A random walk with a branching system in random environments
Institute of Scientific and Technical Information of China (English)
Ying-qiu LI; Xu LI; Quan-sheng LIU
2007-01-01
We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on Z with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.
Phenomenological picture of fluctuations in branching random walks.
Mueller, A H; Munier, S
2014-10-01
We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the 1/sqrt[t] correction to the average position of the rightmost particle of a branching random walk for large times t≫1, computed by Ebert and Van Saarloos, as fluctuations on top of the mean-field approximation of this process with a Brunet-Derrida cutoff at the tip that simulates discreteness. Our analytical formulas successfully compare to numerical simulations of a particular model of a branching random walk. PMID:25375474
Branching structure for an (L-1) random walk in random environment and its applications
Hong, Wenming
2010-01-01
By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching structure. Firstly, we specify the explicit invariant density by a method different with the one used in Br\\'emont [3] and reprove the law of large numbers of the random walk by a method known as the environment viewed from particles". Secondly, the branching structure enables us to prove a stable limit law, generalizing the result of Kesten-Kozlov-Spitzer [11] for the nearest random walk in random environment. As a byproduct, we also prove that the total population of a multitype branching process in random environment with immigration before the first regeneration belongs to the domain of attraction of some \\kappa -stable law.
Institute of Scientific and Technical Information of China (English)
Yan Xia REN
2008-01-01
The global supports of super-Poisson processes and super-random walks with a branching mechanism ψ(z)=z2 and constant branching rate are known to be noncompact. It turns out that, for any spatially dependent branching rate, this property remains true. However, the asymptotic extinction property for these two kinds of superprocesses depends on the decay rate of the branching-rate function at infinity.
Convergence in law for the branching random walk seen from its tip
Madaule, Thomas
2011-01-01
Considering a critical branching random walk on the real line. In a recent paper, Aidekon [3] developed a powerful method to obtain the convergence in law of its minimum after a log-factor normalization. By an adaptation of this method, we show that the point process formed by the branching random walk and its minimum converge in law to a Poisson point process colored by a certain point process. This result, confirming a conjecture of Brunet and Derrida [10], can be viewed as a discrete analog of the corresponding results for the branching brownian motion, previously established by Arguin et al. [5] [6] and Aidekon et al. [2].
Grübel, Rudolf; Kabluchko, Zakhar
2014-01-01
Let $W_{\\infty}(\\beta)$ be the limit of the Biggins martingale $W_n(\\beta)$ associated to a supercritical branching random walk with mean number of offspring $m$. We prove a functional central limit theorem stating that as $n\\to\\infty$ the process $$ D_n(u):= m^{\\frac 12 n} \\left(W_{\\infty}\\left(\\frac{u}{\\sqrt n}\\right) - W_{n}\\left(\\frac{u}{\\sqrt n}\\right) \\right) $$ converges weakly, on a suitable space of analytic functions, to a Gaussian random analytic function with random variance. Usin...
Randomized random walk on a random walk
International Nuclear Information System (INIS)
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)
Cooper, Colin; Frieze, Alan
The aim of this article is to discuss some of the notions and applications of random walks on finite graphs, especially as they apply to random graphs. In this section we give some basic definitions, in Section 2 we review applications of random walks in computer science, and in Section 3 we focus on walks in random graphs.
Durhuus, B; Wheater, J; Durhuus, Bergfinnur; Jonsson, Thordur; Wheater, John
2006-01-01
We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length. We also calculate exactly the spectral dimension of some fixed non-translationally invariant combs. We relate the spectral dimension to the critical exponent of the mass of the two-point function for random walks on random combs, and compute mean displacements as a function of walk duration. We prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension.
Fixed points of a generalized smoothing transformation and applications to the branching random walk
Liu, Quansheng
1998-01-01
Let {Ai : i ≥ 1} be a sequence of non-negative random variables and let M be the class of all probability measures on [0,∞]. Define a transformation T on M by letting Tμ be the distribution of ∑i=1∞AiZi, where the Zi are independent random variables with distribution μ, which are also independent of {Ai}. Under first moment assumptions imposed on {Ai}, we determine exactly when T has a non-trivial fixed point (of finite or infinite mean) and we prove that all fixed ...
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...
Fractional random walk lattice dynamics
Michelitsch, Thomas; Riascos, Alejandro Perez; Nowakowski, Andrzeij; Nicolleau, Franck
2016-01-01
We analyze time-discrete and continuous `fractional' random walks on undirected regular networks with special focus on cubic periodic lattices in $n=1,2,3,..$ dimensions.The fractional random walk dynamics is governed by a master equation involving {\\it fractional powers of Laplacian matrices $L^{\\frac{\\alpha}{2}}$}where $\\alpha=2$ recovers the normal walk.First we demonstrate thatthe interval $0\\textless{}\\alpha\\leq 2$ is admissible for the fractional random walk. We derive analytical expressions for fractional transition matrix and closely related the average return probabilities. We further obtain thefundamental matrix $Z^{(\\alpha)}$, and the mean relaxation time (Kemeny constant) for the fractional random walk.The representation for the fundamental matrix $Z^{(\\alpha)}$ relates fractional random walks with normal random walks.We show that the fractional transition matrix elements exihibit for large cubic $n$-dimensional lattices a power law decay of an $n$-dimensional infinite spaceRiesz fractional deriva...
Snakes and perturbed random walks
Basak, Gopal
2011-01-01
In this paper we study some properties of random walks perturbed at extrema, which are generalizations of the walks considered e.g., in Davis (1999). This process can also be viewed as a version of {\\em excited random walk}, studied recently by many authors. We obtain a few properties related to the range of the process with infinite memory. We also prove the Strong law, Central Limit Theorem, and the criterion for the recurrence of the perturbed walk with finite memory.
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.
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.
RENEWAL THEOREM FOR (L, 1)-RANDOM WALK IN RANDOM ENVIRONMENT
Institute of Scientific and Technical Information of China (English)
洪文明; 孙鸿雁
2013-01-01
We consider a random walk on Z in random environment with possible jumps{-L, · · · ,-1, 1}, in the case that the environment{ωi: i∈Z}are i.i.d.. We establish the renewal theorem for the Markov chain of “the environment viewed from the particle” in both annealed probability and quenched probability, which generalize partially the results of Kesten (1977) and Lalley (1986) for the nearest random walk in random environment on Z, respectively. Our method is based on the intrinsic branching structure within the (L, 1)-RWRE formulated in Hong and Wang (2013).
Topics in random walks in random environment
International Nuclear Information System (INIS)
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)
Quantum Random Walks do not need a Coin Toss
Patel, Apoorva; Raghunathan, K. S.; Rungta, Pranaw
2004-01-01
Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete quantum random walks, studied in the literature, have nonetheless used both superposition and a quantum coin toss instruction. This is not necessary, and a discrete quantum random walk without a quantum coin toss instruction is defined and analyzed here. O...
When Human Walking is a Random Walk
Hausdorff, J. M.
1998-03-01
The complex, hierarchical locomotor system normally does a remarkable job of controlling an inherently unstable, multi-joint system. Nevertheless, the stride interval --- the duration of a gait cycle --- fluctuates from one stride to the next, even under stationary conditions. We used random walk analysis to study the dynamical properties of these fluctuations under normal conditions and how they change with disease and aging. Random walk analysis of the stride-to-stride fluctuations of healthy, young adult men surprisingly reveals a self-similar pattern: fluctuations at one time scale are statistically similar to those at multiple other time scales (Hausdorff et al, J Appl Phsyiol, 1995). To study the stability of this fractal property, we analyzed data obtained from healthy subjects who walked for 1 hour at their usual pace, as well as at slower and faster speeds. The stride interval fluctuations exhibited long-range correlations with power-law decay for up to a thousand strides at all three walking rates. In contrast, during metronomically-paced walking, these long-range correlations disappeared; variations in the stride interval were uncorrelated and non-fractal (Hausdorff et al, J Appl Phsyiol, 1996). To gain insight into the mechanism(s) responsible for this fractal property, we examined the effects of aging and neurological impairment. Using detrended fluctuation analysis (DFA), we computed α, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. α was significantly lower in healthy elderly subjects compared to young adults (p < .003) and in subjects with Huntington's disease, a neuro-degenerative disorder of the central nervous system, compared to disease-free controls (p < 0.005) (Hausdorff et al, J Appl Phsyiol, 1997). α was also significantly related to degree of functional impairment in subjects with Huntington's disease (r=0.78). Recently, we have observed that just as
随机环境中的分枝随机游动的若干极限定理%Some limit theorems on branching random walks in random environments
Institute of Scientific and Technical Information of China (English)
方亮; 胡晓予
2011-01-01
假设{Zn;n=0,1,2,…}是一个随机环境中的分枝随机游动(即质点在产生后代的过程中,还作直线上随机游动),ξ={ξ0,ξ1,ξ2,…}为环境过程.记Z(n,x)为落在区间(-∞,x]中的第n代质点的个数,∫ξn(s)=∑∞j=o pξn(j)Sj为第n代个体的生成函数,mξn=∫1ξn(1).证明了在特定条件下,存在随机序列{tn}使得Z(n,tn)(∏n-1 i=0 mξi)-1均方收敛到一个随机变量.对于依赖于代的分枝随机游动,仍有类似的结论.%Suppose {Zn;n = 0,1,2,…} is a branching random walk in the random environment, and ξ ={ξ0,ξ1 ,ξ2, … } is the environment process. Let Z(n,x) be the number of the nth generation located in the interval ( - ∞, x ], fξn (s) = ∑j=0 ∞ Pξn (j) sj be the generating function of the distribution of the particle in the nth generation, and mξn = fξn' ( 1 ). We show that under the specific conditions, there exists a sequence of random variables { tn } , so that Z( n,tn) ( Πi=0 n-1 mξi )-1 converges in L2. For branching random walks in varying environments, we have similar results.
Localization of reinforced random walks
Tarrès, Pierre
2011-01-01
We describe and analyze how reinforced random walks can eventually localize, i.e. only visit finitely many sites. After introducing vertex and edge self-interacting walks on a discrete graph in a general setting, and stating the main results and conjectures so far on the topic, we present martingale techniques that provide an alternative proof of the a.s. localization of vertex-reinforced random walks (VRRWs) on the integers on finitely many sites and, with positive probability, on five consecutive sites, initially proved by Pemantle and Volkov (1999). Next we introduce the continuous time-lines representation (sometimes called Rubin construction) and its martingale counterpart, and explain how it has been used to prove localization of some reinforced walks on one attracting edge. Then we show how a modified version of this construction enables one to propose a new short proof of the a.s. localization of VRRWs on five sites on Z.
Numerical studies of planar closed random walks
International Nuclear Information System (INIS)
Lattice numerical simulations for planar closed random walks and their winding sectors are presented. The frontiers of the random walks and of their winding sectors have a Hausdorff dimension dH = 4/3. However, when properly defined by taking into account the inner 0-winding sectors, the frontiers of the random walks have a Hausdorff dimension dH≈1.77
Korneta, W.; Pytel, Z.
1988-07-01
The random walk of a particle on a three-dimensional semi-infinite lattice is considered. In order to study the effect of the surface on the random walk, it is assumed that the velocity of the particle depends on the distance to the surface. Moreover it is assumed that at any point the particle may be absorbed with a certain probability. The probability of the return of the particle to the starting point and the average time of eventual return are calculated. The dependence of these quantities on the distance to the surface, the probability of absorption and the properties of the surface is discussed. The method of generating functions is used.
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.
Perturbing transient Random Walk in a Random Environment with cookies of maximal strength
Bauernschubert, Elisabeth
2011-01-01
We consider a left-transient random walk in a random environment on Z that will be disturbed by cookies inducing a drift to the right of strength 1. The number of cookies per site is i.i.d. and independent of the environment. Criteria for recurrence and transience of the random walk are obtained. For this purpose we use subcritical branching processes in random environments with immigration and formulate criteria for recurrence and transience for these processes.
Numerical studies of planar closed random walks
Desbois, Jean; Ouvry, Stephane
2008-01-01
Lattice numerical simulations for planar closed random walks and their winding sectors are presented. The frontiers of the random walks and of their winding sectors have a Hausdorff dimension $d_H=4/3$. However, when properly defined by taking into account the inner 0-winding sectors, the frontiers of the random walks have a Hausdorff dimension $d_H\\approx 1.77$.
Biased random walks on multiplex networks
Battiston, Federico; Latora, Vito
2015-01-01
Biased random walks on complex networks are a particular type of walks whose motion is biased on properties of the destination node, such as its degree. In recent years they have been exploited to design efficient strategies to explore a network, for instance by constructing maximally mixing trajectories or by sampling homogeneously the nodes. In multiplex networks, the nodes are related through different types of links (layers or communication channels), and the presence of connections at different layers multiplies the number of possible paths in the graph. In this work we introduce biased random walks on multiplex networks and provide analytical solutions for their long-term properties such as the stationary distribution and the entropy rate. We focus on degree-biased walks and distinguish between two subclasses of random walks: extensive biased walks consider the properties of each node separately at each layer, intensive biased walks deal instead with intrinsically multiplex variables. We study the effec...
Quantum random walks - an introductory overview
Kempe, J
2003-01-01
This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions.
Transition matrix from a random walk
Schulman, Lawrence S
2016-01-01
Given a random walk a method is presented to produce a matrix of transition probabilities that is consistent with that random walk. The method is tested by using a transition matrix to produce a path and then using that path to create the estimate. The two matrices are then compared.
Random recursive trees and the elephant random walk
Kürsten, Rüdiger
2016-03-01
One class of random walks with infinite memory, so-called elephant random walks, are simple models describing anomalous diffusion. We present a surprising connection between these models and bond percolation on random recursive trees. We use a coupling between the two models to translate results from elephant random walks to the percolation process. We calculate, besides other quantities, exact expressions for the first and the second moment of the root cluster size and of the number of nodes in child clusters of the first generation. We further introduce another model, the skew elephant random walk, and calculate the first and second moment of this process.
ON THE RANGE OF RANDOM WALKS IN RANDOM ENVIRONMENT
Institute of Scientific and Technical Information of China (English)
ZHOUXIANYIN
1995-01-01
The range of roaldom walk on Zd in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk oil Zd in some random environments holds if d > 3, and a weak law of large numbers holds for d = 1.
Scaling of random walk betweenness in networks
Narayan, O
2016-01-01
The betweenness centrality of graphs using random walk paths instead of geodesics is studied. A scaling collapse with no adjustable parameters is obtained as the graph size $N$ is varied; the scaling curve depends on the graph model. A normalized random betweenness, that counts each walk passing through a node only once, is also defined. It is argued to be more useful and seen to have simpler scaling behavior. In particular, the probability for a random walk on a preferential attachment graph to pass through the root node is found to tend to unity as $N\\rightarrow\\infty.$
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
Random walk of second class particles in product shock measures
Balazs, Marton; Kovacs, Peter; Rakos, Attila
2009-01-01
We consider shock measures in a class of conserving stochastic particle systems on Z. These shock measures have a product structure with a step-like density profile and include a second class particle at the shock position. We show for the asymmetric simple exclusion process, for the exponential bricklayers' process, and for a generalized zero range process, that under certain conditions these shocks, and therefore the second class particles, perform a simple random walk. Some previous results, including random walks of product shock measures and stationary shock measures seen from a second class particle, are direct consequences of our more general theorem. Multiple shocks can also be handled easily in this framework. Similar shock structure is also found in a nonconserving model, the branching coalescing random walk, where the role of the second class particle is played by the rightmost (or leftmost) particle.
Quenched moderate deviations principle for random walk in random environment
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We derive a quenched moderate deviations principle for the one-dimensional nearest random walk in random environment,where the environment is assumed to be stationary and ergodic.The approach is based on hitting time decomposition.
