight line trajectories, with constant speed v, which are interrupted by scattering, originating from interaction of spores with the field and wind variations, which randomly change its direction. To characterize the spore dispersal gradients, we have derived analytical expressions of the deposition probability epsilon (r|v) of airborne spores as a function of the distance r from the spore source in an infinite free space and in a disk of radius R with an absorbing edge that mimics an agricultural field surrounded with fields of nonhost plants and bare land. It is found in the free space that epsilon (r|v) approximately e(-alphar/l), with alpha a function of l(d)/l, where l and l(d) are the scattering and deposition mean free paths, respectively. In the disk, however, epsilon (r|v) is an infinite series of Bessel functions and, exhibits three regimes: absorbing (Rl(d)).
The relationship between randomness and power-law distributed move lengths in random walk algorithms
Sakiyama, Tomoko; Gunji, Yukio-Pegio
2014-05-01
Recently, we proposed a new random walk algorithm, termed the REV algorithm, in which the agent alters the directional rule that governs it using the most recent four random numbers. Here, we examined how a non-bounded number, i.e., "randomness" regarding move direction, was important for optimal searching and power-law distributed step lengths in rule change. We proposed two algorithms: the REV and REV-bounded algorithms. In the REV algorithm, one of the four random numbers used to change the rule is non-bounded. In contrast, all four random numbers in the REV-bounded algorithm are bounded. We showed that the REV algorithm exhibited more consistent power-law distributed step lengths and flexible searching behavior.
A Monotonicity Result for the Range of a Perturbed Random Walk
Chen, Lung-Chi; Sun, Rongfeng
2012-01-01
We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of sites visited by the perturbed random walk up to time n is always larger than or equal to that for the unperturbed walk. This intriguing problem arises from the study of a particle among a Poisson system of moving traps with sub-diffusive trap motion. In pa...
Random Walk Particle Tracking For Multiphase Heat Transfer
Lattanzi, Aaron; Yin, Xiaolong; Hrenya, Christine
2017-11-01
As computing capabilities have advanced, direct numerical simulation (DNS) has become a highly effective tool for quantitatively predicting the heat transfer within multiphase flows. Here we utilize a hybrid DNS framework that couples the lattice Boltzmann method (LBM) to the random walk particle tracking (RWPT) algorithm. The main challenge of such a hybrid is that discontinuous fields pose a significant challenge to the RWPT framework and special attention must be given to the handling of interfaces. We derive a method for addressing discontinuities in the diffusivity field, arising at the interface between two phases. Analytical means are utilized to develop an interfacial tracer balance and modify the RWPT algorithm. By expanding the modulus of the stochastic (diffusive) step and only allowing a subset of the tracers within the high diffusivity medium to undergo a diffusive step, the correct equilibrium state can be restored (globally homogeneous tracer distribution). The new RWPT algorithm is implemented within the SUSP3D code and verified against a variety of systems: effective diffusivity of a static gas-solids mixture, hot sphere in unbounded diffusion, cooling sphere in unbounded diffusion, and uniform flow past a hot sphere.
Identifying diseases-related metabolites using random walk.
Hu, Yang; Zhao, Tianyi; Zhang, Ningyi; Zang, Tianyi; Zhang, Jun; Cheng, Liang
2018-04-11
Metabolites disrupted by abnormal state of human body are deemed as the effect of diseases. In comparison with the cause of diseases like genes, these markers are easier to be captured for the prevention and diagnosis of metabolic diseases. Currently, a large number of metabolic markers of diseases need to be explored, which drive us to do this work. The existing metabolite-disease associations were extracted from Human Metabolome Database (HMDB) using a text mining tool NCBO annotator as priori knowledge. Next we calculated the similarity of a pair-wise metabolites based on the similarity of disease sets of them. Then, all the similarities of metabolite pairs were utilized for constructing a weighted metabolite association network (WMAN). Subsequently, the network was utilized for predicting novel metabolic markers of diseases using random walk. Totally, 604 metabolites and 228 diseases were extracted from HMDB. From 604 metabolites, 453 metabolites are selected to construct the WMAN, where each metabolite is deemed as a node, and the similarity of two metabolites as the weight of the edge linking them. The performance of the network is validated using the leave one out method. As a result, the high area under the receiver operating characteristic curve (AUC) (0.7048) is achieved. The further case studies for identifying novel metabolites of diabetes mellitus were validated in the recent studies. In this paper, we presented a novel method for prioritizing metabolite-disease pairs. The superior performance validates its reliability for exploring novel metabolic markers of diseases.
Anomalous transport in turbulent plasmas and continuous time random walks
Balescu, R.
1995-01-01
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 t 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
Stochastic calculus for uncoupled continuous-time random walks.
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.
From elongated spanning trees to vicious random walks
Gorsky, A. [ITEP, B. Cheryomushkinskaya 25, 117218 Moscow (Russian Federation); Nechaev, S., E-mail: nechaev@lptms.u-psud.fr [LPTMS, Université Paris Sud, 91405 Orsay Cedex (France); P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 119991 Moscow (Russian Federation); Poghosyan, V.S. [Institute for Informatics and Automation Problems NAS of Armenia, 375044 Yerevan (Armenia); Priezzhev, V.B. [Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)
2013-05-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of k paths (k is odd) along branches of trees or, equivalently, k loop-erased random walks. Starting and ending points of the paths are grouped such that they form a k-leg watermelon. For large distance r between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as r{sup −ν}logr with ν=(k{sup 2}−1)/2. Considering the spanning forest stretched along the meridian of this watermelon, we show that the two-dimensional k-leg loop-erased watermelon exponent ν is converting into the scaling exponent for the reunion probability (at a given point) of k(1+1)-dimensional vicious walkers, ν{sup -tilde=}k{sup 2}/2. At the end, we express the conjectures about the possible relation to integrable systems.
Random walks on the braid group B3 and magnetic translations in hyperbolic geometry
Voituriez, Raphaeel
2002-01-01
We study random walks on the three-strand braid group B 3 , and in particular compute the drift, or average topological complexity of a random braid, as well as the probability of trivial entanglement. These results involve the study of magnetic random walks on hyperbolic graphs (hyperbolic Harper-Hofstadter problem), what enables to build a faithful representation of B 3 as generalized magnetic translation operators for the problem of a quantum particle on the hyperbolic plane
The linking number and the writhe of uniform random walks and polygons in confined spaces
Panagiotou, E; Lambropoulou, S; Millett, K C
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(n 2 ). 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(√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.
Visser, Andre
2008-01-01
The movement of plankton, either by turbulent mixing or their own inherent motility, can be simulated in a Lagrangian framework as a random walk. Validation of random walk simulations is essential. There is a continuum of mathematically valid stochastic integration schemes upon which random walk...
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.
Self-Trapping Self-Repelling Random Walks
Grassberger, Peter
2017-10-01
Although the title seems self-contradictory, it does not contain a misprint. The model we study is a seemingly minor modification of the "true self-avoiding walk" model of Amit, Parisi, and Peliti in two dimensions. The walks in it are self-repelling up to a characteristic time T* (which depends on various parameters), but spontaneously (i.e., without changing any control parameter) become self-trapping after that. For free walks, T* is astronomically large, but on finite lattices the transition is easily observable. In the self-trapped regime, walks are subdiffusive and intermittent, spending longer and longer times in small areas until they escape and move rapidly to a new area. In spite of this, these walks are extremely efficient in covering finite lattices, as measured by average cover times.
Walking adaptability therapy after stroke: study protocol for a randomized controlled trial.
Timmermans, Celine; Roerdink, Melvyn; van Ooijen, Marielle W; Meskers, Carel G; Janssen, Thomas W; Beek, Peter J
2016-08-26
Walking in everyday life requires the ability to adapt walking to the environment. This adaptability is often impaired after stroke, and this might contribute to the increased fall risk after stroke. To improve safe community ambulation, walking adaptability training might be beneficial after stroke. This study is designed to compare the effects of two interventions for improving walking speed and walking adaptability: treadmill-based C-Mill therapy (therapy with augmented reality) and the overground FALLS program (a conventional therapy program). We hypothesize that C-Mill therapy will result in better outcomes than the FALLS program, owing to its expected greater amount of walking practice. This is a single-center parallel group randomized controlled trial with pre-intervention, post-intervention, retention, and follow-up tests. Forty persons after stroke (≥3 months) with deficits in walking or balance will be included. Participants will be randomly allocated to either C-Mill therapy or the overground FALLS program for 5 weeks. Both interventions will incorporate practice of walking adaptability and will be matched in terms of frequency, duration, and therapist attention. Walking speed, as determined by the 10 Meter Walking Test, will be the primary outcome measure. Secondary outcome measures will pertain to walking adaptability (10 Meter Walking Test with context or cognitive dual-task and Interactive Walkway assessments). Furthermore, commonly used clinical measures to determine walking ability (Timed Up-and-Go test), walking independence (Functional Ambulation Category), balance (Berg Balance Scale), and balance confidence (Activities-specific Balance Confidence scale) will be used, as well as a complementary set of walking-related assessments. The amount of walking practice (the number of steps taken per session) will be registered using the treadmill's inbuilt step counter (C-Mill therapy) and video recordings (FALLS program). This process measure will
Transduction on Directed Graphs via Absorbing Random Walks.
De, Jaydeep; Zhang, Xiaowei; Lin, Feng; Cheng, Li
2017-08-11
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications.Different from existing research efforts that either only deal with undirected graphs or circumvent directionality by means of symmetrization, we propose a novel random walk approach on directed graphs using absorbing Markov chains, which can be regarded as maximizing the accumulated expected number of visits from the unlabeled transient states. Our algorithm is simple, easy to implement, and works with large-scale graphs on binary, multiclass, and multi-label prediction problems. Moreover, it is capable of preserving the graph structure even when the input graph is sparse and changes over time, as well as retaining weak signals presented in the directed edges. We present its intimate connections to a number of existing methods, including graph kernels, graph Laplacian based methods, and interestingly, spanning forest of graphs. Its computational complexity and the generalization error are also studied. Empirically our algorithm is systematically evaluated on a wide range of applications, where it has shown to perform competitively comparing to a suite of state-of-the-art methods. In particular, our algorithm is shown to work exceptionally well with large sparse directed graphs with e.g. millions of nodes and tens of millions of edges, where it significantly outperforms other state-of-the-art methods. In the dynamic graph setting involving insertion or deletion of nodes and edge-weight changes over time, it also allows efficient online updates that produce the same results as of the batch update counterparts.
Movie Recommendation using Random Walks over the Contextual Graph
Bogers, Toine
Recommender systems have become an essential tool in fighting information overload. However, the majority of recommendation algorithms focus only on using ratings information, while disregarding information about the context of the recommendation process. We present ContextWalk, a recommendation...
Covering Ground: Movement Patterns and Random Walk Behavior in Aquilonastra anomala Sea Stars.
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.
Random walks with shape prior for cochlea segmentation in ex vivo μCT
Ruiz Pujadas, Esmeralda; Kjer, Hans Martin; Piella, Gemma
2016-01-01
Purpose Cochlear implantation is a safe and effective surgical procedure to restore hearing in deaf patients. However, the level of restoration achieved may vary due to differences in anatomy, implant type and surgical access. In order to reduce the variability of the surgical outcomes, we...... propose a new framework for cochlea segmentation in ex vivo μCT images using random walks where a distance-based shape prior is combined with a region term estimated by a Gaussian mixture model. The prior is also weighted by a confidence map to adjust its influence according to the strength of the image...... contour. Random walks is performed iteratively, and the prior mask is aligned in every iteration. Results We tested the proposed approach in ten μCT data sets and compared it with other random walks-based segmentation techniques such as guided random walks (Eslami et al. in Med Image Anal 17...
Mathematical conversations multicolor problems, problems in the theory of numbers, and random walks
Dynkin, E B
2006-01-01
Comprises Multicolor Problems, dealing with map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; Random Walks, addressing basic problems in probability theory. 1963 edition.
A Realization of a Quasi-Random Walk for Atoms in Time-Dependent Optical Potentials
Torsten Hinkel
2015-09-01
Full Text Available We consider the time dependent dynamics of an atom in a two-color pumped cavity, longitudinally through a side mirror and transversally via direct driving of the atomic dipole. The beating of the two driving frequencies leads to a time dependent effective optical potential that forces the atom into a non-trivial motion, strongly resembling a discrete random walk behavior between lattice sites. We provide both numerical and analytical analysis of such a quasi-random walk behavior.
Genetic Analysis of Daily Maximum Milking Speed by a Random Walk Model in Dairy Cows
Karacaören, Burak; Janss, Luc; Kadarmideen, Haja
Data were obtained from dairy cows stationed at research farm ETH Zurich for maximum milking speed. The main aims of this paper are a) to evaluate if the Wood curve is suitable to model mean lactation curve b) to predict longitudinal breeding values by random regression and random walk models of ...... filter applications: random walk model could give online prediction of breeding values. Hence without waiting for whole lactation records, genetic evaluation could be made when the daily or monthly data is available......Data were obtained from dairy cows stationed at research farm ETH Zurich for maximum milking speed. The main aims of this paper are a) to evaluate if the Wood curve is suitable to model mean lactation curve b) to predict longitudinal breeding values by random regression and random walk models...... of maximum milking speed. Wood curve did not provide a good fit to the data set. Quadratic random regressions gave better predictions compared with the random walk model. However random walk model does not need to be evaluated for different orders of regression coefficients. In addition with the Kalman...
Human mammary epithelial cells exhibit a bimodal correlated random walk pattern.
Potdar, Alka A; Jeon, Junhwan; Weaver, Alissa M; Quaranta, Vito; Cummings, Peter T
2010-03-10
Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells) that exist in multi-cellular organisms (humans) follow a bimodal correlated random walk (BCRW). Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases) each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation). Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.
Human mammary epithelial cells exhibit a bimodal correlated random walk pattern.
Alka A Potdar
2010-03-01
Full Text Available Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells that exist in multi-cellular organisms (humans follow a bimodal correlated random walk (BCRW.Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation.Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.
Kiskis, J.; Narayanan, R.; Vranas, P.
1993-01-01
The authors study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments, the authors show that the critical exponent v describing the vanishing of the physical mass at the critical point is equal to v θ /d w , where d w is the Hausdorff dimension of the walk, and v θ = var-phi, where var-phi is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is var-phi/v for O(N) models. 3 refs
Walking improves sleep in individuals with cancer: a meta-analysis of randomized, controlled trials.
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.
Diffusion coefficients for multi-step persistent random walks on lattices
Gilbert, Thomas; Sanders, David P
2010-01-01
We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with a two-step memory on different classes of one-, two- and higher dimensional lattices.
Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications
Zhongtuan Zheng
2017-01-01
Full Text Available This paper investigates, both theoretically and numerically, preferential random walks (PRW on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW. Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.
Richards, Elizabeth A; Ogata, Niwako; Cheng, Ching-Wei
2016-01-01
To facilitate physical activity (PA) adoption and maintenance, promotion of innovative population-level strategies that focus on incorporating moderate-intensity lifestyle PAs are needed. The purpose of this randomized controlled trial was to evaluate the Dogs, Physical Activity, and Walking intervention, a 3-month, social cognitive theory (SCT), e-mail-based PA intervention. In a longitudinal, repeated-measures design, 49 dog owners were randomly assigned to a control (n = 25) or intervention group (n = 24). The intervention group received e-mail messages (twice weekly for 4 weeks and weekly for 8 weeks) designed to influence SCT constructs of self-efficacy, self-regulation, outcome expectations and expectancies, and social support. At baseline and every 3 months through 1 year, participants completed self-reported questionnaires of individual, interpersonal, and PA variables. Linear mixed models were used to assess for significant differences in weekly minutes of dog walking and theoretical constructs between groups (intervention and control) across time. To test self-efficacy as a mediator of social support for dog walking, tests for mediation were conducted using the bootstrapping technique. With the exception of Month 9, participants in the intervention group accumulated significantly more weekly minutes of dog walking than the control group. On average, the intervention group accumulated 58.4 more minutes (SD = 18.1) of weekly dog walking than the control group (p dog walking. Results indicate that a simple SCT-based e-mail intervention is effective in increasing and maintaining an increase in dog walking among dog owners at 12-month follow-up. In light of these findings, it may be advantageous to design dog walking interventions that focus on increasing self-efficacy for dog walking by fostering social support.
A Non-Random Walk Down Hollywood Boulevard
Lepori, Gabriele
affect (i.e. grief, proxied by the death of Hollywood Walk of Fame celebrities) on people’s willingness to invest in risky assets (proxied by the daily performance of the U.S. stock market). Using a sample of 1,374 celebrity deaths over the period 1926-2009 and controlling for seasonalities, economic....../environmental factors, and market liquidity, I find that the death of popular and beloved celebrities is immediately followed by a 16 basis point increase in stock returns, which is consistent with a rise in the net demand for risky instruments. I also find evidence that the size of this celebrity-death effect...
Chaos, periodic chaos, and the random-walk problem
Kozak, J.J.; Musho, M.K.; Hatlee, M.D.
1982-01-01
The authors have studied whether numerically generated sequences from the logistic parabola f/sub b/(x) = 4bx(1-x) with b,xelement of[0,1], for values of b above the Feigenbaum critical value b/sub infinity/, are truly chaotic or whether they are periodic but with exceedingly large periods and very long transients. Using the logistic parabola the authors calculate via Monte Carlo simulation the average walk length for trapping on a one-dimensional lattice with a centrosymmetric trap. Comparison with exact results suggests that the only ''truly chaotic'' sequence is the one for which b = 1
Evolution of the concentration PDF in random environments modeled by global random walk
Suciu, Nicolae; Vamos, Calin; Attinger, Sabine; Knabner, Peter
2013-04-01
The evolution of the probability density function (PDF) of concentrations of chemical species transported in random environments is often modeled by ensembles of notional particles. The particles move in physical space along stochastic-Lagrangian trajectories governed by Ito equations, with drift coefficients given by the local values of the resolved velocity field and diffusion coefficients obtained by stochastic or space-filtering upscaling procedures. A general model for the sub-grid mixing also can be formulated as a system of Ito equations solving for trajectories in the composition space. The PDF is finally estimated by the number of particles in space-concentration control volumes. In spite of their efficiency, Lagrangian approaches suffer from two severe limitations. Since the particle trajectories are constructed sequentially, the demanded computing resources increase linearly with the number of particles. Moreover, the need to gather particles at the center of computational cells to perform the mixing step and to estimate statistical parameters, as well as the interpolation of various terms to particle positions, inevitably produce numerical diffusion in either particle-mesh or grid-free particle methods. To overcome these limitations, we introduce a global random walk method to solve the system of Ito equations in physical and composition spaces, which models the evolution of the random concentration's PDF. The algorithm consists of a superposition on a regular lattice of many weak Euler schemes for the set of Ito equations. Since all particles starting from a site of the space-concentration lattice are spread in a single numerical procedure, one obtains PDF estimates at the lattice sites at computational costs comparable with those for solving the system of Ito equations associated to a single particle. The new method avoids the limitations concerning the number of particles in Lagrangian approaches, completely removes the numerical diffusion, and
Simulation of quantum systems with random walks: A new algorithm for charged systems
Ceperley, D.
1983-01-01
Random walks with branching have been used to calculate exact properties of the ground state of quantum many-body systems. In this paper, a more general Green's function identity is derived which relates the potential energy, a trial wavefunction, and a trial density matrix to the rules of a branched random walk. It is shown that an efficient algorithm requires a good trial wavefunction, a good trial density matrix, and a good sampling of this density matrix. An accurate density matrix is constructed for Coulomb systems using the path integral formula. The random walks from this new algorithm diffuse through phase space an order of magnitude faster than the previous Green's Function Monte Carlo method. In contrast to the simple diffusion Monte Carlo algorithm, it is exact method. Representative results are presented for several molecules
Novel pseudo-random number generator based on quantum random walks
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.
Novel pseudo-random number generator based on quantum random walks.
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.
High Dimensional Spectral Graph Theory and Non-backtracking Random Walks on Graphs
Kempton, Mark
This thesis has two primary areas of focus. First we study connection graphs, which are weighted graphs in which each edge is associated with a d-dimensional rotation matrix for some fixed dimension d, in addition to a scalar weight. Second, we study non-backtracking random walks on graphs, which are random walks with the additional constraint that they cannot return to the immediately previous state at any given step. Our work in connection graphs is centered on the notion of consistency, that is, the product of rotations moving from one vertex to another is independent of the path taken, and a generalization called epsilon-consistency. We present higher dimensional versions of the combinatorial Laplacian matrix and normalized Laplacian matrix from spectral graph theory, and give results characterizing the consistency of a connection graph in terms of the spectra of these matrices. We generalize several tools from classical spectral graph theory, such as PageRank and effective resistance, to apply to connection graphs. We use these tools to give algorithms for sparsification, clustering, and noise reduction on connection graphs. In non-backtracking random walks, we address the question raised by Alon et. al. concerning how the mixing rate of a non-backtracking random walk to its stationary distribution compares to the mixing rate for an ordinary random walk. Alon et. al. address this question for regular graphs. We take a different approach, and use a generalization of Ihara's Theorem to give a new proof of Alon's result for regular graphs, and to extend the result to biregular graphs. Finally, we give a non-backtracking version of Polya's Random Walk Theorem for 2-dimensional grids.
Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile
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.
Ding, Jian; Li, Li
2018-06-01
We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.
First-passage time asymptotics over moving boundaries for random walk bridges
Sloothaak, F.; Zwart, B.; Wachtel, V.
2017-01-01
We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent -1/2, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the re...
Emergence of an optimal search strategy from a simple random walk.
Sakiyama, Tomoko; Gunji, Yukio-Pegio
2013-09-06
In reports addressing animal foraging strategies, it has been stated that Lévy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths.
Pólya number and first return of bursty random walk: Rigorous solutions
Wan, J.; Xu, X. P.
2012-03-01
The recurrence properties of random walks can be characterized by Pólya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we investigate Pólya number and first return for bursty random walk on a line, in which the walk has different step size and moving probabilities. Using the concept of the Catalan number, we obtain exact results for first return probability, the average first return time and Pólya number for the first time. We show that Pólya number displays two different functional behavior when the walk deviates from the recurrent point. By utilizing the Lagrange inversion formula, we interpret our findings by transferring Pólya number to the closed-form solutions of an inverse function. We also calculate Pólya number using another approach, which corroborates our results and conclusions. Finally, we consider the recurrence properties and Pólya number of two variations of the bursty random walk model.
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.
Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki
2018-03-01
We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2}). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3}) and the level sets of the Gaussian free field ({d≥ 3}). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.
Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs
Salimi, S.; Jafarizadeh, M. A.
2009-01-01
In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product Cayley graphs (complete cycle, complete K n , charter and n-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as t → ∞ but for quantum state is not always satisfied. (general)
Regularity of the Speed of Biased Random Walk in a One-Dimensional Percolation Model
Gantert, Nina; Meiners, Matthias; Müller, Sebastian
2018-03-01
We consider biased random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. Axelson-Fisk and Häggström established for this model a phase transition for the asymptotic linear speed \\overline{v} of the walk. Namely, there exists some critical value λ c>0 such that \\overline{v}>0 if λ \\in (0,λ c) and \\overline{v}=0 if λ ≥ λ c. We show that the speed \\overline{v} is continuous in λ on (0,∞) and differentiable on (0,λ c/2). Moreover, we characterize the derivative as a covariance. For the proof of the differentiability of \\overline{v} on (0,λ c/2), we require and prove a central limit theorem for the biased random walk. Additionally, we prove that the central limit theorem fails to hold for λ ≥ λ c/2.
Recurrence and Polya Number of General One-Dimensional Random Walks
Zhang Xiaokun; Wan Jing; Lu Jingju; Xu Xinping
2011-01-01
The recurrence properties of random walks can be characterized by Polya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random walk on a line, in which at each time step the walker can move to the left or right with probabilities l and r, or remain at the same position with probability o (l + r + o = 1). We calculate Polya number P of this model and find a simple expression for P as, P = 1 - Δ, where Δ is the absolute difference of l and r (Δ = |l - r|). We prove this rigorous expression by the method of creative telescoping, and our result suggests that the walk is recurrent if and only if the left-moving probability l equals to the right-moving probability r. (general)
Nordic Walking and chronic low back pain: design of a randomized clinical trial
Hartvigsen Jan
2006-10-01
Full Text Available Abstract 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
Elliptic equation for random walks. Application to transport in microporous media
Shapiro, Alexander
2007-01-01
We consider a process of random walks with arbitrary residence time distribution. We show that in many cases this process may not be described by the classical (Fick) parabolic diffusion equation, but an elliptic equation. An additional term proportional to the second time derivative takes into a...
Wiesner, Ivo; Wiesnerová, Dana
2010-01-01
Roč. 54, č. 2 (2010), s. 353-356 ISSN 0006-3134 R&D Projects: GA AV ČR 1QS500510566 Institutional research plan: CEZ:AV0Z50510513 Keywords : begonia germplasm identification * random walk * primary sequence analysis Subject RIV: EB - Genetics ; Molecular Biology Impact factor: 1.582, year: 2010
A note on the random walk theory of recoil movement in prolonged ion bombardment
Koponen, Ismo
1994-01-01
A characteristic function is derived for the probability distribution of final positions of recoil atoms in prolonged ion bombardment of dense matter. The derivation is done within the framework of Poissonian random walk theory using a jump distribution, which is somewhat more general than those studied previously. ((orig.))
Cai, Bingjing; Wang, Haiying; Zheng, Huiru; Wang, Hui
2015-01-01
Systematic identification of protein complexes from protein-protein interaction networks (PPIs) is an important application of data mining in life science. Over the past decades, various new clustering techniques have been developed based on modelling PPIs as binary relations. Non-binary information of co-complex relations (prey/bait) in PPIs data derived from tandem affinity purification/mass spectrometry (TAP-MS) experiments has been unfairly disregarded. In this paper, we propose a Biased Random Walk based algorithm for detecting protein complexes from TAP-MS data, resulting in the random walk with restarting baits (RWRB). RWRB is developed based on Random walk with restart. The main contribution of RWRB is the incorporation of co-complex relations in TAP-MS PPI networks into the clustering process, by implementing a new restarting strategy during the process of random walk. Through experimentation on un-weighted and weighted TAP-MS data sets, we validated biological significance of our results by mapping them to manually curated complexes. Results showed that, by incorporating non-binary, co-membership information, significant improvement has been achieved in terms of both statistical measurements and biological relevance. Better accuracy demonstrates that the proposed method outperformed several state-of-the-art clustering algorithms for the detection of protein complexes in TAP-MS data.
Do exchange rates follow random walks? A variance ratio test of the ...
The random-walk hypothesis in foreign-exchange rates market is one of the most researched areas, particularly in developed economies. However, emerging markets in sub-Saharan Africa have received little attention in this regard. This study applies Lo and MacKinlay's (1988) conventional variance ratio test and Wright's ...
The Hidden Flow Structure and Metric Space of Network Embedding Algorithms Based on Random Walks.
Gu, Weiwei; Gong, Li; Lou, Xiaodan; Zhang, Jiang
2017-10-13
Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a network, such as the clustering and linking prediction but also learns the latent vector representation of the nodes which provides theoretical support for a variety of applications, such as visualization, link prediction, node classification, and recommendation. As the latest progress of the research, several algorithms based on random walks have been devised. Although those algorithms have drawn much attention for their high scores in learning efficiency and accuracy, there is still a lack of theoretical explanation, and the transparency of those algorithms has been doubted. Here, we propose an approach based on the open-flow network model to reveal the underlying flow structure and its hidden metric space of different random walk strategies on networks. We show that the essence of embedding based on random walks is the latent metric structure defined on the open-flow network. This not only deepens our understanding of random- walk-based embedding algorithms but also helps in finding new potential applications in network embedding.
Random walks and a simple chirally invariant lattice Hamiltonian without fermion doubling
Belyea, C.I.
1992-01-01
It is shown that there is a simple chirally-invariant lattice Hamiltonian for fermions which is doubling-free but non-Hermitian and which may be valuable in lattice Hamiltonian studies of quantum chromodynamics. A connection is established between the existence of random walk representations of spinor propagators and this doubling-free formulation, in analogy with Wilson fermions. 15 refs
Random Walk Model for the Growth of Monolayer in Dip Pen Nanolithography
Kim, H; Ha, S; Jang, J
2013-01-01
By using a simple random-walk model, we simulate the growth of a self-assembled monolayer (SAM) pattern generated in dip pen nanolithography (DPN). In this model, the SAM pattern grows mainly via the serial pushing of molecules deposited from the tip. We examine various SAM patterns, such as lines, crosses, and letters by changing the tip scan speed.
Durrett, Richard; Kesten, Harry; Spitzer, Frank
1991-01-01
..., made the transparency used in the printing process. STUDENTS OF FRANK SPITZERSTUDENTS OF FRANK SPITZER 1957 J. W. Lamperti, On the asymptotic behavior of recurrent and almostrecurrent events. 1964 W. W. Whitman, Some strong laws for random walks and Brownian motion. 1965 J. C. Mineka, The existence and uniqueness of positive solutions to the Wien...
Choon Sen Seah
2017-12-01
Full Text Available Microarray technology has become one of the elementary tools for researchers to study the genome of organisms. As the complexity and heterogeneity of cancer is being increasingly appreciated through genomic analysis, cancerous classification is an emerging important trend. Significant directed random walk is proposed as one of the cancerous classification approach which have higher sensitivity of risk gene prediction and higher accuracy of cancer classification. In this paper, the methodology and material used for the experiment are presented. Tuning parameter selection method and weight as parameter are applied in proposed approach. Gene expression dataset is used as the input datasets while pathway dataset is used to build a directed graph, as reference datasets, to complete the bias process in random walk approach. In addition, we demonstrate that our approach can improve sensitive predictions with higher accuracy and biological meaningful classification result. Comparison result takes place between significant directed random walk and directed random walk to show the improvement in term of sensitivity of prediction and accuracy of cancer classification.
Efficient tests for equivalence of hidden Markov processes and quantum random walks
U. Faigle; A. Schönhuth (Alexander)
2011-01-01
htmlabstractWhile two hidden Markov process (HMP) resp.~quantum random walk (QRW) parametrizations can differ from one another, the stochastic processes arising from them can be equivalent. Here a polynomial-time algorithm is presented which can determine equivalence of two HMP parametrizations
The supremuim of a negative drift random walk with dependent heavy-tailed steps
Mikosch, T; Smorodnitsky, G
Many important probabilistic models in queuing theory, insurance and finance deal with partial sums of a negative mean stationary process (a negative drift random walk), and the law of the supremum of such a process is used to calculate, depending on the context, the ruin probability, the steady
One-dimensional random walk of nanosized liquid Pb inclusions on dislocations in Al
Johnson, E.; Levinsen, M.T.; Steenstrup, S.
2004-01-01
to and perpendicular to the dislocations respectively. Movements parallel to the dislocation lines display properties of partially confined one-dimensional random walks where smaller inclusions can be seen to move over distances that are many times their own sizes. In contrast, the trajectories perpendicular...
The invariant measure of random walks in the quarter-plane: respresentation in geometric terms
Chen, Y.; Boucherie, Richardus J.; Goseling, Jasper
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these linear combinations such that the resulting measure may
Continuous-time random walk as a guide to fractional Schroedinger equation
Lenzi, E. K.; Ribeiro, H. V.; Mukai, H.; Mendes, R. S.
2010-01-01
We argue that the continuous-time random walk approach may be a useful guide to extend the Schroedinger equation in order to incorporate nonlocal effects, avoiding the inconsistencies raised by Jeng et al. [J. Math. Phys. 51, 062102 (2010)]. As an application, we work out a free particle in a half space, obtaining the time dependent solution by considering an arbitrary initial condition.
Necessary conditions for the invariant measure of a random walk to be a sum of geometric terms
Chen, Y.; Boucherie, Richardus J.; Goseling, Jasper
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as an infinite sum of geometric terms. We present necessary conditions for the invariant measure of a random walk to be a sum of geometric terms. We
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.
On the genealogy of branching random walks and of directed polymers
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.
Brownian Motion Problem: Random Walk and Beyond -RE ...
by their continuous bombardment by the surrounding molecules of much smaller size (Figure 1). This effect .... of continuous impacts of the randomly moving surround- ing molecules of the fluid (the 'npise'); (ii) these ..... ually increasing range of values due to integration and, thus, keeping it alive. Consequently, the observed ...
Burton Nicola W
2009-07-01
Full Text Available Abstract Background Interventions designed to increase workplace physical activity may not automatically reduce high volumes of sitting, a behaviour independently linked to chronic diseases such as obesity and type II diabetes. This study compared the impact two different walking strategies had on step counts and reported sitting times. Methods Participants were white-collar university employees (n = 179; age 41.3 ± 10.1 years; 141 women, who volunteered and undertook a standardised ten-week intervention at three sites. Pre-intervention step counts (Yamax SW-200 and self-reported sitting times were measured over five consecutive workdays. Using pre-intervention step counts, employees at each site were randomly allocated to a control group (n = 60; maintain normal behaviour, a route-based walking group (n = 60; at least 10 minutes sustained walking each workday or an incidental walking group (n = 59; walking in workday tasks. Workday step counts and reported sitting times were re-assessed at the beginning, mid- and endpoint of intervention and group mean± SD steps/day and reported sitting times for pre-intervention and intervention measurement points compared using a mixed factorial ANOVA; paired sample-t-tests were used for follow-up, simple effect analyses. Results A significant interactive effect (F = 3.5; p t = 3.9, p t = 2.5, p Conclusion Compared to controls, both route and incidental walking increased physical activity in white-collar employees. Our data suggests that workplace walking, particularly through incidental movement, also has the potential to decrease employee sitting times, but there is a need for on-going research using concurrent and objective measures of sitting, standing and walking.
Koschate, J; Drescher, U; Thieschäfer, L; Heine, O; Baum, K; Hoffmann, U
2016-12-01
This study aims to compare cardiorespiratory kinetics as a response to a standardised work rate protocol with pseudo-random binary sequences between cycling and walking in young healthy subjects. Muscular and pulmonary oxygen uptake (V̇O 2 ) kinetics as well as heart rate kinetics were expected to be similar for walking and cycling. Cardiac data and V̇O 2 of 23 healthy young subjects were measured in response to pseudo-random binary sequences. Kinetics were assessed applying time series analysis. Higher maxima of cross-correlation functions between work rate and the respective parameter indicate faster kinetics responses. Muscular V̇O 2 kinetics were estimated from heart rate and pulmonary V̇O 2 using a circulatory model. Muscular (walking vs. cycling [mean±SD in arbitrary units]: 0.40±0.08 vs. 0.41±0.08) and pulmonary V̇O 2 kinetics (0.35±0.06 vs. 0.35±0.06) were not different, although the time courses of the cross-correlation functions of pulmonary V̇O 2 showed unexpected biphasic responses. Heart rate kinetics (0.50±0.14 vs. 0.40±0.14; P=0.017) was faster for walking. Regarding the biphasic cross-correlation functions of pulmonary V̇O 2 during walking, the assessment of muscular V̇O 2 kinetics via pseudo-random binary sequences requires a circulatory model to account for cardio-dynamic distortions. Faster heart rate kinetics for walking should be considered by comparing results from cycle and treadmill ergometry. © Georg Thieme Verlag KG Stuttgart · New York.
Test of Random Walk Behavior in Karachi Stock Exchange
Muhammad Mudassar
2013-05-01
Full Text Available Study was carried out to check the random behavior of the Karachi Stock Exchange (KSE 100 Index during the period of past three financial years to know whether investors could generate abnormal profits during the period or otherwise. Tests used were Runs Test, ADF Test, PP Test and Autocorrelation Function Test. During the study it was found that the performance of KSE 100 Index remained in weak form of inefficiency and investors have been able to generate excessive returns on their investment most of the times.
Limit theorems for random walks on a strip in subdiffusive regimes
Dolgopyat, D; Goldsheid, I
2013-01-01
We study the asymptotic behaviour of occupation times of a transient random walk (RW) in a quenched random environment (RE) on a strip in a subdiffusive regime. The asymptotic behaviour of hitting times, which is a more traditional object of study, is exactly the same. As a particular case, we solve a long standing problem of describing the asymptotic behaviour of a RW with bounded jumps on a one-dimensional lattice. Our technique results from the development of ideas from our previous work (Dolgopyat and Goldsheid 2012 Commun. Math. Phys. 315 241–77) on the simple RWs in RE and those used in Bolthausen and Goldsheid (2000 Commun. Math. Phys. 214 429–47; 2008 Commun. Math. Phys. 278 253–88) and Goldsheid (2008 Probab. Theory Relat. Fields 141 471–511) for the study of random walks on a strip. (paper)
Continuous-Time Random Walk with multi-step memory: an application to market dynamics
Gubiec, Tomasz; Kutner, Ryszard
2017-11-01
An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary number of successive jumps of the process while waiting times between jumps are considered as i.i.d. random variables. This dependence was established analyzing empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale. Then, it was justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model appeared exactly analytically solvable. Therefore, it enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus, the present research significantly extends capabilities of the CTRW formalism. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Correlated random walks induced by dynamical wavefunction collapse
Bedingham, Daniel
2015-03-01
Wavefunction collapse models modify Schrödinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a genuine physical process [PRA 42, 78 (1990)]. 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. Furthermore, the diffusions of two sufficiently nearby particles are positively correlated -- it is more likely that the particles diffuse in the same direction than would happen if they behaved independently [PRA 89, 032713 (2014)]. The use of this effect is proposed as an experimental test of wave function collapse models in which pairs of nanoparticles are simultaneously released from nearby traps and allowed a brief period of free fall. The random displacements of the particles are then measured. The experiment must be carried out at sufficiently low temperature and pressure 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 class of viable wavefunction collapse models. Work supported by the Templeton World Charity Foundation.
A random walk on water (Henry Darcy Medal Lecture)
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
Interrelations between random walks on diagrams (graphs) with and without cycles.
Hill, T L
1988-05-01
Three topics are discussed. A discrete-state, continuous-time random walk with one or more absorption states can be studied by a presumably new method: some mean properties, including the mean time to absorption, can be found from a modified diagram (graph) in which each absorption state is replaced by a one-way cycle back to the starting state. The second problem is a random walk on a diagram (graph) with cycles. The walk terminates on completion of the first cycle. This walk can be replaced by an equivalent walk on a modified diagram with absorption. This absorption diagram can in turn be replaced by another modified diagram with one-way cycles back to the starting state, just as in the first problem. The third problem, important in biophysics, relates to a long-time continuous walk on a diagram with cycles. This diagram can be transformed (in two steps) to a modified, more-detailed, diagram with one-way cycles only. Thus, the one-way cycle fluxes of the original diagram can be found from the state probabilities of the modified diagram. These probabilities can themselves be obtained by simple matrix inversion (the probabilities are determined by linear algebraic steady-state equations). Thus, a simple method is now available to find one-way cycle fluxes exactly (previously Monte Carlo simulation was required to find these fluxes, with attendant fluctuations, for diagrams of any complexity). An incidental benefit of the above procedure is that it provides a simple proof of the one-way cycle flux relation Jn +/- = IIn +/- sigma n/sigma, where n is any cycle of the original diagram.
Conformal invariance self-avoiding walks in the plane or on a random surface
Duplantier, B.
1988-01-01
The two-dimensional (2D) properties of polymers embedded in a solvent, are studied. They are modeled on a lattice by self-avoiding walks. The polymer properties either in the plane with a fixed metric, or on a random 2D surface, where the metric has critical fluctuations, are considered. In the scope of the work, the following topics are discussed: the watermelon topology; the O(n) model and Coulomb gas technique; the model and critical behaviours of polymers on a two-dimensional random lattice; the conformal invariance in a random surface and higher topologies
Mikosch, Thomas Valentin; Moser, Martin
2013-01-01
We investigate the maximum increment of a random walk with heavy-tailed jump size distribution. Here heavy-tailedness is understood as regular variation of the finite-dimensional distributions. The jump sizes constitute a strictly stationary sequence. Using a continuous mapping argument acting...... on the point processes of the normalized jump sizes, we prove that the maximum increment of the random walk converges in distribution to a Fréchet distributed random variable....
Continuous-time random walks on networks with vertex- and time-dependent forcing.
Angstmann, C N; Donnelly, I C; Henry, B I; Langlands, T A M
2013-08-01
We have investigated the transport of particles moving as random walks on the vertices of a network, subject to vertex- and time-dependent forcing. We have derived the generalized master equations for this transport using continuous time random walks, characterized by jump and waiting time densities, as the underlying stochastic process. The forcing is incorporated through a vertex- and time-dependent bias in the jump densities governing the random walking particles. As a particular case, we consider particle forcing proportional to the concentration of particles on adjacent vertices, analogous to self-chemotactic attraction in a spatial continuum. Our algebraic and numerical studies of this system reveal an interesting pair-aggregation pattern formation in which the steady state is composed of a high concentration of particles on a small number of isolated pairs of adjacent vertices. The steady states do not exhibit this pair aggregation if the transport is random on the vertices, i.e., without forcing. The manifestation of pair aggregation on a transport network may thus be a signature of self-chemotactic-like forcing.
Intermittent random walks for an optimal search strategy: one-dimensional case
Oshanin, G; Wio, H S; Lindenberg, K; Burlatsky, S F
2007-01-01
We study the search kinetics of an immobile target by a concentration of randomly moving searchers. The object of the study is to optimize the probability of detection within the constraints of our model. The target is hidden on a one-dimensional lattice in the sense that searchers have no a priori information about where it is, and may detect it only upon encounter. The searchers perform random walks in discrete time n = 0,1,2,...,N, where N is the maximal time the search process is allowed to run. With probability α the searchers step on a nearest-neighbour, and with probability (1-α) they leave the lattice and stay off until they land back on the lattice at a fixed distance L away from the departure point. The random walk is thus intermittent. We calculate the probability P N that the target remains undetected up to the maximal search time N, and seek to minimize this probability. We find that P N is a non-monotonic function of α, and show that there is an optimal choice α opt (N) of α well within the intermittent regime, 0 opt (N) N can be orders of magnitude smaller compared to the 'pure' random walk cases α = 0 and α = 1
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.
Musho, M.K.; Kozak, J.J.
1984-01-01
A method is presented for calculating exactly the relative width (sigma 2 )/sup 1/2// , the skewness γ 1 , and the kurtosis γ 2 characterizing the probability distribution function for three random-walk models of diffusion-controlled processes. For processes in which a diffusing coreactant A reacts irreversibly with a target molecule B situated at a reaction center, three models are considered. The first is the traditional one of an unbiased, nearest-neighbor random walk on a d-dimensional periodic/confining lattice with traps; the second involves the consideration of unbiased, non-nearest-neigh bor (i.e., variable-step length) walks on the same d-dimensional lattice; and, the third deals with the case of a biased, nearest-neighbor walk on a d-dimensional lattice (wherein a walker experiences a potential centered at the deep trap site of the lattice). Our method, which has been described in detail elsewhere [P.A. Politowicz and J. J. Kozak, Phys. Rev. B 28, 5549 (1983)] is based on the use of group theoretic arguments within the framework of the theory of finite Markov processes
A partially reflecting random walk on spheres algorithm for electrical impedance tomography
Maire, Sylvain, E-mail: maire@univ-tln.fr [Laboratoire LSIS Equipe Signal et Image, Université du Sud Toulon-Var, Av. Georges Pompidou, BP 56, 83162 La Valette du Var Cedex (France); Simon, Martin, E-mail: simon@math.uni-mainz.de [Institute of Mathematics, Johannes Gutenberg University, 55099 Mainz (Germany)
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.
The continuous time random walk, still trendy: fifty-year history, state of art and outlook
Kutner, Ryszard; Masoliver, Jaume
2017-03-01
In this article we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism, the numerous modifications permitted by its flexibility, its various applications, and the promising perspectives in the various fields of knowledge. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We focused on a pivotal role of CTRWs mainly in anomalous stochastic processes discovered in physics and beyond. This article plays the role of an extended announcement of the Eur. Phys. J. B Special Issue [open-calls-for-papers/123-epj-b/1090-ctrw-50-years-on">http://epjb.epj.org/open-calls-for-papers/123-epj-b/1090-ctrw-50-years-on] containing articles which show incredible possibilities of the CTRWs. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Random walk, diffusion and mixing in simulations of scalar transport in fluid flows
Klimenko, A Y
2008-01-01
Physical similarity and mathematical equivalence of continuous diffusion and particle random walk form one of the cornerstones of modern physics and the theory of stochastic processes. In many applied models used in simulation of turbulent transport and turbulent combustion, mixing between particles is used to reflect the influence of the continuous diffusion terms in the transport equations. We show that the continuous scalar transport and diffusion can be accurately specified by means of mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme. This gives an alternative formulation for the stochastic process which is selected to represent the continuous diffusion. This paper focuses on statistical errors and deals with relatively simple cases, where one-particle distributions are sufficient for a complete description of the problem.
Effective degrees of freedom of a random walk on a fractal
Balankin, Alexander S.
2015-12-01
We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.
Stationary Probability and First-Passage Time of Biased Random Walk
Li Jing-Wen; Tang Shen-Li; Xu Xin-Ping
2016-01-01
In this paper, we consider the stationary probability and first-passage time of biased random walk on 1D chain, where at each step the walker moves to the left and right with probabilities p and q respectively (0 ⩽ p, q ⩽ 1, p + q = 1). We derive exact analytical results for the stationary probability and first-passage time as a function of p and q for the first time. Our results suggest that the first-passage time shows a double power-law F ∼ (N − 1) γ , where the exponent γ = 2 for N < |p − q| −1 and γ = 1 for N > |p − q| −1 . Our study sheds useful insights into the biased random-walk process. (paper)
The area distribution of two-dimensional random walks and non-Hermitian Hofstadter quantum mechanics
Matveenko, Sergey; Ouvry, Stéphane
2014-01-01
When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be obtained exactly (Mashkevich and Ouvry 2009 J. Stat. Phys. 137 71). We explicitly map this biased classical random system onto a non-Hermitian Hofstadter-like quantum model where a charged particle on a square lattice coupled to a perpendicular magnetic field hops only to the right. For the commensurate case, when the magnetic flux per unit cell is rational, an exact solution of the quantum model is obtained. The periodicity of the lattice allows one to relate traces of the Nth power of the Hamiltonian to probability distribution generating functions of biased walks of length N. (paper)
On Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment
Cao Xiaofeng; Deng Zongwei; Yang Chunbin
2008-01-01
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. We assume that the variation of the number of active sites has three possibilities in each update: to increase by 1 with probability f 1 , to decrease by 1 with probability f 2 , or remain unchanged with probability 1-f 1 -f 2 . This mimics the dynamics in the system. Power-law distributions of the lifetime are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions.
Effects of systematic phase errors on optimized quantum random-walk search algorithm
Zhang Yu-Chao; Bao Wan-Su; Wang Xiang; Fu Xiang-Qun
2015-01-01
This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover’s algorithm. (paper)
On properties of continuous-time random walks with non-Poissonian jump-times
Villarroel, Javier; Montero, Miquel
2009-01-01
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary time by recourse to renewal theory. The case of Erlang distributed times is analyzed in detail. Several concrete examples are considered.
Angular Random Walk Estimation of a Time-Domain Switching Micromachined Gyroscope
2016-10-19
angular random walk (ARW), bias instability, and scale factor instability. While there are methods to address issues with bias and scale factor...effects. Thus, it is expected that it will have low bias and scale factor instabilities. Simulated ARW performance of a particular incarnation of the...1 2. PARAMETRIC SYSTEM IDENTIFICATION BASED ON TIME-DOMAIN SWITCHING ........ 2 3. FINITE ELEMENT MODELING OF RESONATOR
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…
Accumulator and random-walk models of psychophysical discrimination: a counter-evaluation.
Vickers, D; Smith, P
1985-01-01
In a recent assessment of models of psychophysical discrimination, Heath criticises the accumulator model for its reliance on computer simulation and qualitative evidence, and contrasts it unfavourably with a modified random-walk model, which yields exact predictions, is susceptible to critical test, and is provided with simple parameter-estimation techniques. A counter-evaluation is presented, in which the approximations employed in the modified random-walk analysis are demonstrated to be seriously inaccurate, the resulting parameter estimates to be artefactually determined, and the proposed test not critical. It is pointed out that Heath's specific application of the model is not legitimate, his data treatment inappropriate, and his hypothesis concerning confidence inconsistent with experimental results. Evidence from adaptive performance changes is presented which shows that the necessary assumptions for quantitative analysis in terms of the modified random-walk model are not satisfied, and that the model can be reconciled with data at the qualitative level only by making it virtually indistinguishable from an accumulator process. A procedure for deriving exact predictions for an accumulator process is outlined.
Distributed clone detection in static wireless sensor networks: random walk with network division.
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.
Empirical scaling of the length of the longest increasing subsequences of random walks
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.
Distributed clone detection in static wireless sensor networks: random walk with network division.
Wazir Zada Khan
Full Text Available 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.
Bridging Weighted Rules and Graph Random Walks for Statistical Relational Models
Seyed Mehran Kazemi
2018-02-01
Full Text Available The aim of statistical relational learning is to learn statistical models from relational or graph-structured data. Three main statistical relational learning paradigms include weighted rule learning, random walks on graphs, and tensor factorization. These paradigms have been mostly developed and studied in isolation for many years, with few works attempting at understanding the relationship among them or combining them. In this article, we study the relationship between the path ranking algorithm (PRA, one of the most well-known relational learning methods in the graph random walk paradigm, and relational logistic regression (RLR, one of the recent developments in weighted rule learning. We provide a simple way to normalize relations and prove that relational logistic regression using normalized relations generalizes the path ranking algorithm. This result provides a better understanding of relational learning, especially for the weighted rule learning and graph random walk paradigms. It opens up the possibility of using the more flexible RLR rules within PRA models and even generalizing both by including normalized and unnormalized relations in the same model.
Gatto, Riccardo
2017-12-01
This article considers the random walk over Rp, with p ≥ 2, where a given particle starts at the origin and moves stepwise with uniformly distributed step directions and step lengths following a common distribution. Step directions and step lengths are independent. The case where the number of steps of the particle is fixed and the more general case where it follows an independent continuous time inhomogeneous counting process are considered. Saddlepoint approximations to the distribution of the distance from the position of the particle to the origin are provided. Despite the p-dimensional nature of the random walk, the computations of the saddlepoint approximations are one-dimensional and thus simple. Explicit formulae are derived with dimension p = 3: for uniformly and exponentially distributed step lengths, for fixed and for Poisson distributed number of steps. In these situations, the high accuracy of the saddlepoint approximations is illustrated by numerical comparisons with Monte Carlo simulation. Contribution to the "Topical Issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Mannerkorpi, Kaisa; Nordeman, Lena; Cider, ?sa; Jonsson, Gunilla
2010-01-01
Introduction The objective of this study was to investigate the effects of moderate-to-high intensity Nordic walking (NW) on functional capacity and pain in fibromyalgia (FM). Methods A total of 67 women with FM were recruited to the study and randomized either to moderate-to-high intensity Nordic Walking (n = 34, age 48 ? 7.8 years) or to a control group engaging in supervised low-intensity walking (LIW, n = 33, age 50 ? 7.6 years). Primary outcomes were the six-minute walk test (6MWT) and t...
Random walks in nanotube composites: Improved algorithms and the role of thermal boundary resistance
Duong, Hai M.; Papavassiliou, Dimitrios V.; Lee, Lloyd L.; Mullen, Kieran J.
2005-01-01
Random walk simulations of thermal walkers are used to study the effect of interfacial resistance on heat flow in randomly dispersed carbon nanotube composites. The adopted algorithm effectively makes the thermal conductivity of the nanotubes themselves infinite. The probability that a walker colliding with a matrix-nanotube interface reflects back into the matrix phase or crosses into the carbon nanotube phase is determined by the thermal boundary (Kapitza) resistance. The use of 'cold' and 'hot' walkers produces a steady state temperature profile that allows accurate determination of the thermal conductivity. The effects of the carbon nanotube orientation, aspect ratio, volume fraction, and Kapitza resistance on the composite effective conductivity are quantified
Random Walk Model for Cell-To-Cell Misalignments in Accelerator Structures
Stupakov, Gennady
2000-01-01
Due to manufacturing and construction errors, cells in accelerator structures can be misaligned relative to each other. As a consequence, the beam generates a transverse wakefield even when it passes through the structure on axis. The most important effect is the long-range transverse wakefield that deflects the bunches and causes growth of the bunch train projected emittance. In this paper, the effect of the cell-to-cell misalignments is evaluated using a random walk model that assumes that each cell is shifted by a random step relative to the previous one. The model is compared with measurements of a few accelerator structures
Random walks on a fluctuating lattice: A renormalization group approach applied in one dimension
Levermore, C.D.; Nadler, W.; Stein, D.L.
1995-01-01
We study the problem of a random walk on a lattice in which bonds connecting nearest-neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to solve for the effective diffusive behavior at long times. For one-dimensional lattices we obtain better quantitative agreement with simulation data than earlier effective medium results. Our technique works in principle in any dimension, although the amount of computation required rises with the dimensionality of the lattice
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
Vamos, C; Vereecken, H
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
Vamos, Calin; Suciu, Nicolae; Vereecken, Harry
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested
Random-walk approach to the d -dimensional disordered Lorentz gas
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.
Distribution of sizes of erased loops for loop-erased random walks
Dhar, Deepak; Dhar, Abhishek
1997-01-01
We study the distribution of sizes of erased loops for loop-erased random walks on regular and fractal lattices. We show that for arbitrary graphs the probability $P(l)$ of generating a loop of perimeter $l$ is expressible in terms of the probability $P_{st}(l)$ of forming a loop of perimeter $l$ when a bond is added to a random spanning tree on the same graph by the simple relation $P(l)=P_{st}(l)/l$. On $d$-dimensional hypercubical lattices, $P(l)$ varies as $l^{-\\sigma}$ for large $l$, whe...
GLOBAL RANDOM WALK SIMULATIONS FOR SENSITIVITY AND UNCERTAINTY ANALYSIS OF PASSIVE TRANSPORT MODELS
Nicolae Suciu
2011-07-01
Full Text Available The Global Random Walk algorithm (GRW performs a simultaneoustracking on a fixed grid of huge numbers of particles at costscomparable to those of a single-trajectory simulation by the traditional Particle Tracking (PT approach. Statistical ensembles of GRW simulations of a typical advection-dispersion process in groundwater systems with randomly distributed spatial parameters are used to obtain reliable estimations of the input parameters for the upscaled transport model and of their correlations, input-output correlations, as well as full probability distributions of the input and output parameters.
Combs-Miller, Stephanie A; Kalpathi Parameswaran, Anu; Colburn, Dawn; Ertel, Tara; Harmeyer, Amanda; Tucker, Lindsay; Schmid, Arlene A
2014-09-01
To compare the effects of body weight-supported treadmill training and overground walking training when matched for task and dose (duration/frequency/intensity) on improving walking function, activity, and participation after stroke. Single-blind, pilot randomized controlled trial with three-month follow-up. University and community settings. A convenience sample of participants (N = 20) at least six months post-stroke and able to walk independently were recruited. Thirty-minute walking interventions (body weight-supported treadmill training or overground walking training) were administered five times a week for two weeks. Intensity was monitored with the Borg Rating of Perceived Exertion Scale at five-minute increments to maintain a moderate training intensity. Walking speed (comfortable/fast 10-meter walk), walking endurance (6-minute walk), spatiotemporal symmetry, and the ICF Measure of Participation and ACTivity were assessed before, immediately after, and three months following the intervention. The overground walking training group demonstrated significantly greater improvements in comfortable walking speed compared with the body weight-supported treadmill training group immediately (change of 0.11 m/s vs. 0.06 m/s, respectively; p = 0.047) and three months (change of 0.14 m/s vs. 0.08 m/s, respectively; p = 0.029) after training. Only the overground walking training group significantly improved comfortable walking speed (p = 0.001), aspects of gait symmetry (p = 0.032), and activity (p = 0.003) immediately after training. Gains were maintained at the three-month follow-up (p training was more beneficial than body weight-supported treadmill training at improving self-selected walking speed for the participants in this study. © The Author(s) 2014.
A novel Random Walk algorithm with Compulsive Evolution for heat exchanger network synthesis
Xiao, Yuan; Cui, Guomin
2017-01-01
Highlights: • A novel Random Walk Algorithm with Compulsive Evolution is proposed for HENS. • A simple and feasible evolution strategy is presented in RWCE algorithm. • The integer and continuous variables of HEN are optimized simultaneously in RWCE. • RWCE is demonstrated a relatively strong global search ability in HEN optimization. - Abstract: The heat exchanger network (HEN) synthesis can be characterized as highly combinatorial, nonlinear and nonconvex, contributing to unmanageable computational time and a challenge in identifying the global optimal network design. Stochastic methods are robust and show a powerful global optimizing ability. Based on the common characteristic of different stochastic methods, namely randomness, a novel Random Walk algorithm with Compulsive Evolution (RWCE) is proposed to achieve the best possible total annual cost of heat exchanger network with the relatively simple and feasible evolution strategy. A population of heat exchanger networks is first randomly initialized. Next, the heat load of heat exchanger for each individual is randomly expanded or contracted in order to optimize both the integer and continuous variables simultaneously and to obtain the lowest total annual cost. Besides, when individuals approach to local optima, there is a certain probability for them to compulsively accept the imperfect networks in order to keep the population diversity and ability of global optimization. The presented method is then applied to heat exchanger network synthesis cases from the literature to compare the best results published. RWCE consistently has a lower computed total annual cost compared to previously published results.
Continuous-time random walks with reset events. Historical background and new perspectives
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.
Merom, Dafna; Grunseit, Anne; Eramudugolla, Ranmalee; Jefferis, Barbara; Mcneill, Jade; Anstey, Kaarin J
2016-01-01
A physically active lifestyle has the potential to prevent cognitive decline and dementia, yet the optimal type of physical activity/exercise remains unclear. Dance is of special interest as it complex sensorimotor rhythmic activity with additional cognitive, social, and affective dimensions. To determine whether dance benefits executive function more than walking, an activity that is simple and functional. Two-arm randomized controlled trial among community-dwelling older adults. The intervention group received 1 h of ballroom dancing twice weekly over 8 months (~69 sessions) in local community dance studios. The control group received a combination of a home walking program with a pedometer and optional biweekly group-based walking in local community park to facilitate socialization. Executive function tests: processing speed and task shift by the Trail Making Tests, response inhibition by the Stroop Color-Word Test, working memory by the Digit Span Backwards test, immediate and delayed verbal recall by the Rey Auditory Verbal Learning Test, and visuospatial recall by the Brief Visuospatial Memory Test (BVST). One hundred and fifteen adults (mean 69.5 years, SD 6.4) completed baseline and delayed baseline (3 weeks apart) before being randomized to either dance (n = 60) or walking (n = 55). Of those randomized, 79 (68%) completed the follow-up measurements (32 weeks from baseline). In the dance group only, "non-completers" had significantly lower baseline scores on all executive function tests than those who completed the full program. Intention-to-treat analyses showed no group effect. In a random effects model including participants who completed all measurements, adjusted for baseline score and covariates (age, education, estimated verbal intelligence, and community), a between-group effect in favor of dance was noted only for BVST total learning (Cohen's D Effect size 0.29, p = 0.07) and delayed recall (Cohen's D Effect size = 0
Banck-Petersen, Anna; Olsen, Cecilie K; Djurhuus, Sissal S; Herrstedt, Anita; Thorsen-Streit, Sarah; Ried-Larsen, Mathias; Østerlind, Kell; Osterkamp, Jens; Krarup, Peter-Martin; Vistisen, Kirsten; Mosgaard, Camilla S; Pedersen, Bente K; Højman, Pernille; Christensen, Jesper F
2018-03-01
Low physical activity level is associated with poor prognosis in patients with colorectal cancer (CRC). To increase physical activity, technology-based platforms are emerging and provide intriguing opportunities to prescribe and monitor active lifestyle interventions. The "Interval Walking in Colorectal Cancer"(I-WALK-CRC) study explores the feasibility and efficacy a home-based interval-walking intervention delivered by a smart-phone application in order to improve cardio-metabolic health profile among CRC survivors. The aim of the present report is to describe the design, methods and recruitment results of the I-WALK-CRC study.Methods/Results: The I-WALK-CRC study is a randomized controlled trial designed to evaluate the feasibility and efficacy of a home-based interval walking intervention compared to a waiting-list control group for physiological and patient-reported outcomes. Patients who had completed surgery for local stage disease and patients who had completed surgery and any adjuvant chemotherapy for locally advanced stage disease were eligible for inclusion. Between October 1st , 2015, and February 1st , 2017, 136 inquiries were recorded; 83 patients were eligible for enrollment, and 42 patients accepted participation. Age and employment status were associated with participation, as participants were significantly younger (60.5 vs 70.8 years, P CRC survivors was feasible but we aim to better the recruitment rate in future studies. Further, the study clearly favored younger participants. The I-WALK-CRC study will provide important information regarding feasibility and efficacy of a home-based walking exercise program in CRC survivors.
A random walk model for evaluating clinical trials involving serial observations.
Hopper, J L; Young, G P
1988-05-01
For clinical trials where the variable of interest is ordered and categorical (for example, disease severity, symptom scale), and where measurements are taken at intervals, it might be possible to achieve a greater discrimination between the efficacy of treatments by modelling each patient's progress as a stochastic process. The random walk is a simple, easily interpreted model that can be fitted by maximum likelihood using a maximization routine with inference based on standard likelihood theory. In general the model can allow for randomly censored data, incorporates measured prognostic factors, and inference is conditional on the (possibly non-random) allocation of patients. Tests of fit and of model assumptions are proposed, and application to two therapeutic trials of gastroenterological disorders are presented. The model gave measures of the rate of, and variability in, improvement for patients under different treatments. A small simulation study suggested that the model is more powerful than considering the difference between initial and final scores, even when applied to data generated by a mechanism other than the random walk model assumed in the analysis. It thus provides a useful additional statistical method for evaluating clinical trials.
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.
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.
Testing self-regulation interventions to increase walking using factorial randomized N-of-1 trials.
Sniehotta, Falko F; Presseau, Justin; Hobbs, Nicola; Araújo-Soares, Vera
2012-11-01
To investigate the suitability of N-of-1 randomized controlled trials (RCTs) as a means of testing the effectiveness of behavior change techniques based on self-regulation theory (goal setting and self-monitoring) for promoting walking in healthy adult volunteers. A series of N-of-1 RCTs in 10 normal and overweight adults ages 19-67 (M = 36.9 years). We randomly allocated 60 days within each individual to text message-prompted daily goal-setting and/or self-monitoring interventions in accordance with a 2 (step-count goal prompt vs. alternative goal prompt) × 2 (self-monitoring: open vs. blinded Omron-HJ-113-E pedometer) factorial design. Aggregated data were analyzed using random intercept multilevel models. Single cases were analyzed individually. The primary outcome was daily pedometer step counts over 60 days. Single-case analyses showed that 4 participants significantly increased walking: 2 on self-monitoring days and 2 on goal-setting days, compared with control days. Six participants did not benefit from the interventions. In aggregated analyses, mean step counts were higher on goal-setting days (8,499.9 vs. 7,956.3) and on self-monitoring days (8,630.3 vs. 7,825.9). Multilevel analyses showed a significant effect of the self-monitoring condition (p = .01), the goal-setting condition approached significance (p = .08), and there was a small linear increase in walking over time (p = .03). N-of-1 randomized trials are a suitable means to test behavioral interventions in individual participants.
Randomized controlled trial of physical activity, cognition, and walking in multiple sclerosis.
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.
Quantitative characterisation of an engineering write-up using random walk analysis
Sunday A. Oke
2008-02-01
Full Text Available This contribution reports on the investigation of correlation properties in an English scientific text (engineering write-up by means of a random walk. Though the idea to use a random walk to characterise correlations is not new (it was used e.g. in the genome analysis and in the analysis of texts, a random walk approach to the analysis of an English scientific text is still far from being exploited in its full strength as demonstrated in this paper. A method of high-dimensional embedding is proposed. Case examples were drawn arbitrarily from four engineering write-ups (Ph.D. synopsis of three engineering departments in the Faculty of Technology, University of Ibadan, Nigeria. Thirteen additional analyses of non-engineering English texts were made and the results compared to the engineering English texts. Thus, a total of seventeen write-ups of eight Faculties and sixteen Departments of the University of Ibadan were considered. The characterising exponents which relate the average distance of random walkers away from a known starting position to the elapsed time steps were estimated for the seventeen cases according to the power law and in three different dimensional spaces. The average characteristic exponent obtained for the seventeen cases and over three different dimensional spaces studied was 1.42 to 2-decimal with a minimum and a maximum coefficient of determination (R2 of 0.9495 and 0.9994 respectively. This is found to be 284% of the average characterising exponent value (0.5, as supported by the literature for random walkers based on the pseudo-random number generator. The average characteristic exponent obtained for the four cases that were engineering-based and over the three different dimensional studied spaces was 1.41 to 2-decimal (closer by 99.3% to 1.42 with a minimum and a maximum coefficient of determination (R2 of 0.9507 and 0.9974 respectively. This is found to be 282% of the average characterising exponent value (0.5, as
Intra-fraction motion of the prostate is a random walk
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 test rejected the null hypothesis ρ = 1 in 25% to 32% of cases. On average, the Kwiatkowski-Phillips-Schmidt-Shin test rejected the null hypothesis ρ = 0 with a probability of 93% to 96%. The variance in prostate position increased linearly over time (r2 = 0.9 ± 0.1). Variance kept increasing and did not settle at a maximum as would be expected from a stationary process. There was substantial variability in motility between fractions and patients with maximum aberrations from isocenter ranging from 0.5 mm to over 10 mm in one patient alone. In conclusion, evidence strongly suggests that intra-fraction motion of the prostate is a random walk and neither static (like inter-fraction setup errors) nor stationary (like a cyclic motion such as breathing, for example). The prostate tends to drift away from the isocenter during a fraction, and
Intra-fraction motion of the prostate is a random walk
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 (r 2 = 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
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.