Levy random walks on multiplex networks
Guo, Quantong; Zheng, Zhiming; Moreno, Yamir
2016-01-01
Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical processes that occur on top of them. Here, inspired by one specific model of random walks that seems to be ubiquitous across many scientific fields, the Levy flight, we study a new navigation strategy on top of multiplex networks. Capitalizing on spectral graph and stochastic matrix theories, we derive analytical expressions for the mean first passage time and the average time to reach a node on these networks. Moreover, we also explore the efficiency of Levy random walks, which we found to be very different as compared to the single layer scenario, accounting for the structure and dynamics inherent to the multiplex network. Finally, by comparing with some other important random walk processes defined on multiplex networks, we find that in some region of the parameters, a ...
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.
On a directionally reinforced random walk
Ghosh, Arka; Roitershtein, Alexander
2011-01-01
We consider a generalized version of a directionally reinforced random walk, which was originally introduced by Mauldin, Monticino, and von Weizs\\"{a}cker in \\cite{drw}. Our main result is a stable limit theorem for the position of the random walk in higher dimensions. This extends a result of Horv\\'{a}th and Shao \\cite{limits} that was previously obtained in dimension one only (however, in a more stringent functional form).
Branching diffusions in random environment
Böinghoff, Christian
2011-01-01
We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obtain the exact asymptotic behavior of the survival probability. As in the case of BPREs, there is a phase transition in the subcritical regime due to different survival opportunities. In addition, we characterize the process conditioned to never go extinct and establish a backbone construction. In the strongly subcritical regime, mean offspring numbers are increased but still subcritical in the process conditioned to never go extinct. Here survival is solely due to an immortal individual, whose offspring are the ancestors of additional families. In the weakly subcritical regime, the mean offspring number is supercritical in the process conditioned to never go extinct. Thus this process survives with positive probability even if there was no immortal individual.
Gaussian Networks Generated by Random Walks
Javarone, Marco Alberto
2014-01-01
We propose a random walks based model to generate complex networks. Many authors studied and developed different methods and tools to analyze complex networks by random walk processes. Just to cite a few, random walks have been adopted to perform community detection, exploration tasks and to study temporal networks. Moreover, they have been used also to generate scale-free networks. In this work, we define a random walker that plays the role of "edges-generator". In particular, the random walker generates new connections and uses these ones to visit each node of a network. As result, the proposed model allows to achieve networks provided with a Gaussian degree distribution, and moreover, some features as the clustering coefficient and the assortativity show a critical behavior. Finally, we performed numerical simulations to study the behavior and the properties of the cited model.
The associated random walk and martingales in random walks with stationary increments
Grey, D R
2010-01-01
We extend the notion of the associated random walk and the Wald martingale in random walks where the increments are independent and identically distributed to the more general case of stationary ergodic increments. Examples are given where the increments are Markovian or Gaussian, and an application in queueing is considered.
Equal Superposition Transformations and Quantum Random Walks
Parashar, Preeti
2007-01-01
The largest ensemble of qubits which satisfy the general transformation of equal superposition is obtained by different methods, namely, linearity, no-superluminal signalling and non-increase of entanglement under LOCC. We also consider the associated quantum random walk and show that all unitary balanced coins give the same asymmetric spatial probability distribution. It is further illustrated that unbalanced coins, upon appropriate superposition, lead to new unbiased walks which have no cla...
Scaling Argument of Anisotropic Random Walk
Institute of Scientific and Technical Information of China (English)
XU Bing-Zhen; JIN Guo-Jun; WANG Fei-Feng
2005-01-01
In this paper, we analytically discuss the scaling properties of the average square end-to-end distance for anisotropic random walk in D-dimensional space ( D ≥ 2), and the returning probability Pn(ro) for the walker into a certain neighborhood of the origin. We will not only give the calculating formula for and Pn (ro), 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 ～ n, where ⊥ 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 ～ 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 ～ n2 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.
Navigation by anomalous random walks on complex networks
Weng, Tongfeng; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan
2016-01-01
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Levy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Levy walks and the underlying network structure. Interestingly, applying our framework to the famous PageRank search, we can explain why its damping factor empirically chosen to be around 0.85. The framework for analyzing anomalous random walks on complex networks offers a new us...
A Note on Multitype Branching Process with Bounded Immigration in Random Environment
Institute of Scientific and Technical Information of China (English)
Hua Ming WANG
2013-01-01
In this paper,we study the total number of progeny,W,before regenerating of multitype branching process with immigration in random environment.We show that the tail probability of |W| is of order t-κ as t → ∞,with κ some constant.As an application,we prove a stable law for (L-1) random walk in random environment,generalizing the stable law for the nearest random walk in random environment (see "Kesten,Kozlov,Spitzer:A limit law for random walk in a random environment.Compositio Math.,30,145-168 (1975)").
Supercritical branching diffusions in random environment
Hutzenthaler, Martin
2011-01-01
Supercritical branching processes in constant environment conditioned on eventual extinction are known to be subcritical branching processes. The case of random environment is more subtle. A supercritical branching diffusion in random environment (BDRE) conditioned on eventual extinction of the population is not a BDRE. However the quenched law of the population size of a supercritical BDRE conditioned on eventual extinction is equal to the quenched law of the population size of a subcritical BDRE. As a consequence, supercritical BDREs have a phase transition which is similar to a well-known phase transition of subcritical branching processes in random environment.
Random Walk Method for Potential Problems
Krishnamurthy, T.; Raju, I. S.
2002-01-01
A local Random Walk Method (RWM) for potential problems governed by Lapalace's and Paragon's equations is developed for two- and three-dimensional problems. The RWM is implemented and demonstrated in a multiprocessor parallel environment on a Beowulf cluster of computers. A speed gain of 16 is achieved as the number of processors is increased from 1 to 23.
Iterated random walks with shape prior
DEFF Research Database (Denmark)
Pujadas, Esmeralda Ruiz; Kjer, Hans Martin; Piella, Gemma;
2016-01-01
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 th...
Random walk term weighting for information retrieval
DEFF Research Database (Denmark)
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...
Exact Random Walk Distributions using Noncommutative Geometry
Bellissard, J; Barelli, A; Claro, F; Bellissard, Jean; Camacho, Carlos J; Barelli, Armelle; Claro, Francisco
1997-01-01
Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $ N $ on a two-dimensional square lattice for large $ N $, taking into account finite size contributions.
A Random Walk to Economic Freedom?
Directory of Open Access Journals (Sweden)
Witte, Mark David
2013-04-01
Full Text Available Given the wide use of economic freedom in economic literature it is imperative to understand how economic freedom evolves. Results suggest that levels of economic freedom are dominated by random shocks. Using a test for stationarity devised by Westerlund and Larsson (2012 we are unable to reject the null hypothesis of a random walk. The changes to economic freedom also are mostly driven by random shocks with only a minor role played by country specific characteristics. Additionally, changes to economic freedom are partially reversed as increases (decreases in one year are partially offset by decreases (increases in the next year.
Random Walks on Stochastic Temporal Networks
Hoffmann, Till; Lambiotte, Renaud
2013-01-01
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.
Random walk centrality in interconnected multilayer networks
Solé-Ribalta, Albert; De Domenico, Manlio; Gómez, Sergio; Arenas, Alex
2016-06-01
Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in many fields, from economics to biology and from urban planning to social sciences, to identify the most (or the less) influent nodes in a network using centrality measures. However, defining the centrality of actors in interconnected complex networks is not trivial. In this paper, we rely on the tensorial formalism recently proposed to characterize and investigate this kind of complex topologies, and extend two well known random walk centrality measures, the random walk betweenness and closeness centrality, to interconnected multilayer networks. For each of the measures we provide analytical expressions that completely agree with numerically results.
Random Walk on the Prime Numbers
International Nuclear Information System (INIS)
The one-dimensional random walk (RW), where steps up and down are performed according to the occurrence of special primes is defined. Some quantities characterizing RW are investigated. The mean fluctuation function F(l) displays perfect power law dependence F(l) ∼ l1/2 indicating that the defined RW is not correlated. The number of returns of this special RW to the origin is investigated. It turns out, that this single, very special, realization of RW is typical one in the sense, that the usual characteristics used to measure RW, take the values close to the ones averaged over all random walks. The fractal structure on the subset of primes is also found. (author)
Environment-dependent continuous time random walk
Institute of Scientific and Technical Information of China (English)
Lin Fang; Bao Jing-Dong
2011-01-01
A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory:the jumping distance and the waiting time, are replaced by two new ones:the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement ～tα is realized numerically and analysed theoretically, where the value of the power index a is in a region of 0<α<2. Particularly, the damping leads to a sub-diffusion when the impact velocities are drawn from a Gaussian density function and the super-diffusive effect is related to statistical extremes, which are called rare-though-dominant events.
Random Walk Picture of Basketball Scoring
Gabel, Alan
2011-01-01
We present evidence, based on play-by-play data from all 6087 games from the 2006/07--2009/10 seasons of the National Basketball Association (NBA), that basketball scoring is well described by a weakly-biased continuous-time random walk. The time between successive scoring events follows an exponential distribution, with little memory between different scoring intervals. Using this random-walk picture that is augmented by features idiosyncratic to basketball, 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. By further including the heterogeneity of team strengths, we build a computational model that accounts for essentially all statistical features of game scoring data and season win/loss records of each team.
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
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.
Deterministic Random Walks on Regular Trees
Cooper, Joshua; Friedrich, Tobias; Spencer, Joel; 10.1002/rsa.20314
2010-01-01
Jim Propp's rotor router model is a deterministic analogue of a random walk on a graph. Instead of distributing chips randomly, each vertex serves its neighbors in a fixed order. Cooper and Spencer (Comb. Probab. Comput. (2006)) show a remarkable similarity of both models. If an (almost) arbitrary population of chips is placed on the vertices of a grid $\\Z^d$ and does a simultaneous walk in the Propp model, then at all times and on each vertex, the number of chips on this vertex deviates from the expected number the random walk would have gotten there by at most a constant. This constant is independent of the starting configuration and the order in which each vertex serves its neighbors. This result raises the question if all graphs do have this property. With quite some effort, we are now able to answer this question negatively. For the graph being an infinite $k$-ary tree ($k \\ge 3$), we show that for any deviation $D$ there is an initial configuration of chips such that after running the Propp model for a ...
FRACTAL DIMENSION RESULTS FOR CONTINUOUS TIME RANDOM WALKS.
Meerschaert, Mark M; Nane, Erkan; Xiao, Yimin
2013-04-01
Continuous time random walks impose random waiting times between particle jumps. This paper computes the fractal dimensions of their process limits, which represent particle traces in anomalous diffusion.
Coupled continuous time random walks in finance
Meerschaert, M M; Meerschaert, Mark M.; Scalas, Enrico
2006-01-01
Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typically not independent. For these coupled CTRW models, we can now compute the limiting stochastic process (just like Brownian motion is the limit of a simple random walk), even in the case of heavy tailed (power-law) price jumps and/or waiting times. The probability density functions for this limit process solve fractional partial differential equations. In some cases, these equations can be explicitly solved to yield descriptions of long-term price changes, based on a high-resolution model of individual trades that includes the statistical dependence between waiting times and the subsequent log-returns. In the heavy tailed case, this involves operator stable space-time random vectors that genera...
Random walk search in unstructured P2P
Institute of Scientific and Technical Information of China (English)
Jia Zhaoqing; You Jinyuan; Rao Ruonan; Li Minglu
2006-01-01
Unstructured P2P has power-law link distribution, and the random walk in power-law networks is analyzed. The analysis results show that the probability that a random walker walks through the high degree nodes is high in the power-law network, and the information on the high degree nodes can be easily found through random walk. Random walk spread and random walk search method (RWSS) is proposed based on the analysis result. Simulation results show that RWSS achieves high success rates at low cost and is robust to high degree node failure.
Random walk of passive tracers among randomly moving obstacles
Gori, Matteo; 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 environment is here considered in the case of a passively diffusing particle in a crowded environment made of randomly moving and interacting obstacles. Results: The relevant physical quantity which is worked out is the diffusion cofficient of the passive tracer which is computed as a function of the average inter-obstacles distance. Coclusions: 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 m...
Random walks on dual Sierpinski gaskets
Wu, Shunqi; Zhang, Zhongzhi; Chen, Guanrong
2011-07-01
We study an unbiased random walk on dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces. We first determine the mean first-passage time (MFPT) between a particular pair of nodes based on the connection between the MFPTs and the effective resistance. Then, by using the Laplacian spectra, we evaluate analytically the global MFPT (GMFPT), i.e., MFPT between two nodes averaged over all node pairs. Concerning these two quantities, we obtain explicit solutions and show how they vary with the number of network nodes. Finally, we relate our results for the case of d = 2 to the well-known Hanoi Towers problem.
Random walk immunization strategy on scale-free networks
Institute of Scientific and Technical Information of China (English)
Weidong PEI; Zengqiang CHEN; Zhuzhi YUAN
2009-01-01
A novel immunization strategy called the random walk immunization strategy on scale-free networks is proposed. Different from other known immunization strategies, this strategy works as follows: a node is randomly chosen from the network. Starting from this node, randomly walk to one of its neighbor node; if the present node is not immunized, then immunize it and continue the random walk; otherwise go back to the previous node and randomly walk again. This process is repeated until a certain fraction of nodes is immunized. By theoretical analysis and numerical simulations, we found that this strategy is very effective in comparison with the other known immunization strategies.
Implement Quantum Random Walks with Linear Optics Elements
Zhao, Z; Li, H; Yang, T; Chen, Z B; Pan, J W; Zhao, Zhi; Du, Jiangfeng; Li, Hui; Yang, Tao; Chen, Zeng-Bing; Pan, Jian-Wei
2002-01-01
The quantum random walk has drawn special interests because its remarkable features to the classical counterpart could lead to new quantum algorithms. In this paper, we propose a feasible scheme to implement quantum random walks on a line using only linear optics elements. With current single-photon interference technology, the steps that could be experimentally implemented can be extended to very large numbers. We also show that, by decohering the quantum states, our scheme for quantum random walk tends to be classical.
Stability of Cellular Automata Trajectories Revisited: Branching Walks and Lyapunov Profiles
Baetens, Jan M.; Gravner, Janko
2016-10-01
We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects accumulate at different exponential rates in different directions, giving rise to the Lyapunov profile. This profile quantifies instability of a cellular automaton evolution and is connected to the theory of large deviations. We rigorously and empirically study Lyapunov profiles generated from random initial states. We also introduce explicit and computationally feasible variational methods to compute the Lyapunov profiles for periodic configurations, thus developing an analog of Floquet theory for cellular automata.
Concave Majorants of Random Walks and Related Poisson Processes
Abramson, Josh
2010-01-01
We offer a unified approach to the theory of concave majorants of random walks by providing a path transformation for a walk of finite length that leaves the law of the walk unchanged whilst providing complete information about the concave majorant. This leads to a description of a walk of random geometric length as a Poisson point process of excursions away from its concave majorant, which is then used to find a complete description of the concave majorant for a walk of infinite length. In the case where subsets of increments may have the same arithmetic mean, we investigate three nested compositions that naturally arise from our construction of the concave majorant.
Optimal paths as correlated random walks
Perlsman, E.; Havlin, S.
2006-01-01
A numerical study of optimal paths in the directed polymer model shows that the paths are similar to correlated random walks. It is shown that when a directed optimal path of length t is divided into 3 segments whose length is t/3, the correlation between the transversal movements along the first and last path segments is independent of the path length t. It is also shown that the transversal correlations along optimal paths decrease as the paths approach their endpoints. The numerical results obtained for optimal paths in 1+4 dimensions are qualitatively similar to those obtained for optimal paths in lower dimensions, and the data supplies a strong numerical indication that 1+4 is not the upper critical dimension of this model, and of the associated KPZ equation.