Geometrically biased random walks in bacteria-driven micro-shuttles
Angelani, Luca; Di Leonardo, Roberto
2010-01-01
Micron-sized objects having asymmetric boundaries can rectify the chaotic motions of an active bacterial suspension and perform geometrically biased random walks. Using numerical simulations in a planar geometry, we show that arrow-shaped micro-shuttles, constrained to move in one dimension (1D) in a bath of self-propelled micro-organisms, spontaneously perform unidirectional translational motions with a strongly shape-dependent speed. Relaxing the 1D constraint, a random motion in the whole plane sets in at long times, due to random changes in shuttle orientation caused by bacterial collisions. The complex dynamics arising from the mechanical interactions between bacteria and the object boundaries can be described by a Gaussian stochastic force with a shape-dependent mean and a self-correlation decaying exponentially on the timescale of seconds.
Applications of a general random-walk theory for confined diffusion.
Calvo-Muñoz, Elisa M; Selvan, Myvizhi Esai; Xiong, Ruichang; Ojha, Madhusudan; Keffer, David J; Nicholson, Donald M; Egami, Takeshi
2011-01-01
A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.
Random-walk simulation of diffusion-controlled processes among static traps
Lee, S.B.; Kim, I.C.; Miller, C.A.; Torquato, S.; Department of Mechanical and Aerospace Engineering and Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910)
1989-01-01
We present computer-simulation results for the trapping rate (rate constant) k associated with diffusion-controlled reactions among identical, static spherical traps distributed with an arbitrary degree of impenetrability using a Pearson random-walk algorithm. We specifically consider the penetrable-concentric-shell model in which each trap of diameter σ is composed of a mutually impenetrable core of diameter λσ, encompassed by a perfectly penetrable shell of thickness (1-λ)σ/2: λ=0 corresponding to randomly centered or ''fully penetrable'' traps and λ=1 corresponding to totally impenetrable traps. Trapping rates are calculated accurately from the random-walk algorithm at the extreme limits of λ (λ=0 and 1) and at an intermediate value (λ=0.8), for a wide range of trap densities. Our simulation procedure has a relatively fast execution time. It is found that k increases with increasing impenetrability at fixed trap concentration. These ''exact'' data are compared with previous theories for the trapping rate. Although a good approximate theory exists for the fully-penetrable-trap case, there are no currently available theories that can provide good estimates of the trapping rate for a moderate to high density of traps with nonzero hard cores (λ>0)
Tan, Zhi-Jie; Zou, Xian-Wu; Huang, Sheng-You; Zhang, Wei; Jin, Zhun-Zhi
2002-07-01
We investigate the pattern of particle distribution and its evolution with time in multiparticle systems using the model of random walks with memory enhancement and decay. This model describes some biological intelligent walks. With decrease in the memory decay exponent α, the distribution of particles changes from a random dispersive pattern to a locally dense one, and then returns to the random one. Correspondingly, the fractal dimension Df,p characterizing the distribution of particle positions increases from a low value to a maximum and then decreases to the low one again. This is determined by the degree of overlap of regions consisting of sites with remanent information. The second moment of the density ρ(2) was introduced to investigate the inhomogeneity of the particle distribution. The dependence of ρ(2) on α is similar to that of Df,p on α. ρ(2) increases with time as a power law in the process of adjusting the particle distribution, and then ρ(2) tends to a stable equilibrium value.
Marcelo Cardoso de Souza
Full Text Available ABSTRACT Objective: The purpose was to evaluate the effectiveness of a progressive muscle strengthening program using a Swiss ball for AS patients. Methods: Sixty patients with AS were randomized into the intervention group (IG or the control group (CG. Eight exercises were performed by the IG patients with free weights on a Swiss ball two times per week for 16 weeks. The evaluations were performed by a blinded evaluator at baseline and after 4, 8, 12 and 16 weeks using the following instruments: the one-repetition maximum test (1 RM, BASMI, BASFI, HAQ-S, SF-36, 6-minute walk test, time up and go test, BASDAI, ASDAS, ESR and CRP dosage and Likert scale. Results: There was a statistical difference between groups for: strength (1 RM capacity in the following exercises: abdominal, rowing, squat, triceps and reverse fly (p < 0.005; 6-minute walk test (p < 0.001; timed up and go test (p = 0.025 and Likert scale (p < 0.001, all of them with better results for the IG. No differences were observed between the groups with respect to the functional capacity evaluation using the BASFI, HAQ-S, BASMI, SF-36, TUG, ASDAS, ESR and CPR dosage. Conclusions: Progressive muscle strengthening using a Swiss ball is effective for improving muscle strength and walking performance in patients with AS.
Rote, Aubrianne E; Klos, Lori A; Brondino, Michael J; Harley, Amy E; Swartz, Ann M
2015-06-16
Facebook may be a useful tool to provide a social support group to encourage increases in physical activity. This study examines the efficacy of a Facebook social support group to increase steps/day in young women. Female college freshmen (N = 63) were randomized to one of two 8-week interventions: a Facebook Social Support Group (n = 32) or a Standard Walking Intervention (n = 31). Participants in both groups received weekly step goals and tracked steps/day with a pedometer. Women in the Facebook Social Support Group were also enrolled in a Facebook group and asked to post information about their steps/day and provide feedback to one another. Women in both intervention arms significantly increased steps/day pre- to postintervention (F(8,425) = 94.43, P Facebook Social Support Group increased steps/day significantly more (F(1,138) = 11.34, P Facebook to offer a social support group to increase physical activity in young women. Women in the Facebook Social Support Group increased walking by approximately 1.5 miles/day more than women in the Standard Walking Intervention which, if maintained, could have a profound impact on their future health.
Scaling Law for Photon Transmission through Optically Turbid Slabs Based on Random Walk Theory
Xuesong Li
2012-03-01
Full Text Available Past work has demonstrated the value of a random walk theory (RWT to solve multiple-scattering problems arising in numerous contexts. This paper’s goal is to investigate the application range of the RWT using Monte Carlo simulations and extending it to anisotropic media using scaling laws. Meanwhile, this paper also reiterates rules for converting RWT formulas to real physical dimensions, and corrects some errors which appear in an earlier publication. The RWT theory, validated by the Monte Carlo simulations and combined with the scaling law, is expected to be useful to study multiple scattering and to greatly reduce the computation cost.
Random walk in degree space and the time-dependent Watts-Strogatz model
Grande, H. L. Casa; Cotacallapa, M.; Hase, M. O.
2016-01-01
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 Erd\\"os-R\\'enyi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical for...
Random walk in degree space and the time-dependent Watts-Strogatz model
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.
A stylistic classification of Russian-language texts based on the random walk model
Kramarenko, A. A.; Nekrasov, K. A.; Filimonov, V. V.; Zhivoderov, A. A.; Amieva, A. A.
2017-09-01
A formal approach to text analysis is suggested that is based on the random walk model. The frequencies and reciprocal positions of the vowel letters are matched up by a process of quasi-particle migration. Statistically significant difference in the migration parameters for the texts of different functional styles is found. Thus, a possibility of classification of texts using the suggested method is demonstrated. Five groups of the texts are singled out that can be distinguished from one another by the parameters of the quasi-particle migration process.
Papáček, Š.; Matonoha, Ctirad; Štumbauer, V.; Štys, D.
2012-01-01
Roč. 82, č. 10 (2012), s. 2022-2032 ISSN 0378-4754. [Modelling 2009. IMACS Conference on Mathematical Modelling and Computational Methods in Applied Sciences and Engineering /4./. Rožnov pod Radhoštěm, 22.06.2009-26.06.2009] Grant - others:CENAKVA(CZ) CZ.1.05/2.1.00/01.0024; GA JU(CZ) 152//2010/Z Institutional research plan: CEZ:AV0Z10300504 Keywords : multiscale modelling * distributed parameter system * boundary value problem * random walk * photosynthetic factory Subject RIV: EI - Biotechnology ; Bionics Impact factor: 0.836, year: 2012
Lu Dawei; Peng Xinhua; Du Jiangfeng; Zhu Jing; Zou Ping; Yu Yihua; Zhang Shanmin; Chen Qun
2010-01-01
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.
Visser, Andre
1997-01-01
Random walk simulation has the potential to be an extremely powerful tool in the investigation of turbulence in environmental processes. However, care must be taken in applying such simulations to the motion of particles in turbulent marine systems where turbulent diffusivity is commonly spatially...... are incorrect, and a simple technique that can properly simulate turbulent diffusion in the marine environment is discussed...... non-uniform. The problems associated with this nonuniformity are far from negligible and have been recognised for quite some time. However, incorrect implementations continue to appear in the Literature. In this note computer simulations are presented to illustrate how and why these implementations...
Elliptic random-walk equation for suspension and tracer transport in porous media
Shapiro, Alexander; Bedrikovetsky, P. G.
2008-01-01
. The new theory predicts delay of the maximum of the tracer, compared to the velocity of the flow, while its forward "tail" contains much more particles than in the solution of the classical parabolic (advection-dispersion) equation. This is in agreement with the experimental observations and predictions......We propose a new approach to transport of the suspensions and tracers in porous media. The approach is based on a modified version of the continuous time random walk (CTRW) theory. In the framework of this theory we derive an elliptic transport equation. The new equation contains the time...... of the CTRW theory. (C) 2008 Elsevier B.V. All rights reserved....
Dafna eMerom
2016-02-01
Full Text Available Background: A physically active lifestyle has the potential to prevent cognitive decline and dementia, yet the optimal type of physical activity/exercise remains unclear. Dance is of special interest as it complex sensorimotor rhythmic activity with additional cognitive, social and affective dimensions. Objectives: to determine whether dance benefits executive function more than walking, an activity that is simple and functional. Methods: Two-arm randomised controlled trial among community-dwelling older adults. The intervention group received 1 hour of ballroom dancing twice weekly over 8 months (~69sessions in local community dance studios. The control group received a combination of a home walking program with a pedometer and optional biweekly group-based walking in local community park to facilitate socialisation. Main outcomes: Main outcomes: executive function tests: processing speed and task shift by the Trail Making Tests (TMT, response inhibition by the Stroop Colour-Word Test (SCWT, working memory by the Digit Span Backwards (DSB test, immediate and delayed verbal recall by the Rey Auditory Verbal Learning Test (RAVLT and visuospatial recall by the Brief Visuospatial Memory Test (BVST. Results: One hundred and fifteen adults (69.5 years, SD6.4 completed baseline and delayed baseline (3 weeks apart before being randomised to either dance (n=60 or walking (n=55. Of those randomized, 79 (68% completed the follow-up measurements (32 weeks from baseline. In the dance group only, ‘non-completers’ had significant lower baseline scores on all executive function tests than those completed the full program. Intention-to-treat analyses showed no group effect. In a random effects model including participants who completed all measurements, adjusted for baseline score and covariates (age, education, estimated verbal intelligence, community, a between group effect in favour of dance was noted only for BVST total learning (Cohen’s D Effect size
Wollschlaeger, A.
1996-12-31
The presented particle tracking model is for the numerical calculation of heavy metal transport in natural waters. The Navier-Stokes-Equations are solved with the Finite-Element-Method. The advective movement of the particles is interpolated from the velocities on the discrete mesh. The influence of turbulence is simulated with a Random-Walk-Model where particles are distributed due to a given probability function. Both parts are added and lead to the new particle position. The characteristics of the heavy metals are assigned to the particules as their attributes. Dissolved heavy metals are transported only by the flow. Heavy metals which are bound to particulate matter have an additional settling velocity. The sorption and the remobilization processes are approximated through a probability law which maintains the proportionality ratio between dissolved heavy metals and those which are bound to particulate matter. At the bed heavy metals bound to particulate matter are subjected to deposition and erosion processes. The model treats these processes by considering the absorption intensity of the heavy metals to the bottom sediments. Calculations of the Weser estuary show that the particle tracking model allows the simulation of the heavy metal behaviour even under complex flow conditions. (orig.) [Deutsch] Das vorgestellte Partikelmodell dient zur numerischen Berechnung des Schwermetalltransports in natuerlichen Gewaessern. Die Navier-Stokes-Gleichungen werden mit der Methode der Finiten Elemente geloest. Die advektive Bewegung der Teilchen ergibt sich aus der Interpolation der Geschwindigkeiten auf dem diskreten Netz. Der Einfluss der Turbulenz wird mit einem Random-Walk-Modell simuliert, bei dem sich die Partikel anhand einer vorgegebenen Wahrscheinlichkeitsfunktion verteilen. Beide Bewegungsanteile werden zusammengefasst und ergeben die neue Partikelposition. Die Eigenschaften der Schwermetalle werden den Partikeln als Attribute zugeordnet. Geloeste Schwermetalle
Simulation of a directed random-walk model: the effect of pseudo-random-number correlations
Shchur, L. N.; Heringa, J. R.; Blöte, H. W. J.
1996-01-01
We investigate the mechanism that leads to systematic deviations in cluster Monte Carlo simulations when correlated pseudo-random numbers are used. We present a simple model, which enables an analysis of the effects due to correlations in several types of pseudo-random-number sequences. This model provides qualitative understanding of the bias mechanism in a class of cluster Monte Carlo algorithms.
A continuous-time random-walk approach to the Cole-Davidson dielectric response of dipolar liquids
Szabat, B.; Langner, K. M.; Klösgen-Buchkremer, Beate Maria
2004-01-01
We show how the Cole-Davidson relaxation response, characteristic of alcoholic systems, can be derived within the framework of the continuous-time random walk (CTRW). Using the random-variable formalism, we indicate that the high-frequency power law of dielectric spectra is determined by the heavy...
A continuous-time random-walk approach to the Cole-Davidson dielectric response of dipolar liquids
Szabat, Bozena; Langner, Karol M.; Klösgen, Beate Maria
2005-01-01
We show how the Cole-Davidson relaxation response, characteristic of alcoholic systems, can be derived within the framework of the continuous-time random walk 4CTRW). Using the random-variable formalism, we indicate that the high-frequency power law of dielectric spectra is determined by the heav...
Walking Away from Type 2 diabetes: a cluster randomized controlled trial.
Yates, T; Edwardson, C L; Henson, J; Gray, L J; Ashra, N B; Troughton, J; Khunti, K; Davies, M J
2017-05-01
This study aimed to investigate whether an established behavioural intervention, Walking Away from Type 2 Diabetes, is effective at promoting and sustaining increased walking activity when delivered within primary care. Cluster randomized controlled trial involving 10 general practices recruited from Leicestershire, UK, in 2009-2010. Eight hundred and eight (36% female) individuals with a high risk of Type 2 diabetes mellitus, identified through a validated risk score, were included. Participants in five practices were randomized to Walking Away from Type 2 Diabetes, a pragmatic 3-h group-based structured education programme incorporating pedometer use with annual follow-on refresher sessions. The primary outcome was accelerometer assessed ambulatory activity (steps/day) at 12 months. Longer term maintenance was assessed at 24 and 36 months. Results were analysed using generalized estimating equation models, accounting for clustering. Complete accelerometer data for the primary outcome were available for 571 (71%) participants. Increases in ambulatory activity of 411 steps/day [95% confidence interval (CI): 117, 704] and self-reported vigorous-intensity physical activity of 218 metabolic equivalent min/week (95% CI: 6, 425) at 12 months were observed in the intervention group compared with control; differences between groups were not sustained at 36 months. No differences between groups were observed for markers of cardiometabolic health. Replacing missing data with multiple imputation did not affect the results. A pragmatic low-resource group-based structured education programme with pedometer use resulted in modest increases in ambulatory activity compared with control conditions after 12 months when implemented within a primary care setting to those at high risk of Type 2 diabetes mellitus; however, the results were not maintained over 36 months. © 2016 Diabetes UK.
Personalized PageRank Clustering: A graph clustering algorithm based on random walks
A. Tabrizi, Shayan; Shakery, Azadeh; Asadpour, Masoud; Abbasi, Maziar; Tavallaie, Mohammad Ali
2013-11-01
Graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications. In addition, exponential growth of real-world graphs such as social networks, biological networks and electrical circuits demands clustering algorithms with nearly-linear time and space complexity. In this paper we propose Personalized PageRank Clustering (PPC) that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph. We combine random walks and modularity to precisely and efficiently reveal the clusters of a graph. PPC is a top-down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly-linear approaches that are mainly bottom-up. It also gives a hierarchy of clusters that is useful in many applications. PPC has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets. Furthermore, its top-down approach makes it a flexible solution for clustering problems with different requirements.
Two-state random walk model of lattice diffusion - 1. Self-correlation function
Balakrishnan, V.; Venkataraman, G.
1981-01-01
Diffusion with interruptions (arising from localized oscillations, or traps, or mixing between jump diffusion and fluid-like diffusion, etc.) is a very general phenomenon. Its manifestations range from superionic conductance to the behaviour of hydrogen in metals. Based on a continuous-time random walk approach, we present a comprehensive two-state random walk model for the diffusion of a particle on a lattice, incorporating arbitrary holding-time distributions for both localized residence at the sites and inter-site flights, and also the correct first-waiting-time distributions. A synthesis is thus achieved of the two extremes of jump diffusion (zero flight time) and fluid-like diffusion (zero residence time). Various earlier models emerge as special cases of our theory. Among the noteworthy results obtained are: closed-form solutions (in d dimensions, and with arbitrary directional bias) for temporarily uncorrelated jump diffusion and for the fluid diffusion counterpart; a compact, general formula for the mean square displacement; the effects of a continuous spectrum of time scales in the holding-time distributions, etc. The dynamic mobility and the structure factor for 'oscillatory diffusion' are taken up in part 2. (author)
Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?
Czégel, Dániel; Palla, Gergely
2015-01-01
Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or connections between the fundamental units of the studied system. Although a number of notable methods are already available, their vast majority is treating all directed acyclic graphs as already maximally hierarchical. Here we propose a hierarchy measure based on random walks on the network. The novelty of our approach is that directed trees corresponding to multi level pyramidal structures obtain higher hierarchy scores compared to directed chains and directed stars. Furthermore, in the thermodynamic limit the hierarchy measure of regular trees is converging to a well defined limit depending only on the branching number. When applied to real networks, our method is computationally very effective, as the result can be evaluated with arbitrary precision by subsequent multiplications of the transition matrix describing the random walk process. In addition, the tests on real world networks provided very intuitive results, e.g., the trophic levels obtained from our approach on a food web were highly consistent with former results from ecology. PMID:26657012
Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?
Czégel, Dániel; Palla, Gergely
2015-12-10
Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or connections between the fundamental units of the studied system. Although a number of notable methods are already available, their vast majority is treating all directed acyclic graphs as already maximally hierarchical. Here we propose a hierarchy measure based on random walks on the network. The novelty of our approach is that directed trees corresponding to multi level pyramidal structures obtain higher hierarchy scores compared to directed chains and directed stars. Furthermore, in the thermodynamic limit the hierarchy measure of regular trees is converging to a well defined limit depending only on the branching number. When applied to real networks, our method is computationally very effective, as the result can be evaluated with arbitrary precision by subsequent multiplications of the transition matrix describing the random walk process. In addition, the tests on real world networks provided very intuitive results, e.g., the trophic levels obtained from our approach on a food web were highly consistent with former results from ecology.
A lattice-model representation of continuous-time random walks
Campos, Daniel; Mendez, Vicenc
2008-01-01
We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied
Counting the corners of a random walk and its application to traffic flow
Knorr, Florian; Schreckenberg, Michael
2012-01-01
We study a system with two types of interacting particles on a one-dimensional lattice. Particles of the first type, which we call ‘active’, are able to detect particles of the second type (called ‘passive’). By relating the problem to a discrete random walk in one dimension with a fixed number of steps we determine the fraction of active and detected particles for both open and periodic boundary conditions as well as for the case where passive particles interact with both or only one neighbors. In the random walk picture, where the two particles types stand for steps in opposite directions, passive particles are detected whenever the resulting path has a corner. For open boundary conditions, it turns out that a simple mean field approximation reproduces the exact result if the particles interact with one neighbor only. A practical application of this problem is heterogeneous traffic flow with communicating and non-communicating vehicles. In this context communicating vehicles can be thought of as active particles which can by front (and rear) sensors detect the vehicle ahead (and behind) although these vehicles do not actively share information. Therefore, we also present simulation results which show the validity of our analysis for real traffic flow. (paper)
A lattice-model representation of continuous-time random walks
Campos, Daniel [School of Mathematics, Department of Applied Mathematics, University of Manchester, Manchester M60 1QD (United Kingdom); Mendez, Vicenc [Grup de Fisica Estadistica, Departament de Fisica, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain)], E-mail: daniel.campos@uab.es, E-mail: vicenc.mendez@uab.es
2008-02-29
We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied.
Anomalous diffusion and Levy random walk of magnetic field lines in three dimensional turbulence
Zimbardo, G.; Veltri, P.; Basile, G.; Principato, S.
1995-01-01
The transport of magnetic field lines is studied numerically where three dimensional (3-D) magnetic fluctuations, with a power law spectrum, and periodic over the simulation box are superimposed on an average uniform magnetic field. The weak and the strong turbulence regime, δB∼B 0 , are investigated. In the weak turbulence case, magnetic flux tubes are separated from each other by percolating layers in which field lines undergo a chaotic motion. In this regime the field lines may exhibit Levy, rather than Gaussian, random walk, changing from Levy flights to trapped motion. The anomalous diffusion laws left-angle Δx 2 i right-angle ∝s α with α>1 and α<1, are obtained for a number of cases, and the non-Gaussian character of the field line random walk is pointed out by computing the kurtosis. Increasing the fluctuation level, and, therefore stochasticity, normal diffusion (α congruent 1) is recovered and the kurtoses reach their Gaussian value. However, the numerical results show that neither the quasi-linear theory nor the two dimensional percolation theory can be safely extrapolated to the considered 3-D strong turbulence regime. copyright 1995 American Institute of Physics
Mean first passage time for random walk on dual structure of dendrimer
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.
Wei, Kun; Zhong, Suchuan
2017-08-01
Phenomenologically inspired by dolphins' unihemispheric sleep, we introduce a minimal model for random walks with physiological memory. The physiological memory consists of long-term memory which includes unconscious implicit memory and conscious explicit memory, and working memory which serves as a multi-component system for integrating, manipulating and managing short-term storage. The model assumes that the sleeping state allows retrievals of episodic objects merely from the episodic buffer where these memory objects are invoked corresponding to the ambient objects and are thus object-oriented, together with intermittent but increasing use of implicit memory in which decisions are unconsciously picked up from historical time series. The process of memory decay and forgetting is constructed in the episodic buffer. The walker's risk attitude, as a product of physiological heuristics according to the performance of objected-oriented decisions, is imposed on implicit memory. The analytical results of unihemispheric random walks with the mixture of object-oriented and time-oriented memory, as well as the long-time behavior which tends to the use of implicit memory, are provided, indicating the common sense that a conservative risk attitude is inclinable to slow movement.
Modeling spreading of oil slicks based on random walk methods and Voronoi diagrams
Durgut, İsmail; Reed, Mark
2017-01-01
We introduce a methodology for representation of a surface oil slick using a Voronoi diagram updated at each time step. The Voronoi cells scale the Gaussian random walk procedure representing the spreading process by individual particle stepping. The step length of stochastically moving particles is based on a theoretical model of the spreading process, establishing a relationship between the step length of diffusive spreading and the thickness of the slick at the particle locations. The Voronoi tessellation provides the areal extent of the slick particles and in turn the thicknesses of the slick and the diffusive-type spreading length for all particles. The algorithm successfully simulates the spreading process and results show very good agreement with the analytical solution. Moreover, the results are robust for a wide range of values for computational time step and total number of particles. - Highlights: • A methodology for representation of a surface oil slick using a Voronoi diagram • An algorithm simulating the spreading of oil slick with the Voronoi diagram representation • The algorithm employs the Gaussian random walk method through individual particle stepping. • The diffusive spreading is based on a theoretical model of the spreading process. • Algorithm is computationally robust and successfully reproduces analytical solutions to the spreading process.
Navigational efficiency in a biased and correlated random walk model of individual animal movement.
Bailey, Joseph D; Wallis, Jamie; Codling, Edward A
2018-01-01
Understanding how an individual animal is able to navigate through its environment is a key question in movement ecology that can give insight into observed movement patterns and the mechanisms behind them. Efficiency of navigation is important for behavioral processes at a range of different spatio-temporal scales, including foraging and migration. Random walk models provide a standard framework for modeling individual animal movement and navigation. Here we consider a vector-weighted biased and correlated random walk (BCRW) model for directed movement (taxis), where external navigation cues are balanced with forward persistence. We derive a mathematical approximation of the expected navigational efficiency for any BCRW of this form and confirm the model predictions using simulations. We demonstrate how the navigational efficiency is related to the weighting given to forward persistence and external navigation cues, and highlight the counter-intuitive result that for low (but realistic) levels of error on forward persistence, a higher navigational efficiency is achieved by giving more weighting to this indirect navigation cue rather than direct navigational cues. We discuss and interpret the relevance of these results for understanding animal movement and navigation strategies. © 2017 by the Ecological Society of America.
Asymptotic results for the semi-Markovian random walk with delay
Khaniyev, T.A.; Aliyev, R.T.
2006-12-01
In this study, the semi-Markovian random walk with a discrete interference of chance (X(t) ) is considered and under some weak assumptions the ergodicity of this process is discussed. Characteristic function of the ergodic distribution of X(t) is expressed by means of the probability characteristics of the boundary functionals (N,S N ). Some exact formulas for first and second moments of ergodic distribution of the process X(t) are obtained when the random variable ζ 1 - s, which is describing a discrete interference of chance, has Gamma distribution on the interval [0, ∞) with parameter (α,λ) . Based on these results, the asymptotic expansions with three terms for the first two moments of the ergodic distribution of the process X(t) are obtained, as λ → 0. (author)
Random walk analysis of grain motion during superplastic deformation of TZP
Okamoto, T; Yasuda, K; Shiota, T
2009-01-01
This study focuses on grain motion in TZP (Tetragonal Zirconia Polycrystal) ceramics during superplastic deformation. The specimen was 16 times elongated repeatedly at 1400 0 C in air. The increment of true plastic strain was set to be 2%, and the specimen was deformed up to 30.3% true plastic strain finally. After each deformation, displacement vectors of specified 748 grains were measured from their position vectors determined by FE-SEM micrographs. As a result, the grains move to the tensile loading direction in zigzag way. And also, the zigzag motion changes with plastic strain: The grains move randomly (random walk motion) by the first 15% true plastic strain, and then grain motion becomes spatially uniform gradually. It is related to changes of constraint of surrounding matrix.
Avena, L.; Hollander, den W.Th.F.; Redig, F.H.J.
2009-01-01
Consider a one-dimensional shift-invariant attractive spin-ip system in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on vacant sites has a local drift to the left. In [2] we proved a law
Avena, L.; Hollander, den W.Th.F.; Redig, F.H.J.
2010-01-01
Consider a one-dimensional shift-invariant attractive spin-flip system in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on vacant sites has a local drift to the left. In previous work we
Müller, Christian L.; Sbalzarini, Ivo F.; van Gunsteren, Wilfred F.; Žagrović, Bojan; Hünenberger, Philippe H.
2009-06-01
The concept of high-resolution shapes (also referred to as folds or states, depending on the context) of a polymer chain plays a central role in polymer science, structural biology, bioinformatics, and biopolymer dynamics. However, although the idea of shape is intuitively very useful, there is no unambiguous mathematical definition for this concept. In the present work, the distributions of high-resolution shapes within the ideal random-walk ensembles with N =3,…,6 beads (or up to N =10 for some properties) are investigated using a systematic (grid-based) approach based on a simple working definition of shapes relying on the root-mean-square atomic positional deviation as a metric (i.e., to define the distance between pairs of structures) and a single cutoff criterion for the shape assignment. Although the random-walk ensemble appears to represent the paramount of homogeneity and randomness, this analysis reveals that the distribution of shapes within this ensemble, i.e., in the total absence of interatomic interactions characteristic of a specific polymer (beyond the generic connectivity constraint), is significantly inhomogeneous. In particular, a specific (densest) shape occurs with a local probability that is 1.28, 1.79, 2.94, and 10.05 times (N =3,…,6) higher than the corresponding average over all possible shapes (these results can tentatively be extrapolated to a factor as large as about 1028 for N =100). The qualitative results of this analysis lead to a few rather counterintuitive suggestions, namely, that, e.g., (i) a fold classification analysis applied to the random-walk ensemble would lead to the identification of random-walk "folds;" (ii) a clustering analysis applied to the random-walk ensemble would also lead to the identification random-walk "states" and associated relative free energies; and (iii) a random-walk ensemble of polymer chains could lead to well-defined diffraction patterns in hypothetical fiber or crystal diffraction experiments
Effects of exercise on brain activity during walking in older adults: a randomized controlled trial.
Shimada, Hiroyuki; Ishii, Kenji; Makizako, Hyuma; Ishiwata, Kiichi; Oda, Keiichi; Suzukawa, Megumi
2017-05-30
Physical activity may preserve neuronal plasticity, increase synapse formation, and cause the release of hormonal factors that promote neurogenesis and neuronal function. Previous studies have reported enhanced neurocognitive function following exercise training. However, the specific cortical regions activated during exercise training remain largely undefined. In this study, we quantitatively and objectively evaluated the effects of exercise on brain activity during walking in healthy older adults. A total of 24 elderly women (75-83 years old) were randomly allocated to either an intervention group or a control group. Those in the intervention group attended 3 months of biweekly 90-min sessions focused on aerobic exercise, strength training, and physical therapy. We monitored changes in regional cerebral glucose metabolism during walking in both groups using positron emission tomography (PET) and [ 18 F]fluorodeoxyglucose (FDG). All subjects completed the 3-month experiment and the adherence to the exercise program was 100%. Compared with the control group, the intervention group showed a significantly greater step length in the right foot after 3 months of physical activity. The FDG-PET assessment revealed a significant post-intervention increase in regional glucose metabolism in the left posterior entorhinal cortex, left superior temporal gyrus, and right superior temporopolar area in the intervention group. Interestingly, the control group showed a relative increase in regional glucose metabolism in the left premotor and supplemental motor areas, left and right somatosensory association cortex, and right primary visual cortex after the 3-month period. We found no significant differences in FDG uptake between the intervention and control groups before vs. after the intervention. Exercise training increased activity in specific brain regions, such as the precuneus and entorhinal cortices, which play an important role in episodic and spatial memory. Further
Høyer, Ellen; Jahnsen, Reidun; Stanghelle, Johan Kvalvik; Strand, Liv Inger
2012-01-01
Treadmill training with body weight support (TTBWS) for relearning walking ability after brain damage is an approach under current investigation. Efficiency of this method beyond traditional training is lacking evidence, especially in patients needing walking assistance after stroke. The objective of this study was to investigate change in walking and transfer abilities, comparing TTBWS with traditional walking training. A single-blinded, randomized controlled trial was conducted. Sixty patients referred for multi-disciplinary primary rehabilitation were assigned into one of two intervention groups, one received 30 sessions of TTBWS plus traditional training, the other traditional training alone. Daily training was 1 hr. Outcome measures were Functional Ambulation Categories (FAC), Walking, Functional Independence Measure (FIM); shorter transfer and stairs, 10 m and 6-min walk tests. Substantial improvements in walking and transfer were shown within both groups after 5 and 11 weeks of intervention. Overall no statistical significant differences were found between the groups, but 12 of 17 physical measures tended to show improvements in favour of the treadmill approach. Both training strategies provided significant improvements in the tested activities, suggesting that similar outcomes can be obtained in the two modalities by systematic, intensive and goal directed training.
Mikosch, Thomas Valentin; Rackauskas, Alfredas
2010-01-01
In this paper, we deal with the asymptotic distribution of the maximum increment of a random walk with a regularly varying jump size distribution. This problem is motivated by a long-standing problem on change point detection for epidemic alternatives. It turns out that the limit distribution...... of the maximum increment of the random walk is one of the classical extreme value distributions, the Fréchet distribution. We prove the results in the general framework of point processes and for jump sizes taking values in a separable Banach space...
Generalized Pareto for Pattern-Oriented Random Walk Modelling of Organisms' Movements.
Sophie Bertrand
Full Text Available 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.
Bantoft, Christina; Summers, Mathew J; Tranent, Peter J; Palmer, Matthew A; Cooley, P Dean; Pedersen, Scott J
2016-02-01
In the present study, we examined the effect of working while seated, while standing, or while walking on measures of short-term memory, working memory, selective and sustained attention, and information-processing speed. The advent of computer-based technology has revolutionized the adult workplace, such that average adult full-time employees spend the majority of their working day seated. Prolonged sitting is associated with increasing obesity and chronic health conditions in children and adults. One possible intervention to reduce the negative health impacts of the modern office environment involves modifying the workplace to increase incidental activity and exercise during the workday. Although modifications, such as sit-stand desks, have been shown to improve physiological function, there is mixed information regarding the impact of such office modification on individual cognitive performance and thereby the efficiency of the work environment. In a fully counterbalanced randomized control trial, we assessed the cognitive performance of 45 undergraduate students for up to a 1-hr period in each condition. The results indicate that there is no significant change in the measures used to assess cognitive performance associated with working while seated, while standing, or while walking at low intensity. These results indicate that cognitive performance is not degraded with short-term use of alternate workstations. © 2015, Human Factors and Ergonomics Society.
Generalized Pareto for Pattern-Oriented Random Walk Modelling of Organisms' Movements.
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.
Continuous time random walk: Galilei invariance and relation for the nth moment
Fa, Kwok Sau
2011-01-01
We consider a decoupled continuous time random walk model with a generic waiting time probability density function (PDF). For the force-free case we derive an integro-differential diffusion equation which is related to the Galilei invariance for the probability density. We also derive a general relation which connects the nth moment in the presence of any external force to the second moment without external force, i.e. it is valid for any waiting time PDF. This general relation includes the generalized second Einstein relation, which connects the first moment in the presence of any external force to the second moment without any external force. These expressions for the first two moments are verified by using several kinds of the waiting time PDF. Moreover, we present new anomalous diffusion behaviours for a waiting time PDF given by a product of power-law and exponential function.
Random walk-based similarity measure method for patterns in complex object
Liu Shihu
2017-04-01
Full Text Available This paper discusses the similarity of the patterns in complex objects. The complex object is composed both of the attribute information of patterns and the relational information between patterns. Bearing in mind the specificity of complex object, a random walk-based similarity measurement method for patterns is constructed. In this method, the reachability of any two patterns with respect to the relational information is fully studied, and in the case of similarity of patterns with respect to the relational information can be calculated. On this bases, an integrated similarity measurement method is proposed, and algorithms 1 and 2 show the performed calculation procedure. One can find that this method makes full use of the attribute information and relational information. Finally, a synthetic example shows that our proposed similarity measurement method is validated.
Ni Xiaohui; Jiang Zhiqiang; Zhou Weixing
2009-01-01
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.
A random walk approach to the diffusion of positrons in gaseous media
Girardi-Schappo, M.; Tenfen, W.; Arretche, F.
2013-01-01
In this work, we present a random walk model to study the positron diffusion in gaseous media. The positron-atom interaction is described through positron-target cross sections. The main idea is to obtain how much energy a positron transfer to the environment atoms, through ionizations and electronic excitations until its annihilation, taking the ratio between each energetically available collision channel to the total one as the probability for each process to occur. As a first application, we studied how the positron diffuse in gases of helium, neon, argon and their mixtures. To characterize the positron dynamics in each system, we calculated the radiation profile generated from the annihilation, their diffusion profiles and the most probable distances for excitation and ionization. (authors)
A random walk evolution model of wireless sensor networks and virus spreading
Wang Ya-Qi; Yang Xiao-Yuan
2013-01-01
In this paper, considering both cluster heads and sensor nodes, we propose a novel evolving a network model based on a random walk to study the fault tolerance decrease of wireless sensor networks (WSNs) due to node failure, and discuss the spreading dynamic behavior of viruses in the evolution model. A theoretical analysis shows that the WSN generated by such an evolution model not only has a strong fault tolerance, but also can dynamically balance the energy loss of the entire network. It is also found that although the increase of the density of cluster heads in the network reduces the network efficiency, it can effectively inhibit the spread of viruses. In addition, the heterogeneity of the network improves the network efficiency and enhances the virus prevalence. We confirm all the theoretical results with sufficient numerical simulations. (general)
Fragmentation of polarized 23Na on 208Pb and the random-walk model
Clarke, N.M.; Karban, O.; Blyth, C.O.; Choi, H.D.; Hall, S.J.; Roman, S.; Tungate, G.; Cole, A.J.; Davis, N.J.; Shotter, A.C.; Connell, K.A.
1993-01-01
Inclusive measurements are presented for the differential cross sections and tensor analyzing powers ( TT 20 and T 20 ) of ions produced by the fragmentation of a beam of polarized 23 Na incident on a 208 Pb target at an energy of 195.5 MeV (8.5 MeV/nucleon). The data are discussed in terms of a simple ''shape-effect'' model, and compared to the predictions of the nuclear random-walk model which has been extended to the calculation of aligned, deformed projectiles. This model reproduces the principal features of the differential cross sections and the trends as a function of mass loss, but gives poorer agreement for the analyzing powers
Cvetkovic, V.; Molin, S.
2012-02-01
We present a methodology that combines numerical simulations of groundwater flow and advective transport in heterogeneous porous media with analytical retention models for computing the infection risk probability from pathogens in aquifers. The methodology is based on the analytical results presented in [1,2] for utilising the colloid filtration theory in a time-domain random walk framework. It is shown that in uniform flow, the results from the numerical simulations of advection yield comparable results as the analytical TDRW model for generating advection segments. It is shown that spatial variability of the attachment rate may be significant, however, it appears to affect risk in a different manner depending on if the flow is uniform or radially converging. In spite of the fact that numerous issues remain open regarding pathogen transport in aquifers on the field scale, the methodology presented here may be useful for screening purposes, and may also serve as a basis for future studies that would include greater complexity.
Microstructure-based characterization of permeability using a random walk model
Chen, F F; Yang, Y S
2012-01-01
Quantitative transport properties of materials are analysed using a random walk model, based on the microscopic compositional distribution of compositions in the materials. A material sample is defined on a simple-cubic lattice, with volume fractions specified for each composition on every volume pixel (voxel). The quantitative relation between bulk permeability and fine-scale anisotropy is investigated by assuming fully anisotropic and fully isotropic voxel morphology. Such a study has prompted an analytic approximate formulation to predict bulk permeability range for a heterogeneous multi-component system that lacks detailed microstructure information. The numerical approach is verified on synthetic structures with known permeability. The analysis technique is applied to a real-world rock sample, as illustrated by a case study detailed in this paper. The investigations show that the bulk permeability is affected significantly by fine length scale anisotropy. (paper)
A random-walk model for pore pressure accumulation in marine soils
Sumer, B. Mutlu; Cheng, Niang-Sheng
1999-01-01
A numerical random-walk model has been developed for the pore-water pressure. The model is based on the analogy between the variation of the pore pressure and the diffusion process of any passive quantity such as concentration. The pore pressure in the former process is analogous...... to the concentration in the latter. In the simulation, particles are released in the soil, and followed as they travel through the statistical field variables. The model has been validated (1) against the Terzaghi consolidation process, and (2) against the process where the pore pressure builds up under progressive...... waves. The model will apparently enable the researcher to handle complex geometries (such as a pipeline buried in a soil) relatively easily. Early results with regard to the latter example, namely the buildup of pore pressure around a buried pipeline subject to a progressive wave, are encouraging....
Penentuan Distribusi Suhu pada Permukaan Geometri Tak Tentu Menggunakan Metode Random Walk
Balduyanus Yosep Godja
2016-05-01
Full Text Available Telah dilakukan penentuan distribusi suhu dalam keadaan tunak pada sebuah plat bergeometri tak tentu menggunakan metode Random Walk yang dilengkapi fungsi green. Setiap sisi plat dikondisikan bervariasi terhadap suhu dalam rentang 10°C sampai 100°C dengan 4 (empat konfigurasi berkeadaan steady. Persamaan Laplace yang mendeskripsikan permasalahan ini dihampiri dengan mensimulasikan sejumlah walker pada setiap titik domain permasalahan untuk kemudian secara acak disebar menuju ke setiap sisi plat. Hasil yang diperoleh untuk setiap kondisi plat menunjukkan kesalahan relatif terhadap solusi numerik metode iterasi jacobi yang telah menghampiri solusi analitik, secara rata-rata adalah 0,85%. Nilai kesalahan tersebut diperoleh dengan menggunakan 5000 walker. Penelitian ini juga mendapatkan bahwa akurasi hampiran ditentukan oleh banyaknya walker yang digunakan. Secara umum, semakin banyak jumlah walker yang digunakan maka akurasi hampiran akan semakin baik.
Magnetic field line random walk in two-dimensional dynamical turbulence
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.
Estimating filtration coefficients for straining from percolation and random walk theories
Yuan, Hao; Shapiro, Alexander; You, Zhenjiang
2012-01-01
In this paper, laboratory challenge tests are carried out under unfavorable attachment conditions, so that size exclusion or straining is the only particle capture mechanism. The experimental results show that far above the percolation threshold the filtration coefficients are not proportional...... size exclusion theory or the model of parallel tubes with mixing chambers, where the filtration coefficients are proportional to the flux through smaller pores, and the predicted penetration depths are much lower. A special capture mechanism is proposed, which makes it possible to explain...... the experimentally observed power law dependencies of filtration coefficients and large penetration depths of particles. Such a capture mechanism is realized in a 2D pore network model with periodical boundaries with the random walk of particles on the percolation lattice. Geometries of infinite and finite clusters...
SU-F-BRD-09: A Random Walk Model Algorithm for Proton Dose Calculation
Yao, W; Farr, J
2015-01-01
Purpose: To develop a random walk model algorithm for calculating proton dose with balanced computation burden and accuracy. Methods: Random walk (RW) model is sometimes referred to as a density Monte Carlo (MC) simulation. In MC proton dose calculation, the use of Gaussian angular distribution of protons due to multiple Coulomb scatter (MCS) is convenient, but in RW the use of Gaussian angular distribution requires an extremely large computation and memory. Thus, our RW model adopts spatial distribution from the angular one to accelerate the computation and to decrease the memory usage. From the physics and comparison with the MC simulations, we have determined and analytically expressed those critical variables affecting the dose accuracy in our RW model. Results: Besides those variables such as MCS, stopping power, energy spectrum after energy absorption etc., which have been extensively discussed in literature, the following variables were found to be critical in our RW model: (1) inverse squared law that can significantly reduce the computation burden and memory, (2) non-Gaussian spatial distribution after MCS, and (3) the mean direction of scatters at each voxel. In comparison to MC results, taken as reference, for a water phantom irradiated by mono-energetic proton beams from 75 MeV to 221.28 MeV, the gamma test pass rate was 100% for the 2%/2mm/10% criterion. For a highly heterogeneous phantom consisting of water embedded by a 10 cm cortical bone and a 10 cm lung in the Bragg peak region of the proton beam, the gamma test pass rate was greater than 98% for the 3%/3mm/10% criterion. Conclusion: We have determined key variables in our RW model for proton dose calculation. Compared with commercial pencil beam algorithms, our RW model much improves the dose accuracy in heterogeneous regions, and is about 10 times faster than MC simulations
Efficiency analysis of diffusion on T-fractals in the sense of random walks.
Peng, Junhao; Xu, Guoai
2014-04-07
Efficiently controlling the diffusion process is crucial in the study of diffusion problem in complex systems. In the sense of random walks with a single trap, mean trapping time (MTT) and mean diffusing time (MDT) are good measures of trapping efficiency and diffusion efficiency, respectively. They both vary with the location of the node. In this paper, we analyze the effects of node's location on trapping efficiency and diffusion efficiency of T-fractals measured by MTT and MDT. First, we provide methods to calculate the MTT for any target node and the MDT for any source node of T-fractals. The methods can also be used to calculate the mean first-passage time between any pair of nodes. Then, using the MTT and the MDT as the measure of trapping efficiency and diffusion efficiency, respectively, we compare the trapping efficiency and diffusion efficiency among all nodes of T-fractal and find the best (or worst) trapping sites and the best (or worst) diffusing sites. Our results show that the hub node of T-fractal is the best trapping site, but it is also the worst diffusing site; and that the three boundary nodes are the worst trapping sites, but they are also the best diffusing sites. Comparing the maximum of MTT and MDT with their minimums, we find that the maximum of MTT is almost 6 times of the minimum of MTT and the maximum of MDT is almost equal to the minimum for MDT. Thus, the location of target node has large effect on the trapping efficiency, but the location of source node almost has no effect on diffusion efficiency. We also simulate random walks on T-fractals, whose results are consistent with the derived results.
Learning of Multimodal Representations With Random Walks on the Click Graph.
Wu, Fei; Lu, Xinyan; Song, Jun; Yan, Shuicheng; Zhang, Zhongfei Mark; Rui, Yong; Zhuang, Yueting
2016-02-01
In multimedia information retrieval, most classic approaches tend to represent different modalities of media in the same feature space. With the click data collected from the users' searching behavior, existing approaches take either one-to-one paired data (text-image pairs) or ranking examples (text-query-image and/or image-query-text ranking lists) as training examples, which do not make full use of the click data, particularly the implicit connections among the data objects. In this paper, we treat the click data as a large click graph, in which vertices are images/text queries and edges indicate the clicks between an image and a query. We consider learning a multimodal representation from the perspective of encoding the explicit/implicit relevance relationship between the vertices in the click graph. By minimizing both the truncated random walk loss as well as the distance between the learned representation of vertices and their corresponding deep neural network output, the proposed model which is named multimodal random walk neural network (MRW-NN) can be applied to not only learn robust representation of the existing multimodal data in the click graph, but also deal with the unseen queries and images to support cross-modal retrieval. We evaluate the latent representation learned by MRW-NN on a public large-scale click log data set Clickture and further show that MRW-NN achieves much better cross-modal retrieval performance on the unseen queries/images than the other state-of-the-art methods.
Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach
Comolli, Alessandro; Dentz, Marco
2017-09-01
We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy's law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in
Avrachenkov, Konstantin; Borkar, Vivek S; Kadavankandy, Arun; Sreedharan, Jithin K
2018-01-01
In the framework of network sampling, random walk (RW) based estimation techniques provide many pragmatic solutions while uncovering the unknown network as little as possible. Despite several theoretical advances in this area, RW based sampling techniques usually make a strong assumption that the samples are in stationary regime, and hence are impelled to leave out the samples collected during the burn-in period. This work proposes two sampling schemes without burn-in time constraint to estimate the average of an arbitrary function defined on the network nodes, for example, the average age of users in a social network. The central idea of the algorithms lies in exploiting regeneration of RWs at revisits to an aggregated super-node or to a set of nodes, and in strategies to enhance the frequency of such regenerations either by contracting the graph or by making the hitting set larger. Our first algorithm, which is based on reinforcement learning (RL), uses stochastic approximation to derive an estimator. This method can be seen as intermediate between purely stochastic Markov chain Monte Carlo iterations and deterministic relative value iterations. The second algorithm, which we call the Ratio with Tours (RT)-estimator, is a modified form of respondent-driven sampling (RDS) that accommodates the idea of regeneration. We study the methods via simulations on real networks. We observe that the trajectories of RL-estimator are much more stable than those of standard random walk based estimation procedures, and its error performance is comparable to that of respondent-driven sampling (RDS) which has a smaller asymptotic variance than many other estimators. Simulation studies also show that the mean squared error of RT-estimator decays much faster than that of RDS with time. The newly developed RW based estimators (RL- and RT-estimators) allow to avoid burn-in period, provide better control of stability along the sample path, and overall reduce the estimation time. Our
Hurley, Jane C; Hollingshead, Kevin E; Todd, Michael; Jarrett, Catherine L; Tucker, Wesley J; Angadi, Siddhartha S; Adams, Marc A
2015-09-11
Walking is a widely accepted and frequently targeted health promotion approach to increase physical activity (PA). Interventions to increase PA have produced only small improvements. Stronger and more potent behavioral intervention components are needed to increase time spent in PA, improve cardiometabolic risk markers, and optimize health. Our aim is to present the rationale and methods from the WalkIT Trial, a 4-month factorial randomized controlled trial (RCT) in inactive, overweight/obese adults. The main purpose of the study was to evaluate whether intensive adaptive components result in greater improvements to adults' PA compared to the static intervention components. Participants enrolled in a 2x2 factorial RCT and were assigned to one of four semi-automated, text message-based walking interventions. Experimental components included adaptive versus static steps/day goals, and immediate versus delayed reinforcement. Principles of percentile shaping and behavioral economics were used to operationalize experimental components. A Fitbit Zip measured the main outcome: participants' daily physical activity (steps and cadence) over the 4-month duration of the study. Secondary outcomes included self-reported PA, psychosocial outcomes, aerobic fitness, and cardiorespiratory risk factors assessed pre/post in a laboratory setting. Participants were recruited through email listservs and websites affiliated with the university campus, community businesses and local government, social groups, and social media advertising. This study has completed data collection as of December 2014, but data cleaning and preliminary analyses are still in progress. We expect to complete analysis of the main outcomes in late 2015 to early 2016. The Walking Interventions through Texting (WalkIT) Trial will further the understanding of theory-based intervention components to increase the PA of men and women who are healthy, insufficiently active and are overweight or obese. WalkIT is one of
Fayolle, Guy; Malyshev, Vadim
2017-01-01
This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts. Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows spec...
B. Chen (Bohan); J. Blanchet; C.H. Rhee (Chang-Han); A.P. Zwart (Bert)
2017-01-01
textabstractWe propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based on an importance sampling strategy that hinges
Reike, Dennis; Schwarz, Wolf
2016-01-01
The time required to determine the larger of 2 digits decreases with their numerical distance, and, for a given distance, increases with their magnitude (Moyer & Landauer, 1967). One detailed quantitative framework to account for these effects is provided by random walk models. These chronometric models describe how number-related noisy…
Schippers, P.; Verboom, J.; Knaapen, J.P.; Apeldoorn, van R.
1996-01-01
A grid-based random walk model has been developed to simulate animal dispersal, taking landscape heterogeneity and linear barriers such as roads and rivers into account. The model can be used to estimate connectivity and has been parameterized for thebadger in the central part of the Netherlands.
Scholtes, V.A.; Becher, J.G.; Janssen-Potten, Y.J.; Dekkers, H.; Smallenbroek, L.; Dallmeijer, A.J.
2012-01-01
The objective of the study was to evaluate the effectiveness of functional progressive resistance exercise (PRE) training on walking ability in children with cerebral palsy (CP).Fifty-one ambulant children with spastic CP (mean age 10 years 5 months, 29 boys) were randomized to an intervention (n=
Reynolds, A M
2009-01-01
The movement patterns of a diverse range of animals have scale-free characteristics. These characteristics provide necessary but not sufficient conditions for the presence of movement patterns that can be approximated by Levy walks. Nevertheless, it has been widely assumed that the occurrence of scale-free animal movements can indeed be attributed to the presence of Levy walks. This is, in part, because it is known that the super-diffusive properties of Levy walks can be advantageous in random search scenarios when searchers have little or no prior knowledge of target locations. However, fractional Brownian motions (fBms) and fractional Levy motions (fLms) are both scale-free and super-diffusive, and so it is possible that these motions rather than Levy walks underlie some or all occurrences of scale-free animal movement patterns. Here this possibility is examined in numerical simulations through a determination of the searching efficiencies of fBm and fLm searches. It is shown that these searches are less efficient than Levy walk searches. This finding does not rule out the possibility that some animals with scale-free movement patterns are executing fBm and fLm searches, but it does make Levy walk searches the more likely possibility.
G. Morone
2012-01-01
Full Text Available Foot drop is a quite common problem in nervous system disorders. Neuromuscular electrical stimulation (NMES has showed to be an alternative approach to correct foot drop improving walking ability in patients with stroke. In this study, twenty patients with stroke in subacute phase were enrolled and randomly divided in two groups: one group performing the NMES (i.e. Walkaide Group, WG and the Control Group (CG performing conventional neuromotor rehabilitation. Both groups underwent the same amount of treatment time. Significant improvements of walking speed were recorded for WG (% than for CG (%, as well as in terms of locomotion (Functional Ambulation Classification score: . In terms of mobility and force, ameliorations were recorded, even if not significant (Rivermead Mobility Index: ; Manual Muscle Test: . Similar changes between groups were observed for independence in activities of daily living, neurological assessments, and spasticity reduction. These results highlight the potential efficacy for patients affected by a droop foot of a walking training performed with a neurostimulator in subacute phase.
Kalron, Alon; Rosenblum, Uri; Frid, Lior; Achiron, Anat
2017-03-01
Evaluate the effects of a Pilates exercise programme on walking and balance in people with multiple sclerosis and compare this exercise approach to conventional physical therapy sessions. Randomized controlled trial. Multiple Sclerosis Center, Sheba Medical Center, Tel-Hashomer, Israel. Forty-five people with multiple sclerosis, 29 females, mean age (SD) was 43.2 (11.6) years; mean Expanded Disability Status Scale (S.D) was 4.3 (1.3). Participants received 12 weekly training sessions of either Pilates ( n=22) or standardized physical therapy ( n=23) in an outpatient basis. Spatio-temporal parameters of walking and posturography parameters during static stance. Functional tests included the Time Up and Go Test, 2 and 6-minute walk test, Functional Reach Test, Berg Balance Scale and the Four Square Step Test. In addition, the following self-report forms included the Multiple Sclerosis Walking Scale and Modified Fatigue Impact Scale. At the termination, both groups had significantly increased their walking speed ( P=0.021) and mean step length ( P=0.023). According to the 2-minute and 6-minute walking tests, both groups at the end of the intervention program had increased their walking speed. Mean (SD) increase in the Pilates and physical therapy groups were 39.1 (78.3) and 25.3 (67.2) meters, respectively. There was no effect of group X time in all instrumented and clinical balance and gait measures. Pilates is a possible treatment option for people with multiple sclerosis in order to improve their walking and balance capabilities. However, this approach does not have any significant advantage over standardized physical therapy.
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
A Markov random walk under constraint for discovering overlapping communities in complex networks
Jin, Di; Yang, Bo; Liu, Dayou; He, Dongxiao; Liu, Jie; Baquero, Carlos
2011-01-01
The detection of overlapping communities in complex networks has motivated recent research in relevant fields. Aiming to address this problem, we propose a Markov-dynamics-based algorithm, called UEOC, which means 'unfold and extract overlapping communities'. In UEOC, when identifying each natural community that overlaps, a Markov random walk method combined with a constraint strategy, which is based on the corresponding annealed network (degree conserving random network), is performed to unfold the community. Then, a cutoff criterion with the aid of a local community function, called conductance, which can be thought of as the ratio between the number of edges inside the community and those leaving it, is presented to extract this emerged community from the entire network. The UEOC algorithm depends on only one parameter whose value can be easily set, and it requires no prior knowledge of the hidden community structures. The proposed UEOC has been evaluated both on synthetic benchmarks and on some real-world networks, and has been compared with a set of competing algorithms. The experimental result has shown that UEOC is highly effective and efficient for discovering overlapping communities
Range walk error correction and modeling on Pseudo-random photon counting system
Shen, Shanshan; Chen, Qian; He, Weiji
2017-08-01
Signal to noise ratio and depth accuracy are modeled for the pseudo-random ranging system with two random processes. The theoretical results, developed herein, capture the effects of code length and signal energy fluctuation are shown to agree with Monte Carlo simulation measurements. First, the SNR is developed as a function of the code length. Using Geiger-mode avalanche photodiodes (GMAPDs), longer code length is proven to reduce the noise effect and improve SNR. Second, the Cramer-Rao lower bound on range accuracy is derived to justify that longer code length can bring better range accuracy. Combined with the SNR model and CRLB model, it is manifested that the range accuracy can be improved by increasing the code length to reduce the noise-induced error. Third, the Cramer-Rao lower bound on range accuracy is shown to converge to the previously published theories and introduce the Gauss range walk model to range accuracy. Experimental tests also converge to the presented boundary model in this paper. It has been proven that depth error caused by the fluctuation of the number of detected photon counts in the laser echo pulse leads to the depth drift of Time Point Spread Function (TPSF). Finally, numerical fitting function is used to determine the relationship between the depth error and the photon counting ratio. Depth error due to different echo energy is calibrated so that the corrected depth accuracy is improved to 1cm.
Random Walk on a Perturbation of the Infinitely-Fast Mixing Interchange Process
Salvi, Michele; Simenhaus, François
2018-03-01
We consider a random walk in dimension d≥1 in a dynamic random environment evolving as an interchange process with rate γ >0 . We prove that, if we choose γ large enough, almost surely the empirical velocity of the walker X_t/t eventually lies in an arbitrary small ball around the annealed drift. This statement is thus a perturbation of the case γ =+∞ where the environment is refreshed between each step of the walker. We extend three-way part of the results of Huveneers and Simenhaus (Electron J Probab 20(105):42, 2015), where the environment was given by the 1-dimensional exclusion process: (i) We deal with any dimension d≥1 ; (ii) We treat the much more general interchange process, where each particle carries a transition vector chosen according to an arbitrary law μ ; (iii) We show that X_t/t is not only in the same direction of the annealed drift, but that it is also close to it.
A random walk model to simulate the atmospheric dispersion of radionuclide
Zhuo, Jun; Huang, Liuxing; Niu, Shengli; Xie, Honggang; Kuang, Feihong
2018-01-01
To investigate the atmospheric dispersion of radionuclide in large-medium scale, a numerical simulation method based on random walk model for radionuclide atmospheric dispersion was established in the paper. The route of radionuclide migration and concentration distribution of radionuclide can be calculated out by using the method with the real-time or historical meteorological fields. In the simulation, a plume of radionuclide is treated as a lot of particles independent of each other. The particles move randomly by the fluctuations of turbulence, and disperse, so as to enlarge the volume of the plume and dilute the concentration of radionuclide. The dispersion of the plume over time is described by the variance of the particles. Through statistical analysis, the relationships between variance of the particles and radionuclide dispersion characteristics can be derived. The main mechanisms considered in the physical model are: (1) advection of radionuclide by mean air motion, (2) mixing of radionuclide by atmospheric turbulence, (3) dry and wet deposition, (4) disintegration. A code named RADES was developed according the method. And then, the European Tracer Experiment (ETEX) in 1994 is simulated by the RADES and FLEXPART codes, the simulation results of the concentration distribution of tracer are in good agreement with the experimental data.
Random Walk on a Perturbation of the Infinitely-Fast Mixing Interchange Process
Salvi, Michele; Simenhaus, François
2018-05-01
We consider a random walk in dimension d≥ 1 in a dynamic random environment evolving as an interchange process with rate γ >0. We prove that, if we choose γ large enough, almost surely the empirical velocity of the walker X_t/t eventually lies in an arbitrary small ball around the annealed drift. This statement is thus a perturbation of the case γ =+∞ where the environment is refreshed between each step of the walker. We extend three-way part of the results of Huveneers and Simenhaus (Electron J Probab 20(105):42, 2015), where the environment was given by the 1-dimensional exclusion process: (i) We deal with any dimension d≥1; (ii) We treat the much more general interchange process, where each particle carries a transition vector chosen according to an arbitrary law μ ; (iii) We show that X_t/t is not only in the same direction of the annealed drift, but that it is also close to it.
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. Copyright Â© 2011 Elsevier Ltd. All rights reserved.
Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.
2017-12-01
We analyze a Markovian random walk strategy on undirected regular networks involving power matrix functions of the type L\\frac{α{2}} where L indicates a ‘simple’ Laplacian matrix. We refer to such walks as ‘fractional random walks’ with admissible interval 0walk. From these analytical results we establish a generalization of Polya’s recurrence theorem for fractional random walks on d-dimensional infinite lattices: The fractional random walk is transient for dimensions d > α (recurrent for d≤slantα ) of the lattice. As a consequence, for 0walk is transient for all lattice dimensions d=1, 2, .. and in the range 1≤slantα walk is transient only for lattice dimensions d≥slant 3 . The generalization of Polya’s recurrence theorem remains valid for the class of random walks with Lévy flight asymptotics for long-range steps. We also analyze the mean first passage probabilities, mean residence times, mean first passage times and global mean first passage times (Kemeny constant) for the fractional random walk. For an infinite 1D lattice (infinite ring) we obtain for the transient regime 0walk is generated by the non-diagonality of the fractional Laplacian matrix with Lévy-type heavy tailed inverse power law decay for the probability of long-range moves. This non-local and asymptotic behavior of the fractional random walk introduces small-world properties with the emergence of Lévy flights on large (infinite) lattices.
Anson, Eric; Ma, Lei; Meetam, Tippawan; Thompson, Elizabeth; Rathore, Roshita; Dean, Victoria; Jeka, John
2018-05-01
Virtual reality and augmented feedback have become more prevalent as training methods to improve balance. Few reports exist on the benefits of providing trunk motion visual feedback (VFB) during treadmill walking, and most of those reports only describe within session changes. To determine whether trunk motion VFB treadmill walking would improve over-ground balance for older adults with self-reported balance problems. 40 adults (75.8 years (SD 6.5)) with self-reported balance difficulties or a history of falling were randomized to a control or experimental group. Everyone walked on a treadmill at a comfortable speed 3×/week for 4 weeks in 2 min bouts separated by a seated rest. The control group was instructed to look at a stationary bulls-eye target while the experimental group also saw a moving cursor superimposed on the stationary bulls-eye that represented VFB of their walking trunk motion. The experimental group was instructed to keep the cursor in the center of the bulls-eye. Somatosensory (monofilaments and joint position testing) and vestibular function (canal specific clinical head impulses) was evaluated prior to intervention. Balance and mobility were tested before and after the intervention using Berg Balance Test, BESTest, mini-BESTest, and Six Minute Walk. There were no significant differences between groups before the intervention. The experimental group significantly improved on the BESTest (p = 0.031) and the mini-BEST (p = 0.019). The control group did not improve significantly on any measure. Individuals with more profound sensory impairments had a larger improvement on dynamic balance subtests of the BESTest. Older adults with self-reported balance problems improve their dynamic balance after training using trunk motion VFB treadmill walking. Individuals with worse sensory function may benefit more from trunk motion VFB during walking than individuals with intact sensory function. Copyright © 2018 Elsevier B.V. All rights reserved.
2013-01-01
Background Regaining independent ambulation is the top priority for individuals recovering from stroke. Thus, physical rehabilitation post-stroke should focus on improving walking function and endurance. However, the amount of walking completed by individuals with stroke attending rehabilitation is far below that required for independent community ambulation. There has been increased interest in accelerometer-based monitoring of walking post-stroke. Walking monitoring could be integrated within the goal-setting process for those with ambulation goals in rehabilitation. The feedback from these devices can be downloaded to a computer to produce reports. The purpose of this study is to determine the effect of accelerometer-based feedback of daily walking activity during rehabilitation on the frequency and duration of walking post-stroke. Methods Participants will be randomly assigned to one of two groups: feedback or no feedback. Participants will wear accelerometers daily during in- and out-patient rehabilitation and, for participants in the feedback group, the participants’ treating physiotherapist will receive regular reports of walking activity. The primary outcome measures are the amount of daily walking completed, as measured using the accelerometers, and spatio-temporal characteristics of walking (e.g. walking speed). We will also examine goal attainment, satisfaction with progress towards goals, stroke self-efficacy, and community-integration. Discussion Increased walking activity during rehabilitation is expected to improve walking function and community re-integration following discharge. In addition, a focus on altering walking behaviour within the rehabilitation setting may lead to altered behaviour and increased activity patterns after discharge. Trial registration ClinicalTrials.gov NCT01521234 PMID:23865593
Karstoft, Kristian; Winding, Kamilla; Knudsen, Sine H; Nielsen, Jens S; Thomsen, Carsten; Pedersen, Bente K; Solomon, Thomas P J
2013-02-01
To evaluate the feasibility of free-living walking training in type 2 diabetic patients and to investigate the effects of interval-walking training versus continuous-walking training upon physical fitness, body composition, and glycemic control. Subjects with type 2 diabetes were randomized to a control (n = 8), continuous-walking (n = 12), or interval-walking group (n = 12). Training groups were prescribed five sessions per week (60 min/session) and were controlled with an accelerometer and a heart-rate monitor. Continuous walkers performed all training at moderate intensity, whereas interval walkers alternated 3-min repetitions at low and high intensity. Before and after the 4-month intervention, the following variables were measured: VO(2)max, body composition, and glycemic control (fasting glucose, HbA(1c), oral glucose tolerance test, and continuous glucose monitoring [CGM]). Training adherence was high (89 ± 4%), and training energy expenditure and mean intensity were comparable. VO(2)max increased 16.1 ± 3.7% in the interval-walking group (P Body mass and adiposity (fat mass and visceral fat) decreased in the interval-walking group only (P interval-walking group. The continuous walkers showed no changes in glycemic control. Free-living walking training is feasible in type 2 diabetic patients. Continuous walking offsets the deterioration in glycemia seen in the control group, and interval walking is superior to energy expenditure-matched continuous walking for improving physical fitness, body composition, and glycemic control.