Renewal theorems for random walks in random scenery
Guillotin-Plantard, Nadine
2011-01-01
Random walks in random scenery are processes defined by $Z_n:=\\sum_{k=1}^n\\xi_{X_1+...+X_k}$, where $(X_k,k\\ge 1)$ and $(\\xi_y,y\\in\\mathbb Z)$ are two independent sequences of i.i.d. random variables. We suppose that the distributions of $X_1$ and $\\xi_0$ belong to the normal domain of attraction of strictly stable distributions with index $\\alpha\\in[1,2]$ and $\\beta\\in(0,2)$ respectively. We are interested in the asymptotic behaviour as $|a|$ goes to infinity of quantities of the form $\\sum_{n\\ge 1}{\\mathbb E}[h(Z_n-a)]$ (when $(Z_n)_n$ is transient) or $\\sum_{n\\ge 1}{\\mathbb E}[h(Z_n)-h(Z_n-a)]$ (when $(Z_n)_n$ is recurrent) where $h$ is some complex-valued function defined on $\\mathbb{R}$ or $\\mathbb{Z}$.
The parabolic Anderson model random walk in random potential
König, Wolfgang
2016-01-01
This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.
Random walk models for top-N recommendation task
Institute of Scientific and Technical Information of China (English)
Yin ZHANG; Jiang-qin WU; Yue-ting ZHUANG
2009-01-01
Recently there has been an increasing interest in applying random walk based methods to recommender systems.We employ a Gaussian random field to model the top-N recommendation task as a semi-supervised learning problem.taking into account the degree of each node on the user-item bipartite graph,and induce an effective absorbing random walk (ARW) algorithm for the top-N recommendation task.Our random walk approach directly generates the top-N recommendations for individuals,rather than predicting the ratings of the recommendations.Experimental results on the two real data sets show that our random walk algorithm significantly outperforms the state-of-the-art random walk based personalized ranking algorithm as well as the popular item-based collaborative filtering method.
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
Pseudo memory effects, majorization and entropy in quantum random walks
Energy Technology Data Exchange (ETDEWEB)
Bracken, Anthony J [Centre for Mathematical Physics and Department of Mathematics, University of Queensland, Brisbane 4072 (Australia); Ellinas, Demosthenes [Division of Mathematics, Technical University of Crete, GR-73100 Chania Crete (Greece); Tsohantjis, Ioannis [Division of Physics, Technical University of Crete, GR-73100 Chania Crete (Greece)
2004-02-25
A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial distribution. In a classical walk, entropy increase can be regarded as a consequence of the majorization ordering of successive distributions. The Lorenz curves of successive distributions for a symmetric quantum walk reveal no majorization ordering in general. Nevertheless, entropy can increase, and computer experiments show that it does so on average. Varying the stages at which the quantum coin system is traced out leads to new quantum walks, including a symmetric walk for which majorization ordering is valid but the spreading rate exceeds that of the usual symmetric quantum walk. (letter to the editor)
Pseudo Memory Effects, Majorization and Entropy in Quantum Random Walks
Bracken, A J; Tsohantjis, I; Bracken, Anthony J.; Ellinas, Demosthenes; Tsohantjis, Ioannis
2004-01-01
A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial distribution. In a classical walk, entropy increase can be regarded as a consequence of the majorization ordering of successive distributions. The Lorenz curves of successive distributions for a symmetric quantum walk reveal no majorization ordering in general. Nevertheless, entropy can increase, and computer experiments show that it does so on average. Varying the stages at which the quantum coin system is traced out leads to new quantum walks, including a symmetric walk for which majorization ordering is valid but the spreading rate exceeds that of the usual symmetric quantum walk.
Random walk in random environment in a two-dimensional stratified medium with orientations
Devulder, Alexis
2011-01-01
We consider a model of random walk in ${\\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with iid probability to stay on these lines. We prove the transience of the walk for any fixed orientations under general hypotheses. We also establish a result of convergence in distribution for this walk with suitable normalizations under more precise assumptions.
Testing Random Walk Behavior in the Damascus Securities Exchange
Ghada Abbas
2014-01-01
The majority of empirical literature on random walk behavior has interested on developed and emerging markets. However, few studies have been carried out to test the randomness of returns series on less developed markets. Damascus securities exchange is a young and nascent market in the Middle Eastern, started its operations in 2009; therefore, there is no empirical evidence testing the validity of random walk process. This paper examines whether daily stock returns on Damascus Securities Exc...
Deuschel, Jean-Dominique; Kösters, Holger
2008-01-01
We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman (Probab. Theory Related Fields 129 (2004) 219--244) to the non-reversible setting.
Random walks on the BMW monoid: an algebraic approach
Wolff, Sarah
2016-01-01
We consider Metropolis-based systematic scan algorithms for generating Birman-Murakami-Wenzl (BMW) monoid basis elements of the BMW algebra. As the BMW monoid consists of tangle diagrams, these scanning strategies can be rephrased as random walks on links and tangles. We translate these walks into left multiplication operators in the corresponding BMW algebra. Taking this algebraic perspective enables the use of tools from representation theory to analyze the walks; in particular, we develop ...
Algebraic area enclosed by random walks on a lattice
Desbois, Jean
2015-10-01
We compute the moments ≤ft of the area enclosed by an N-steps random walk on a 2D lattice. We consider separately the cases where the walk comes back to the origin or not. We also compute, for both cases, the characteristic function ≤ft at order 1/{N}2.
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.
Large deviations for random walk in a random environment
Yilmaz, Atilla
2008-01-01
In this work, we study the large deviation properties of random walk in a random environment on $\\mathbb{Z}^d$ with $d\\geq1$. We start with the quenched case, take the point of view of the particle, and prove the large deviation principle (LDP) for the pair empirical measure of the environment Markov chain. By an appropriate contraction, we deduce the quenched LDP for the mean velocity of the particle and obtain a variational formula for the corresponding rate function $I_q$. We propose an Ansatz for the minimizer of this formula. This Ansatz is easily verified when $d=1$. In his 2003 paper, Varadhan proves the averaged LDP for the mean velocity and gives a variational formula for the corresponding rate function $I_a$. Under the non-nestling assumption (resp. Kalikow's condition), we show that $I_a$ is strictly convex and analytic on a non-empty open set $\\mathcal{A}$, and that the true velocity $\\xi_o$ is an element (resp. in the closure) of $\\mathcal{A}$. We then identify the minimizer of Varadhan's variati...
Random walks of cytoskeletal motors in open and closed compartments
R. Lipowsky; S. Klumpp
2001-01-01
Random walks of molecular motors, which bind to and unbind from cytoskeletal filaments, are studied theoretically. The bound and unbound motors undergo directed and nondirected motion, respectively. Motors in open compartments exhibit anomalous drift velocities. Motors in closed compartments generat
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.
Implement Quantum Random Walks with Linear Optics Elements
Zhao, Zhi; Du, Jiangfeng; Li, Hui; Yang, Tao; Chen, Zeng-Bing; Pan, Jian-Wei
2002-01-01
The quantum random walk has drawn special interests because its remarkable features to the classical counterpart could lead to new quantum algorithms. In this paper, we propose a feasible scheme to implement quantum random walks on a line using only linear optics elements. With current single-photon interference technology, the steps that could be experimentally implemented can be extended to very large numbers. We also show that, by decohering the quantum states, our scheme for quantum rando...
Improving Random Walk Estimation Accuracy with Uniform Restarts
Avrachenkov, Konstantin; Ribeiro, Bruno; Towsley, Don
2010-01-01
This work proposes and studies the properties of a hybrid sampling scheme that mixes independent uniform node sampling and random walk (RW)-based crawling. We show that our sampling method combines the strengths of both uniform and RW sampling while minimizing their drawbacks. In particular, our method increases the spectral gap of the random walk, and hence, accelerates convergence to the stationary distribution. The proposed method resembles PageRank but unlike PageRank preserves time-rever...
Statistics of branched flow in a weak correlated random potential
Kaplan, Lev
2002-01-01
Recent images of electron flow through a two-dimensional electron gas (2DEG) device show branching behavior that is reproduced in numerical simulations of motion in a correlated random potential [cond-mat/0010348]. We show how such branching naturally arises from caustics in the classical flow and find a simple scaling behavior of the branching under variation of the random potential strength. Analytic results describing the statistical properties of the branching are confirmed by classical a...
ENHANCED RANDOM WALK WITH CHOICE: AN EMPIRICAL STUDY
Directory of Open Access Journals (Sweden)
John Alexandris
2014-03-01
Full Text Available The Random Walk with d Choice RWC d( is a recently proposed variation of the simple Random Walk that first selects a subset of d neighbor nodes and then decides to move to the node which minimizes the value of a certain parameter; this parameter captures the number of past visits of the walk to that node. In this paper, we propose the Enhanced Random Walk with d Choice algorithm ERWC d h ( , which first selects a subset of d neighbor nodes and then decides to move to the node which minimizes a value H defined at every node; this H value depends on a parameter h and captures information about past visits of the walk to that node and - with a certain weight - to its neighbors. Simulations of the Enhanced Random Walk with d Choice algorithm on various types of graphs indicate beneficial results with respect to Cover Time and Load Balancing. The graph types used are the Random Geometric Graph, Torus, Grid, Hypercube, Lollipop and Bernoulli.
Search for Directed Networks by Different Random Walk Strategies
Institute of Scientific and Technical Information of China (English)
ZHU Zi-Qi; JIN Xiao-Ling; HUANG Zhi-Long
2012-01-01
A comparative study is carried out on the effciency of five different random walk strategies searching on directed networks constructed based on several typical complex networks.Due to the difference in search effciency of the strategies rooted in network clustering,the clustering coeFfcient 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 Erd(o)s-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 effcient. However,no-triangle-loop and no-quadrangle-loop random walks do not improve the search effciency 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; 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. PMID:27409082
A random walk down Main Street
Directory of Open Access Journals (Sweden)
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.
Riemann Hypothesis and Random Walks: the Zeta case
LeClair, André
2016-01-01
In previous work it was shown that if certain series based on sums over primes of non-principal Dirichlet characters have a conjectured random walk behavior, then the Euler product formula for its $L$-function is valid to the right of the critical line $\\Re (s) > 1/2$, and the Riemann Hypothesis for this class of $L$-functions follows. Building on this work, here we propose how to extend this line of reasoning to the Riemann zeta function and other principal Dirichlet $L$-functions. We use our results to argue that $ S_\\delta (t) \\equiv \\lim_{\\delta \\to 0^+} \\dfrac{1}{\\pi} \\arg \\zeta (\\tfrac{1}{2}+ \\delta + i t ) = O(1)$, and that it is nearly always on the principal branch. We conjecture that a 1-point correlation function of the Riemann zeros has a normal distribution. This leads to the construction of a probabilistic model for the zeros. Based on these results we describe a new algorithm for computing very high Riemann zeros as a kind of stochastic process, and we calculate the $10^{100}$-th zero to over 1...
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
Generalized Quantum Random Walk in Momentum Space
Romanelli, A; Siri, R; Abal, G; Donangelo, R
2004-01-01
We introduce a discrete-time quantum walk on a one-dimensional momentum space including both discrete jumps and continuous drift. Its time evolution has two diferent stages. Initially a Markovian diffusion develops during a characteristic time interval, after which dynamical localization sets in, as in the well known Quantum Kicked Rotor system. For some exceptional values of the model's parameter the system exhibits resonant behavior and the system model behaves as the standard discrete time quantum walker on the line.
Random walk in random environment in a two-dimensional stratified medium with orientations
Devulder, Alexis; Pene, Francoise
2012-01-01
We consider a model of random walk in ${\\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed orientations under general hypotheses. This contrasts with the model of Campanino and Petritis, in which probabilities to stay on these lines are all equal. We also establish a result of convergence in distribution for this walk with suitable normalizations under...
The Cover Time of Deterministic Random Walks for General Transition Probabilities
Shiraga, Takeharu
2016-01-01
The deterministic random walk is a deterministic process analogous to a random walk. While there are some results on the cover time of the rotor-router model, which is a deterministic random walk corresponding to a simple random walk, nothing is known about the cover time of deterministic random walks emulating general transition probabilities. This paper is concerned with the SRT-router model with multiple tokens, which is a deterministic process coping with general transition probabilities ...
Tail estimates for one-dimensional non-nearest-neighbor random walk in random environment
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Suppose that the integers are assigned i.i.d. random variables {(β gx , . . . , β 1x , α x )} (each taking values in the unit interval and the sum of them being 1), which serve as an environment. This environment defines a random walk {X n } (called RWRE) which, when at x, moves one step of length 1 to the right with probability α x and one step of length k to the left with probability β kx for 1≤ k≤ g. For certain environment distributions, we determine the almost-sure asymptotic speed of the RWRE and show that the chance of the RWRE deviating below this speed has a polynomial rate of decay. This is the generalization of the results by Dembo, Peres and Zeitouni in 1996. In the proof we use a large deviation result for the product of random matrices and some tail estimates and moment estimates for the total population size in a multi-type branching process with random environment.
Visual Tracking via Random Walks on Graph Model.
Li, Xiaoli; Han, Zhifeng; Wang, Lijun; Lu, Huchuan
2016-09-01
In this paper, we formulate visual tracking as random walks on graph models with nodes representing superpixels and edges denoting relationships between superpixels. We integrate two novel graphs with the theory of Markov random walks, resulting in two Markov chains. First, an ergodic Markov chain is enforced to globally search for the candidate nodes with similar features to the template nodes. Second, an absorbing Markov chain is utilized to model the temporal coherence between consecutive frames. The final confidence map is generated by a structural model which combines both appearance similarity measurement derived by the random walks and internal spatial layout demonstrated by different target parts. The effectiveness of the proposed Markov chains as well as the structural model is evaluated both qualitatively and quantitatively. Experimental results on challenging sequences show that the proposed tracking algorithm performs favorably against state-of-the-art methods. PMID:26292358
Limited Random Walk Algorithm for Big Graph Data Clustering
Zhang, Honglei; Kiranyaz, Serkan; Gabbouj, Moncef
2016-01-01
Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the walking agent using an inflation function and a normalization function. We analyze the behavior of the limited random walk procedure and propose a novel algorithm for both global and local graph clustering problems. Previous random-walk-based algorithms depend on the chosen fitness function to find the clusters around a seed vertex. The proposed algorithm tackles the problem in an entirely different manner. We use the limited random walk procedure to find attracting vertices in a graph and use them as features to cluster the vertices. According to the experimental results on the simulated graph data and the real-world big graph data, the proposed method is superior to the state-of-the-art methods in solving graph clustering problems. Since the proposed method uses the embarrass...
A local limit theorem for random walks in random scenery and on randomly oriented lattices
Castell, Fabienne; Pène, Françoise; Schapira, Bruno
2010-01-01
Random walks in random scenery are processes defined by $Z_n:=\\sum_{k=1}^n\\xi_{X_1+...+X_k}$, where $(X_k,k\\ge 1)$ and $(\\xi_y,y\\in\\mathbb Z)$ are two independent sequences of i.i.d. random variables. We assume here that their distributions belong to the normal domain of attraction of stable laws with index $\\alpha\\in (0,2]$ and $\\beta\\in (0,2]$ respectively. These processes were first studied by H. Kesten and F. Spitzer, who proved the convergence in distribution when $\\alpha\
On a zero-drift nearest-neighbour random walk
Cohen, J.W.