Grebenkov, Denis S
2011-02-01
A new method for computing the signal attenuation due to restricted diffusion in a linear magnetic field gradient is proposed. A fast random walk (FRW) algorithm for simulating random trajectories of diffusing spin-bearing particles is combined with gradient encoding. As random moves of a FRW are continuously adapted to local geometrical length scales, the method is efficient for simulating pulsed-gradient spin-echo experiments in hierarchical or multiscale porous media such as concrete, sandstones, sedimentary rocks and, potentially, brain or lungs. Copyright © 2010 Elsevier Inc. All rights reserved.
From medium heterogeneity to flow and transport: A time-domain random walk approach
Hakoun, V.; Comolli, A.; Dentz, M.
2017-12-01
The prediction of flow and transport processes in heterogeneous porous media is based on the qualitative and quantitative understanding of the interplay between 1) spatial variability of hydraulic conductivity, 2) groundwater flow and 3) solute transport. Using a stochastic modeling approach, we study this interplay through direct numerical simulations of Darcy flow and advective transport in heterogeneous media. First, we study flow in correlated hydraulic permeability fields and shed light on the relationship between the statistics of log-hydraulic conductivity, a medium attribute, and the flow statistics. Second, we determine relationships between Eulerian and Lagrangian velocity statistics, this means, between flow and transport attributes. We show how Lagrangian statistics and thus transport behaviors such as late particle arrival times are influenced by the medium heterogeneity on one hand and the initial particle velocities on the other. We find that equidistantly sampled Lagrangian velocities can be described by a Markov process that evolves on the characteristic heterogeneity length scale. We employ a stochastic relaxation model for the equidistantly sampled particle velocities, which is parametrized by the velocity correlation length. This description results in a time-domain random walk model for the particle motion, whose spatial transitions are characterized by the velocity correlation length and temporal transitions by the particle velocities. This approach relates the statistical medium and flow properties to large scale transport, and allows for conditioning on the initial particle velocities and thus to the medium properties in the injection region. The approach is tested against direct numerical simulations.
Ahlstrom, S.W.; Foote, H.P.; Arnett, R.C.; Cole, C.R.; Serne, R.J.
1977-05-01
The Multicomponent Mass Transfer (MMT) Model is a generic computer code, currently in its third generation, that was developed to predict the movement of radiocontaminants in the saturated and unsaturated sediments of the Hanford Site. This model was designed to use the water movement patterns produced by the unsaturated and saturated flow models coupled with dispersion and soil-waste reaction submodels to predict contaminant transport. This report documents the theorical foundation and the numerical solution procedure of the current (third) generation of the MMT Model. The present model simulates mass transport processes using an analog referred to as the Discrete-Parcel-Random-Walk (DPRW) algorithm. The basic concepts of this solution technique are described and the advantages and disadvantages of the DPRW scheme are discussed in relation to more conventional numerical techniques such as the finite-difference and finite-element methods. Verification of the numerical algorithm is demonstrated by comparing model results with known closed-form solutions. A brief error and sensitivity analysis of the algorithm with respect to numerical parameters is also presented. A simulation of the tritium plume beneath the Hanford Site is included to illustrate the use of the model in a typical application. 32 figs
Occupation times and ergodicity breaking in biased continuous time random walks
Bel, Golan; Barkai, Eli
2005-01-01
Continuous time random walk (CTRW) models are widely used to model diffusion in condensed matter. There are two classes of such models, distinguished by the convergence or divergence of the mean waiting time. Systems with finite average sojourn time are ergodic and thus Boltzmann-Gibbs statistics can be applied. We investigate the statistical properties of CTRW models with infinite average sojourn time; in particular, the occupation time probability density function is obtained. It is shown that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point exhibits bimodal U or trimodal W shape, related to the arcsine law. The key points are as follows. (a) In a CTRW with finite or infinite mean waiting time, the distribution of the number of visits on a lattice point is determined by the probability that a member of an ensemble of particles in equilibrium occupies the lattice point. (b) The asymmetry parameter of the probability distribution function of occupation times is related to the Boltzmann probability and to the partition function. (c) The ensemble average is given by Boltzmann-Gibbs statistics for either finite or infinite mean sojourn time, when detailed balance conditions hold. (d) A non-ergodic generalization of the Boltzmann-Gibbs statistical mechanics for systems with infinite mean sojourn time is found
Backward jump continuous-time random walk: An application to market trading
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.
How Far Is Quasar UV/Optical Variability from a Damped Random Walk at Low Frequency?
Guo Hengxiao; Wang Junxian; Cai Zhenyi; Sun Mouyuan, E-mail: hengxiaoguo@gmail.com, E-mail: jxw@ustc.edu.cn [CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei 230026 (China)
2017-10-01
Studies have shown that UV/optical light curves of quasars can be described using the prevalent damped random walk (DRW) model, also known as the Ornstein–Uhlenbeck process. A white noise power spectral density (PSD) is expected at low frequency in this model; however, a direct observational constraint to the low-frequency PSD slope is difficult due to the limited lengths of the light curves available. Meanwhile, quasars show scatter in their DRW parameters that is too large to be attributed to uncertainties in the measurements and dependence on the variation of known physical factors. In this work we present simulations showing that, if the low-frequency PSD deviates from the DRW, the red noise leakage can naturally produce large scatter in the variation parameters measured from simulated light curves. The steeper the low-frequency PSD slope, the larger scatter we expect. Based on observations of SDSS Stripe 82 quasars, we find that the low-frequency PSD slope should be no steeper than −1.3. The actual slope could be flatter, which consequently requires that the quasar variabilities should be influenced by other unknown factors. We speculate that the magnetic field and/or metallicity could be such additional factors.
Coverage maximization under resource constraints using a nonuniform proliferating random walk.
Saha, Sudipta; Ganguly, Niloy
2013-02-01
Information management services on networks, such as search and dissemination, play a key role in any large-scale distributed system. One of the most desirable features of these services is the maximization of the coverage, i.e., the number of distinctly visited nodes under constraints of network resources as well as time. However, redundant visits of nodes by different message packets (modeled, e.g., as walkers) initiated by the underlying algorithms for these services cause wastage of network resources. In this work, using results from analytical studies done in the past on a K-random-walk-based algorithm, we identify that redundancy quickly increases with an increase in the density of the walkers. Based on this postulate, we design a very simple distributed algorithm which dynamically estimates the density of the walkers and thereby carefully proliferates walkers in sparse regions. We use extensive computer simulations to test our algorithm in various kinds of network topologies whereby we find it to be performing particularly well in networks that are highly clustered as well as sparse.
The influence of gap distance on the random walk of cathode spot in vacuum arc
Shi Zongqian; Xiao Jia; Jia Shenli; Liu Zhigang; Wang Lijun
2007-01-01
Experiments were conducted in a detachable vacuum chamber for Cu vacuum arc with arc current in the range 19-24 A. Experimental results indicated that the gap distance had a distinct influence on the characteristics of the random walk of the cathode spot (CS) for the gap distance adopted, i.e. d = 4.8 mm and d = 6.8 mm. It was found that the increase in the gap distance could lead to a larger diffusion parameter. Based on the dynamics of fragments constituting the CS, it was proposed that with a longer gap distance, the magnetic interaction between fragments would be strengthened. It would result in the increase of the mean step length of the CS and the decrease of the mean step time, which would lead to a larger diffusion parameter as observed. The plasma density in the region of the CS was also found to decrease with the increase in the gap distance. It would result in the CS having a higher probability of jumping to the contaminated region but not to the vicinity of the existing crater
Fluctuations around equilibrium laws in ergodic continuous-time random walks.
Schulz, Johannes H P; Barkai, Eli
2015-06-01
We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.
Continuous time random walk analysis of solute transport in fractured porous media
Cortis, Andrea; Cortis, Andrea; Birkholzer, Jens
2008-06-01
The objective of this work is to discuss solute transport phenomena in fractured porous media, where the macroscopic transport of contaminants in the highly permeable interconnected fractures can be strongly affected by solute exchange with the porous rock matrix. We are interested in a wide range of rock types, with matrix hydraulic conductivities varying from almost impermeable (e.g., granites) to somewhat permeable (e.g., porous sandstones). In the first case, molecular diffusion is the only transport process causing the transfer of contaminants between the fractures and the matrix blocks. In the second case, additional solute transfer occurs as a result of a combination of advective and dispersive transport mechanisms, with considerable impact on the macroscopic transport behavior. We start our study by conducting numerical tracer experiments employing a discrete (microscopic) representation of fractures and matrix. Using the discrete simulations as a surrogate for the 'correct' transport behavior, we then evaluate the accuracy of macroscopic (continuum) approaches in comparison with the discrete results. However, instead of using dual-continuum models, which are quite often used to account for this type of heterogeneity, we develop a macroscopic model based on the Continuous Time Random Walk (CTRW) framework, which characterizes the interaction between the fractured and porous rock domains by using a probability distribution function of residence times. A parametric study of how CTRW parameters evolve is presented, describing transport as a function of the hydraulic conductivity ratio between fractured and porous domains.
Geiger, S.; Cortis, A.; Birkholzer, J.T.
2010-04-01
Solute transport in fractured porous media is typically 'non-Fickian'; that is, it is characterized by early breakthrough and long tailing and by nonlinear growth of the Green function-centered second moment. This behavior is due to the effects of (1) multirate diffusion occurring between the highly permeable fracture network and the low-permeability rock matrix, (2) a wide range of advection rates in the fractures and, possibly, the matrix as well, and (3) a range of path lengths. As a consequence, prediction of solute transport processes at the macroscale represents a formidable challenge. Classical dual-porosity (or mobile-immobile) approaches in conjunction with an advection-dispersion equation and macroscopic dispersivity commonly fail to predict breakthrough of fractured porous media accurately. It was recently demonstrated that the continuous time random walk (CTRW) method can be used as a generalized upscaling approach. Here we extend this work and use results from high-resolution finite element-finite volume-based simulations of solute transport in an outcrop analogue of a naturally fractured reservoir to calibrate the CTRW method by extracting a distribution of retention times. This procedure allows us to predict breakthrough at other model locations accurately and to gain significant insight into the nature of the fracture-matrix interaction in naturally fractured porous reservoirs with geologically realistic fracture geometries.
Anta, Juan A; Mora-Seró, Iván; Dittrich, Thomas; Bisquert, Juan
2008-08-14
We make use of the numerical simulation random walk (RWNS) method to compute the "jump" diffusion coefficient of electrons in nanostructured materials via mean-square displacement. First, a summary of analytical results is given that relates the diffusion coefficient obtained from RWNS to those in the multiple-trapping (MT) and hopping models. Simulations are performed in a three-dimensional lattice of trap sites with energies distributed according to an exponential distribution and with a step-function distribution centered at the Fermi level. It is observed that once the stationary state is reached, the ensemble of particles follow Fermi-Dirac statistics with a well-defined Fermi level. In this stationary situation the diffusion coefficient obeys the theoretical predictions so that RWNS effectively reproduces the MT model. Mobilities can be also computed when an electrical bias is applied and they are observed to comply with the Einstein relation when compared with steady-state diffusion coefficients. The evolution of the system towards the stationary situation is also studied. When the diffusion coefficients are monitored along simulation time a transition from anomalous to trap-limited transport is observed. The nature of this transition is discussed in terms of the evolution of electron distribution and the Fermi level. All these results will facilitate the use of RW simulation and related methods to interpret steady-state as well as transient experimental techniques.
RRW: repeated random walks on genome-scale protein networks for local cluster discovery
Can Tolga
2009-09-01
Full Text Available Abstract Background We propose an efficient and biologically sensitive algorithm based on repeated random walks (RRW for discovering functional modules, e.g., complexes and pathways, within large-scale protein networks. Compared to existing cluster identification techniques, RRW implicitly makes use of network topology, edge weights, and long range interactions between proteins. Results We apply the proposed technique on a functional network of yeast genes and accurately identify statistically significant clusters of proteins. We validate the biological significance of the results using known complexes in the MIPS complex catalogue database and well-characterized biological processes. We find that 90% of the created clusters have the majority of their catalogued proteins belonging to the same MIPS complex, and about 80% have the majority of their proteins involved in the same biological process. We compare our method to various other clustering techniques, such as the Markov Clustering Algorithm (MCL, and find a significant improvement in the RRW clusters' precision and accuracy values. Conclusion RRW, which is a technique that exploits the topology of the network, is more precise and robust in finding local clusters. In addition, it has the added flexibility of being able to find multi-functional proteins by allowing overlapping clusters.
The stretch to stray on time: Resonant length of random walks in a transient
Falcke, Martin; Friedhoff, Victor Nicolai
2018-05-01
First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average first-passage time or control might be applied to reduce noise. We investigate moments of the first-passage time distribution under an exponential transient describing relaxation of environmental conditions. We solve the Laplace-transformed (generalized) master equation analytically using a novel method that is applicable to general state schemes. The first-passage time from one end to the other of a linear chain of states is our application for the solutions. The dependence of its average on the relaxation rate obeys a power law for slow transients. The exponent ν depends on the chain length N like ν = - N / ( N + 1 ) to leading order. Slow transients substantially reduce the noise of first-passage times expressed as the coefficient of variation (CV), even if the average first-passage time is much longer than the transient. The CV has a pronounced minimum for some lengths, which we call resonant lengths. These results also suggest a simple and efficient noise control strategy and are closely related to the timing of repetitive excitations, coherence resonance, and information transmission by noisy excitable systems. A resonant number of steps from the inhibited state to the excitation threshold and slow recovery from negative feedback provide optimal timing noise reduction and information transmission.
Calibration of Discrete Random Walk (DRW) Model via G.I Taylor's Dispersion Theory
Javaherchi, Teymour; Aliseda, Alberto
2012-11-01
Prediction of particle dispersion in turbulent flows is still an important challenge with many applications to environmental, as well as industrial, fluid mechanics. Several models of dispersion have been developed to predict particle trajectories and their relative velocities, in combination with a RANS-based simulation of the background flow. The interaction of the particles with the velocity fluctuations at different turbulent scales represents a significant difficulty in generalizing the models to the wide range of flows where they are used. We focus our attention on the Discrete Random Walk (DRW) model applied to flow in a channel, particularly to the selection of eddies lifetimes as realizations of a Poisson distribution with a mean value proportional to κ / ɛ . We present a general method to determine the constant of this proportionality by matching the DRW model dispersion predictions for fluid element and particle dispersion to G.I Taylor's classical dispersion theory. This model parameter is critical to the magnitude of predicted dispersion. A case study of its influence on sedimentation of suspended particles in a tidal channel with an array of Marine Hydrokinetic (MHK) turbines highlights the dependency of results on this time scale parameter. Support from US DOE through the Northwest National Marine Renewable Energy Center, a UW-OSU partnership.
Learning by random walks in the weight space of the Ising perceptron
Huang, Haiping; Zhou, Haijun
2010-01-01
Several variants of a stochastic local search process for constructing the synaptic weights of an Ising perceptron are studied. In this process, binary patterns are sequentially presented to the Ising perceptron and are then learned as the synaptic weight configuration is modified through a chain of single- or double-weight flips within the compatible weight configuration space of the earlier learned patterns. This process is able to reach a storage capacity of α≈0.63 for pattern length N = 101 and α≈0.41 for N = 1001. If in addition a relearning process is exploited, the learning performance is further improved to a storage capacity of α≈0.80 for N = 101 and α≈0.42 for N = 1001. We found that, for a given learning task, the solutions constructed by the random walk learning process are separated by a typical Hamming distance, which decreases with the constraint density α of the learning task; at a fixed value of α, the width of the Hamming distance distribution decreases with N
Mandujano-Ramírez, Humberto J; González-Vázquez, José P; Oskam, Gerko; Dittrich, Thomas; Garcia-Belmonte, Germa; Mora-Seró, Iván; Bisquert, Juan; Anta, Juan A
2014-03-07
Many recent advances in novel solar cell technologies are based on charge separation in disordered semiconductor heterojunctions. In this work we use the Random Walk Numerical Simulation (RWNS) method to model the dynamics of electrons and holes in two disordered semiconductors in contact. Miller-Abrahams hopping rates and a tunnelling distance-dependent electron-hole annihilation mechanism are used to model transport and recombination, respectively. To test the validity of the model, three numerical "experiments" have been devised: (1) in the absence of constant illumination, charge separation has been quantified by computing surface photovoltage (SPV) transients. (2) By applying a continuous generation of electron-hole pairs, the model can be used to simulate a solar cell under steady-state conditions. This has been exploited to calculate open-circuit voltages and recombination currents for an archetypical bulk heterojunction solar cell (BHJ). (3) The calculations have been extended to nanostructured solar cells with inorganic sensitizers to study, specifically, non-ideality in the recombination rate. The RWNS model in combination with exponential disorder and an activated tunnelling mechanism for transport and recombination is shown to reproduce correctly charge separation parameters in these three "experiments". This provides a theoretical basis to study relevant features of novel solar cell technologies.
The Random Walk of Cars and Their Collision Probabilities with Planets
Hanno Rein
2018-05-01
Full Text Available On 6 February 2018, SpaceX launched a Tesla Roadster on a Mars-crossing orbit. We perform N-body simulations to determine the fate of the object over the next 15 Myr. The orbital evolution is initially dominated by close encounters with the Earth. While a precise orbit can not be predicted beyond the next several centuries due to these repeated chaotic scatterings, one can reliably predict the long-term outcomes by statistically analyzing a large suite of possible trajectories with slightly perturbed initial conditions. Repeated gravitational scatterings with Earth lead to a random walk. Collisions with the Earth, Venus and the Sun represent primary sinks for the Roadster’s orbital evolution. Collisions with Mercury and Mars, or ejections from the Solar System by Jupiter, are highly unlikely. We calculate a dynamical half-life of the Tesla of approximately 15 Myr, with some 22%, 12% and 12% of Roadster orbit realizations impacting the Earth, Venus, and the Sun within one half-life, respectively. Because the eccentricities and inclinations in our ensemble increase over time due to mean-motion and secular resonances, the impact rates with the terrestrial planets decrease beyond a few million years, whereas the impact rate on the Sun remains roughly constant.
Identifying and Analyzing Novel Epilepsy-Related Genes Using Random Walk with Restart Algorithm
Wei Guo
2017-01-01
Full Text Available As a pathological condition, epilepsy is caused by abnormal neuronal discharge in brain which will temporarily disrupt the cerebral functions. Epilepsy is a chronic disease which occurs in all ages and would seriously affect patients’ personal lives. Thus, it is highly required to develop effective medicines or instruments to treat the disease. Identifying epilepsy-related genes is essential in order to understand and treat the disease because the corresponding proteins encoded by the epilepsy-related genes are candidates of the potential drug targets. In this study, a pioneering computational workflow was proposed to predict novel epilepsy-related genes using the random walk with restart (RWR algorithm. As reported in the literature RWR algorithm often produces a number of false positive genes, and in this study a permutation test and functional association tests were implemented to filter the genes identified by RWR algorithm, which greatly reduce the number of suspected genes and result in only thirty-three novel epilepsy genes. Finally, these novel genes were analyzed based upon some recently published literatures. Our findings implicate that all novel genes were closely related to epilepsy. It is believed that the proposed workflow can also be applied to identify genes related to other diseases and deepen our understanding of the mechanisms of these diseases.
Sharp Trapping Boundaries in the Random Walk of Interplanetary Magnetic Field Lines
Ruffolo, D.; Chuychai, P.; Meechai, J.; Pongkitiwanichkul, P.; Kimpraphan, N.; Matthaeus, W. H.; Rowlands, G.
2004-05-01
Although magnetic field lines in space are believed to undergo a diffusive random walk in the long-distance limit, observed dropouts of solar energetic particles, as well as computer simulations, indicate sharply defined filaments in which interplanetary magnetic field lines have been temporarily trapped. We identify mechanisms that can explain such sharp boundaries in the framework of 2D+slab turbulence, a model that provides a good explanation of solar wind turbulence spectra and the parallel transport of solar energetic particles. Local trapping boundaries (LTBs) are empirically defined as trajectories of 2D turbulence where the mean 2D field is a local maximum. In computer simulations, the filaments (or ``islands'' in the two dimensions perpendicular to the mean field) that are most resistant to slab diffusion correspond closely to the mathematically defined LTBs, that is, there is a mathematical prescription for defining the trapping regions. Furthermore, we provide computational evidence and a theoretical explanation that strong 2D turbulence can inhibit diffusion due to the slab component. Therefore, while these filaments are basically defined by the small-scale topology of 2D turbulence, there can be sharp trapping boundaries where the 2D field is strongest. This work was supported by the Thailand Research Fund, the Rachadapisek Sompoj Fund of Chulalongkorn University, and NASA Grant NAG5-11603. G.R. thanks Mahidol University for its hospitality and the Thailand Commission for Higher Education for travel support.
Pfingsten, W.
1996-01-01
Safety assessments for radioactive waste repositories require a detailed knowledge of physical, chemical, hydrological, and geological processes for long time spans. In the past, individual models for hydraulics, transport, or geochemical processes were developed more or less separately to great sophistication for the individual processes. Such processes are especially important in the near field of a waste repository. Attempts have been made to couple at least two individual processes to get a more adequate description of geochemical systems. These models are called coupled codes; they couple predominantly a multicomponent transport model with a chemical reaction model. Here reactive transport is modeled by the sequentially coupled code MCOTAC that couples one-dimensional advective, dispersive, and diffusive transport with chemical equilibrium complexation and precipitation/dissolution reactions in a porous medium. Transport, described by a random walk of multispecies particles, and chemical equilibrium calculations are solved separately, coupled only by an exchange term. The modular-structured code was applied to incongruent dissolution of hydrated silicate gels, to movement of multiple solid front systems, and to an artificial, numerically difficult heterogeneous redox problem. These applications show promising features with respect to applicability to relevant problems and possibilities of extensions
Zhu, Zhizhong; Cui, Liling; Yin, Miaomiao; Yu, Yang; Zhou, Xiaona; Wang, Hongtu; Yan, Hua
2016-06-01
To investigate the effects of hydrotherapy on walking ability and balance in patients with chronic stroke. Single-blind, randomized controlled pilot trial. Outpatient rehabilitation clinic at a tertiary neurological hospital in China. A total of 28 participants with impairments in walking and controlling balance more than six months post-stroke. After baseline evaluations, participants were randomly assigned to a land-based therapy (control group, n = 14) or hydrotherapy (study group, n = 14). Participants underwent individual sessions for four weeks, five days a week, for 45 minutes per session. After four weeks of rehabilitation, all participants were evaluated by a blinded assessor. Functional assessments included the Functional Reach Test, Berg Balance Scale, 2-minute walk test, and Timed Up and Go Test. After four weeks of treatment, the Berg Balance Scale, functional reach test, 2-minute walk test, and the Timed Up and Go Test scores had improved significantly in each group (P aquatic group than in the control group (P stroke. © The Author(s) 2015.
A non-Lévy random walk in chacma baboons: what does it mean?
Cédric Sueur
Full Text Available The Lévy walk is found from amoebas to humans and has been described as the optimal strategy for food research. Recent results, however, have generated controversy about this conclusion since animals also display alternatives to the Lévy walk such as the Brownian walk or mental maps and because movement patterns found in some species only seem to depend on food patches distribution. Here I show that movement patterns of chacma baboons do not follow a Lévy walk but a Brownian process. Moreover this Brownian walk is not the main process responsible for movement patterns of baboons. Findings about their speed and trajectories show that baboons use metal maps and memory to find resources. Thus the Brownian process found in this species appears to be more dependent on the environment or might be an alternative when known food patches are depleted and when animals have to find new resources.
Complementarity and quantum walks
Kendon, Viv; Sanders, Barry C.
2005-01-01
We show that quantum walks interpolate between a coherent 'wave walk' and a random walk depending on how strongly the walker's coin state is measured; i.e., the quantum walk exhibits the quintessentially quantum property of complementarity, which is manifested as a tradeoff between knowledge of which path the walker takes vs the sharpness of the interference pattern. A physical implementation of a quantum walk (the quantum quincunx) should thus have an identifiable walker and the capacity to demonstrate the interpolation between wave walk and random walk depending on the strength of measurement
Esophagus segmentation in CT via 3D fully convolutional neural network and random walk.
Fechter, Tobias; Adebahr, Sonja; Baltas, Dimos; Ben Ayed, Ismail; Desrosiers, Christian; Dolz, Jose
2017-12-01
the results of this model can be refined by a random walk step taking pixel intensities and neighborhood relationships into account. One of the main advantages of our network over previous methods is that it performs 3D convolutions, thus fully exploiting the 3D spatial context and performing an efficient volume-wise prediction. The whole segmentation process is fully automatic and yields esophagus delineations in very good agreement with the gold standard, showing that it can compete with previously published methods. © 2017 American Association of Physicists in Medicine.
Applicability of the condensed-random-walk Monte Carlo method at low energies in high-Z materials
Berger, Martin J.
1998-01-01
The predictions of several Monte Carlo codes were compared with each other and with experimental results pertaining to the penetration of through gold foils of electrons incident with energies from 128 to 8 keV. The main purpose was to demonstrate that reflection and transmission coefficients, for number and energy, can be estimated reliably with a simple Monte Carlo code based on the condensed-random-walk and continuous-slowing-down approximations
Soufi, M [Shahid Beheshti University, Tehran, Tehran (Iran, Islamic Republic of); Asl, A Kamali [Shahid Beheshti University, Tehran, Iran., Tehran, Tehran (Iran, Islamic Republic of); Geramifar, P [Shariati Hospital, Tehran, Iran., Tehran, Tehran (Iran, Islamic Republic of)
2015-06-15
Purpose: The objective of this study was to find the best seed localization parameters in random walk algorithm application to lung tumor delineation in Positron Emission Tomography (PET) images. Methods: PET images suffer from statistical noise and therefore tumor delineation in these images is a challenging task. Random walk algorithm, a graph based image segmentation technique, has reliable image noise robustness. Also its fast computation and fast editing characteristics make it powerful for clinical purposes. We implemented the random walk algorithm using MATLAB codes. The validation and verification of the algorithm have been done by 4D-NCAT phantom with spherical lung lesions in different diameters from 20 to 90 mm (with incremental steps of 10 mm) and different tumor to background ratios of 4:1 and 8:1. STIR (Software for Tomographic Image Reconstruction) has been applied to reconstruct the phantom PET images with different pixel sizes of 2×2×2 and 4×4×4 mm{sup 3}. For seed localization, we selected pixels with different maximum Standardized Uptake Value (SUVmax) percentages, at least (70%, 80%, 90% and 100%) SUVmax for foreground seeds and up to (20% to 55%, 5% increment) SUVmax for background seeds. Also, for investigation of algorithm performance on clinical data, 19 patients with lung tumor were studied. The resulted contours from algorithm have been compared with nuclear medicine expert manual contouring as ground truth. Results: Phantom and clinical lesion segmentation have shown that the best segmentation results obtained by selecting the pixels with at least 70% SUVmax as foreground seeds and pixels up to 30% SUVmax as background seeds respectively. The mean Dice Similarity Coefficient of 94% ± 5% (83% ± 6%) and mean Hausdorff Distance of 1 (2) pixels have been obtained for phantom (clinical) study. Conclusion: The accurate results of random walk algorithm in PET image segmentation assure its application for radiation treatment planning and
Soufi, M; Asl, A Kamali; Geramifar, P
2015-01-01
Purpose: The objective of this study was to find the best seed localization parameters in random walk algorithm application to lung tumor delineation in Positron Emission Tomography (PET) images. Methods: PET images suffer from statistical noise and therefore tumor delineation in these images is a challenging task. Random walk algorithm, a graph based image segmentation technique, has reliable image noise robustness. Also its fast computation and fast editing characteristics make it powerful for clinical purposes. We implemented the random walk algorithm using MATLAB codes. The validation and verification of the algorithm have been done by 4D-NCAT phantom with spherical lung lesions in different diameters from 20 to 90 mm (with incremental steps of 10 mm) and different tumor to background ratios of 4:1 and 8:1. STIR (Software for Tomographic Image Reconstruction) has been applied to reconstruct the phantom PET images with different pixel sizes of 2×2×2 and 4×4×4 mm 3 . For seed localization, we selected pixels with different maximum Standardized Uptake Value (SUVmax) percentages, at least (70%, 80%, 90% and 100%) SUVmax for foreground seeds and up to (20% to 55%, 5% increment) SUVmax for background seeds. Also, for investigation of algorithm performance on clinical data, 19 patients with lung tumor were studied. The resulted contours from algorithm have been compared with nuclear medicine expert manual contouring as ground truth. Results: Phantom and clinical lesion segmentation have shown that the best segmentation results obtained by selecting the pixels with at least 70% SUVmax as foreground seeds and pixels up to 30% SUVmax as background seeds respectively. The mean Dice Similarity Coefficient of 94% ± 5% (83% ± 6%) and mean Hausdorff Distance of 1 (2) pixels have been obtained for phantom (clinical) study. Conclusion: The accurate results of random walk algorithm in PET image segmentation assure its application for radiation treatment planning and
Godrèche, Claude
2017-05-01
The probability distribution of the longest interval between two zeros of a simple random walk starting and ending at the origin, and of its continuum limit, the Brownian bridge, was analysed in the past by Rosén and Wendel, then extended by the latter to stable processes. We recover and extend these results using simple concepts of renewal theory, which allows to revisit past and recent works of the physics literature.
Godrèche, Claude
2017-01-01
The probability distribution of the longest interval between two zeros of a simple random walk starting and ending at the origin, and of its continuum limit, the Brownian bridge, was analysed in the past by Rosén and Wendel, then extended by the latter to stable processes. We recover and extend these results using simple concepts of renewal theory, which allows to revisit past and recent works of the physics literature. (paper)
Haroldo Valetin Ribeiro
2012-03-01
Full Text Available We investigate how it is possible to obtain different diffusive regimes from the Continuous Time Random Walk (CTRW approach performing suitable changes for the waiting time and jumping distributions in order to get two or more regimes for the same diffusive process. We also obtain diffusion-like equations related to these processes and investigate the connection of the results with anomalous diffusion.
Fast Inbound Top-K Query for Random Walk with Restart.
Zhang, Chao; Jiang, Shan; Chen, Yucheng; Sun, Yidan; Han, Jiawei
2015-09-01
Random walk with restart (RWR) is widely recognized as one of the most important node proximity measures for graphs, as it captures the holistic graph structure and is robust to noise in the graph. In this paper, we study a novel query based on the RWR measure, called the inbound top-k (Ink) query. Given a query node q and a number k , the Ink query aims at retrieving k nodes in the graph that have the largest weighted RWR scores to q . Ink queries can be highly useful for various applications such as traffic scheduling, disease treatment, and targeted advertising. Nevertheless, none of the existing RWR computation techniques can accurately and efficiently process the Ink query in large graphs. We propose two algorithms, namely Squeeze and Ripple, both of which can accurately answer the Ink query in a fast and incremental manner. To identify the top- k nodes, Squeeze iteratively performs matrix-vector multiplication and estimates the lower and upper bounds for all the nodes in the graph. Ripple employs a more aggressive strategy by only estimating the RWR scores for the nodes falling in the vicinity of q , the nodes outside the vicinity do not need to be evaluated because their RWR scores are propagated from the boundary of the vicinity and thus upper bounded. Ripple incrementally expands the vicinity until the top- k result set can be obtained. Our extensive experiments on real-life graph data sets show that Ink queries can retrieve interesting results, and the proposed algorithms are orders of magnitude faster than state-of-the-art method.
Directional migration of recirculating lymphocytes through lymph nodes via random walks.
Niclas Thomas
Full Text Available Naive T lymphocytes exhibit extensive antigen-independent recirculation between blood and lymph nodes, where they may encounter dendritic cells carrying cognate antigen. We examine how long different T cells may spend in an individual lymph node by examining data from long term cannulation of blood and efferent lymphatics of a single lymph node in the sheep. We determine empirically the distribution of transit times of migrating T cells by applying the Least Absolute Shrinkage & Selection Operator (LASSO or regularised S-LASSO to fit experimental data describing the proportion of labelled infused cells in blood and efferent lymphatics over time. The optimal inferred solution reveals a distribution with high variance and strong skew. The mode transit time is typically between 10 and 20 hours, but a significant number of cells spend more than 70 hours before exiting. We complement the empirical machine learning based approach by modelling lymphocyte passage through the lymph node insilico. On the basis of previous two photon analysis of lymphocyte movement, we optimised distributions which describe the transit times (first passage times of discrete one dimensional and continuous (Brownian three dimensional random walks with drift. The optimal fit is obtained when drift is small, i.e. the ratio of probabilities of migrating forward and backward within the node is close to one. These distributions are qualitatively similar to the inferred empirical distribution, with high variance and strong skew. In contrast, an optimised normal distribution of transit times (symmetrical around mean fitted the data poorly. The results demonstrate that the rapid recirculation of lymphocytes observed at a macro level is compatible with predominantly randomised movement within lymph nodes, and significant probabilities of long transit times. We discuss how this pattern of migration may contribute to facilitating interactions between low frequency T cells and antigen
Bodin, Jacques
2015-03-01
In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.