1996-01-01
The present study concerns the analysis of the hitting point identity for a nearest-neighbour random walk of which the one-step transition to the $NE$, $SE$, $SW$ and $NW$ are the only transitions with nonzero probabilities. The one-step transition vector has a symmetrical probability distribution with zero drifts. The state space of the random walk is the set of lattice points in the first quarter plane, the point at the coordinate axes are all absorbing states. The distribution of the hitti...
Application of continuous-time random walk to statistical arbitrage
Directory of Open Access Journals (Sweden)
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
Existence of the harmonic measure for random walks on graphs and in random environments
Boivin, Daniel
2011-01-01
We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on $\\Z^d$, $d\\geq 3$, when the conductances are i.i.d. and the bonds with positive conductance percolate. The harmonic measure from infinity also exists for random walks on supercritical clusters of ${\\mathbb Z}^2$. This is proved using results of Barlow (2004).
Law of large numbers for non-elliptic random walks in dynamic random environments
Hollander, Frank den; Sidoravicius, Vladas
2011-01-01
We prove a law of large numbers for a class of $\\Z^d$-valued random walks in dynamic random environments, including \\emph{non-elliptic} examples. We assume that the random environment has a mixing property called \\emph{conditional cone-mixing} and that the random walk tends to stay inside space-time cones. The proof is based on a generalization of the regeneration scheme developed by Comets and Zeitouni for static random environments, which was adapted by Avena, den Hollander and Redig to dynamic random environments. We exhibit some one-dimensional examples to which our result applies. In some cases, the sign of the speed can be determined.
Measuring the fractal dimension of an optical random walk
Savo, Romolo; Svensson, Tomas; Vynck, Kevin; Wiersma, Diederik S
2013-01-01
Random walks often grasp the essence of transport processes in complex systems, representing a model for a large variety of phenomena, from human travel, to molecular kinetics, to the propagation of light and sound in disordered media. Transport is generally driven by the topology of the system, which can range from a simply random distribution of scattering elements, to very rich self-similar structures like random fractals. In this context the fractal dimension of the random walk trajectory, $d_\\mathrm{w}$, crucially determines the nature of the resulting transport process and provides information on the way the spatial evolution scales with time. In living cells and turbulent flow it has been possible to study anomalous dynamics showing $d_\\mathrm{w}\
Random walks of a quantum particle on a circle
International Nuclear Information System (INIS)
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
On the recurrence set of planar Markov Random Walks
Hervé, Loïc
2012-01-01
In this paper, we investigate the properties of recurrent planar Markov random walks. More precisely, we study the set of recurrent points with the use of local limit theorems. The Nagaev-Guivarc'h spectral method provides several examples for which these local limit theorems are satisfied as soon as the (standard or non-standard) central limit theorem holds.
Movie Recommendation using Random Walks over the Contextual Graph
DEFF Research Database (Denmark)
Bogers, Toine
algorithm that makes it easy to include different types of contextual information. It models the browsing process of a user on a movie database website by taking random walks over the contextual graph. We present our approach in this paper and highlight a number of future extensions with additional...
Quantum random walk approximation on locally compact quantum groups
Lindsay, J Martin; Skalski, Adam G.
2011-01-01
A natural scheme is established for the approximation of quantum Levy processes on locally compact quantum groups by quantum random walks. We work in the somewhat broader context of discrete approximations of completely positive quantum stochastic convolution cocycles on C*-bialgebras.
Adaptive importance sampling of random walks on continuous state spaces
International Nuclear Information System (INIS)
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
Inference of random walk models to describe leukocyte migration
Jones, Phoebe J. M.; Sim, Aaron; Taylor, Harriet B.; Bugeon, Laurence; Dallman, Magaret J.; Pereira, Bernard; Stumpf, Michael P. H.; Liepe, Juliane
2015-12-01
While the majority of cells in an organism are static and remain relatively immobile in their tissue, migrating cells occur commonly during developmental processes and are crucial for a functioning immune response. The mode of migration has been described in terms of various types of random walks. To understand the details of the migratory behaviour we rely on mathematical models and their calibration to experimental data. Here we propose an approximate Bayesian inference scheme to calibrate a class of random walk models characterized by a specific, parametric particle re-orientation mechanism to observed trajectory data. We elaborate the concept of transition matrices (TMs) to detect random walk patterns and determine a statistic to quantify these TM to make them applicable for inference schemes. We apply the developed pipeline to in vivo trajectory data of macrophages and neutrophils, extracted from zebrafish that had undergone tail transection. We find that macrophage and neutrophils exhibit very distinct biased persistent random walk patterns, where the strengths of the persistence and bias are spatio-temporally regulated. Furthermore, the movement of macrophages is far less persistent than that of neutrophils in response to wounding.
Generalized (c,d-Entropy and Aging Random Walks
Directory of Open Access Journals (Sweden)
Rudolf Hanel
2013-12-01
Full Text Available Complex systems are often inherently non-ergodic and non-Markovian and Shannon entropy loses its applicability. Accelerating, path-dependent and aging random walks offer an intuitive picture for non-ergodic and non-Markovian systems. It was shown that the entropy of non-ergodic systems can still be derived from three of the Shannon–Khinchin axioms and by violating the fourth, the so-called composition axiom. The corresponding entropy is of the form Sc,d ~ ∑iΓ(1 + d, 1 − cln pi and depends on two system-specific scaling exponents, c and d. This entropy contains many recently proposed entropy functionals as special cases, including Shannon and Tsallis entropy. It was shown that this entropy is relevant for a special class of non-Markovian random walks. In this work, we generalize these walks to a much wider class of stochastic systems that can be characterized as “aging” walks. These are systems whose transition rates between states are path- and time-dependent. We show that for particular aging walks, Sc,d is again the correct extensive entropy. Before the central part of the paper, we review the concept of (c,d-entropy in a self-contained way.
Avena, L
2012-01-01
We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on the asymptotic speeds and the scaling limits of such random walks. We observe different behaviors depending on the dynamics of the underlying random environment and the ratio between the jump rate of the random walk and the one of the environment. We compare our data with well known results for static random environment. We observe that the non-diffusive regime known so far only for the static case can occur in the dynamic setup too. Such anomalous fluctuations emerge in a new phase diagram. Further we discuss possible consequences for general static and dynamic random environments.
Maximum occupation time of a transient excited random walk on Z
Rastegar, Reza
2011-01-01
We consider a transient excited random walk on $Z$ and study the asymptotic behavior of the occupation time of a currently most visited site. In particular, our results imply that, in contrast to the random walks in random environment, a transient excited random walk does not spend an asymptotically positive fraction of time at its favorite (most visited up to a date) sites.
Prostate Cancer Segmentation Using Multispectral Random Walks
Artan, Yusuf; Haider, Masoom A.; Yetik, Imam Samil
Several studies have shown the advantages of multispectral magnetic resonance imaging (MRI) as a noninvasive imaging technique for prostate cancer localization. However, a large proportion of these studies are with human readers. There is a significant inter and intra-observer variability for human readers, and it is substantially difficult for humans to analyze the large dataset of multispectral MRI. To solve these problems a few studies were proposed for fully automated cancer localization in the past. However, fully automated methods are highly sensitive to parameter selection and often may not produce desirable segmentation results. In this paper, we present a semi-supervised segmentation algorithm by extending a graph based semi-supervised random walker algorithm to perform prostate cancer segmentation with multispectral MRI. Unlike classical random walker which can be applied only to dataset of single type of MRI, we develop a new method that can be applied to multispectral images. We prove the effectiveness of the proposed method by presenting the qualitative and quantitative results of multispectral MRI datasets acquired from 10 biopsy-confirmed cancer patients. Our results demonstrate that the multispectral MRI noticeably increases the sensitivity and jakkard measures of prostate cancer localization compared to single MR images; 0.71 sensitivity and 0.56 jakkard for multispectral images compared to 0.51 sensitivity and 0.44 jakkard for single MR image based segmentation.
An Analysis of Random-Walk Cuckoo Hashing
Frieze, Alan; Melsted, Páll; Mitzenmacher, Michael
In this paper, we provide a polylogarithmic bound that holds with high probability on the insertion time for cuckoo hashing under the random-walk insertion method. Cuckoo hashing provides a useful methodology for building practical, high-performance hash tables. The essential idea of cuckoo hashing is to combine the power of schemes that allow multiple hash locations for an item with the power to dynamically change the location of an item among its possible locations. Previous work on the case where the number of choices is larger than two has required a breadth-first search analysis, which is both inefficient in practice and currently has only a polynomial high probability upper bound on the insertion time. Here we significantly advance the state of the art by proving a polylogarithmic bound on the more efficient random-walk method, where items repeatedly kick out random blocking items until a free location for an item is found.
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.
Sub-Markov Random Walk for Image Segmentation.
Dong, Xingping; Shen, Jianbing; Shao, Ling; Van Gool, Luc
2016-02-01
A novel sub-Markov random walk (subRW) algorithm with label prior is proposed for seeded image segmentation, which can be interpreted as a traditional random walker on a graph with added auxiliary nodes. Under this explanation, we unify the proposed subRW and other popular random walk (RW) algorithms. This unifying view will make it possible for transferring intrinsic findings between different RW algorithms, and offer new ideas for designing novel RW algorithms by adding or changing auxiliary nodes. To verify the second benefit, we design a new subRW algorithm with label prior to solve the segmentation problem of objects with thin and elongated parts. The experimental results on both synthetic and natural images with twigs demonstrate that the proposed subRW method outperforms previous RW algorithms for seeded image segmentation.
Coverage maximization under resource constraints using proliferating random walks
Indian Academy of Sciences (India)
Sudipta Saha; Niloy Ganguly; Abhijit Guria
2015-02-01
Dissemination of information has been one of the prime needs in almost every kind of communication network. The existing algorithms for this service, try to maximize the coverage, i.e., the number of distinct nodes to which a given piece of information could be conveyed under the constraints of time and energy. However, the problem becomes challenging for unstructured and decentralized environments. Due to its simplicity and adaptability, random walk (RW) has been a very useful tool for such environments. Different variants of this technique have been studied. In this paper, we study a history-based non-uniform proliferating random strategy where new walkers are dynamically introduced in the sparse regions of the network. Apart from this, we also study the breadth-first characteristics of the random walk-based algorithms through an appropriately designed metrics.
Metadisorder for designer light in random-walk systems
Yu, Sunkyu; Hong, Jiho; Park, Namkyoo
2015-01-01
Disorder plays a critical role in signal transport, by controlling the correlation of systems. In wave physics, disordered potentials suppress wave transport due to their localized eigenstates from random-walk scattering. Although the variation of localization with tunable disorder has been intensively studied as a bridge between ordered and disordered media, the general trend of disorder-enhanced localization has remained unchanged, failing in envisaging the existence of delocalization in highly-disordered potentials. Here, we propose the concept of 'metadisorder': tunable random-walk systems having a designed eigenstate with unnatural localization. We demonstrate that one of the eigenstates in a randomly-coupled system can always be arbitrarily molded, regardless of the degree of disorder, by adjusting the self-energy of each element. Ordered waves are then achieved in highly-disordered systems, including planewaves and globally- collective resonances. We also devise counterintuitive functionalities in diso...
Bounds of Deviation for Branching Chains in Random Environments
Institute of Scientific and Technical Information of China (English)
Wei Gang WANG
2011-01-01
We consider non-extinct branching processes in general random environments. Under the condition of means and second moments of each generation being bounded, we give the upper bounds and lower bounds for some form deviations of the process.
Level 1 quenched large deviation principle for random walk in dynamic random environment
Drewitz, David Campos Alexander
2011-01-01
Consider a random walk on a continuous time-dependent random environment on the hiper-cubic lattice. Recently, Rassoul-Agha, Seppalainen and Yilmaz proved a general large deviation principle under mild ergodicity assumptions on the random environment for such a random walk, establishing first a level 2 and 3 large deviation principle. Here we present an alternative short proof of the level 1 large deviations under mild ergodicity assumptions on the environment, which provides the existence and convexity of the rate function, in the continuous time case. Our methods are based on the use of sub-additive ergodic theorem as presented by Varadhan in 2003.
Quantum decomposition of random walk on Cayley graph of finite group
Kang, Yuanbao
2016-09-01
In the paper, A quantum decomposition (QD, for short) of random walk on Cayley graph of finite group is introduced, which contains two cases. One is QD of quantum random walk operator (QRWO, for short), another is QD of Quantum random walk state (QRWS, for short). Using these findings, I finally obtain some applications for quantum random walk (QRW, for short), which are of interest in the study of QRW, highlighting the role played by QRWO and QRWS.
On the pertinence to Physics of random walks induced by random dynamical systems: a survey
Petritis, Dimitri
2016-08-01
Let be an abstract space and a denumerable (finite or infinite) alphabet. Suppose that is a family of functions such that for all we have and a family of transformations . The pair ((Sa)a , (pa)a ) is termed an iterated function system with place dependent probabilities. Such systems can be thought as generalisations of random dynamical systems. As a matter of fact, suppose we start from a given ; we pick then randomly, with probability pa (x), the transformation Sa and evolve to Sa (x). We are interested in the behaviour of the system when the iteration continues indefinitely. Random walks of the above type are omnipresent in both classical and quantum Physics. To give a small sample of occurrences we mention: random walks on the affine group, random walks on Penrose lattices, random walks on partially directed lattices, evolution of density matrices induced by repeated quantum measurements, quantum channels, quantum random walks, etc. In this article, we review some basic properties of such systems and provide with a pathfinder in the extensive bibliography (both on mathematical and physical sides) where the main results have been originally published.
Chover-Type Laws of the Iterated Logarithm for Continuous Time Random Walks
Kyo-Shin Hwang; Wensheng Wang
2012-01-01
A continuous time random walk is a random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper, we establish Chover-type laws of the iterated logarithm for continuous time random walks with jumps and waiting times in the domains of attraction of stable laws.
Visual Saliency and Attention as Random Walks on Complex Networks
Costa, L F
2006-01-01
The unmatched versatility of vision in mammals is totally dependent on purposive eye movements and selective attention guided by saliencies in the presented images. The current article shows how concepts and tools from the areas of random walks, Markov chains, complex networks and artificial image analysis can be naturally combined in order to provide a unified and biologically plausible model for saliency detection and visual attention, which become indistinguishable in the process. Images are converted into complex networks by considering pixels as nodes while connections are established in terms of fields of influence defined by visual features such as tangent fields induced by luminance contrasts, distance, and size. Random walks are performed on such networks in order to emulate attentional shifts and even eye movements in the case of large shapes, and the frequency of visits to each node is conveniently obtained from the eigenequation defined by the stochastic matrix associated to the respectively drive...
Linearly Bounded Liars, Adaptive Covering Codes, and Deterministic Random Walks
Cooper, Joshua N
2009-01-01
We analyze a deterministic form of the random walk on the integer line called the {\\em liar machine}, similar to the rotor-router model, finding asymptotically tight pointwise and interval discrepancy bounds versus random walk. This provides an improvement in the best-known winning strategies in the binary symmetric pathological liar game with a linear fraction of responses allowed to be lies. Equivalently, this proves the existence of adaptive binary block covering codes with block length $n$, covering radius $\\leq fn$ for $f\\in(0,1/2)$, and cardinality $O(\\sqrt{\\log \\log n}/(1-2f))$ times the sphere bound $2^n/\\binom{n}{\\leq \\lfloor fn\\rfloor}$.
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.
Continuous Time Random Walks for the Evolution of Lagrangian Velocities
Dentz, Marco; Comolli, Alessandro; Borgne, Tanguy Le; Lester, Daniel R
2016-01-01
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have non-stationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and non-stationary conditions. We provide explicit expressions for the Lagrangian velocity statistics, and determine the behaviors of...
On the Emergence of Shortest Paths by Reinforced Random Walks
Figueiredo, Daniel R
2016-01-01
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate the interplay between the efficiency of network navigation (i.e., path lengths) and network structure (i.e., edge weights). We propose a simple and tractable model based on iterative biased random walks where edge weights increase over time as function of the traversed path length. Under mild assumptions, we prove that biased random walks will eventually only traverse shortest paths in their journey towards the destination. We further characterize the transient regime proving that the probability to traverse non-shortest paths decays according to a power-law. We also highlight various properties in this dynamic, such as the trade-off between exploration and convergence, and preservation of initial network plasticity. We believe the proposed model and results can be of inter...
Biasing the random walk of a molecular motor
Energy Technology Data Exchange (ETDEWEB)
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%.
Simple Random Walk Statistics. Part I: Discrete Time Results
Katzenbeisser, Walter; Panny, Wolfgang
1990-01-01
In a famous paper Dwass [I9671 proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows to extend Dwass's results in several ways, viz. arbitrary endpoints, horizontal steps, and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. T...
Random Walk Hypothesis (Rwh) In The Bursa Malaysia Stock Exchange
Ng, Swee Khiang
2005-01-01
The assumptions of the random walk hypothesis (RWH) are tested for Bursa Malaysia Stock Exchange (formerly known as Kuala Lumpur Stock Exchange) indices during the sample period of 1990 to 2005. The entire period is divided into two sub-periods, which are before and after the Asian financial crisis. The findings suggested that the stock price indices did not follow the assumptions of RWH during the entire period. In the sample period before the Asian financial crisis, the behaviour of stock p...
Bose-Einstein Correlations from Random Walk Models
Tomasik, Boris; Pisút, J; Tomasik, Boris; Heinz, Ulrich; Pisut, Jan
1998-01-01
We argue that the recently suggested ``random walk models'' for the extrapolation of hadronic transverse mass spectra from pp or pA to AB collisions fail to describe existing data on Bose-Einstein correlations. In particular they are unable to reproduce the measured magnitude and K_\\perp-dependence of R_s in Pb+Pb collisions and the increase of R_l with increasing size of the collision system.
Random walks, liquidity molasses and critical response in financial markets
J. -P. Bouchaud; J. Kockelkoren; Potters, M
2004-01-01
Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged fluctuations in liquidity, with an otherwise permanent market impact, challenging the scenario proposed in Quantitative Finance 4, 176 (2004), where the impact is *transient*, with a power-law decay in time. The exponent of this decay is precisely tuned to a criti...
Random Walk Routing in WSNs with Regular Topologies
Institute of Scientific and Technical Information of China (English)
Hui Tian; Hong Shen; Teruo Matsuzawa
2006-01-01
Topology is one of the most important characteristics for any type of networks because it represents the network's inherent properties and has great impact on the performance of the network. For wireless sensor networks (WSN),a well-deployed regular topology can help save more energy than what a random topology can do. WSNs with regular topologies can prolong network lifetime as studied in many previous work. However, little work has been done in developing effective routing algorithms for WSNs with regular topologies, except routing along a shortest path with the knowledge of global location information of sensor nodes. In this paper, a new routing protocol based on random walk is proposed. It does not require global location information. It also achieves load balancing property inherently for WSNs which is difficult to achieve by other routing protocols. In the scenarios where the message required to be sent to the base station is in comparatively small size with the inquiry message among neighboring nodes, it is proved that the random walk routing protocol can guarantee high probability of successful transmission from the source to the base station with the same amount of energy consumption as the shortest path routing. Since in many applications of WSNs, sensor nodes often send only beep-like small messages to the base station to report their status, our proposed random walk routing is thus a viable scheme and can work very efficiently especially in these application scenarios. The random walk routing provides load balancing in the WSN as mentioned, however, the nodes near to the base station are inevitably under heavier burden than those far away from the base station. Therefore, a density-aware deployment scheme is further proposed to guarantee that the heavy-load nodes do not affect the network lifetime even if their energy is exhausted. The main idea is deploying sensors with different densities according to their distance to the base station. It will be
Holey random walks: optics of heterogeneous turbid composites.
Svensson, Tomas; Vynck, Kevin; Grisi, Marco; Savo, Romolo; Burresi, Matteo; Wiersma, Diederik S
2013-02-01
We present a probabilistic theory of random walks in turbid media with nonscattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics, and void spacings can be analytically predicted. The theory is validated using Monte Carlo simulations of light transport in heterogeneous systems in the form of random sphere packings and good agreement is found. The role of step correlations is discussed and differences between unbounded and bounded systems are investigated. Our results are relevant to the optics of heterogeneous systems in general and represent an important step forward in the understanding of media with strong (fractal) heterogeneity in particular. PMID:23496473
Existence of the Harmonic Measure for Random Walks on Graphs and in Random Environments
Boivin, Daniel; Rau, Clément
2013-01-01
We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on ℤ d , d≥3, when the conductances are i.i.d. and the bonds with positive conductance percolate. The harmonic measure from infinity also exists for random walks on supercritical clusters of ℤ2. This is proved using results of Barlow (Ann. Probab. 32:3024-3084, 2004) and Barlow and Hambly (Electron. J. Probab. 14(1):1-27, 2009).
Some Probability Properties of Random Walk in Time-Random Environment
Institute of Scientific and Technical Information of China (English)
Zhang Xiao-min; Li Bo
2004-01-01
A general formulation of the stochastic model for random walk in time-random environment and an equivalent definition is established in this paper. Moreover, some basic probability relations similar to the classical case which are very useful in the corresponding research of fractal properties are given. At the end, a typical example is provided to show the recurrence and transience.
Strong approximation for the general Kesten-Spitzer random walk in independent random scenery
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper is to prove that, if a one-dimensional random wa lkcan be approximated by a Brownian motion, then the related random walk in a g eneral independent scenery can be approximated by a Brownian motion in Brownian scenery.
A Novel Algorithm of Quantum Random Walk in Server Traffic Control and Task Scheduling
Directory of Open Access Journals (Sweden)
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.
Law of large numbers for a class of random walks in dynamic random environments
Avena, L; Redig, F
2009-01-01
In this paper we consider a class of one-dimensional interacting particle systems in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied/vacant sites has a local drift to the right/left. We adapt a regeneration-time argument originally developed by Comets and Zeitouni for static random environments to prove that, under a space-time mixing property for the dynamic random environment called cone-mixing, the random walk has an a.s. constant global speed. In addition, we show that if the dynamic random environment is exponentially mixing in space-time and the local drifts are small, then the global speed can be written as a power series in the size of the local drifts. From the first term in this series the sign of the global speed can be read off. The results can be easily extended to higher dimensions.
Free Dirac evolution as a quantum random walk
Bracken, A J; Smyrnakis, I
2006-01-01
Any positive-energy state of a free Dirac particle that is initially highly-localized, evolves in time by spreading at speeds close to the speed of light. This general phenomenon is explained by the fact that the Dirac evolution can be approximated arbitrarily closely by a quantum random walk, where the roles of coin and walker systems are naturally attributed to the spin and position degrees of freedom of the particle. Initially entangled and spatially localized spin-position states evolve with asymptotic two-horned distributions of the position probability, familiar from earlier studies of quantum walks. For the Dirac particle, the two horns travel apart at close to the speed of light.
Infinitely dimensional control Markov branching chains in random environments
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
First of all we introduce the concepts of infinitely dimensional control Markov branching chains in random environments (β-MBCRE) and prove the existence of such chains, then we introduce the concepts of conditional generating functionals and random Markov transition functions of such chains and investigate their branching property. Base on these concepts we calculate the moments of the β-MBCRE and obtain the main results of this paper such as extinction probabilities, polarization and proliferation rate. Finally we discuss the classification ofβ-MBCRE according to the different standards.
Tests of the random walk hypothesis for financial data
Nakamura, Tomomichi; Small, Michael
2007-04-01
We propose a method from the viewpoint of deterministic dynamical systems to investigate whether observed data follow a random walk (RW) and apply the method to several financial data. Our method is based on the previously proposed small-shuffle surrogate method. Hence, our method does not depend on the specific data distribution, although previously proposed methods depend on properties of the data distribution. The data we use are stock market (Standard & Poor's 500 in US market and Nikkei225 in Japanese market), exchange rate (British Pound/US dollar and Japanese Yen/US dollar), and commodity market (gold price and crude oil price). We found that these financial data are RW whose first differences are independently distributed random variables or time-varying random variables.
Nonlocal operators, parabolic-type equations, and ultrametric random walks
Energy Technology Data Exchange (ETDEWEB)
Chacón-Cortes, L. F., E-mail: fchaconc@math.cinvestav.edu.mx; Zúñiga-Galindo, W. A., E-mail: wazuniga@math.cinvestav.edu.mx [Centro de Investigacion y de Estudios Avanzados del I.P.N., Departamento de Matematicas, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Mexico D.F., C.P. 07360 (Mexico)
2013-11-15
In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the number of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.
Memory biased random walk approach to synthetic clickstream generation
Antulov-Fantulin, Nino; Zlatic, Vinko; Grcar, Miha; Smuc, Tomislav
2012-01-01
Personalized recommender systems rely on personal usage data of each user in the system. However, privacy policies protecting users' rights prevent this data of being publicly available to a wider researcher audience. In this work, we propose a memory biased random walk model (MBRW) based on real clickstream graphs, as a generator of synthetic clickstreams that conform to statistical properties of the real clickstream data, while, at the same time, adhering to the privacy protection policies. We show that synthetic clickstreams can be used to learn recommender system models which achieve high recommender performance on real data and at the same time assuring that strong de-minimization guarantees are provided.
Universality in random-walk models with birth and death
International Nuclear Information System (INIS)
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 Walks and Boundaries of CAT(0) Cubical complexes
Fernós, Talia; Lécureux, Jean; Mathéus, Fréderic
2016-01-01
We show under weak hypotheses that the pushforward $\\{Z_no\\}$ of a random-walk to a CAT(0) cube complex converges to a point on the boundary. We introduce the notion of squeezing points, which allows us to consider the convergence in either the Roller boundary or the visual boundary, with the appropriate hypotheses. This study allows us to show that any nonelementary action necessarily contains regular elements, that is, elements that act as rank-1 hyperbolic isometries in each irreducible fa...
Turbulent pair dispersion as a continuous-time random walk
Thalabard, Simon; Bec, Jeremie
2014-01-01
The phenomenology of turbulent relative dispersion is revisited. A heuristic scenario is proposed, in which pairs of tracers undergo a succession of independent ballistic separations during time intervals whose lengths fluctuate. This approach suggests that the logarithm of the distance between tracers self-averages and performs a continuous-time random walk. This leads to specific predictions for the probability distribution of separations, that differ from those obtained using scale-dependent eddy-diffusivity models (e.g. in the framework of Richardson's approach). Such predictions are tested against high-resolution simulations and shed new lights on the explosive separation between tracers.
Time-delayed fronts from biased random walks
Energy Technology Data Exchange (ETDEWEB)
Fort, Joaquim [Departament de Fisica, Campus de Montilivi, Universitat de Girona, 17071 Girona, Catalonia (Spain); Pujol, Toni [Departament de Mecanica, Campus de Montilivi, Universitat de Girona, 17071 Girona, Catalonia (Spain)
2007-07-15
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.
A General Random Walk Model of Molecular Motor
Institute of Scientific and Technical Information of China (English)
WANG Xian-Ju; AI Bao-Quan; LIU Guo-Tao; LIU Liang-Gang
2003-01-01
A general random walk model framework is presented which can be used to statistically describe the internaldynamics and external mechanical movement of molecular motors along filament track. The motion of molecular motorin a periodic potential and a constant force is considered. We show that the molecular motor's movement becomesslower with the potential barrier increasing, but if the forceis increased, the molecular motor's movement becomesfaster. The relation between the effective rate constant and the potential barrier's height, and that between the effectiverate constant and the value of the force are discussed. Our results are consistent with the experiments and relevanttheoretical consideration, and can be used to explain some physiological phenomena.
Bisexual Galton-Watson Branching Processes in Random Environments
Institute of Scientific and Technical Information of China (English)
Shi-xia Ma
2006-01-01
In this paper, we consider a bisexual Galton-Watson branching process whose offspring probability distribution is controlled by a random environment process. Some results for the probability generating functions associated with the process are obtained and sufficient conditions for certain extinction and for non-certain extinction are established.
Random-walk baryogenesis via primordial black holes
Semiz, İbrahim
2016-01-01
Gravitation violates baryon number $B$: A star has a huge amount of it, while a black hole forming from the star has none. Consider primordial black holes before the hadronic annihiliation in the early universe, encountering and absorbing baryons and antibaryons: Each such absorption changes $B$ of the universe by one unit, up or down. But the absorption events are $uncorrelated$ $and$ $random$, hence they amount to a random walk in $B$-space, leading to the expectation of a net $|B|$ at the end. While the scale of this effect is most uncertain, it must exist. We explore some ramifications, including the change of net $|B|$ with expansion, connection with universe topology, and possible observational signatures.
Do MENA stock market returns follow a random walk process?
Directory of Open Access Journals (Sweden)
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.
Combinatorial Approximation Algorithms for MaxCut using Random Walks
Kale, Satyen
2010-01-01
We give the first combinatorial approximation algorithm for Maxcut that beats the trivial 0.5 factor by a constant. The main partitioning procedure is very intuitive, natural, and easily described. It essentially performs a number of random walks and aggregates the information to provide the partition. We can control the running time to get an approximation factor-running time tradeoff. We show that for any constant b > 1.5, there is an O(n^{b}) algorithm that outputs a (0.5+delta)-approximation for Maxcut, where delta = delta(b) is some positive constant. One of the components of our algorithm is a weak local graph partitioning procedure that may be of independent interest. Given a starting vertex $i$ and a conductance parameter phi, unless a random walk of length ell = O(log n) starting from i mixes rapidly (in terms of phi and ell), we can find a cut of conductance at most phi close to the vertex. The work done per vertex found in the cut is sublinear in n.
THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Suppose {Xn} is a random walk in time-random environment with state space Zd, |Xn| approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α.Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.
Random walks in nonuniform environments with local dynamic interactions
Baker, Christopher M.; Hughes, Barry D.; Landman, Kerry A.
2013-10-01
We consider a class of lattice random walk models in which the random walker is initially confined to a finite connected set of allowed sites but has the opportunity to enlarge this set by colliding with its boundaries, each such collision having a given probability of breaking through. The model is motivated by an analogy to cell motility in tissue, where motile cells have the ability to remodel extracellular matrix, but is presented here as a generic model for stochastic erosion. For the one-dimensional case, we report some exact analytic results, some mean-field type analytic approximate results and simulations. We compute exactly the mean and variance of the time taken to enlarge the interval from a single site to a given size. The problem of determining the statistics of the interval length and the walker's position at a given time is more difficult and we report several interesting observations from simulations. Our simulations include the case in which the initial interval length is random and the case in which the initial state of the lattice is a random mixture of allowed and forbidden sites, with the walker placed at random on an allowed site. To illustrate the extension of these ideas to higher-dimensional systems, we consider the erosion of the simple cubic lattice commencing from a single site and report simulations of measures of cluster size and shape and the mean-square displacement of the walker.
The Laplace Functional and Moments for Markov Branching Chains in Random Environments
Institute of Scientific and Technical Information of China (English)
HU Di-he; ZHANG Shu-lin
2005-01-01
The concepts of random Markov matrix, Markov branching chain in random environment (MBCRE) and Laplace functional of Markov branching chain in random environment (LFMBCRE) are introduced. The properties of LFMBCRE and the explicit formulas of moments of MBCRE are given.