Anisotropy of the monomer random walk in a polymer melt: local-order and connectivity effects
Bernini, S; Leporini, D
2016-01-01
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. (paper)
Identifying co-targets to fight drug resistance based on a random walk model
Chen Liang-Chun
2012-01-01
Full Text Available Abstract Background Drug resistance has now posed more severe and emergent threats to human health and infectious disease treatment. However, wet-lab approaches alone to counter drug resistance have so far still achieved limited success due to less knowledge about the underlying mechanisms of drug resistance. Our approach apply a heuristic search algorithm in order to extract active network under drug treatment and use a random walk model to identify potential co-targets for effective antibacterial drugs. Results We use interactome network of Mycobacterium tuberculosis and gene expression data which are treated with two kinds of antibiotic, Isoniazid and Ethionamide as our test data. Our analysis shows that the active drug-treated networks are associated with the trigger of fatty acid metabolism and synthesis and nicotinamide adenine dinucleotide (NADH-related processes and those results are consistent with the recent experimental findings. Efflux pumps processes appear to be the major mechanisms of resistance but SOS response is significantly up-regulation under Isoniazid treatment. We also successfully identify the potential co-targets with literature confirmed evidences which are related to the glycine-rich membrane, adenosine triphosphate energy and cell wall processes. Conclusions With gene expression and interactome data supported, our study points out possible pathways leading to the emergence of drug resistance under drug treatment. We develop a computational workflow for giving new insights to bacterial drug resistance which can be gained by a systematic and global analysis of the bacterial regulation network. Our study also discovers the potential co-targets with good properties in biological and graph theory aspects to overcome the problem of drug resistance.
Recchia, Stephen
Kevlar is the most common high-end plastic filament yarn used in body armor, tire reinforcement, and wear resistant applications. Kevlar is a trade name for an aramid fiber. These are fibers in which the chain molecules are highly oriented along the fiber axis, so the strength of the chemical bond can be exploited. The bulk material is extruded into filaments that are bound together into yarn, which may be chorded with other materials as in car tires, woven into a fabric, or layered in an epoxy to make composite panels. The high tensile strength to low weight ratio makes this material ideal for designs that decrease weight and inertia, such as automobile tires, body panels, and body armor. For designs that use Kevlar, increasing the strength, or tenacity, to weight ratio would improve performance or reduce cost of all products that are based on this material. This thesis computationally and experimentally investigates the tenacity and stiffness of Kevlar yarns with varying twist ratios. The test boundary conditions were replicated with a geometrically accurate finite element model, resulting in a customized code that can reproduce tortuous filaments in a yarn was developed. The solid model geometry capturing filament tortuosity was implemented through a random walk method of axial geometry creation. A finite element analysis successfully recreated the yarn strength and stiffness dependency observed during the tests. The physics applied in the finite element model was reproduced in an analytical equation that was able to predict the failure strength and strain dependency of twist ratio. The analytical solution can be employed to optimize yarn design for high strength applications.
Kittas, Aristotelis; Delobelle, Aurélien; Schmitt, Sabrina; Breuhahn, Kai; Guziolowski, Carito; Grabe, Niels
2016-01-01
An effective means to analyze mRNA expression data is to take advantage of established knowledge from pathway databases, using methods such as pathway-enrichment analyses. However, pathway databases are not case-specific and expression data could be used to infer gene-regulation patterns in the context of specific pathways. In addition, canonical pathways may not always describe the signaling mechanisms properly, because interactions can frequently occur between genes in different pathways. Relatively few methods have been proposed to date for generating and analyzing such networks, preserving the causality between gene interactions and reasoning over the qualitative logic of regulatory effects. We present an algorithm (MCWalk) integrated with a logic programming approach, to discover subgraphs in large-scale signaling networks by random walks in a fully automated pipeline. As an exemplary application, we uncover the signal transduction mechanisms in a gene interaction network describing hepatocyte growth factor-stimulated cell migration and proliferation from gene-expression measured with microarray and RT-qPCR using in-house perturbation experiments in a keratinocyte-fibroblast co-culture. The resulting subgraphs illustrate possible associations of hepatocyte growth factor receptor c-Met nodes, differentially expressed genes and cellular states. Using perturbation experiments and Answer Set programming, we are able to select those which are more consistent with the experimental data. We discover key regulator nodes by measuring the frequency with which they are traversed when connecting signaling between receptors and significantly regulated genes and predict their expression-shift consistently with the measured data. The Java implementation of MCWalk is publicly available under the MIT license at: https://bitbucket.org/akittas/biosubg. © 2015 FEBS.
Aittasalo Minna
2012-06-01
Full Text Available Abstract Background The purpose of the study was to evaluate a 6-month intervention to promote office-employees’ walking with pedometers and e-mail messages. Methods Participants were recruited by 10 occupational health care units (OHC from 20 worksites with 2,230 employees. Voluntary and insufficiently physically active employees (N = 241 were randomized to a pedometer (STEP, N = 123 and a comparison group (COMP, N = 118. STEP included one group meeting, log-monitored pedometer-use and six e-mail messages from OHC. COMP participated in data collection. Reach, effectiveness, adoption, implementation, maintenance (RE-AIM and costs were assessed with questionnaires (0, 2, 6, 12 months, process evaluation and interviews (12 months. Results The intervention reached 29% (N = 646 of employees in terms of participation willingness. Logistic regression showed that the proportion of walkers tended to increase more in STEP than in COMP at 2 months in “walking for transportation” (Odds ratio 2.12, 95%CI 0.94 to 4.81 and at 6 months in “walking for leisure” (1.86, 95%CI 0.94 to 3.69. Linear model revealed a modest increase in the mean duration of “walking stairs” at 2 and 6 months (Geometric mean ratio 1.26, 95%CI 0.98 to 1.61; 1.27, 0.98 to 1.64. Adoption and implementation succeeded as intended. At 12 months, some traces of the intervention were sustained in 15 worksites, and a slightly higher number of walkers in STEP in comparison with COMP was observed in “walking stairs” (OR 2.24, 95%CI 0.94 to 5.31 and in “walking for leisure” (2.07, 95%CI 0.99 to 4.34. The direct costs of the intervention were 43 Euros per participant. Conclusions The findings indicate only modest impact on some indicators of walking. Future studies should invest in reaching the employees, minimizing attrition rate and using objective walking assessment. Trial registeration ISRCTN79432107
Matzer, Franziska; Nagele, Eva; Lerch, Nikolaus; Vajda, Christian; Fazekas, Christian
2018-04-01
Both physical activity and relaxation have stress-relieving potential. This study investigates their combined impact on the relaxation response while considering participants' initial stress level. In a randomized cross-over trial, 81 healthy adults completed 4 types of short-term interventions for stress reduction, each lasting for 1 hr: (1) physical activity (walking) combined with resting, (2) walking combined with balneotherapy, (3) combined resting and balneotherapy, and (4) resting only. Saliva cortisol, blood pressure, state of mood, and relaxation were measured preintervention and postintervention. Stress levels were determined by validated questionnaires. All interventions were associated with relaxation responses in the variables saliva cortisol, blood pressure, state of mood, and subjective relaxation. No significant differences were found regarding the reduction of salivary cortisol (F = 1.30; p = .281). The systolic blood pressure was reduced best when walking was combined with balneotherapy or resting (F = 7.34; p stress levels (n = 25) felt more alert after interventions including balneotherapy, whereas they reported an increase of tiredness when walking was combined with resting (F = 3.20; p = .044). Results suggest that combining physical activity and relaxation (resting or balneotherapy) is an advantageous short-term strategy for stress reduction as systolic blood pressure is reduced best while similar levels of relaxation can be obtained. Copyright © 2017 John Wiley & Sons, Ltd.
Continuous-time random-walk model for anomalous diffusion in expanding media
Le Vot, F.; Abad, E.; Yuste, S. B.
2017-09-01
Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium
Continuous-time random-walk model for anomalous diffusion in expanding media.
Le Vot, F; Abad, E; Yuste, S B
2017-09-01
Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium
Alghadir, Ahmad; Anwer, Shahnawaz
2016-04-12
Walking, a closed kinetic chain (CKC) activity, is widely used in knee rehabilitation as it allows early weight bearing and movement. It has been suggested that retro-walking may provide additional benefits beyond those experienced by forward-walking. The present study will investigate the effect of retro- and forward-walking on quadriceps muscle strength, pain, function, balance and mobility in knee Osteoarthritis (OA) subjects. Sixty-nine participants with knee OA will be recruited from the outpatient department in this randomized controlled trial. The participants will be randomly assigned to one of three groups; retro walking, forward walking or control group. The training program will be 3 days/week for 6 weeks. In addition, all the participants will receive a standard physiotherapy training program. An independent assessor blinded to group assignment will measure quadriceps muscle strength, knee pain intensity, functional disability, and mobility at baseline and 6 weeks after training. The results of this study will enhance our understanding on the therapeutic effects of walking (retro- or forward-walking) in knee OA. The findings from this study will help determine whether retro- or forward-walking or both are effective in the rehabilitation of subjects with knee OA. Controlled Trials ISRCTN12850845, Registered 26 January 2015.
Meirovitch, Hagai
1985-12-01
The scanning method proposed by us [J. Phys. A 15, L735 (1982); Macromolecules 18, 563 (1985)] for simulation of polymer chains is further developed and applied, for the first time, to a model with finite interactions. In addition to ``importance sampling,'' we remove the bias introduced by the scanning method with a procedure suggested recently by Schmidt [Phys. Rev. Lett. 51, 2175 (1983)]; this procedure has the advantage of enabling one to estimate the statistical error. We find these two procedures to be equally efficient. The model studied is an N-step random walk on a lattice, in which a random walk i has a statistical weight &, where p∞ for any dimension d by Donsker and Varadhan (DV) and by others. and lnφ, where φ is the survival probability in the trapping problem, diverge like Nα with α=d/(d+2). Most numerical studies, however, have failed to reach the DV regime in which d/(d+2) becomes a good approximation for α. On the other hand, our results for α (obtained for Nzero, and that the probability of a walk returning to the origin behaves approximately as N-1/3 for both d=2 and 3.
Thøgersen-Ntoumani, C; Loughren, E A; Kinnafick, F-E; Taylor, I M; Duda, J L; Fox, K R
2015-12-01
Physical activity may regulate affective experiences at work, but controlled studies are needed and there has been a reliance on retrospective accounts of experience. The purpose of the present study was to examine the effect of lunchtime walks on momentary work affect at the individual and group levels. Physically inactive employees (N = 56; M age = 47.68; 92.86% female) from a large university in the UK were randomized to immediate treatment or delayed treatment (DT). The DT participants completed both a control and intervention period. During the intervention period, participants partook in three weekly 30-min lunchtime group-led walks for 10 weeks. They completed twice daily affective reports at work (morning and afternoon) using mobile phones on two randomly chosen days per week. Multilevel modeling was used to analyze the data. Lunchtime walks improved enthusiasm, relaxation, and nervousness at work, although the pattern of results differed depending on whether between-group or within-person analyses were conducted. The intervention was effective in changing some affective states and may have broader implications for public health and workplace performance. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Cameron-Tucker HL
2016-08-01
Full Text Available Helen Laura Cameron-Tucker,1 Richard Wood-Baker,1 Lyn Joseph,1 Julia A Walters,1 Natalie Schüz,2 E Haydn Walters1 1Centre of Research Excellence for Chronic Respiratory Disease and Lung Aging, School of Medicine, 2School of Health Sciences, Faculty of Health, University of Tasmania, Hobart, Tasmania, Australia Purpose: With the limited reach of pulmonary rehabilitation (PR and low levels of daily physical activity in chronic obstructive pulmonary disease (COPD, a need exists to increase daily exercise. This study evaluated telephone health-mentoring targeting home-based walking (tele-rehab compared to usual waiting time (usual care followed by group PR. Patients and methods: People with COPD were randomized to tele-rehab (intervention or usual care (controls. Tele-rehab delivered by trained nurse health-mentors supported participants’ home-based walking over 8–12 weeks. PR, delivered to both groups simultaneously, included 8 weeks of once-weekly education and self-management skills, with separate supervised exercise. Data were collected at three time-points: baseline (TP1, before (TP2, and after (TP3 PR. The primary outcome was change in physical capacity measured by 6-minute walk distance (6MWD with two tests performed at each time-point. Secondary outcomes included changes in self-reported home-based walking, health-related quality of life, and health behaviors. Results: Of 65 recruits, 25 withdrew before completing PR. Forty attended a median of 6 (4 education sessions. Seventeen attended supervised exercise (5±2 sessions. Between TP1 and TP2, there was a statistically significant increase in the median 6MWD of 12 (39.1 m in controls, but no change in the tele-rehab group. There were no significant changes in 6MWD between other time-points or groups, or significant change in any secondary outcomes. Participants attending supervised exercise showed a nonsignificant improvement in 6MWD, 12.3 (71 m, while others showed no change, 0 (33 m
Pastor, María-Ángeles; López-Roig, Sofía; Lledó, Ana; Peñacoba, Cecilia; Velasco, Lilian; Schweiger-Gallo, Inge; Cigarán, Margarita; Ecija, Carmen; Limón, Ramón; Sanz, Yolanda
2014-04-11
Fibromyalgia patients are often advised to engage in regular low- to moderate-intensity physical exercise. The need of fibromyalgia patients to walk has been stressed in previous research. Behavioral self-regulation theories suggest that a combination of motivational aspects (to develop or strengthen a behavioral intention: Theory of Planned Behavior) and volitional aspects (engagement of intention in behavior: implementation intentions) is more effective than a single intervention. In this paper, we describe a protocol for identifying the motivational processes (using the Theory of Planned Behavior) involved in the practice of walking (phase I) and for studying the efficacy of an intervention that combines motivational and volitional contents to enhance the acquisition and continuation of this exercise behavior (phase II). The paper also shows the characteristics of eligible individuals (women who do not walk) and ineligible populations (women who walk or do not walk because of comorbidity without medical recommendation to walk). Both groups consist of members of any of four patients' associations in Spain who are between 18 and 70 years of age and meet the London Fibromyalgia Epidemiology Study Screening Questionnaire criteria for fibromyalgia. Furthermore, using this study protocol, we will explore the characteristics of participants (eligible women who agreed to participate in the study) and nonparticipants (eligible women who refused to participate). Two studies will be conducted: Phase I will be a cross-sectional study, and phase II will be a triple-blind, randomized longitudinal study with two treatment groups and one active control group. The questionnaires were sent to a total of 2,227 members of four patients' associations in Spain. A total of 920 participants with fibromyalgia returned the questionnaires, and 582 were ultimately selected to participate. The first data gathered have allowed us to identify the characteristics of the study population and
Maki, Yohko; Ura, Chiaki; Yamaguchi, Tomoharu; Murai, Tatsuhiko; Isahai, Mikie; Kaiho, Ayumi; Yamagami, Tetsuya; Tanaka, Satoshi; Miyamae, Fumiko; Sugiyama, Mika; Awata, Shuichi; Takahashi, Ryutaro; Yamaguchi, Haruyasu
2012-03-01
To evaluate the efficacy of a municipality-led walking program under the Japanese public Long-Term Care Insurance Act to prevent mental decline. Randomized controlled trial. The city of Takasaki. One hundred fifty community members aged 72.0 ± 4.0 were randomly divided into intervention (n = 75) and control (n = 75) groups. A walking program was conducted once a week for 90 minutes for 3 months. The program encouraged participants to walk on a regular basis and to increase their steps per day gradually. The intervention was conducted in small groups of approximately six, so combined benefits of exercise and social interaction were expected. Cognitive function was evaluated focusing on nine tests in five domains: memory, executive function, word fluency, visuospatial abilities, and sustained attention. Quality of life (QOL), depressive state, functional capacity, range of activities, and social network were assessed using questionnaires, and motor function was evaluated. Significant differences between the intervention and control groups were shown in word fluency related to frontal lobe function (F(1, 128) = 6.833, P = .01), QOL (F(1,128) = 9.751, P = .002), functional capacity including social interaction (F(1,128) = 13.055, P < .001), and motor function (Timed Up and Go Test: F(1,127) = 10.117, P = .002). No significant differences were observed in other cognitive tests. Walking programs may provide benefits in some aspects of cognition, QOL, and functional capacity including social interaction in elderly community members. This study could serve as the basis for implementation of a community-based intervention to prevent mental decline. © 2012, Copyright the Authors Journal compilation © 2012, The American Geriatrics Society.
MODELING THE TIME VARIABILITY OF SDSS STRIPE 82 QUASARS AS A DAMPED RANDOM WALK
MacLeod, C. L.; Ivezic, Z.; Bullock, E.; Kimball, A.; Sesar, B.; Westman, D.; Brooks, K.; Gibson, R.; Becker, A. C.; Kochanek, C. S.; Kozlowski, S.; Kelly, B.; De Vries, W. H.
2010-01-01
We model the time variability of ∼9000 spectroscopically confirmed quasars in SDSS Stripe 82 as a damped random walk (DRW). Using 2.7 million photometric measurements collected over 10 yr, we confirm the results of Kelly et al. and Kozlowski et al. that this model can explain quasar light curves at an impressive fidelity level (0.01-0.02 mag). The DRW model provides a simple, fast (O(N) for N data points), and powerful statistical description of quasar light curves by a characteristic timescale (τ) and an asymptotic rms variability on long timescales (SF ∞ ). We searched for correlations between these two variability parameters and physical parameters such as luminosity and black hole mass, and rest-frame wavelength. Our analysis shows SF ∞ to increase with decreasing luminosity and rest-frame wavelength as observed previously, and without a correlation with redshift. We find a correlation between SF ∞ and black hole mass with a power-law index of 0.18 ± 0.03, independent of the anti-correlation with luminosity. We find that τ increases with increasing wavelength with a power-law index of 0.17, remains nearly constant with redshift and luminosity, and increases with increasing black hole mass with a power-law index of 0.21 ± 0.07. The amplitude of variability is anti-correlated with the Eddington ratio, which suggests a scenario where optical fluctuations are tied to variations in the accretion rate. However, we find an additional dependence on luminosity and/or black hole mass that cannot be explained by the trend with Eddington ratio. The radio-loudest quasars have systematically larger variability amplitudes by about 30%, when corrected for the other observed trends, while the distribution of their characteristic timescale is indistinguishable from that of the full sample. We do not detect any statistically robust differences in the characteristic timescale and variability amplitude between the full sample and the small subsample of quasars detected
Helmstetter, A.; Sornette, D.
2002-01-01
The epidemic-type aftershock sequence (ETAS) model is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power-law decay ∼1/t 1+θ of seismicity after an earthquake) and Gutenberg-Richter law (power-law distribution of earthquake energies). In order to describe also the space distribution of seismicity, we use in addition a power-law distribution ∼1/r 1+μ of distances between triggered and triggering earthquakes. The ETAS model has been studied for the last two decades to model real seismicity catalogs and to obtain short-term probabilistic forecasts. Here, we present a mapping between the ETAS model and a class of CTRW (continuous time random walk) models, based on the identification of their corresponding master equations. This mapping allows us to use the wealth of results previously obtained on anomalous diffusion of CTRW. After translating into the relevant variable for the ETAS model, we provide a classification of the different regimes of diffusion of seismic activity triggered by a mainshock. Specifically, we derive the relation between the average distance between aftershocks and the mainshock as a function of the time from the mainshock and of the joint probability distribution of the times and locations of the aftershocks. The different regimes are fully characterized by the two exponents θ and μ. Our predictions are checked by careful numerical simulations. We stress the distinction between the 'bare' Omori law describing the seismic rate activated directly by a mainshock and the 'renormalized' Omori law taking into account all possible cascades from mainshocks to aftershocks of aftershock of aftershock, and so on. In particular, we predict that seismic diffusion or subdiffusion occurs and should be observable only when the observed Omori exponent is less than 1, because this signals the operation of the renormalization of the bare Omori law, also at the origin of seismic diffusion in
Interval-walking training for the treatment of type 2 diabetes: a randomized, controlled trial
Karstoft, Kristian; Winding, Kamilla; Knudsen, Sine H.
Formål: To evaluate the feasibility of free-living walking training in type 2 diabetes patients, and to investigate the effects of interval-walking training (IWT) versus continuous-walking training (CWT) upon self reported health, physical fitness, body composition and glycemic control. Metoder...... alternated 3-min repetitions at low and high intensity. Before and after the 4-month intervention, the following variables were measured: Self-reported health, Physical fitness (VO2max), body composition, and glycemic control (fasting glucose, HbA1c, oral glucose tolerance test, continuous glucose monitoring...... [CGM]). Resultater: Training adherence was high (89 + 4%), and training energy expenditure and mean intensity were comparable between training groups. Nine and four of the subjects reported “Improved Health” in the IWT and CWT group, respectively. VO2max increased 16.1 + 3.7% in the IWT group (P
Imam, Bita; Miller, William C; Finlayson, Heather; Eng, Janice J; Jarus, Tal
2017-01-01
To assess the feasibility of Wii.n.Walk for improving walking capacity in older adults with lower limb amputation. A parallel, evaluator-blind randomized controlled feasibility trial. Community-living. Individuals who were ⩾50 years old with a unilateral lower limb amputation. Wii.n.Walk consisted of Wii Fit training, 3x/week (40 minute sessions), for 4 weeks. Training started in the clinic in groups of 3 and graduated to unsupervised home training. Control group were trained using cognitive games. Feasibility indicators: trial process (recruitment, retention, participants' perceived benefit from the Wii.n.Walk intervention measured by exit questionnaire), resources (adherence), management (participant processing, blinding), and treatment (adverse event, and Cohen's d effect size and variance). Primary clinical outcome: walking capacity measured using the 2 Minute Walk Test at baseline, end of treatment, and 3-week retention. Of 28 randomized participants, 24 completed the trial (12/arm). Median (range) age was 62.0 (50-78) years. Mean (SD) score for perceived benefit from the Wii.n.Walk intervention was 38.9/45 (6.8). Adherence was 83.4%. The effect sizes for the 2 Minute Walk Test were 0.5 (end of treatment) and 0.6 (3-week retention) based on intention to treat with imputed data; and 0.9 (end of treatment) and 1.2 (3-week retention) based on per protocol analysis. The required sample size for a future larger RCT was deemed to be 72 (36 per arm). The results suggested the feasibility of the Wii.n.Walk with a medium effect size for improving walking capacity. Future larger randomized controlled trials investigating efficacy are warranted.
3D exemplar-based random walks for tooth segmentation from cone-beam computed tomography images
Pei, Yuru, E-mail: peiyuru@cis.pku.edu.cn; Ai, Xingsheng; Zha, Hongbin [Department of Machine Intelligence, School of EECS, Peking University, Beijing 100871 (China); Xu, Tianmin [School of Stomatology, Stomatology Hospital, Peking University, Beijing 100081 (China); Ma, Gengyu [uSens, Inc., San Jose, California 95110 (United States)
2016-09-15
Purpose: Tooth segmentation is an essential step in acquiring patient-specific dental geometries from cone-beam computed tomography (CBCT) images. Tooth segmentation from CBCT images is still a challenging task considering the comparatively low image quality caused by the limited radiation dose, as well as structural ambiguities from intercuspation and nearby alveolar bones. The goal of this paper is to present and discuss the latest accomplishments in semisupervised tooth segmentation with adaptive 3D shape constraints. Methods: The authors propose a 3D exemplar-based random walk method of tooth segmentation from CBCT images. The proposed method integrates semisupervised label propagation and regularization by 3D exemplar registration. To begin with, the pure random walk method is to get an initial segmentation of the teeth, which tends to be erroneous because of the structural ambiguity of CBCT images. And then, as an iterative refinement, the authors conduct a regularization by using 3D exemplar registration, as well as label propagation by random walks with soft constraints, to improve the tooth segmentation. In the first stage of the iteration, 3D exemplars with well-defined topologies are adapted to fit the tooth contours, which are obtained from the random walks based segmentation. The soft constraints on voxel labeling are defined by shape-based foreground dentine probability acquired by the exemplar registration, as well as the appearance-based probability from a support vector machine (SVM) classifier. In the second stage, the labels of the volume-of-interest (VOI) are updated by the random walks with soft constraints. The two stages are optimized iteratively. Instead of the one-shot label propagation in the VOI, an iterative refinement process can achieve a reliable tooth segmentation by virtue of exemplar-based random walks with adaptive soft constraints. Results: The proposed method was applied for tooth segmentation of twenty clinically captured CBCT
Merom, D; Gebel, K; Fahey, P; Astell-Burt, T; Voukelatos, A; Rissel, C; Sherrington, C
2015-01-01
In older adults the relationships between health, fall-related risk factors, perceived neighborhood walkability, walking behavior and intervention impacts are poorly understood. To determine whether: i) health and fall-related risk factors were associated with perceptions of neighborhood walkability; ii) perceived environmental attributes, and fall-related risk factors predicted change in walking behavior at 12 months; and iii) perceived environmental attributes and fall-related risk factors moderated the effect of a self-paced walking program on walking behavior. Randomized trial on walking and falls conducted between 2009 and 2012 involving 315 community-dwelling inactive adults ≥ 65 years living in Sydney, Australia. Measures were: mobility status, fall history, injurious fall and fear of falling (i.e., fall-related risk factors), health status, walking self-efficacy and 11 items from the neighborhood walkability scale and planned walking ≥ 150 min/week at 12 months. Participants with poorer mobility, fear of falling, and poor health perceived their surroundings as less walkable. Walking at 12 months was significantly greater in "less greenery" (AOR = 3.3, 95% CI: 1.11-9.98) and "high traffic" (AOR = 1.98, 95% CI: 1.00-3.91) neighborhoods. The intervention had greater effects in neighborhoods perceived to have poorer pedestrian infrastructure (p for interaction = 0.036). Low perceived walkability was shaped by health status and did not appear to be a barrier to walking behavior. There appears to be a greater impact of, and thus, need for, interventions to encourage walking in environments perceived not to have supportive walking infrastructure. Future studies on built environments and walking should gather information on fall-related risk factors to better understand how these characteristics interact.
Mawanga Freddie Festo
2017-04-01
Full Text Available Since the 1990s exports of fresh agricultural products by air from Uganda have been increasing and making a significant contribution to her International trade. Products include mostly fish, flowers, papain, and vanilla constituting over 95% of all air exports. Farming of the items is mainly by small scale farmers who depend on the natural climate of the country. Consequently, monthly yields are also climate dependent making individual export volumes unpredictable. In spite of these uncertainties, this study was intended to investigate possible existence of a model in the trends. Monthly data were collected from Uganda Civil Aviation Authority from 2009 to 2012. Analysis was by using ARIMA Approach with the help of Eviews 8. Visually the data exhibited irregular patterns and without a trend or seasonality. First order differencing stationarised the data and the residuals had a random non-significant noise suggesting a Random Walk Model expressed as ARIMA (0, 1, 0 and a negative drift. The model shows a link between current and one lag export volumes and the negative drift is a convergence of successive differences in export volumes. These findings have policy implications in expansion and forecasting of the exports potential of applicability of Random Walk Theory in practice.
Effects of nordic walking and exercise in type 2 diabetes mellitus: a randomized controlled trial
Gram, Bibi; Christensen, Robin; Christiansen, Christian
2010-01-01
Both Nordic walking and Exercise on Prescription have potential as elements in the management of type 2 diabetes mellitus. These programs are recommended, but their effectiveness has not yet been established. The aim was to evaluate the efficacy of these 2 interventions compared with standard...
Beck, Eric N; Intzandt, Brittany N; Almeida, Quincy J
2018-01-01
It may be possible to use attention-based exercise to decrease demands associated with walking in Parkinson's disease (PD), and thus improve dual task walking ability. For example, an external focus of attention (focusing on the effect of an action on the environment) may recruit automatic control processes degenerated in PD, whereas an internal focus (limb movement) may recruit conscious (nonautomatic) control processes. Thus, we aimed to investigate how externally and internally focused exercise influences dual task walking and symptom severity in PD. Forty-seven participants with PD were randomized to either an Externally (n = 24) or Internally (n = 23) focused group and completed 33 one-hour attention-based exercise sessions over 11 weeks. In addition, 16 participants were part of a control group. Before, after, and 8 weeks following the program (pre/post/washout), gait patterns were measured during single and dual task walking (digit-monitoring task, ie, walking while counting numbers announced by an audio-track), and symptom severity (UPDRS-III) was assessed ON and OFF dopamine replacement. Pairwise comparisons (95% confidence intervals [CIs]) and repeated-measures analyses of variance were conducted. Pre to post: Dual task step time decreased in the external group (Δ = 0.02 seconds, CI 0.01-0.04). Dual task step length (Δ = 2.3 cm, CI 0.86-3.75) and velocity (Δ = 4.5 cm/s, CI 0.59-8.48) decreased (became worse) in the internal group. UPDRS-III scores (ON and OFF) decreased (improved) in only the External group. Pre to washout: Dual task step time ( P = .005) and percentage in double support ( P = .014) significantly decreased (improved) in both exercise groups, although only the internal group increased error on the secondary counting task (ie, more errors monitoring numbers). UPDRS-III scores in both exercise groups significantly decreased ( P = .001). Since dual task walking improvements were found immediately, and 8 weeks after the cessation of an
Steeves, Jeremy A; Bassett, David R; Fitzhugh, Eugene C; Raynor, Hollie A; Thompson, Dixie L
2012-08-06
There is a growing problem of physical inactivity in America, and approximately a quarter of the population report being completely sedentary during their leisure time. In the U.S., TV viewing is the most common leisure-time activity. Stepping in place during TV commercials (TV Commercial Stepping) could increase physical activity. The purpose of this study was to examine the feasibility of incorporating physical activity (PA) into a traditionally sedentary activity, by comparing TV Commercial Stepping during 90 min/d of TV programming to traditional exercise (Walking). A randomized controlled pilot study of the impact of 6 months of TV Commercial Stepping versus Walking 30 min/day in adults was conducted. 58 sedentary, overweight (body mass index 33.5 ± 4.8 kg/m2) adults (age 52.0 ± 8.6 y) were randomly assigned to one of two 6-mo behavioral PA programs: 1) TV Commercial Stepping; or 2) Walking 30 min/day. To help facilitate behavior changes participants received 6 monthly phone calls, attended monthly meetings for the first 3 months, and received monthly newsletters for the last 3 months. Using intent-to-treat analysis, changes in daily steps, TV viewing, diet, body weight, waist and hip circumference, and percent fat were compared at baseline, 3, and 6 mo. Data were collected in 2010-2011, and analyzed in 2011. Of the 58 subjects, 47 (81%) were retained for follow-up at the completion of the 6-mo program. From baseline to 6-mo, both groups significantly increased their daily steps [4611 ± 1553 steps/d vs. 7605 ± 2471 steps/d (TV Commercial Stepping); 4909 ± 1335 steps/d vs. 7865 ± 1939 steps/d (Walking); P TV viewing and dietary intake decreased significantly in both groups. Body weight did not change, but both groups had significant decreases in percent body fat (3-mo to 6-mo), and waist and hip circumference (baseline to 6-mo) over time. Participants in both the TV Commercial Stepping and Walking groups had favorable changes in
Steeves Jeremy A
2012-08-01
Full Text Available Abstract Background There is a growing problem of physical inactivity in America, and approximately a quarter of the population report being completely sedentary during their leisure time. In the U.S., TV viewing is the most common leisure-time activity. Stepping in place during TV commercials (TV Commercial Stepping could increase physical activity. The purpose of this study was to examine the feasibility of incorporating physical activity (PA into a traditionally sedentary activity, by comparing TV Commercial Stepping during 90 min/d of TV programming to traditional exercise (Walking. Methods A randomized controlled pilot study of the impact of 6 months of TV Commercial Stepping versus Walking 30 min/day in adults was conducted. 58 sedentary, overweight (body mass index 33.5 ± 4.8 kg/m2 adults (age 52.0 ± 8.6 y were randomly assigned to one of two 6-mo behavioral PA programs: 1 TV Commercial Stepping; or 2 Walking 30 min/day. To help facilitate behavior changes participants received 6 monthly phone calls, attended monthly meetings for the first 3 months, and received monthly newsletters for the last 3 months. Using intent-to-treat analysis, changes in daily steps, TV viewing, diet, body weight, waist and hip circumference, and percent fat were compared at baseline, 3, and 6 mo. Data were collected in 2010–2011, and analyzed in 2011. Results Of the 58 subjects, 47 (81% were retained for follow-up at the completion of the 6-mo program. From baseline to 6-mo, both groups significantly increased their daily steps [4611 ± 1553 steps/d vs. 7605 ± 2471 steps/d (TV Commercial Stepping; 4909 ± 1335 steps/d vs. 7865 ± 1939 steps/d (Walking; P Conclusions Participants in both the TV Commercial Stepping and Walking groups had favorable changes in daily steps, TV viewing, diet, and anthropometrics. PA can be performed while viewing TV commercials and this may be a feasible alternative to traditional approaches for
Griffith, Garett; Klaren, Rachel E; Motl, Robert W; Baynard, Tracy; Fernhall, Bo
2015-03-01
This randomized controlled trial (RCT) will investigate the effects of a home-based aerobic exercise training regimen (i.e., cycle ergometry) on subclinical atherosclerosis and walking mobility in persons with multiple sclerosis (MS) and minimal disability. This RCT will recruit 54 men and women who have an Expanded Disability Status Scale characteristic of the 1st stage of MS (i.e., 0-4.0) to participate in a 3 month exercise or stretching intervention, with assessments of subclinical atherosclerosis and walking mobility conducted at baseline, week 6 (midpoint), and week 12 (conclusion) of the program. The exercise intervention will consist of 3 days/week of cycling, with a gradual increase of duration followed by an increase in intensity across the 3 month period. The attention-control condition will incorporate stretching activities and will require the same contact time commitment as the exercise condition. Both study groups will participate in weekly video chat sessions with study personnel in order to monitor and track program adherence. Primary outcomes will consist of assessments of vascular structure and function, as well as several walking tasks. Additional outcomes will include questionnaires, cardiorespiratory fitness assessment, and a 1-week free-living physical activity assessment. This investigation will increase understanding of the role of aerobic exercise as part of a treatment plan for managing subclinical atherosclerosis and improving walking mobility persons in the 1st stage of MS. Overall, this study design has the potential to lead to effective aerobic exercise intervention strategies for this population and improve program adherence. Copyright © 2015 Elsevier Inc. All rights reserved.