From chromosome crumpling to the interacting randomly branched polymers
Everaers, Ralf
The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for non-concatenated unknotted rings, which are known to crumple and segregate and which have been implicated as models for the generic behavior of interphase chromosomes. In we have used a computationally efficient multi-scale approach to identify the subtle physics underlying their behavior, where we combine massive Molecular Dynamics simulations on the fiber level with Monte Carlo simulations of a wide range of lattice models for the large scale structure. This allowed us to show that ring melts can be quantitatively mapped to coarse-grained melts of interacting randomly branched primitive paths. To elucidate the behavior of interacting branched polymers, we use a combination of scaling arguments and computer simulations. The simulations are carried out for different statistical ensembles: ideal randomly branching polymers, melts of interacting randomly branching polymers, and self-avoiding trees with annealed and quenched connectivities. In all cases, we perform a detailed analysis of the tree connectivities and conformations. We find that the scaling behaviour of average properties is very well described by the Flory theory of Gutin et al. [Macromolecules 26, 1293 (1993)]. A detailed study of the corresponding distribution functions allows us to propose a coherent framework of the behavior of interacting trees, including generalised Fisher-Pincus relationships and the detailed analysis of contacts statistics.
Upper large deviations for Branching Processes in Random Environment with heavy tails
Bansaye, Vincent
2010-01-01
Branching Processes in a Random Environment (BPREs) $(Z_n:n\\geq0)$ are a generalization of Galton Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. We determine here the upper large deviation of the process when the reproduction law may have heavy tails. The behavior of BPREs is related to the associated random walk of the environment, whose increments are distributed like the logarithmic mean of the offspring distributions. We obtain an expression of the upper rate function of $(Z_n:n\\geq0)$, that is the limit of $-\\log \\mathbb{P}(Z_n\\geq e^{\\theta n})/n$ when $n\\to \\infty$. It depends on the rate function of the associated random walk of the environment, the logarithmic cost of survival $\\gamma:=-\\lim_{n\\to\\infty} \\log \\mathbb{P}(Z_n>0)/n$ and the polynomial decay $\\beta$ of the tail distribution of $Z_1$. We give interpretations of this rate function in terms of the least costly ways for the process $(Z_n: n \\geq 0)$ of attaining extraordinarily large va...
Large deviations for the local times of a random walk among random conductances
König, Wolfgang; Wolff, Tilman
2011-01-01
We derive an annealed large deviation principle for the normalised local times of a continuous-time random walk among random conductances in a finite domain in $\\Z^d$ in the spirit of Donsker-Varadhan \\cite{DV75}. We work in the interesting case that the conductances may assume arbitrarily small values. Thus, the underlying picture of the principle is a joint strategy of small values of the conductances and large holding times of the walk. The speed and the rate function of our principle are explicit in terms of the lower tails of the conductance distribution. As an application, we identify the logarithmic asymptotics of the lower tails of the principal eigenvalue of the randomly perturbed negative Laplace operator in the domain.
Limit theorems for one and two-dimensional random walks in random scenery
Castell, Fabienne; Pène, Françoise
2011-01-01
Random walks in random scenery are processes defined by $Z_n:=\\sum_{k=1}^n\\xi_{X_1+...+X_k}$, where $(X_k,k\\ge 1)$ and $(\\xi_y,y\\in{\\mathbb Z}^d)$ are two independent sequences of i.i.d. random variables with values in ${\\mathbb Z}^d$ and $\\mathbb R$ respectively. We suppose that the distributions of $X_1$ and $\\xi_0$ belong to the normal basin of attraction of stable distribution of index $\\alpha\\in(0,2]$ and $\\beta\\in(0,2]$. When $d=1$ and $\\alpha\
The average inter-crossing number of equilateral random walks and polygons
Diao, Y.; Dobay, A.; Stasiak, A.
2005-09-01
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=\\frac{3\\ln 2}{8}\\approx 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.
Fractal Dimension of Randomly Branched Polymers in a Good Solvent
Institute of Scientific and Technical Information of China (English)
巴信武; 张书文; 王海军; 王素娟; 韩颖慧
2002-01-01
We propose a concept of subchains for randomly branched polymers. As a direct application of this concept,the asymptotic expression of the average mean square radius of gyration is determined to give the fractal dimensions, in which the excluded volume effect is taken into consideration. Furthermore, we investigate a scaling relation that is associated with the Flory exponent v, the fractal dimension df and the polydispersity exponent τ.
When human walking becomes random walking: fractal analysis and modeling of gait rhythm fluctuations
Hausdorff, Jeffrey M.; Ashkenazy, Yosef; Peng, Chang-K.; Ivanov, Plamen Ch.; Stanley, H. Eugene; Goldberger, Ary L.
2001-12-01
We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases. Stochastic modeling of the gait rhythm dynamics, based on transitions between different “neural centers”, reproduces distinctive statistical properties of the gait pattern. By tuning one model parameter, the hopping (transition) range, the model can describe alterations in gait dynamics from childhood to adulthood - including a decrease in the correlation and volatility exponents with maturation.
A simplified analytical random walk model for proton dose calculation
Yao, Weiguang; Merchant, Thomas E.; Farr, Jonathan B.
2016-10-01
We propose an analytical random walk model for proton dose calculation in a laterally homogeneous medium. A formula for the spatial fluence distribution of primary protons is derived. The variance of the spatial distribution is in the form of a distance-squared law of the angular distribution. To improve the accuracy of dose calculation in the Bragg peak region, the energy spectrum of the protons is used. The accuracy is validated against Monte Carlo simulation in water phantoms with either air gaps or a slab of bone inserted. The algorithm accurately reflects the dose dependence on the depth of the bone and can deal with small-field dosimetry. We further applied the algorithm to patients’ cases in the highly heterogeneous head and pelvis sites and used a gamma test to show the reasonable accuracy of the algorithm in these sites. Our algorithm is fast for clinical use.
Dynamics of market indices, Markov chains, and random walking problem
Krivoruchenko, M I
2001-01-01
Dynamics of the major USA market indices DJIA, S&P, Nasdaq, and NYSE is analyzed from the point of view of the random walking problem with two-step correlations of the market moves. The parameters characterizing the stochastic dynamics are determined empirically from the historical quotes for the daily, weekly, and monthly series. The results show existence of statistically significant correlations between the subsequent market moves. The weekly and monthly parameters are calculated in terms of the daily parameters, assuming that the Markov chains with two-step correlations give a complete description of the market stochastic dynamics. We show that the macro- and micro-parameters obey the renorm group equation. The comparison of the parameters determined from the renorm group equation with the historical values shows that the Markov chains approach gives reasonable predictions for the weekly quotes and underestimates the probability for continuation of the down trend in the monthly quotes. The return and ...
Asteroid orbits with Gaia using random-walk statistical ranging
Muinonen, Karri; Fedorets, Grigori; Pentikäinen, Hanna; Pieniluoma, Tuomo; Oszkiewicz, Dagmara; Granvik, Mikael; Virtanen, Jenni; Tanga, Paolo; Mignard, François; Berthier, Jérôme; Dell`Oro, Aldo; Carry, Benoit; Thuillot, William
2016-04-01
We describe statistical inverse methods for the computation of initial asteroid orbits within the data processing and analysis pipeline of the ESA Gaia space mission. Given small numbers of astrometric observations across short time intervals, we put forward a random-walk ranging method, in which the orbital-element phase space is uniformly sampled, up to a limiting χ2-value, with the help of the Markov-chain Monte Carlo technique (MCMC). The sample orbits obtain weights from the a posteriori probability density value and the MCMC rejection rate. For the first time, we apply the method to Gaia astrometry of asteroids. The results are nominal in that the method provides realistic estimates for the orbital uncertainties and meets the efficiency requirements for the daily, short-term processing of unknown objects.
Multifractal analysis and simulation of multifractal random walks
Schmitt, Francois G.; Huang, Yongxiang
2016-04-01
Multifractal time series, characterized by a scale invariance and large fluctuations at all scales, are found in many fields of natural and applied sciences. They are found i.e. in many geophysical fields, such as atmospheric and oceanic turbulence, hydrology, earth sciences. Here we consider a quite general type of multifractal time series, called multifractal random walk, as non stationary stochastic processes with intermittent stationary increments. We first quickly recall how such time series can be analyzed and characterized, using structure functions and arbitrary order Hilbert spectral analysis. We then discuss the simulation approach. The main object is to provide a stochastic process generating time series having the same multiscale properties We review recent works on this topic, and provide stochastic simulations in order to verify the theoretical predictions. In the lognormal framework we provide a h - μ plane expressing the scale invariant properties of these simulations. The theoretical plane is compared to simulation results.
Random walks on Sierpinski gaskets of different dimensions
Weber, Sebastian; Klafter, Joseph; Blumen, Alexander
2010-11-01
We study random walks (RWs) on classical and dual Sierpinski gaskets (SG and DSG), naturally embedded in d -dimensional Euclidian spaces (ESs). For large d the spectral dimension ds approaches 2, the marginal RW dimension. In contrast to RW over two-dimensional ES, RWs over SG and DSG show a very rich behavior. First, the time discrete scale invariance leads to logarithmic-periodic (log-periodic) oscillations in the RW properties monitored, which increase in amplitude with d . Second, the asymptotic approach to the theoretically predicted RW power laws is significantly altered depending on d and on the variant of the fractal (SG or DSG) under study. In addition, we discuss the suitability of standard RW properties to determine ds , a question of great practical relevance.
A random walk in the land of precompound decay
International Nuclear Information System (INIS)
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.)
Information Filtering via Biased Random Walk on Coupled Social Network
Directory of Open Access Journals (Sweden)
Da-Cheng Nie
2014-01-01
Full Text Available 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 General Random Walk Model of Molecular Motor
Institute of Scientific and Technical Information of China (English)
WANGXian-Ju; AIBao-Quan; LIUGuo-Tao; LIULiang-Gang
2003-01-01
A general random walk model framework is presented which can be used to statistically describe the internal dynamics and external mechanical movement of molecular motors along filament track. The motion of molecular motor in a periodic potential and a constant force is considered. We show that the molecular motor's movement becomes slower with the potential barrier increasing, but if the force is increased, the molecular motor''s movement becomes faster. The relation between the effective rate constant and the potential battler's height, and that between the effective rate constant and the value of the force are discussed. Our results are consistent with the experiments and relevant theoretical consideration, and can be used to explain some physiological phenomena.
Composition of many spins, random walks and statistics
Polychronakos, Alexios P
2016-01-01
The multiplicities of the decomposition of the product of an arbitrary number $n$ of spin $s$ states into irreducible $SU(2)$ representations are computed. Two complementary methods are presented, one based on random walks in representation space and another based on the partition function of the system in the presence of a magnetic field. The large-$n$ scaling limit of these multiplicities is derived, including nonperturbative corrections, and related to semiclassical features of the system. A physical application of these results to ferromagnetism is explicitly worked out. Generalizations involving several types of spins, as well as spin distributions, are also presented. The corresponding problem for (anti-)symmetric composition of spins is also considered and shown to obey remarkable duality and bosonization relations and exhibit qualitatively different large-$n$ scaling properties.
Correlated continuous-time random walks in external force fields
Magdziarz, Marcin; Metzler, Ralf; Szczotka, Wladyslaw; Zebrowski, Piotr
2012-05-01
We study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated waiting times. In this model the current waiting time Ti is equal to the previous waiting time Ti-1 plus a small increment. Based on the associated coupled Langevin equations the force field is systematically introduced. We show that in a confining potential the relaxation dynamics follows power-law or stretched exponential pattern, depending on the model parameters. The process obeys a generalized Einstein-Stokes-Smoluchowski relation and observes the second Einstein relation. The stationary solution is of Boltzmann-Gibbs form. The case of an harmonic potential is discussed in some detail. We also show that the process exhibits aging and ergodicity breaking.
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.
Maximal Displacement for Bridges of Random Walks in a Random Environment
Gantert, Nina
2009-01-01
It is well known that the distribution of simple random walks on $\\bf{Z}$ conditioned on returning to the origin after $2n$ steps does not depend on $p= P(S_1 = 1)$, the probability of moving to the right. Moreover, conditioned on $\\{S_{2n}=0\\}$ the maximal displacement $\\max_{k\\leq 2n} |S_k|$ converges in distribution when scaled by $\\sqrt{n}$ (diffusive scaling). We consider the analogous problem for transient random walks in random environments on $\\bf{Z}$. We show that under the quenched law $P_\\omega$ (conditioned on the environment $\\omega$), the maximal displacement of the random walk when conditioned to return to the origin at time $2n$ is no longer necessarily of the order $\\sqrt{n}$. If the environment is nestling (both positive and negative local drifts exist) then the maximal displacement conditioned on returning to the origin at time $2n$ is of order $n^{\\kappa/(\\kappa+1)}$, where the constant $\\kappa>0$ depends on the law on environment. On the other hand, if the environment is marginally nestli...
Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?
Czégel, Dániel
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...
Law of large numbers for a transient random walk driven by a symmetric exclusion process
Avena, Luca; Völlering, Florian
2011-01-01
We consider a one-dimensional simple symmetric exclusion process in equilibrium, constituting a dynamic random environment for a nearest-neighbor random walk that on occupied/vacant sites has two different local drifts to the right. We prove that the random walk has an a.s. positive constant global speed by using a regeneration-time argument. This result is part of an ongoing project aiming to analyze the behavior of random walks in slowly mixing dynamic random environments. A brief discussion on this topic is presented.
Stretched Exponential Relaxation in Disordered Complex Systems: Fractal Time Random Walk Model
Institute of Scientific and Technical Information of China (English)
Ekrem Aydmer
2007-01-01
We have analytically derived the relaxation function for one-dimensional disordered complex systems in terms of autocorrelation function of fractal time random walk by using operator formalism. We have shown that the relaxation function has stretched exponential, i.e. the Kohlrausch-Williams-Watts character for a fractal time random walk process.
Ranking Competitors Using Degree-Neutralized Random Walks
Shin, Seungkyu; Park, Juyong
2016-01-01
Competition is ubiquitous in many complex biological, social, and technological systems, playing an integral role in the evolutionary dynamics of the systems. It is often useful to determine the dominance hierarchy or the rankings of the components of the system that compete for survival and success based on the outcomes of the competitions between them. Here we propose a ranking method based on the random walk on the network representing the competitors as nodes and competitions as directed edges with asymmetric weights. We use the edge weights and node degrees to define the gradient on each edge that guides the random walker towards the weaker (or the stronger) node, which enables us to interpret the steady-state occupancy as the measure of the node's weakness (or strength) that is free of unwarranted degree-induced bias. We apply our method to two real-world competition networks and explore the issues of ranking stabilization and prediction accuracy, finding that our method outperforms other methods includ...
Ranking competitors using degree-neutralized random walks.
Shin, Seungkyu; Ahnert, Sebastian E; Park, Juyong
2014-01-01
Competition is ubiquitous in many complex biological, social, and technological systems, playing an integral role in the evolutionary dynamics of the systems. It is often useful to determine the dominance hierarchy or the rankings of the components of the system that compete for survival and success based on the outcomes of the competitions between them. Here we propose a ranking method based on the random walk on the network representing the competitors as nodes and competitions as directed edges with asymmetric weights. We use the edge weights and node degrees to define the gradient on each edge that guides the random walker towards the weaker (or the stronger) node, which enables us to interpret the steady-state occupancy as the measure of the node's weakness (or strength) that is free of unwarranted degree-induced bias. We apply our method to two real-world competition networks and explore the issues of ranking stabilization and prediction accuracy, finding that our method outperforms other methods including the baseline win-loss differential method in sparse networks.
Characteristic times of biased random walks on complex networks
Bonaventura, Moreno; Latora, Vito
2013-01-01
We consider degree-biased random walkers whose probability to move from a node to one of its neighbours of degree k is proportional to k^{\\alpha}, where \\alpha is a tuning parameter. We study both numerically and analytically three types of characteristic times, namely: i) the time the walker needs to come back to the starting node, ii) the time it takes to pass from a given node, and iii) the time it takes to visit all the nodes of the network. We consider a large database of real-world networks and we show that the value of \\alpha which minimizes the three characteristic times is different from the value \\alpha_{min}=-1 analytically found for uncorrelated networks in the mean-field approximation. In addition to this, assortative networks have preferentially a value of \\alpha_{min} in the range [-1,-0.5], while disassortative networks have \\alpha_{min} in the range [-0.5, 0]. When only local information is available, degree-biased random walks can guarantee smaller characteristic times by means of an appropr...
Rosenbluth, Jeffrey M
2008-01-01
We take the point of view of the particle in a multidimensional nearest neighbor random walk in random environment (RWRE). We prove a quenched large deviation principle and derive a variational formula for the quenched rate function. Most of the previous results in this area rely on the subadditive ergodic theorem. We employ a different technique which is based on a minimax theorem. Large deviation principles for RWRE have been proven for i.i.d. nestling environments subject to a moment condition and for ergodic uniformly elliptic environments. We assume only that the environment is ergodic and the transition probabilities satisfy a moment condition.
THE EXISTENCE AND MOMENTS OF CANONICAL BRANCHING CHAIN IN RANDOM ENVIRONMENT
Institute of Scientific and Technical Information of China (English)
胡迪鹤
2004-01-01
The concepts of branching chain in random environmnet and canonical branching chain in random environment axe introduced. Moreover the existence of these chains is proved. Finally the exact formulas of mathematical expectation and variance of branching chain in random environment axe also given.
Giant vacant component left by a random walk in a random d-regular graph
Cerny, Jiri; Windisch, David
2010-01-01
We study the trajectory of a simple random walk on a d-regular graph with d>2 and locally tree-like structure as the number n of vertices grows. Examples of such graphs include random d-regular graphs and large girth expanders. For these graphs, we investigate percolative properties of the set of vertices not visited by the walk until time un, where u>0 is a fixed positive parameter. We show that this so-called vacant set exhibits a phase transition in u in the following sense: there exists an explicitly computable threshold u* such that, with high probability as n grows, if uu*, then it has a volume of order log(n). The critical value u* coincides with the critical intensity of a random interlacement process (introduced by Sznitman [arXiv:0704.2560]) on a d-regular tree. We also show that the random interlacement model describes the structure of the vacant set in local neighbourhoods.
Biggins, J D
2010-01-01
Results on the behaviour of the rightmost particle in the $n$th generation in the branching random walk are reviewed and the phenomenon of anomalous spreading speeds, noticed recently in related deterministic models, is considered. The relationship between such results and certain coupled reaction-diffusion equations is indicated.
Radio Variability and Random Walk Noise Properties of Four Blazars
Park, Jong-Ho
2014-01-01
We present the results of a time series analysis of the long-term radio lightcurves of four blazars: 3C 279, 3C 345, 3C 446, and BL Lacertae. We exploit the data base of the University of Michigan Radio Astronomy Observatory (UMRAO) monitoring program which provides densely sampled lightcurves spanning 32 years in time in three frequency bands located at 4.8, 8, and 14.5 GHz. Our sources show mostly flat or inverted (spectral indices -0.5 < alpha < 0) spectra, in agreement with optically thick emission. All lightcurves show strong variability on all time scales. Analyzing the time lags between the lightcurves from different frequency bands, we find that we can distinguish high-peaking flares and low-peaking flares in accord with the classification of Valtaoja et al. (1992). The periodograms (temporal power spectra) of the observed lightcurves are consistent with random-walk powerlaw noise without any indication of (quasi-)periodic variability. The fact that all four sources studied are in agreement with...
Free-Dirac-particle evolution as a quantum random walk
Bracken, A. J.; Ellinas, D.; Smyrnakis, I.
2007-02-01
It is known that any positive-energy state of a free Dirac particle that is initially highly localized evolves in time by spreading at speeds close to the speed of light. As recently indicated by Strauch, this general phenomenon, and the resulting “two-horned” distributions of position probability along any axis through the point of initial localization, can be interpreted in terms of a quantum random walk, in which the roles of “coin” and “walker” are naturally associated with the spin and translational degrees of freedom in a discretized version of Dirac’s equation. We investigate the relationship between these two evolutions analytically and show how the evolved probability density on the x axis for the Dirac particle at any time t can be obtained from the asymptotic form of the probability distribution for the position of a “quantum walker.” The case of a highly localized initial state is discussed as an example.
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.
Discrete Randomness in Discrete Time Quantum Walk: Study Via Stochastic Averaging
Ellinas, D.; Bracken, A. J.; Smyrnakis, I.
2012-10-01
The role of classical noise in quantum walks (QW) on integers is investigated in the form of discrete dichotomic random variable affecting its reshuffling matrix parametrized as a SU2)/U (1) coset element. Analysis in terms of quantum statistical moments and generating functions, derived by the completely positive trace preserving (CPTP) map governing evolution, reveals a pronounced eventual transition in walk's diffusion mode, from a quantum ballistic regime with rate O(t) to a classical diffusive regime with rate O(√{t}), when condition (strength of noise parameter)2 × (number of steps) = 1, is satisfied. The role of classical randomness is studied showing that the randomized QW, when treated on the stochastic average level by means of an appropriate CPTP averaging map, turns out to be equivalent to a novel quantized classical walk without randomness. This result emphasizes the dual role of quantization/randomization in the context of classical random walk.
Estimates for the Tail Probability of the Supremum of a Random Walk with Independent Increments
Institute of Scientific and Technical Information of China (English)
Yang YANG; Kaiyong WANG
2011-01-01
The authors investigate the tail probability of the supremum of a random walk with independent increments and obtain some equivalent assertions in the case that the increments are independent and identically distributed random variables with Osubexponential integrated distributions.A uniform upper bound is derived for the distribution of the supremum of a random walk with independent but non-identically distributed increments,whose tail distributions are dominated by a common tail distribution with an O-subexponential integrated distribution.
The Limit Theorems for Random Walk with State Space R in a Space-time Random Environment
Institute of Scientific and Technical Information of China (English)
Wei Gang WANG; Zhen Long GAO; Di He HU
2008-01-01
We consider a discrete time random walk on real number space in a space-time random environment. We state that when the random environment is i.i.d., under the marginal annealed law, the law of large numbers, iterated law and CLT of the process are correct. Using a martingale approach, we also state an a.s. invariance principle for random walks in general random environment whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for the environment chain.
Quantum Random Walks and their Convergence to Evans-Hudson Flows
Indian Academy of Sciences (India)
Lingaraj Sahu
2008-08-01
Using coordinate-free basic operators on toy Fock spaces, quantum random walks are defined following the ideas of Attal and Pautrat. Extending the result for one dimensional noise, strong convergence of quantum random walks associated with bounded structure maps to Evans–Hudson flow is proved under suitable assumptions. Starting from the bounded generator of a given uniformly continuous quantum dynamical semigroup on a von Neumann algebra, we have constructed quantum random walks which converges strongly and the strong limit gives an Evans–Hudson dilation for the semigroup.
Universal adaptive self-stabilizing traversal scheme: random walk and reloading wave
Bernard, Thibault; Sohier, Devan
2011-01-01
In this paper, we investigate random walk based token circulation in dynamic environments subject to failures. We describe hypotheses on the dynamic environment that allow random walks to meet the important property that the token visits any node infinitely often. The randomness of this scheme allows it to work on any topology, and require no adaptation after a topological change, which is a desirable property for applications to dynamic systems. For random walks to be a traversal scheme and to answer the concurrence problem, one needs to guarantee that exactly one token circulates in the system. In the presence of transient failures, configurations with multiple tokens or with no token can occur. The meeting property of random walks solves the cases with multiple tokens. The reloading wave mechanism we propose, together with timeouts, allows to detect and solve cases with no token. This traversal scheme is self-stabilizing, and universal, meaning that it needs no assumption on the system topology. We describ...
Age-dependent branching processes in random environments
Institute of Scientific and Technical Information of China (English)
2008-01-01
We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξn) on R+, and reproduce independently new particles according to a probability law p(ξn) on N. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.
Age-dependent branching processes in random environments
Institute of Scientific and Technical Information of China (English)
LI YingQiu; LIU QuanSheng
2008-01-01
We consider an age-dependent branching process in random environments.The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables.Given an environment ξ,the process is a non-homogenous Galton-Watson process,whose particles in n-th generation have a life length distribution G(ξn) on R+,and reproduce independently new particles according to a probability law p(ξn) on N.Let Z(t) be the number of particles alive at time t.We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation,and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process.We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t),and show their exponential growth rates by studying a renewal equation in random environments.
The First Order Correction to the Exit Distribution for Some Random Walks
Kennedy, Tom
2016-07-01
We study three different random walk models on several two-dimensional lattices by Monte Carlo simulations. One is the usual nearest neighbor random walk. Another is the nearest neighbor random walk which is not allowed to backtrack. The final model is the smart kinetic walk. For all three of these models the distribution of the point where the walk exits a simply connected domain D in the plane converges weakly to harmonic measure on partial D as the lattice spacing δ → 0. Let ω (0,\\cdot ;D) be harmonic measure for D, and let ω _δ (0,\\cdot ;D) be the discrete harmonic measure for one of the random walk models. Our definition of the random walk models is unusual in that we average over the orientation of the lattice with respect to the domain. We are interested in the limit of (ω _δ (0,\\cdot ;D)- ω (0,\\cdot ;D))/δ . Our Monte Carlo simulations of the three models lead to the conjecture that this limit equals c_{M,L} ρ _D(z) times Lebesgue measure with respect to arc length along the boundary, where the function ρ _D(z) depends on the domain, but not on the model or lattice, and the constant c_{M,L} depends on the model and on the lattice, but not on the domain. So there is a form of universality for this first order correction. We also give an explicit formula for the conjectured density ρ _D.
Analytic calculation of hadron spectrum by random walk approximation in lattice QCD
International Nuclear Information System (INIS)
The authors explain the detail of how to calculate the meson and baryon spectrum by random walk approximation analytically. The results are compared with experimental values and Monte-Carlo results. (Auth.)
Computer simulations of randomly branching polymers: annealed versus quenched branching structures
Rosa, Angelo; Everaers, Ralf
2016-08-01
We present computer simulations of three systems of randomly branching polymers in d = 3 dimensions: ideal trees and self-avoiding trees with annealed and quenched connectivities. In all cases, we performed a detailed analysis of trees connectivities, spatial conformations and statistical properties of linear paths on trees, and compare the results to the corresponding predictions of Flory theory. We confirm that, overall, the theory predicts correctly that trees with quenched ideal connectivity exhibit less overall swelling in good solvent than corresponding trees with annealed connectivity even though they are more strongly stretched on the path level. At the same time, we emphasize the inadequacy of the Flory theory in predicting the behaviour of other, and equally relevant, observables like contact probabilities between tree nodes. We show, then, that contact probabilities can be aptly characterized by introducing a novel critical exponent, {θ }{path}, which accounts for how they decay as a function of the node-to-node path distance on the tree.
Quantum random walks with multiphoton interference and high order correlation functions
Gard, Bryan T; Anisimov, Petr M; Lee, Hwang; Dowling, Jonathan P
2011-01-01
We show a simulation of quantum random walks with multiple photons using a staggered array of 50/50 beam splitters with a bank of detectors at any desired level. We discuss the multiphoton interference effects that are inherent to this setup, and introduce one, two, and threefold coincidence detection schemes. The use of Feynman diagrams are used to intuitively explain the unique multiphoton interference effects of these quantum random walks.
Random walk study of electron motion in helium in crossed electromagnetic fields
Englert, G. W.
1972-01-01
Random walk theory, previously adapted to electron motion in the presence of an electric field, is extended to include a transverse magnetic field. In principle, the random walk approach avoids mathematical complexity and concomitant simplifying assumptions and permits determination of energy distributions and transport coefficients within the accuracy of available collisional cross section data. Application is made to a weakly ionized helium gas. Time of relaxation of electron energy distribution, determined by the random walk, is described by simple expressions based on energy exchange between the electron and an effective electric field. The restrictive effect of the magnetic field on electron motion, which increases the required number of collisions per walk to reach a terminal steady state condition, as well as the effect of the magnetic field on electron transport coefficients and mean energy can be quite adequately described by expressions involving only the Hall parameter.
Random self-similar trees and a hierarchical branching process
Kovchegov, Yevgeniy
2016-01-01
We study self-similarity in random binary rooted trees. In a well-understood case of Galton-Watson trees, a distribution is called self-similar if it is invariant with respect to the operation of pruning, which cuts the tree leaves. This only happens in the critical case (a constant process progeny), which also exhibits other special symmetries. We extend the prune-invariance set-up to a non-Markov situation and trees with edge lengths. In this general case the class of self-similar processes becomes much richer and covers a variety of practically important situations. The main result is construction of the hierarchical branching processes that satisfy various self-similarity constraints (distributional, mean, in edge-lengths) depending on the process parameters. Taking the limit of averaged stochastic dynamics, as the number of trajectories increases, we obtain a deterministic system of differential equations that describes the process evolution. This system is used to establish a phase transition that separ...
Human mammary epithelial cells exhibit a bimodal correlated random walk pattern.
Directory of Open Access Journals (Sweden)
Alka A Potdar
Full Text Available BACKGROUND: 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. METHODOLOGY/PRINCIPAL FINDINGS: 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. CONCLUSIONS/SIGNIFICANCE: 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.
Genetic Analysis of Daily Maximum Milking Speed by a Random Walk Model in Dairy Cows
DEFF Research Database (Denmark)
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...
Einstein relation for biased random walk on Galton--Watson trees
Arous, Gerard Ben; Olla, Stefano; Zeitouni, Ofer
2011-01-01
We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton--Watson trees. This provides the first example where the Einstein relation is proved for motion in random media with arbitrary deep traps.
Transient superdiffusion in random walks with a q-exponentially decaying memory profile
Moura, Thiago R. S.; Viswanathan, G. M.; da Silva, M. A. A.; Cressoni, J. C.; da Silva, L. R.
2016-07-01
We propose a random walk model with q-exponentially decaying memory profile. The q-exponential function is a generalization of the ordinary exponential function. In the limit q → 1, the q-exponential becomes the ordinary exponential function. This model presents a Markovian diffusive regime that is characterized by finite memory correlations. It is well known, that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. In this problem we report the outcome of a transient superdiffusion for finite sized walks.
A random walk-based method for segmentation of intravascular ultrasound images
Yan, Jiayong; Liu, Hong; Cui, Yaoyao
2014-04-01
Intravascular ultrasound (IVUS) is an important imaging technique that is used to study vascular wall architecture for diagnosis and assessment of the vascular diseases. Segmentation of lumen and media-adventitia boundaries from IVUS images is a basic and necessary step for quantitative assessment of the vascular walls. Due to ultrasound speckles, artifacts and individual differences, automated segmentation of IVUS images represents a challenging task. In this paper, a random walk based method is proposed for fully automated segmentation of IVUS images. Robust and accurate determination of the seed points for different regions is the key to successful use of the random walk algorithm in segmentation of IVUS images and is the focus of our work. The presented method mainly comprises five steps: firstly, the seed points inside the lumen and outside the adventitia are roughly estimated with intensity information, respectively; secondly, the seed points outside the adventitia are refined, and those of the media are determined through the results of applying random walk to the IVUS image with the roughly estimated seed points; thirdly, the media-adventitia boundary is detected by using random walk with the seed points obtained in the second step and the image gradient; fourthly, the seed points for media and lumen are refined; finally, the lumen boundary is extracted by using random walk again with the seed points obtained in the fourth step and the image gradient. The tests of the proposed algorithm on the in vivo dataset demonstrate the effectiveness of the presented IVUS image segmentation approach.