Cocco, S; Monasson, R
2009-01-01
We consider the Sinai model, in which a random walker moves in a random quenched potential V, and ask the following questions: 1. how can the quenched potential V be inferred from the observations of one or more realizations of the random motion? 2. how many observations (walks) are required to make a reliable inference, that is, to be able to distinguish between two similar but distinct potentials, V 1 and V 2 ? We show how question 1 can be easily solved within the Bayesian framework. In addition, we show that the answer to question 2 is, in general, intimately connected to the calculation of the survival probability of a fictitious walker in a potential W defined from V 1 and V 2 , with partial absorption at sites where V 1 and V 2 do not coincide. For the one-dimensional Sinai model, this survival probability can be analytically calculated, in excellent agreement with numerical simulations.
Exact two-point resistance, and the simple random walk on the complete graph minus N edges
Chair, Noureddine
2012-01-01
An analytical approach is developed to obtain the exact expressions for the two-point resistance and the total effective resistance of the complete graph minus N edges of the opposite vertices. These expressions are written in terms of certain numbers that we introduce, which we call the Bejaia and the Pisa numbers; these numbers are the natural generalizations of the bisected Fibonacci and Lucas numbers. The correspondence between random walks and the resistor networks is then used to obtain the exact expressions for the first passage and mean first passage times on this graph. - Highlights: ► We obtain exact formulas for the two-point resistance of the complete graph minus N edges. ► We obtain also the total effective resistance of this graph. ► We modified Schwatt’s formula on trigonometrical power sum to suit our computations. ► We introduced the generalized bisected Fibonacci and Lucas numbers: the Bejaia and the Pisa numbers. ► The first passage and mean first passage times of the random walks have exact expressions.
Wang, Guanglei; Wang, Pengyu; Han, Yechen; Liu, Xiuling; Li, Yan; Lu, Qian
2017-06-01
In recent years, optical coherence tomography (OCT) has developed into a popular coronary imaging technology at home and abroad. The segmentation of plaque regions in coronary OCT images has great significance for vulnerable plaque recognition and research. In this paper, a new algorithm based on K -means clustering and improved random walk is proposed and Semi-automated segmentation of calcified plaque, fibrotic plaque and lipid pool was achieved. And the weight function of random walk is improved. The distance between the edges of pixels in the image and the seed points is added to the definition of the weight function. It increases the weak edge weights and prevent over-segmentation. Based on the above methods, the OCT images of 9 coronary atherosclerotic patients were selected for plaque segmentation. By contrasting the doctor's manual segmentation results with this method, it was proved that this method had good robustness and accuracy. It is hoped that this method can be helpful for the clinical diagnosis of coronary heart disease.
Exact two-point resistance, and the simple random walk on the complete graph minus N edges
Chair, Noureddine, E-mail: n.chair@ju.edu.jo
2012-12-15
An analytical approach is developed to obtain the exact expressions for the two-point resistance and the total effective resistance of the complete graph minus N edges of the opposite vertices. These expressions are written in terms of certain numbers that we introduce, which we call the Bejaia and the Pisa numbers; these numbers are the natural generalizations of the bisected Fibonacci and Lucas numbers. The correspondence between random walks and the resistor networks is then used to obtain the exact expressions for the first passage and mean first passage times on this graph. - Highlights: Black-Right-Pointing-Pointer We obtain exact formulas for the two-point resistance of the complete graph minus N edges. Black-Right-Pointing-Pointer We obtain also the total effective resistance of this graph. Black-Right-Pointing-Pointer We modified Schwatt's formula on trigonometrical power sum to suit our computations. Black-Right-Pointing-Pointer We introduced the generalized bisected Fibonacci and Lucas numbers: the Bejaia and the Pisa numbers. Black-Right-Pointing-Pointer The first passage and mean first passage times of the random walks have exact expressions.
Kendon, Viv
2014-01-01
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. Recent results showing quantum walks are “universal for quantum computation” relate to algorithms, to be run on quantum computers. We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer
Ponomarev, A. L.; Brenner, D.; Hlatky, L. R.; Sachs, R. K.
2000-01-01
DNA double-strand breaks (DSBs) produced by densely ionizing radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. Stochastic DSB clustering at large scales, from > 100 Mbp down to simulations and analytic equations. A random-walk, coarse-grained polymer model for chromatin is combined with a simple track structure model in Monte Carlo software called DNAbreak and is applied to data on alpha-particle irradiation of V-79 cells. The chromatin model neglects molecular details but systematically incorporates an increase in average spatial separation between two DNA loci as the number of base-pairs between the loci increases. Fragment-size distributions obtained using DNAbreak match data on large fragments about as well as distributions previously obtained with a less mechanistic approach. Dose-response relations, linear at small doses of high linear energy transfer (LET) radiation, are obtained. They are found to be non-linear when the dose becomes so large that there is a significant probability of overlapping or close juxtaposition, along one chromosome, for different DSB clusters from different tracks. The non-linearity is more evident for large fragments than for small. The DNAbreak results furnish an example of the RLC (randomly located clusters) analytic formalism, which generalizes the broken-stick fragment-size distribution of the random-breakage model that is often applied to low-LET data.
Imam, Bita; Miller, William C; Finlayson, Heather C; Eng, Janice J; Payne, Michael Wc; Jarus, Tal; Goldsmith, Charles H; Mitchell, Ian M
2014-12-22
The number of older adults living with lower limb amputation (LLA) who require rehabilitation for improving their walking capacity and mobility is growing. Existing rehabilitation practices frequently fail to meet this demand. Nintendo Wii Fit may be a valuable tool to enable rehabilitation interventions. Based on pilot studies, we have developed "Wii.n.Walk", an in-home telehealth Wii Fit intervention targeted to improve walking capacity in older adults with LLA. The objective of this study is to determine whether the Wii.n.Walk intervention enhances walking capacity compared to an attention control group. This project is a multi-site (Vancouver BC, London ON), parallel, evaluator-blind randomized controlled trial. Participants include community-dwelling older adults over the age of 50 years with unilateral transtibial or transfemoral amputation. Participants will be stratified by site and block randomized in triplets to either the Wii.n.Walk intervention or an attention control group employing the Wii Big Brain cognitive software. This trial will include both supervised and unsupervised phases. During the supervised phase, both groups will receive 40-minute sessions of supervised group training three times per week for a duration of 4 weeks. Participants will complete the first week of the intervention in groups of three at their local rehabilitation center with a trainer. The remaining 3 weeks will take place at participants' homes using remote supervision by the trainer using Apple iPad technology. At the end of 4 weeks, the supervised period will end and the unsupervised period will begin. Participants will retain the Wii console and be encouraged to continue using the program for an additional 4 weeks' duration. The primary outcome measure will be the "Two-Minute Walk Test" to measure walking capacity. Outcome measures will be evaluated for all participants at baseline, after the end of both the supervised and unsupervised phases, and after 1-year follow up
Pantoni, Camila Bianca Falasco; Di Thommazo-Luporini, Luciana; Mendes, Renata Gonçalves; Caruso, Flávia Cristina Rossi; Mezzalira, Daniel; Arena, Ross; Amaral-Neto, Othon; Catai, Aparecida Maria; Borghi-Silva, Audrey
2016-01-01
Continuous positive airway pressure (CPAP) has been used as an effective support to decrease the negative pulmonary effects of coronary artery bypass graft (CABG) surgery. However, it is unknown whether CPAP can positively influence patients undergoing CABG during exercise. This study evaluated the effectiveness of CPAP on the first day of ambulation after CABG in patients undergoing inpatient cardiac rehabilitation (CR). Fifty-four patients after CABG surgery were randomly assigned to receive either inpatient CR and CPAP (CPG) or standard CR without CPAP (CG). Cardiac rehabilitation included walking and CPAP pressures were set between 10 to 12 cmH2O. Participants were assessed on the first day of walking at rest and during walking. Outcome measures included breathing pattern variables, exercise time in seconds (ETs), dyspnea/leg effort ratings, and peripheral oxygen saturation (SpO2). Twenty-seven patients (13 CPG vs 14 CG) completed the study. Compared with walking without noninvasive ventilation assistance, CPAP increased ETs by 43.4 seconds (P = .040) during walking, promoted better thoracoabdominal coordination, increased ventilation during walking by 12.5 L/min (P = .001), increased SpO2 values at the end of walking by 2.6% (P = .016), and reduced dyspnea ratings by 1 point (P = .008). Continuous positive airway pressure can positively influence exercise tolerance, ventilatory function, and breathing pattern in response to a single bout of exercise after CABG.
Cooper, M A
2000-01-01
We present various approximations for the angular distribution of particles emerging from an optically thick, purely isotropically scattering region into a vacuum. Our motivation is to use such a distribution for the Fleck-Canfield random walk method [1] for implicit Monte Carlo (IMC) [2] radiation transport problems. We demonstrate that the cosine distribution recommended in the original random walk paper [1] is a poor approximation to the angular distribution predicted by transport theory. Then we examine other approximations that more closely match the transport angular distribution.
Richardson, Caroline R; Buis, Lorraine R; Janney, Adrienne W; Goodrich, David E; Sen, Ananda; Hess, Michael L; Mehari, Kathleen S; Fortlage, Laurie A; Resnick, Paul J; Zikmund-Fisher, Brian J; Strecher, Victor J; Piette, John D
2010-12-17
Approximately half of American adults do not meet recommended physical activity guidelines. Face-to-face lifestyle interventions improve health outcomes but are unlikely to yield population-level improvements because they can be difficult to disseminate, expensive to maintain, and inconvenient for the recipient. In contrast, Internet-based behavior change interventions can be disseminated widely at a lower cost. However, the impact of some Internet-mediated programs is limited by high attrition rates. Online communities that allow participants to communicate with each other by posting and reading messages may decrease participant attrition. Our objective was to measure the impact of adding online community features to an Internet-mediated walking program on participant attrition and average daily step counts. This randomized controlled trial included sedentary, ambulatory adults who used email regularly and had at least 1 of the following: overweight (body mass index [BMI] ≥ 25), type 2 diabetes, or coronary artery disease. All participants (n = 324) wore enhanced pedometers throughout the 16-week intervention and uploaded step-count data to the study server. Participants could log in to the study website to view graphs of their walking progress, individually-tailored motivational messages, and weekly calculated goals. Participants were randomized to 1 of 2 versions of a Web-based walking program. Those randomized to the "online community" arm could post and read messages with other participants while those randomized to the "no online community" arm could not read or post messages. The main outcome measures were participant attrition and average daily step counts over 16 weeks. Multiple regression analyses assessed the effect of the online community access controlling for age, sex, disease status, BMI, and baseline step counts. Both arms significantly increased their average daily steps between baseline and the end of the intervention period, but there were no
The non-random walk of stock prices: the long-term correlation between signs and sizes
La Spada, G.; Farmer, J. D.; Lillo, F.
2008-08-01
We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about 70%, and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-contemporaneous correlation between the signs and sizes of individual returns. We conjecture that this is related to the long-memory of transaction signs and the need to enforce market efficiency.
Transport properties of the continuous-time random walk with a long-tailed waiting-time density
Weissman, H.; Havlin, S.; Weiss, G.H.
1989-01-01
The authors derive asymptotic properties of the propagator p(r, t) of a continuous-time random walk (CTRW) in which the waiting time density has the asymptotic form ψ(t) ∼ T α /t α+1 when t >> T and 0 = ∫ 0 ∞ τψ(τ)dτ is finite. One is that the asymptotic behavior of p(0, t) is demonstrated by the waiting time at the origin rather than by the dimension. The second difference is that in the presence of a field p(r, t) no longer remains symmetric around a moving peak. Rather, it is shown that the peak of this probability always occurs at r = 0, and the effect of the field is to break the symmetry that occurs when < ∞. Finally, they calculate similar properties, although in not such great detail, for the case in which the single-step jump probabilities themselves have an infinite mean
Loew, Laurianne; Brosseau, Lucie; Kenny, Glen P; Durand-Bush, Natalie; Poitras, Stéphane; De Angelis, Gino; Wells, George A
2017-07-01
Knee osteoarthritis is a common joint problem leading to an increase of pain and a loss of function in older individuals. The main objective of this study was to evaluate if a participant who was randomly assigned to his preferred group improved his adherence to an effective walking program compared to a participant who did not receive his preferred group. This was a 9-month pilot randomized clinical trial, based on a patient treatment preferences design. The 69 eligible participants had a diagnosis of knee osteoarthritis. Participants were randomized to one of two groups: a supervised community-based or unsupervised walking program, based on the Ottawa Panel guidelines. At 6 months, participants who expressed a preference, either for the supervised or unsupervised program, and who were assigned to their preferred choice of program showed significantly higher adherence to walking sessions (supervised 60.7 ± 12.3%, P walking program, while ensuring the maintenance of clinical benefits of walking, among older adults susceptible to avoid or not properly engage in physical activity.
Olson, Daniel W.; Dutta, Sarit; Laachi, Nabil; Tian, Mingwei; Dorfman, Kevin D.
2011-01-01
Using the two-state, continuous-time random walk model, we develop expressions for the mobility and the plate height during DNA electrophoresis in an ordered post array that delineate the contributions due to (i) the random distance between collisions and (ii) the random duration of a collision. These contributions are expressed in terms of the means and variances of the underlying stochastic processes, which we evaluate from a large ensemble of Brownian dynamics simulations performed using different electric fields and molecular weights in a hexagonal array of 1 μm posts with a 3 μm center-to-center distance. If we fix the molecular weight, we find that the collision frequency governs the mobility. In contrast, the average collision duration is the most important factor for predicting the mobility as a function of DNA size at constant Péclet number. The plate height is reasonably well-described by a single post rope-over-pulley model, provided that the extension of the molecule is small. Our results only account for dispersion inside the post array and thus represent a theoretical lower bound on the plate height in an actual device. PMID:21290387
Imam, Bita; Finlayson, Heather C; Eng, Janice J; Payne, Michael WC; Jarus, Tal; Goldsmith, Charles H; Mitchell, Ian M
2014-01-01
Background The number of older adults living with lower limb amputation (LLA) who require rehabilitation for improving their walking capacity and mobility is growing. Existing rehabilitation practices frequently fail to meet this demand. Nintendo Wii Fit may be a valuable tool to enable rehabilitation interventions. Based on pilot studies, we have developed “Wii.n.Walk”, an in-home telehealth Wii Fit intervention targeted to improve walking capacity in older adults with LLA. Objective The objective of this study is to determine whether the Wii.n.Walk intervention enhances walking capacity compared to an attention control group. Methods This project is a multi-site (Vancouver BC, London ON), parallel, evaluator-blind randomized controlled trial. Participants include community-dwelling older adults over the age of 50 years with unilateral transtibial or transfemoral amputation. Participants will be stratified by site and block randomized in triplets to either the Wii.n.Walk intervention or an attention control group employing the Wii Big Brain cognitive software. This trial will include both supervised and unsupervised phases. During the supervised phase, both groups will receive 40-minute sessions of supervised group training three times per week for a duration of 4 weeks. Participants will complete the first week of the intervention in groups of three at their local rehabilitation center with a trainer. The remaining 3 weeks will take place at participants’ homes using remote supervision by the trainer using Apple iPad technology. At the end of 4 weeks, the supervised period will end and the unsupervised period will begin. Participants will retain the Wii console and be encouraged to continue using the program for an additional 4 weeks’ duration. The primary outcome measure will be the “Two-Minute Walk Test” to measure walking capacity. Outcome measures will be evaluated for all participants at baseline, after the end of both the supervised and
A not quite random walk: Experimenting with the ethnomethods of the algorithm
Malte Ziewitz
2017-11-01
Full Text Available Algorithms have become a widespread trope for making sense of social life. Science, finance, journalism, warfare, and policing—there is hardly anything these days that has not been specified as “algorithmic.” Yet, although the trope has brought together a variety of audiences, it is not quite clear what kind of work it does. Often portrayed as powerful yet inscrutable entities, algorithms maintain an air of mystery that makes them both interesting and difficult to understand. This article takes on this problem and examines the role of algorithms not as techno-scientific objects to be known, but as a figure that is used for making sense of observations. Following in the footsteps of Harold Garfinkel’s tutorial cases, I shall illustrate the implications of this view through an experiment with algorithmic navigation. Challenging participants to go on a walk, guided not by maps or GPS but by an algorithm developed on the spot, I highlight a number of dynamics typical of reasoning with running code, including the ongoing respecification of rules and observations, the stickiness of the procedure, and the selective invocation of the algorithm as an intelligible object. The materials thus provide an opportunity to rethink key issues at the intersection of the social sciences and the computational, including popular concerns with transparency, accountability, and ethics.
Zhang, Zhongzhi; Dong, Yuze; Sheng, Yibin
2015-10-01
Random walks including non-nearest-neighbor jumps appear in many real situations such as the diffusion of adatoms and have found numerous applications including PageRank search algorithm; however, related theoretical results are much less for this dynamical process. In this paper, we present a study of mixed random walks in a family of fractal scale-free networks, where both nearest-neighbor and next-nearest-neighbor jumps are included. We focus on trapping problem in the network family, which is a particular case of random walks with a perfect trap fixed at the central high-degree node. We derive analytical expressions for the average trapping time (ATT), a quantitative indicator measuring the efficiency of the trapping process, by using two different methods, the results of which are consistent with each other. Furthermore, we analytically determine all the eigenvalues and their multiplicities for the fundamental matrix characterizing the dynamical process. Our results show that although next-nearest-neighbor jumps have no effect on the leading scaling of the trapping efficiency, they can strongly affect the prefactor of ATT, providing insight into better understanding of random-walk process in complex systems.
Fific, Mario; Little, Daniel R.; Nosofsky, Robert M.
2010-01-01
We formalize and provide tests of a set of logical-rule models for predicting perceptual classification response times (RTs) and choice probabilities. The models are developed by synthesizing mental-architecture, random-walk, and decision-bound approaches. According to the models, people make independent decisions about the locations of stimuli…
Williams, Stefanie L; Michie, Susan; Dale, Jeremy; Stallard, Nigel; French, David P
2015-05-01
Perceived behavioral control (PBC) is a consistent predictor of intentions to walk more. A previously successful intervention to promote walking by altering PBC has been adapted for delivery in general practice. This study aimed to evaluate the effect of this intervention on Theory of Planned Behavior (TPB) constructs in this context. Cluster randomized controlled trial, with n = 315 general practice patients. Practice nurses and Healthcare Assistants delivered a self-regulation intervention or information provision (control). Questionnaires assessed TPB variables at baseline, post-intervention, 6 weeks and 6 months. Walking was measured by pedometer. The control group reported significantly higher subjective norm at all follow-up time points. There were no significant differences between the two groups in PBC, intention, attitude or walking behavior. TPB variables significantly predicted intentions to walk more, but not objective walking behavior, after accounting for clustering. The lack of effect of the intervention was probably due to a failure to maintain intervention fidelity, and the unsuitability of the behavior change techniques included in the intervention for the population investigated. This previously successful intervention was not successful when delivered in this context, calling into question whether practice nurses are best placed to deliver such interventions. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.
Aileen W. K. Chan
2016-07-01
Full Text Available Physical inactivity is one of the major modifiable lifestyle risk factors for cardiovascular disease (CVD. This protocol aims to evaluate the effectiveness of Tai Chi versus brisk walking in reducing CVD risk factors. This is a randomized controlled trial with three arms, namely, Tai Chi group, walking group, and control group. The Tai Chi group will receive Tai Chi training, which consists of two 60-min sessions each week for three months, and self-practice for 30 min every day. The walking group will perform brisk walking for 30 min every day. The control group will receive their usual care. 246 subjects with CVD risk factors will be recruited from two outpatient clinics. The primary outcome is blood pressure. Secondary outcomes include fasting blood for lipid profile, sugar and glycated haemoglobin (HbA1c; body mass index, waist circumference, body fat percentage; perceived stress level and quality of life. Data collections will be conducted at baseline, 3-month, 6-month and 9-month. Generalized estimating equations model will be used to compare the changes in outcomes across time between groups. It is expected that both the Tai Chi and walking groups could maintain better health and have improved quality of life, and that Tai Chi will be more effective than brisk walking in reducing CVD risk factors.
Liang, Yingjie; Chen, Wen
2018-04-01
The mean squared displacement (MSD) of the traditional ultraslow diffusion is a logarithmic function of time. Recently, the continuous time random walk model is employed to characterize this ultraslow diffusion dynamics by connecting the heavy-tailed logarithmic function and its variation as the asymptotical waiting time density. In this study we investigate the limiting waiting time density of a general ultraslow diffusion model via the inverse Mittag-Leffler function, whose special case includes the traditional logarithmic ultraslow diffusion model. The MSD of the general ultraslow diffusion model is analytically derived as an inverse Mittag-Leffler function, and is observed to increase even more slowly than that of the logarithmic function model. The occurrence of very long waiting time in the case of the inverse Mittag-Leffler function has the largest probability compared with the power law model and the logarithmic function model. The Monte Carlo simulations of one dimensional sample path of a single particle are also performed. The results show that the inverse Mittag-Leffler waiting time density is effective in depicting the general ultraslow random motion.
Most, S.; Jia, N.; Bijeljic, B.; Nowak, W.
2016-12-01
Pre-asymptotic characteristics are almost ubiquitous when analyzing solute transport processes in porous media. These pre-asymptotic aspects are caused by spatial coherence in the velocity field and by its heterogeneity. For the Lagrangian perspective of particle displacements, the causes of pre-asymptotic, non-Fickian transport are skewed velocity distribution, statistical dependencies between subsequent increments of particle positions (memory) and dependence between the x, y and z-components of particle increments. Valid simulation frameworks should account for these factors. We propose a particle tracking random walk (PTRW) simulation technique that can use empirical pore-space velocity distributions as input, enforces memory between subsequent random walk steps, and considers cross dependence. Thus, it is able to simulate pre-asymptotic non-Fickian transport phenomena. Our PTRW framework contains an advection/dispersion term plus a diffusion term. The advection/dispersion term produces time-series of particle increments from the velocity CDFs. These time series are equipped with memory by enforcing that the CDF values of subsequent velocities change only slightly. The latter is achieved through a random walk on the axis of CDF values between 0 and 1. The virtual diffusion coefficient for that random walk is our only fitting parameter. Cross-dependence can be enforced by constraining the random walk to certain combinations of CDF values between the three velocity components in x, y and z. We will show that this modelling framework is capable of simulating non-Fickian transport by comparison with a pore-scale transport simulation and we analyze the approach to asymptotic behavior.
DePaul, Vincent G; Wishart, Laurie R; Richardson, Julie; Thabane, Lehana; Ma, Jinhui; Lee, Timothy D
2015-05-01
Although task-related walking training has been recommended after stroke, the theoretical basis, content, and impact of interventions vary across the literature. There is a need for a comparison of different approaches to task-related walking training after stroke. To compare the impact of a motor-learning-science-based overground walking training program with body-weight-supported treadmill training (BWSTT) in ambulatory, community-dwelling adults within 1 year of stroke onset. In this rater-blinded, 1:1 parallel, randomized controlled trial, participants were stratified by baseline gait speed. Participants assigned to the Motor Learning Walking Program (MLWP) practiced various overground walking tasks under the supervision of 1 physiotherapist. Cognitive effort was encouraged through random practice and limited provision of feedback and guidance. The BWSTT program emphasized repetition of the normal gait cycle while supported on a treadmill and assisted by 1 to 3 therapy staff. The primary outcome was comfortable gait speed at postintervention assessment (T2). In total, 71 individuals (mean age = 67.3; standard deviation = 11.6 years) with stroke (mean onset = 20.9 [14.1] weeks) were randomized (MLWP, n = 35; BWSTT, n = 36). There was no significant between-group difference in gait speed at T2 (0.002 m/s; 95% confidence interval [CI] = -0.11, 0.12; P > .05). The MLWP group improved by 0.14 m/s (95% CI = 0.09, 0.19), and the BWSTT group improved by 0.14 m/s (95% CI = 0.08, 0.20). In this sample of community-dwelling adults within 1 year of stroke, a 15-session program of varied overground walking-focused training was not superior to a BWSTT program of equal frequency, duration, and in-session step activity. © The Author(s) 2014.
Price Formation Modelling by Continuous-Time Random Walk: An Empirical Study
Frédéric Délèze
2015-01-01
Full Text Available Markovian and non-Markovian\tmodels are presented to\tmodel the futures\tmarket price formation.\tWe show that\tthe\twaiting-time\tand\tthe\tsurvival\tprobabilities\thave\ta\tsignificant\timpact\ton\tthe\tprice\tdynamics.\tThis\tstudy tests\tanalytical\tsolutions\tand\tpresent\tnumerical\tresults for the\tprobability\tdensity function\tof the\tcontinuoustime random\twalk\tusing\ttick-by-tick\tquotes\tprices\tfor\tthe\tDAX\t30\tindex\tfutures.
Analytic random-walk model for the coherence of a frequency comb
Eramo, R.; Cancio Pastor, P.; Cavalieri, S.
2018-03-01
We present an analytical study of the frequency comb coherence due to random noise in the pulses phases. We derive a simple expression for the comb lineshape, which depends on a single parameter Neff with the physical meaning of number of coherent comb pulses, inversely proportional to the variance of the phase jumps between subsequent comb pulses. A comparison to the case of a cw-monomode laser with white noise frequency fluctuations is also presented.
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.
Zimbardo, G.
2005-01-01
Plasma transport in the presence of turbulence depends on a variety of parameters like the fluctuation level ? B/B0, the ratio between the particle Larmor radius and the turbulence correlation lengths, and the turbulence anisotropy. In this presentation, we review the results of numerical simulations of plasma and magnetic field line transport in the case of anisotropic magnetic turbulence, for parameter values close to those of the solar wind. We assume a uniform background magnetic field B0 = B0ez and a Fourier representation for magnetic fluctuations, with wavectors forming any angle with respect to B0. The energy density spectrum is a power law, and in k space the constant amplitude surfaces are ellipsoids, described by the correlation lengths lx, ly, lz, which quantify the anisotropy of turbulence. For magnetic field lines, we find that transport perpendicular to the background field depends on the Kubo number R = ? B B0 lz lx . For small Kubo numbers, R ? 1, we find anomalous, non Gaussian transport regimes (both sub and superdiffusive) which can be described as a Levy random walk. Increasing the Kubo number, i.e., the fluctuation level ? B/B0 and/or the ratio lz/lx, we find first a quasilinear and then a percolative regime, both corresponding to Gaussian diffusion. For particles, we find that transport parallel and perpendicular to the background magnetic field heavily depends on the turbulence anisotropy and on the particle Larmor radius. For turbulence levels typical of the solar wind, ? B/B0 ? 0.5 ?1, when the ratio between the particle Larmor radius and the turbulence correlation lengths is small, anomalous regimes are found in the case lz/lx ? 1, with Levy random walk (superdiffusion) along the magnetic field and subdiffusion in the perpendicular directions. Conversely, for lz/lx > 1 normal, Gaussian diffusion is found. Increasing the ratio between the particle Larmor radius and the turbulence correlation lengths, the parallel superdiffusion is
Baker, Graham; Gray, Stuart R; Wright, Annemarie; Fitzsimons, Claire; Nimmo, Myra; Lowry, Ruth; Mutrie, Nanette
2008-09-05
Recent systematic reviews have suggested that pedometers may be effective motivational tools to promote walking. However, studies tend to be of a relatively short duration, with small clinical based samples. Further research is required to demonstrate their effectiveness in adequately powered, community based studies. Using a randomized controlled trial design, this study assessed the impact of a 12-week graduated pedometer-based walking intervention on daily step-counts, self-reported physical activity and health outcomes in a Scottish community sample not meeting current physical activity recommendations. Sixty-three women and 16 men (49.2 years +/- 8.8) were randomly assigned to either an intervention (physical activity consultation and 12-week pedometer-based walking program) or control (no action) group. Measures for step-counts, 7-day physical activity recall, affect, quality of life (n = 79), body mass, BMI, % body fat, waist and hip circumference (n = 76), systolic/diastolic blood pressure, total cholesterol and HDL cholesterol (n = 66) were taken at baseline and week 12. Analyses were performed on an intention to treat basis using 2-way mixed factorial analyses of variance for parametric data and Mann Whitney and Wilcoxon tests for non-parametric data. Significant increases were found in the intervention group for step-counts (p lack of significant changes in health outcomes. Continued follow-up of this study will examine adherence to the intervention and possible resulting effects on health outcomes.
Martin Rosvall
Full Text Available To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between compression and pattern detection; by compressing a description of a random walker as a proxy for real flow on a network, we find regularities in the network that induce this system-wide flow. Finding the shortest multilevel description of the random walker therefore gives us the best hierarchical clustering of the network--the optimal number of levels and modular partition at each level--with respect to the dynamics on the network. With a novel search algorithm, we extract and illustrate the rich multilevel organization of several large social and biological networks. For example, from the global air traffic network we uncover countries and continents, and from the pattern of scientific communication we reveal more than 100 scientific fields organized in four major disciplines: life sciences, physical sciences, ecology and earth sciences, and social sciences. In general, we find shallow hierarchical structures in globally interconnected systems, such as neural networks, and rich multilevel organizations in systems with highly separated regions, such as road networks.
Disorder and decoherence in coined quantum walks
Zhang Rong; Qin Hao; Tang Bao; Xue Peng
2013-01-01
This article aims to provide a review on quantum walks. Starting form a basic idea of discrete-time quantum walks, we will review the impact of disorder and decoherence on the properties of quantum walks. The evolution of the standard quantum walks is deterministic and disorder introduces randomness to the whole system and change interference pattern leading to the localization effect. Whereas, decoherence plays the role of transmitting quantum walks to classical random walks. (topical review - quantum information)
Park, Hyun-Ju; Oh, Duck-Won; Choi, Jong-Duk; Kim, Jong-Man; Kim, Suhn-Yeop; Cha, Yong-Jun; Jeon, Su-Jin
2017-08-01
To investigate the effects of action observation training involving community-based ambulation for improving walking ability after stroke. Randomized, controlled pilot study. Inpatient rehabilitation hospital. A total of 25 inpatients with post-stroke hemiparesis were randomly assigned to either the experimental group ( n = 12) or control group ( n = 13). Subjects of the experimental group watched video clips demonstrating four-staged ambulation training with a more complex environment factor for 30 minutes, three times a week for four weeks. Meanwhile, subjects of the control group watched video clips, which showed different landscape pictures. Walking function was evaluated before and after the four-week intervention using a 10-m walk test, community walk test, activities-specific balance confidence scale, and spatiotemporal gait measures. Changes in the values for the 10-m walk test (0.17 ±0.19 m/s vs. 0.05 ±0.08 m/s), community walk test (-151.42 ±123.82 seconds vs. 67.08 ±176.77 seconds), and activities-specific balance confidence (6.25 ±5.61 scores vs. 0.72 ±2.24 scores) and the spatiotemporal parameters (i.e. stride length (19.00 ±11.34 cm vs. 3.16 ±11.20 cm), single support (5.87 ±5.13% vs. 0.25 ±5.95%), and velocity (15.66 ±12.34 cm/s vs. 2.96 ±10.54 cm/s)) indicated a significant improvement in the experimental group compared with the control group. In the experimental group, walking function and ambulation confidence was significantly different between the pre- and post-intervention, whereas the control group showed a significant difference only in the 10-m walk test. Action observation training of community ambulation may be favorably used for improving walking function of patients with post-stroke hemiparesis.
Wu, Ming; Kim, Janis; Arora, Pooja; Gaebler-Spira, Deborah J; Zhang, Yunhui
2017-11-01
The aim of the study was to determine whether applying an assistance force to the pelvis and legs during treadmill training can improve walking function in children with cerebral palsy. Twenty-three children with cerebral palsy were randomly assigned to the robotic or treadmill only group. For participants who were assigned to the robotic group, a controlled force was applied to the pelvis and legs during treadmill walking. For participants who were assigned to the treadmill only group, manual assistance was provided as needed. Each participant trained 3 times/wk for 6 wks. Outcome measures included walking speed, 6-min walking distance, and clinical assessment of motor function, which were evaluated before, after training, and 8 wks after the end of training, and were compared between two groups. Significant increases in walking speed and 6-min walking distance were observed after robotic training (P = 0.03), but no significant change was observed after treadmill training only. A greater increase in 6-min walking distance was observed after robotic training than that after treadmill only training (P = 0.01). Applying a controlled force to the pelvis and legs, for facilitating weight-shift and leg swing, respectively, during treadmill training may improve walking speed and endurance in children with cerebral palsy. Complete the self-assessment activity and evaluation online at http://www.physiatry.org/JournalCME CME OBJECTIVES: Upon completion of this article, the reader should be able to: (1) discuss the importance of physical activity at the participation level (sports programs) for children with cerebral palsy; (2) contrast the changes in walking ability and endurance for children in GMFCS level I, II and III following sports programs; and (3) identify the impact of higher frequency of sports program attendance over time on walking ability. Advanced ACCREDITATION: The Association of Academic Physiatrists is accredited by the Accreditation Council for Continuing
Gharib, Nevein Mm; El-Maksoud, Gehan M Abd; Rezk-Allah, Soheir S
2011-10-01
To assess the effects of additional gait trainer assisted walking exercises on walking performance in children with hemiparetic cerebral palsy. A randomized controlled study. Paediatric physical therapy outpatient clinic. Thirty spastic hemiparetic cerebral palsied children of both sexes (10-13 years - 19 girls and 11 boys). Children were randomly assigned into two equal groups; experimental and control groups. Participants in both groups received a traditional physical therapy exercise programme. Those in the experimental group received additional gait trainer based walking exercises which aimed to improve walking performance. Treatment was provided three times per week for three successive months. Children received baseline and post-treatment assessments using Biodex Gait Trainer 2 assessment device to evaluate gait parameters including: average step length, walking speed, time on each foot (% of gait cycle) and ambulation index. Children in the experimental group showed a significant improvement as compared with those in the control group. The ambulation index was 75.53±7.36 (11.93 ± 2.89 change score) for the experimental group and 66.06 ± 5.48 (2.13 ± 4.43 change score) for the control group (t = 3.99 and P = 0.0001). Time of support for the affected side was 42.4 ± 3.37 (7 ± 2.20 change score) for the experimental group and 38.06 ± 4.63 (3.33 ± 6.25 change score) for the control group (t = 2.92 and P = 0.007). Also, there was a significant improvement in step length and walking speed in both groups. Gait trainer combined with traditional physiotherapy increase the chance of improving gait performance in children with spastic hemiparetic cerebral palsy.
Calculation of large Reynolds number two-dimensional flow using discrete vortices with random walk
Milinazzo, F.; Saffman, P.G.
1977-01-01
The numerical calculation of two-dimensional rotational flow at large Reynolds number is considered. The method of replacing a continuous distribution of vorticity by a finite number, N, of discrete vortices is examined, where the vortices move under their mutually induced velocities plus a random component to simulate effects of viscosity. The accuracy of the method is studied by comparison with the exact solution for the decay of a circular vortex. It is found, and analytical arguments are produced in support, that the quantitative error is significant unless N is large compared with a characteristic Reynolds number. The mutually induced velocities are calculated by both direct summation and by the ''cloud in cell'' technique. The latter method is found to produce comparable error and to be much faster
Nimmo Myra
2008-09-01
Full Text Available Abstract Background Recent systematic reviews have suggested that pedometers may be effective motivational tools to promote walking. However, studies tend to be of a relatively short duration, with small clinical based samples. Further research is required to demonstrate their effectiveness in adequately powered, community based studies. Objective Using a randomized controlled trial design, this study assessed the impact of a 12-week graduated pedometer-based walking intervention on daily step-counts, self-reported physical activity and health outcomes in a Scottish community sample not meeting current physical activity recommendations. Method Sixty-three women and 16 men (49.2 years ± 8.8 were randomly assigned to either an intervention (physical activity consultation and 12-week pedometer-based walking program or control (no action group. Measures for step-counts, 7-day physical activity recall, affect, quality of life (n = 79, body mass, BMI, % body fat, waist and hip circumference (n = 76, systolic/diastolic blood pressure, total cholesterol and HDL cholesterol (n = 66 were taken at baseline and week 12. Analyses were performed on an intention to treat basis using 2-way mixed factorial analyses of variance for parametric data and Mann Whitney and Wilcoxon tests for non-parametric data. Results Significant increases were found in the intervention group for step-counts (p p = .02 and positive affect (p = .027. Significant decreases were found in this group for time spent in weekday (p = .003, weekend (p = .001 and total sitting (p = .001 with no corresponding changes in the control group. No significant changes in any other health outcomes were found in either group. In comparison with the control group at week 12, the intervention group reported a significantly greater number of minutes spent in leisure time (p = .008, occupational (p = .045 and total walking (p = .03, and significantly fewer minutes in time spent in weekend (p = .003 and
Violi, F; Marubini, E; Coccheri, S; Nenci, G G
2000-05-01
Defibrotide is an antithrombotic drug which enhances prostacyclin production and activates fibrinolytic system. The aim of this study was to investigate the improvement of walking distance in patients with intermittent claudication treated with defibrotide. DICLIS was a double blind, placebo-controlled study which included patients with walking distance autonomy at a standardized treadmill test or =100 meters. A total of 310 patients were randomly allocated to placebo (n = 101), defibrotide 800 mg/day (n = 104) or defibrotide 1200 mg/day (n = 105). During a one year follow-up, the Absolute Walking Distance (AWD) was measured six times (0, 30, 60, 90, 180, 360 days). Similar improvement in walking distance was found in the three groups until the 90th day; thereafter placebo group showed no further increase, while AWD continued to increase in the defibrotide groups. Between the 180th and 360th day visits, AWD was significantly higher (P defibrotide than in patients given placebo. No difference in efficacy was observed between the two dosages of defibrotide. No differences in side effects were observed among the three groups. The results of the present trial suggest that long-term administration of defibrotide improves walking distance in patients with intermittent claudication.
Zhang, Yunhua; Dai, Li; Liu, Ying; Zhang, YuHang; Wang, ShaoPeng
2017-01-01
Fruit is essential for plant reproduction and is responsible for protection and dispersal of seeds. The development and maturation of fruit is tightly regulated by numerous genetic factors that respond to environmental and internal stimulation. In this study, we attempted to identify novel fruit-related genes in a model organism, Arabidopsis thaliana, using a computational method. Based on validated fruit-related genes, the random walk with restart (RWR) algorithm was applied on a protein-protein interaction (PPI) network using these genes as seeds. The identified genes with high probabilities were filtered by the permutation test and linkage tests. In the permutation test, the genes that were selected due to the structure of the PPI network were discarded. In the linkage tests, the importance of each candidate gene was measured from two aspects: (1) its functional associations with validated genes and (2) its similarity with validated genes on gene ontology (GO) terms and KEGG pathways. Finally, 255 inferred genes were obtained, subsequent extensive analysis of important genes revealed that they mainly contribute to ubiquitination (UBQ9, UBQ8, UBQ11, UBQ10), serine hydroxymethyl transfer (SHM7, SHM5, SHM6) or glycol-metabolism (HXKL2_ARATH, CSY5, GAPCP1), suggesting essential roles during the development and maturation of fruit in Arabidopsis thaliana.
Aref, S
1982-01-01
A study of the migration of fourth stage larvae of the parasite Strongylus vulgaris in the intestinal arteries of the horse is presented. It is established, that the larvae migrate along the arteries in almost straight lines. It is suggested that this is primarily due to their ability to sense the curvature of the vessel wall, and not, as might have been expected, because of an ability to sense the direction of blood flow. A larva will sometimes alter its direction of motion when encountering a small off-branching artery. This behaviour suggests, that the migration of S. vulgaris larvae can be modeled as a one-dimensional discrete random walk on a long time scale. This model is simpler than any deterministic model and, in particular, does not require the existence of a predilection site. The available data is not, however, sufficient for a convincing, quantitative test of the model. The proposed reluctance of the larvae to bend into off-branching arteries is used to explain the crowding of larvae in the cranial mesenteric artery.
Panda, Rashmi; Puhan, N B; Panda, Ganapati
2018-02-01
Accurate optic disc (OD) segmentation is an important step in obtaining cup-to-disc ratio-based glaucoma screening using fundus imaging. It is a challenging task because of the subtle OD boundary, blood vessel occlusion and intensity inhomogeneity. In this Letter, the authors propose an improved version of the random walk algorithm for OD segmentation to tackle such challenges. The algorithm incorporates the mean curvature and Gabor texture energy features to define the new composite weight function to compute the edge weights. Unlike the deformable model-based OD segmentation techniques, the proposed algorithm remains unaffected by curve initialisation and local energy minima problem. The effectiveness of the proposed method is verified with DRIVE, DIARETDB1, DRISHTI-GS and MESSIDOR database images using the performance measures such as mean absolute distance, overlapping ratio, dice coefficient, sensitivity, specificity and precision. The obtained OD segmentation results and quantitative performance measures show robustness and superiority of the proposed algorithm in handling the complex challenges in OD segmentation.
Yao, Weiguang; Merchant, Thomas E.; Farr, Jonathan B.
2016-10-01
The lateral homogeneity assumption is used in most analytical algorithms for proton dose, such as the pencil-beam algorithms and our simplified analytical random walk model. To improve the dose calculation in the distal fall-off region in heterogeneous media, we analyzed primary proton fluence near heterogeneous media and propose to calculate the lateral fluence with voxel-specific Gaussian distributions. The lateral fluence from a beamlet is no longer expressed by a single Gaussian for all the lateral voxels, but by a specific Gaussian for each lateral voxel. The voxel-specific Gaussian for the beamlet of interest is calculated by re-initializing the fluence deviation on an effective surface where the proton energies of the beamlet of interest and the beamlet passing the voxel are the same. The dose improvement from the correction scheme was demonstrated by the dose distributions in two sets of heterogeneous phantoms consisting of cortical bone, lung, and water and by evaluating distributions in example patients with a head-and-neck tumor and metal spinal implants. The dose distributions from Monte Carlo simulations were used as the reference. The correction scheme effectively improved the dose calculation accuracy in the distal fall-off region and increased the gamma test pass rate. The extra computation for the correction was about 20% of that for the original algorithm but is dependent upon patient geometry.
Murase, Yohsuke
2010-06-01
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species, while migrants have no correlation with the resident species. It is found that the dynamics of community assembly with mutations are quite different from the case with migrations. In contrast to mutation models, which show intermittent dynamics of quasi-steady states interrupted by sudden reorganizations of the community, migration models show smooth and gradual renewal of the community. As a consequence, instead of the 1/f diversity fluctuations found for the mutation models, 1/f2, random-walk like fluctuations are observed for the migration models. In addition, a characteristic species-lifetime distribution is found: a power law that is cut off by a "skewed" distribution in the long-lifetime regime. The latter has a longer tail than a simple exponential function, which indicates an age-dependent species-mortality function. Since this characteristic profile has been observed, both in fossil data and in several other mathematical models, we conclude that it is a universal feature of macroevolution. © 2010 Elsevier Ltd.
Nan, Tongchao; Li, Kaixuan; Wu, Jichun; Yin, Lihe
2018-04-01
Sustainability has been one of the key criteria of effective water exploitation. Groundwater exploitation and water-table decline at Haolebaoji water source site in the Ordos basin in NW China has drawn public attention due to concerns about potential threats to ecosystems and grazing land in the area. To better investigate the impact of production wells at Haolebaoji on the water table, an adapted algorithm called the random walk on grid method (WOG) is applied to simulate the hydraulic head in the unconfined and confined aquifers. This is the first attempt to apply WOG to a real groundwater problem. The method can not only evaluate the head values but also the contributions made by each source/sink term. One is allowed to analyze the impact of source/sink terms just as if one had an analytical solution. The head values evaluated by WOG match the values derived from the software Groundwater Modeling System (GMS). It suggests that WOG is effective and applicable in a heterogeneous aquifer with respect to practical problems, and the resultant information is useful for groundwater management.
Vanderbei, Robert J., E-mail: rvdb@princeton.edu [Princeton University, Department of Operations Research and Financial Engineering (United States); P Latin-Small-Letter-Dotless-I nar, Mustafa C., E-mail: mustafap@bilkent.edu.tr [Bilkent University, Department of Industrial Engineering (Turkey); Bozkaya, Efe B. [Sabanc Latin-Small-Letter-Dotless-I University, Faculty of Administrative Sciences (Turkey)
2013-02-15
An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problem as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put.
Roubinet, D.; Russian, A.; Dentz, M.; Gouze, P.
2017-12-01
Characterizing and modeling hydrodynamic reactive transport in fractured rock are critical challenges for various research fields and applications including environmental remediation, geological storage, and energy production. To this end, we consider a recently developed time domain random walk (TDRW) approach, which is adapted to reproduce anomalous transport behaviors and capture heterogeneous structural and physical properties. This method is also very well suited to optimize numerical simulations by memory-shared massive parallelization and provide numerical results at various scales. So far, the TDRW approach has been applied for modeling advective-diffusive transport with mass transfer between mobile and immobile regions and simple (theoretical) reactions in heterogeneous porous media represented as single continuum domains. We extend this approach to dual-continuum representations considering a highly permeable fracture network embedded into a poorly permeable rock matrix with heterogeneous geochemical reactions occurring in both geological structures. The resulting numerical model enables us to extend the range of the modeled heterogeneity scales with an accurate representation of solute transport processes and no assumption on the Fickianity of these processes. The proposed model is compared to existing particle-based methods that are usually used to model reactive transport in fractured rocks assuming a homogeneous surrounding matrix, and is used to evaluate the impact of the matrix heterogeneity on the apparent reaction rates for different 2D and 3D simple-to-complex fracture network configurations.
Liu, Baoshun; Li, Ziqiang; Zhao, Xiujian
2015-02-21
In this research, Monte-Carlo Continuity Random Walking (MC-RW) model was used to study the relation between electron transport and photocatalysis of nano-crystalline (nc) clusters. The effects of defect energy disorder, spatial disorder of material structure, electron density, and interfacial transfer/recombination on the electron transport and the photocatalysis were studied. Photocatalytic activity is defined as 1/τ from a statistical viewpoint with τ being the electron average lifetime. Based on the MC-RW simulation, a clear physical and chemical "picture" was given for the photocatalytic kinetic analysis of nc-clusters. It is shown that the increase of defect energy disorder and material spatial structural disorder, such as the decrease of defect trap number, the increase of crystallinity, the increase of particle size, and the increase of inter-particle connection, can enhance photocatalytic activity through increasing electron transport ability. The increase of electron density increases the electron Fermi level, which decreases the activation energy for electron de-trapping from traps to extending states, and correspondingly increases electron transport ability and photocatalytic activity. Reducing recombination of electrons and holes can increase electron transport through the increase of electron density and then increases the photocatalytic activity. In addition to the electron transport, the increase of probability for electrons to undergo photocatalysis can increase photocatalytic activity through the increase of the electron interfacial transfer speed.
Xing, Lizhi; Dong, Xianlei; Guan, Jun
2017-04-01
Input-output table is very comprehensive and detailed in describing the national economic system with lots of economic relationships, which contains supply and demand information among industrial sectors. The complex network, a theory and method for measuring the structure of complex system, can describe the structural characteristics of the internal structure of the research object by measuring the structural indicators of the social and economic system, revealing the complex relationship between the inner hierarchy and the external economic function. This paper builds up GIVCN-WIOT models based on World Input-Output Database in order to depict the topological structure of Global Value Chain (GVC), and assumes the competitive advantage of nations is equal to the overall performance of its domestic sectors' impact on the GVC. Under the perspective of econophysics, Global Industrial Impact Coefficient (GIIC) is proposed to measure the national competitiveness in gaining information superiority and intermediate interests. Analysis of GIVCN-WIOT models yields several insights including the following: (1) sectors with higher Random Walk Centrality contribute more to transmitting value streams within the global economic system; (2) Half-Value Ratio can be used to measure robustness of open-economy macroeconomics in the process of globalization; (3) the positive correlation between GIIC and GDP indicates that one country's global industrial impact could reveal its international competitive advantage.
Hailin Chen
2013-01-01
Full Text Available Increasing evidence has revealed that microRNAs (miRNAs play important roles in the development and progression of human diseases. However, efforts made to uncover OMIM disease-miRNA associations are lacking and the majority of diseases in the OMIM database are not associated with any miRNA. Therefore, there is a strong incentive to develop computational methods to detect potential OMIM disease-miRNA associations. In this paper, random walk on OMIM disease similarity network is applied to predict potential OMIM disease-miRNA associations under the assumption that functionally related miRNAs are often associated with phenotypically similar diseases. Our method makes full use of global disease similarity values. We tested our method on 1226 known OMIM disease-miRNA associations in the framework of leave-one-out cross-validation and achieved an area under the ROC curve of 71.42%. Excellent performance enables us to predict a number of new potential OMIM disease-miRNA associations and the newly predicted associations are publicly released to facilitate future studies. Some predicted associations with high ranks were manually checked and were confirmed from the publicly available databases, which was a strong evidence for the practical relevance of our method.
Vanderbei, Robert J.; Pınar, Mustafa Ç.; Bozkaya, Efe B.
2013-01-01
An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problem as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put.
Murase, Yohsuke; Shimada, Takashi; Ito, Nobuyasu; Rikvold, Per Arne
2010-01-01
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species, while migrants have no correlation with the resident species. It is found that the dynamics of community assembly with mutations are quite different from the case with migrations. In contrast to mutation models, which show intermittent dynamics of quasi-steady states interrupted by sudden reorganizations of the community, migration models show smooth and gradual renewal of the community. As a consequence, instead of the 1/f diversity fluctuations found for the mutation models, 1/f2, random-walk like fluctuations are observed for the migration models. In addition, a characteristic species-lifetime distribution is found: a power law that is cut off by a "skewed" distribution in the long-lifetime regime. The latter has a longer tail than a simple exponential function, which indicates an age-dependent species-mortality function. Since this characteristic profile has been observed, both in fossil data and in several other mathematical models, we conclude that it is a universal feature of macroevolution. © 2010 Elsevier Ltd.
Schulz, Johannes H P; Chechkin, Aleksei V; Metzler, Ralf
2013-01-01
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. (paper)
McDermott, Mary M; Ferrucci, Luigi; Tian, Lu; Guralnik, Jack M; Lloyd-Jones, Donald; Kibbe, Melina R; Polonsky, Tamar S; Domanchuk, Kathryn; Stein, James H; Zhao, Lihui; Taylor, Doris; Skelly, Christopher; Pearce, William; Perlman, Harris; McCarthy, Walter; Li, Lingyu; Gao, Ying; Sufit, Robert; Bloomfield, Christina L; Criqui, Michael H
2017-12-05
Benefits of granulocyte-macrophage colony-stimulating factor (GM-CSF) for improving walking ability in people with lower extremity peripheral artery disease (PAD) are unclear. Walking exercise may augment the effects of GM-CSF in PAD, since exercise-induced ischemia enhances progenitor cell release and may promote progenitor cell homing to ischemic calf muscle. To determine whether GM-CSF combined with supervised treadmill exercise improves 6-minute walk distance, compared with exercise alone and compared with GM-CSF alone; to determine whether GM-CSF alone improves 6-minute walk more than placebo and whether exercise improves 6-minute walk more than an attention control intervention. Randomized clinical trial with 2 × 2 factorial design. Participants were identified from the Chicago metropolitan area and randomized between January 6, 2012, and December 22, 2016, to 1 of 4 groups: supervised exercise + GM-CSF (exercise + GM-CSF) (n = 53), supervised exercise + placebo (exercise alone) (n = 53), attention control + GM-CSF (GM-CSF alone) (n = 53), attention control + placebo (n = 51). The final follow-up visit was on August 15, 2017. Supervised exercise consisted of treadmill exercise 3 times weekly for 6 months. The attention control consisted of weekly educational lectures by clinicians for 6 months. GM-CSF (250 μg/m2/d) or placebo were administered subcutaneously (double-blinded) 3 times/wk for the first 2 weeks of the intervention. The primary outcome was change in 6-minute walk distance at 12-week follow-up (minimum clinically important difference, 20 m). P values were adjusted based on the Hochberg step-up method. Of 827 persons evaluated, 210 participants with PAD were randomized (mean age, 67.0 [SD, 8.6] years; 141 [67%] black, 82 [39%] women). One hundred ninety-five (93%) completed 12-week follow-up. At 12-week follow-up, exercise + GM-CSF did not significantly improve 6-minute walk distance more than
Ferraz, Daniel Dominguez; Trippo, Karen Valadares; Duarte, Gabriel Pereira; Neto, Mansueto Gomes; Bernardes Santos, Kionna Oliveira; Filho, Jamary Oliveira
2018-05-01
To compare the effects of functional training, bicycle exercise, and exergaming on walking capacity of elderly with Parkinson disease (PD). A pilot randomized, controlled, single-blinded trial. A state reference health care center for elderly, a public reference outpatient clinic for the elderly. Elderly individuals (≥60 years of age; N=62) with idiopathic PD (stage 2 to 3 of modified Hoehn and Yahr staging scale) according to the London Brain Bank. The participants were randomly assigned to three groups. Group 1 (G1) participated in functional training (n=22); group 2 (G2) performed bicycle exercise (n=20), and group 3 (G3) trained with Kinect Adventures (Microsoft, Redmond, WA) exergames (n=20). The primary outcome measure was the 6-minute walk test (6MWT); secondary outcome measures were the 10-m walk test (10MWT), sitting-rising test (SRT), body mass index, Parkinson Disease Questionnaire-39, World Health Organization Disability Assessment Schedule 2.0 (WHODAS 2.0), and 15-item Geriatric Depression Scale. All groups showed significant improvements in 6MWT (G1 P=.008; G2 P=.001; G3 P=.005), SRT (G1 Ptraining had similar outcomes compared with functional training and bicycle exercise. The three physical exercise modalities presented significant improvements on walking capacity, ability to stand up and sit, and functionality of the participants. Copyright © 2018 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.
Reeves, Mark
2014-03-01
Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is dominant contribution of the entropy in driving important biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy) that enable students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce seemingly complex biological processes and structures to be described by tractable models that include deterministic processes and simple probabilistic inference. The students test these models in simulations and in laboratory experiments that are biologically relevant. The students are challenged to bridge the gap between statistical parameterization of their data (mean and standard deviation) and simple model-building by inference. This allows the students to quantitatively describe realistic cellular processes such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront ``random'' forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk
Grebenkov, Denis S.; Nguyen, Hang T.; Li, Jing-Rebecca
2013-01-01
A fast random walk (FRW) algorithm is adapted to compute diffusion-weighted NMR signals in a Menger sponge which is formed by multiple channels of broadly distributed sizes and often considered as a model for soils and porous materials. The self-similar structure of a Menger sponge allows for rapid simulations that were not feasible by other numerical techniques. The role of multiple length scales on diffusion-weighted NMR signals is investigated. (authors)
N. Bayer; O.J. Boxma (Onno)
1995-01-01
textabstractTwo variants of an M/G/1 queue with negative customers lead to the study of a random walk $bmsX_{n+1=ppart{bmsX_n+bmsxi_n$ where the integer-valued $bmsxi_n$ are not bounded from below or from above, and are distributed differently in the interior of the state-space and on the boundary.
Richardson, Caroline R; Mehari, Kathleen S; McIntyre, Laura G; Janney, Adrienne W; Fortlage, Laurie A; Sen, Ananda; Strecher, Victor J; Piette, John D
2007-01-01
Abstract Background The majority of individuals with type 2 diabetes do not exercise regularly. Pedometer-based walking interventions can help; however, pedometer-based interventions targeting only total daily accumulated steps might not yield the same health benefits as physical activity programs specifying a minimum duration and intensity of physical activity bouts. Methods This pilot randomized trial compared two goal-setting strategies: 1) lifestyle goals targeting total daily accumulated...
Chen, Lei; Liu, Tao; Zhao, Xian
2018-06-01
The anatomical therapeutic chemical (ATC) classification system is a widely accepted drug classification scheme. This system comprises five levels and includes several classes in each level. Drugs are classified into classes according to their therapeutic effects and characteristics. The first level includes 14 main classes. In this study, we proposed two network-based models to infer novel potential chemicals deemed to belong in the first level of ATC classification. To build these models, two large chemical networks were constructed using the chemical-chemical interaction information retrieved from the Search Tool for Interactions of Chemicals (STITCH). Two classic network algorithms, shortest path (SP) and random walk with restart (RWR) algorithms, were executed on the corresponding network to mine novel chemicals for each ATC class using the validated drugs in a class as seed nodes. Then, the obtained chemicals yielded by these two algorithms were further evaluated by a permutation test and an association test. The former can exclude chemicals produced by the structure of the network, i.e., false positive discoveries. By contrast, the latter identifies the most important chemicals that have strong associations with the ATC class. Comparisons indicated that the two models can provide quite dissimilar results, suggesting that the results yielded by one model can be essential supplements for those obtained by the other model. In addition, several representative inferred chemicals were analyzed to confirm the reliability of the results generated by the two models. This article is part of a Special Issue entitled: Accelerating Precision Medicine through Genetic and Genomic Big Data Analysis edited by Yudong Cai & Tao Huang. Copyright © 2017 Elsevier B.V. All rights reserved.
Burnell, Daniel K.; Hansen, Scott K.; Xu, Jie
2017-09-01
Contaminants in groundwater may experience a broad spectrum of velocities and multiple rates of mass transfer between mobile and immobile zones during transport. These conditions may lead to non-Fickian plume evolution which is not well described by the advection-dispersion equation (ADE). Simultaneously, many groundwater contaminants are degraded by processes that may be modeled as first-order decay. It is now known that non-Fickian transport and reaction are intimately coupled, with reaction affecting the transport operator. However, closed-form solutions for these important scenarios have not been published for use in applications. In this paper, we present four new Green's function analytic solutions in the uncoupled, uncorrelated continuous time random walk (CTRW) framework for reactive non-Fickian transport, corresponding to the quartet of conservative tracer solutions presented by Kreft and Zuber (1978) for Fickian transport. These consider pulse injection for both resident and flux concentration combined with detection in both resident and flux concentration. A pair of solutions for resident concentration temporal pulses with detection in both flux and resident concentration is also presented. We also derive the relationship between flux and resident concentration for non-Fickian transport with first-order reaction for this CTRW formulation. An explicit discussion of employment of the new solutions to model transport with arbitrary upgradient boundary conditions as well as mobile-immobile mass transfer is then presented. Using the new solutions, we show that first-order reaction has no effect on the anomalous spatial spreading rate of concentration profiles, but produces breakthrough curves at fixed locations that appear to have been generated by Fickian transport. Under the assumption of a Pareto CTRW transition distribution, we present a variety of numerical simulations including results showing coherence of our analytic solutions and CTRW particle
InfAcrOnt: calculating cross-ontology term similarities using information flow by a random walk.
Cheng, Liang; Jiang, Yue; Ju, Hong; Sun, Jie; Peng, Jiajie; Zhou, Meng; Hu, Yang
2018-01-19
Since the establishment of the first biomedical ontology Gene Ontology (GO), the number of biomedical ontology has increased dramatically. Nowadays over 300 ontologies have been built including extensively used Disease Ontology (DO) and Human Phenotype Ontology (HPO). Because of the advantage of identifying novel relationships between terms, calculating similarity between ontology terms is one of the major tasks in this research area. Though similarities between terms within each ontology have been studied with in silico methods, term similarities across different ontologies were not investigated as deeply. The latest method took advantage of gene functional interaction network (GFIN) to explore such inter-ontology similarities of terms. However, it only used gene interactions and failed to make full use of the connectivity among gene nodes of the network. In addition, all existent methods are particularly designed for GO and their performances on the extended ontology community remain unknown. We proposed a method InfAcrOnt to infer similarities between terms across ontologies utilizing the entire GFIN. InfAcrOnt builds a term-gene-gene network which comprised ontology annotations and GFIN, and acquires similarities between terms across ontologies through modeling the information flow within the network by random walk. In our benchmark experiments on sub-ontologies of GO, InfAcrOnt achieves a high average area under the receiver operating characteristic curve (AUC) (0.9322 and 0.9309) and low standard deviations (1.8746e-6 and 3.0977e-6) in both human and yeast benchmark datasets exhibiting superior performance. Meanwhile, comparisons of InfAcrOnt results and prior knowledge on pair-wise DO-HPO terms and pair-wise DO-GO terms show high correlations. The experiment results show that InfAcrOnt significantly improves the performance of inferring similarities between terms across ontologies in benchmark set.
Zimbardo, Gaetano
2005-01-01
Plasma transport in the presence of turbulence depends on a variety of parameters such as the fluctuation level, δB/B 0 , the ratio between the particle Larmor radius and the turbulence correlation length, and the turbulence anisotropy. In this paper, we present the results of numerical simulations of plasma and magnetic field line transport in the case of anisotropic magnetic turbulence, for parameter values close to those of the solar wind. We assume a uniform background magnetic field B 0 = B 0 e z and a Fourier representation for magnetic fluctuations, which includes wavectors oblique with respect to B 0 . The energy density spectrum is a power law, and in k space it is described by the correlation lengths l x , l y , l z , which quantify the anisotropy of turbulence. For magnetic field lines, transport perpendicular to the background field depends on the Kubo number R (δB/B 0 ) (l z /l x ). For small Kubo numbers, R 0 , or the ratio l z /l x , we find first a quasilinear regime and then a percolative regime, both corresponding to Gaussian diffusion. For particles, we find that transport parallel and perpendicular to the background magnetic field depends heavily on the turbulence anisotropy and on the particle Larmor radius. For turbulence levels typical of the solar wind, δB/B 0 ≅ 0.5-1, when the ratio between the particle Larmor radius and the turbulence correlation lengths is small, anomalous regimes are found in the case l z /l x ≤ 1, with a Levy random walk (superdiffusion) along the magnetic field and subdiffusion in the perpendicular directions. Conversely, for l z /l x > 1 normal Gaussian diffusion is found. A possible expression for generalized double diffusion is discussed
Bang, Kyung Sook; Lee, In Sook; Kim, Sung Jae; Song, Min Kyung; Park, Se Eun
2016-02-01
This study was performed to determine the physical and psychological effects of an urban forest-walking program for office workers. For many workers, sedentary lifestyles can lead to low levels of physical activity causing various health problems despite an increased interest in health promotion. Fifty four office workers participated in this study. They were assigned to two groups (experimental group and control group) in random order and the experimental group performed 5 weeks of walking exercise based on Information-Motivation-Behavioral skills Model. The data were collected from October to November 2014. SPSS 21.0 was used for the statistical analysis. The results showed that the urban forest walking program had positive effects on the physical activity level (U=65.00, phealth promotion behavior (t=-2.20, p=.033), and quality of life (t=-2.42, p=.020). However, there were no statistical differences in depression, waist size, body mass index, blood pressure, or bone density between the groups. The current findings of the study suggest the forest-walking program may have positive effects on improving physical activity, health promotion behavior, and quality of life. The program can be used as an effective and efficient strategy for physical and psychological health promotion for office workers.
Bendix Tom
2010-02-01
Full Text Available Abstract Background Active approaches including both specific and unspecific exercise are probably the most widely recommended treatment for patients with chronic low back pain but it is not known exactly which types of exercise provide the most benefit. Nordic Walking - power walking using ski poles - is a popular and fast growing type of exercise in Northern Europe that has been shown to improve cardiovascular metabolism. Until now, no studies have been performed to investigate whether Nordic Walking has beneficial effects in relation to back pain. Methods A total of 151 patients with low back and/or leg pain of greater than eight weeks duration were recruited from a hospital based outpatient back pain clinic. Patients continuing to have pain greater than three on the 11-point numeric rating scale after a multidisciplinary intervention were included. Fifteen patients were unable to complete the baseline evaluation and 136 patients were randomized to receive A Nordic walking supervised by a specially trained instructor twice a week for eight weeks B One-hour instruction in Nordic walking by a specially trained instructor followed by advice to perform Nordic walking at home as much as they liked for eight weeks or C Individual oral information consisting of advice to remain active and about maintaining the daily function level that they had achieved during their stay at the backcenter. Primary outcome measures were pain and disability using the Low Back Pain Rating Scale, and functional limitation further assessed using the Patient Specific Function Scale. Furthermore, information on time off work, use of medication, and concurrent treatment for their low back pain was collected. Objective measurements of physical activity levels for the supervised and unsupervised Nordic walking groups were performed using accelerometers. Data were analyzed on an intention-to-treat basis. Results No mean differences were found between the three groups in