THE CONSTRUCTION OF MULTITYPE CANONICAL MARKOV BRANCHING CHAINS IN RANDOM ENVIRONMENTS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the concepts of the multitype canonical Markov branching chain in random environment (CMBCRE) and multitype Markov branching chain in random environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties.
Rudra Prakash Pradhan
2012-01-01
The paper investigates the random walk properties of foreign trade. The data used in the empirical test correspond to monthly exports and imports of India in the globalization era of 1990s. The test of random walk employed in this study is the variance ratio test, developed by Lo and Mackinlay. The empirical results indicate that the series contain large permanent component and small temporary component for both exports and imports. This suggests that foreign trade follows a random walk.
Random Walks on Directed Networks: Inference and Respondent-driven Sampling
Malmros, Jens; Britton, Tom
2013-01-01
Respondent driven sampling (RDS) is a method often used to estimate population properties (e.g. sexual risk behavior) in hard-to-reach populations. It combines an effective modified snowball sampling methodology with an estimation procedure that yields unbiased population estimates under the assumption that the sampling process behaves like a random walk on the social network of the population. Current RDS estimation methodology assumes that the social network is undirected, i.e. that all edges are reciprocal. However, empirical social networks in general also have non-reciprocated edges. To account for this fact, we develop a new estimation method for RDS in the presence of directed edges on the basis of random walks on directed networks. We distinguish directed and undirected edges and consider the possibility that the random walk returns to its current position in two steps through an undirected edge. We derive estimators of the selection probabilities of individuals as a function of the number of outgoing...
Optimized quantum random-walk search algorithm for multi-solution search
Institute of Scientific and Technical Information of China (English)
张宇超; 鲍皖苏; 汪翔; 付向群
2015-01-01
This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.
Finding passwords by random walks: How long does it take?
Kabatiansky, G
2009-01-01
We compare an efficiency of a deterministic "lawnmower" and random search strategies for finding a prescribed sequence of letters (a password) of length M in which all letters are taken from the same Q-ary alphabet. We show that at best a random search takes two times longer than a "lawnmower" search.
Directed Random Walk on the Lattices of Genus Two
Nazarenko, A. V.
2011-01-01
The object of the present investigation is an ensemble of self-avoiding and directed graphs belonging to eight-branching Cayley tree (Bethe lattice) generated by the Fucsian group of a Riemann surface of genus two and embedded in the Pincar\\'e unit disk. We consider two-parametric lattices and calculate the multifractal scaling exponents for the moments of the graph lengths distribution as functions of these parameters. We show the results of numerical and statistical computations, where the ...
Rate of escape of random walks on wreath products and related groups
Revelle, David
2003-01-01
This article examines the rate of escape for a random walk on $G\\wr \\Z$ and proves laws of the iterated logarithm for both the inner and outer radius of escape. The class of G for which these results hold includes finite, G as well as groups of the form $H\\wr \\Z$, so the construction can be iterated. Laws of the iterated logarithm are also found for random walk on Baumslag--Solitar groups and a discrete version of the Sol geometry.
Bias phase and light power dependence of the random walk coefficient of fiber optic gyroscope
Institute of Scientific and Technical Information of China (English)
Jian Mi; Chunxi Zhang; Zheng Li; Zhanjun Wu
2006-01-01
@@ Taking account of shot noise, thermal noise, dark current noise, and intensity noise that come from broad band light source, the dependence of the random walk coefficient of fiber optic gyroscope (FOG) on bias phase and light power is studied theoretically and experimentally. It is shown that with different optical and electronic parameters, the optimal bias phase is different and should be adjusted accordingly to improve the FOG precision. By choosing appropriate bias phase, the random walk coefficient of the aim FOG is reduced from 0.0026 to 0.0019 deg./h1/2.
A Non-Random Walk Down Hollywood Boulevard
DEFF Research Database (Denmark)
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...... is increasing in the popularity/media coverage of the celebrity in question, and is larger for stocks that are more affected by investor sentiment. Overall, my findings are consistent with the lab research on the affect management model, which maintains that incidental negative affect promotes risk...
Quantum random walk on the line as a markovian process
Romanelli, A; Siri, R; Abal, G; Auyuanet, A; Donangelo, R J
2004-01-01
We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic increase in the variance of the quantum walker's position with time is a direct consequence of the coherence of the quantum evolution. If the evolution is decoherent, as in the classical case, the variance is shown to increase linearly with time, as expected. Furthermore we show that this system has an evolution operator analogous to that of a resonant quantum kicked rotor. As this rotator may be described through a quantum computational algorithm, one may employ this algorithm to describe the time evolution of the quantum walker.
Multitype branching processes with immigration in random environment and polling systems
Vatutin, Vladimir
2010-01-01
For multitype branching processes with immigration evolving in a random environment and producing a final product we find the tail distribution of the size of the final product accumulated in the system for a life period. Using this result we investigate the tail distribution of the busy periods of the branching type polling systems with random service disciplines and random positive switch-over times
Avena, Luca; Blondel, Oriane; Faggionato, Alessandra
2016-10-01
We introduce via perturbation a class of random walks in reversible dynamic environments having a spectral gap. In this setting one can apply the mathematical results derived in Avena et al. (L^2-Perturbed Markov processes and applications to random walks in dynamic random environments, Preprint, 2016). As first results, we show that the asymptotic velocity is antisymmetric in the perturbative parameter and, for a subclass of random walks, we characterize the velocity and a stationary distribution of the environment seen from the walker as suitable series in the perturbative parameter. We then consider as a special case a random walk on the East model that tends to follow dynamical interfaces between empty and occupied regions. We study the asymptotic velocity and density profile for the environment seen from the walker. In particular, we determine the sign of the velocity when the density of the underlying East process is not 1 / 2, and we discuss the appearance of a drift in the balanced setting given by density 1 / 2.
Is walking a random walk? Evidence for long-range correlations in stride interval of human gait
Hausdorff, Jeffrey M.; Peng, C.-K.; Ladin, Zvi; Wei, Jeanne Y.; Goldberger, Ary L.
1995-01-01
Complex fluctuation of unknown origin appear in the normal gait pattern. These fluctuations might be described as being (1) uncorrelated white noise, (2) short-range correlations, or (3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that sucessfully accounts for the experimentally observed long-range correlations.
Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs
Institute of Scientific and Technical Information of China (English)
S. Salimi; M.A. Jafarizadeh
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 Kn, charter and n-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as t→∞ but for quantum state is not always satisfied.
The random walk of a drilling laser beam
Anthony, T. R.
1980-01-01
The disregistry of holes drilled with a pulse laser beam in 330-micron-thick single-crystal silicon-on-sapphire wafers is examined. The exit positions of the holes were displaced from the hole entrance positions on the opposing face of the wafer, and this random displacement increased with the number of laser pulses required. A model in which the bottom of the drill hole experiences small random displacements during each laser pulse is used to describe the experimental observations. It is shown that the average random displacement caused by each pulse is only a few percent of the hole diameter and can be reduced by using as few laser pulses as necessary while avoiding the cracking and spalling of the wafer that occur with a hole drilled with a single pulse.
Simulation of the diffusion process in composite porous media by random walks
Institute of Scientific and Technical Information of China (English)
ZHANG Yong
2005-01-01
A new random-walk interpolation scheme was developed to simulate solute transport through composite porous media with different porosities as well as different diffusivities. The significant influences of the abrupt variations of porosity and diffusivity on solute transport were simulated by tracking random walkers through a linear interpolation domain across the heterogeneity interface. The displacements of the random walkers within the interpolation region were obtained explicitly by establishing the equivalence between the Fokker-Planck equation and the advection-dispersion equation. Applications indicate that the random-walk interpolation method can simulate one- and two-dimensional, 2nd-order diffusion processes in composite media without local mass conservation errors. In addition, both the theoretical derivations and the numerical simulations show that the drift and dispersion of particles depend on the type of Markov process selected to reflect the dynamics of random walkers. If the nonlinear Langevin equation is used, the gradient of porosity and the gradient of diffusivity strongly affect the drift displacement of particles. Therefore, random-walking particles driven by the gradient of porosity,the gradient of diffusivity, and the random diffusion, can imitate the transport of solute under only pure diffusion in composite porous media containing abrupt variations of porosity and diffusivity.
The Random Walk Hypothesis for the Zimbabwe Stock Exchange: January 1998-November 2006
Directory of Open Access Journals (Sweden)
Tafirenyika Sunde
2008-01-01
Full Text Available The main intention of this study was to investigate, using monthly data, whether prices in the Zimbabwe Stock Exchange (ZSE follow a random-walk process as required for there to be market efficiency. The study applied the unit root tests to establish if the ZSE followed a random walk or not. If the ZSE follows a random walk it is said to be efficient and therefore managers of companies and investment specialists cannot take advantage of it to make unnecessarily huge profits. The ZSE was chosen because it represents a typical emerging stock market in Sub-Saharan Africa. The study used the Augmented-Dickey Fuller (ADF tests with a lag length that was necessary to remove autocorrelation from residuals. Using monthly data from January 1998-November 2006 we found that the ZSE did not follow a random walk and therefore was not efficient in the weak form. This meant that past prices had an influence in the determination of future prices and this provided an opportunity for out-performance by skillful financial managers and investment specialists. During the period studied investment analysts and managers of companies were able to take advantage of these investment opportunities to make abnormal returns from the ZSE. The current study helped to corroborate the findings of a similar previous study that was carried out on the Zimbabwean economy for the period 1990-1998[8].
DEFF Research Database (Denmark)
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 spatiall...... are incorrect, and a simple technique that can properly simulate turbulent diffusion in the marine environment is discussed...
Return Probability of the Open Quantum Random Walk with Time-Dependence
Institute of Scientific and Technical Information of China (English)
Clement Ampadu
2013-01-01
We study the open quantum random walk (OQRW) with time-dependence on the one-dimensional lattice space and obtain the associated limit distribution.As an application we study the return probability of the OQRW.We also ask,"What is the average time for the return probability of the OQRW?"
Elliptic random-walk equation for suspension and tracer transport in porous media
DEFF Research Database (Denmark)
Shapiro, Alexander; Bedrikovetsky, P. G.
2008-01-01
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...
Pointwise upper estimates for transition probability of continuous time random walks on graphs
Chen, Xinxing
2013-01-01
Let $X$ be a continuous time random walk on a weighted graph. Given the on-diagonal upper bounds of transition probabilities at two vertices $x_1$ and $x_2$, we use an adapted metric initiated by Davies, and obtain Gaussian upper estimates for the off-diagonal transition probability $P_{x_1}(X_t=x_2)$.
Continuous-time random walk with correlated jumps on stock market
International Nuclear Information System (INIS)
Extension of the classical continuous-time random walk model created for description of share price evolution is presented. The model assumes that consecutive jumps are dependent; in this case it is exactly solvable, reconstructing, for example, the empirical velocity autocorrelation function (vacf). However, the problem of existing the fat tail in the nonlinear vacf is still an open one. (authors)
Nordic Walking and chronic low back pain: design of a randomized clinical trial
Directory of Open Access Journals (Sweden)
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
Institute of Scientific and Technical Information of China (English)
Wang Kaiyong; Wang Yuebao; Yin Chuancun
2011-01-01
This article gives the equivalent conditions of the local asymptotics for the overshoot of a random walk with heavy-tailed increments, from which we find that the above asymptotics are different from the local asymptoties for the supremum of the random walk. To do this, the article first extends and improves some existing results about the solutions of renewal equations.
Persistent random walk on a site-disordered one-dimensional lattice: Photon subdiffusion
Miri, MirFaez; Sadjadi, Zeinab; Fouladvand, M. Ebrahim
2006-01-01
We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density $f(t)$. Depending on the behavior of $f(t)$ near $t=0$, diffusive and subdiffusive transports are predicted by the disorder expansion of the mean square-displacement and the effective medium approximation. Monte Carlo simulations confirm the anomalous diffusion of photons. To observ...
Test of Random Walk Hypothesis in the Nigerian Stock Market
Directory of Open Access Journals (Sweden)
Joel Obayagbona
2015-04-01
Full Text Available The paper investigates the weak-form market hypothesis in the emerging capital market of Nigeria from January 2006 to December 2011. It uses three tests of randomness based on autoregressive technique to check for the presence or otherwise of autocorrelation in daily stock prices and returns from the Nigerian Stock Market. All the tests including the Z-statistics for both stock prices and their returns show significant indications of dependence in return series and hence, of non-randomness. The overall results suggest that the emerging Nigerian Stock Market is not efficient in the weak form. The paper recommends that policy makers and regulatory authorities should enact and implement policy measures and put in place necessary market structures that would promote the efficiency of the Nigerian Stock Market.
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
Growth of Preferential Attachment Random Graphs Via Continuous-Time Branching Processes
Indian Academy of Sciences (India)
Krishna B Athreya; Arka P Ghosh; Sunder Sethuraman
2008-08-01
Some growth asymptotics of a version of `preferential attachment’ random graphs are studied through an embedding into a continuous-time branching scheme. These results complement and extend previous work in the literature.
Test of Random Walk Behavior in Karachi Stock Exchange
Directory of Open Access Journals (Sweden)
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.
δ-exceedance records and random adaptive walks
Park, Su-Chan; Krug, Joachim
2016-08-01
We study a modified record process where the kth record in a series of independent and identically distributed random variables is defined recursively through the condition {Y}k\\gt {Y}k-1-{δ }k-1 with a deterministic sequence {δ }k\\gt 0 called the handicap. For constant {δ }k\\equiv δ and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of δ between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records (Park et al 2015 Phys. Rev. E 91 042707). Here we explore the behavior for general probability distributions and decreasing and increasing sequences {δ }k, focusing in particular on the case when {δ }k matches the typical spacing between subsequent records in the underlying simple record process without handicap. We find that a continuous phase transition occurs only in the exponential case, but a novel kind of first order transition emerges when {δ }k is increasing. The problem is partly motivated by the dynamics of evolutionary adaptation in biological fitness landscapes, where {δ }k corresponds to the change of the deterministic fitness component after k mutational steps. The results for the record process are used to compute the mean number of steps that a population performs in such a landscape before being trapped at a local fitness maximum.
Correlated random walks caused by dynamical wavefunction collapse.
Bedingham, D J; Ulbricht, H
2015-01-01
Wavefunction collapse models modify Schrödinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum measurement problem. An additional generic consequence of the collapse mechanism is that it causes particles to exhibit a tiny random diffusive motion. Here it is shown that for the continuous spontaneous localization (CSL) model—one of the most well developed collapse models—the diffusions of two sufficiently nearby particles are positively correlated. An experimental test of this effect is proposed in which random displacements of pairs of free nanoparticles are measured after they have been simultaneously released from nearby traps. The experiment must be carried out at sufficiently low temperature and pressure in order for the collapse effects to dominate over the ambient environmental noise. It is argued that these constraints can be satisfied by current technologies for a large region of the viable parameter space of the CSL model. The effect disappears as the separation between particles exceeds the CSL length scale. The test therefore provides a means of bounding this length scale. PMID:26303388
Rodriguez-Horta, E.; Estevez-Rams, E.; Lora-Serrano, R.; Fernández, B. Aragón
2016-09-01
The correlated biased random walk with latency in one and two dimensions is discussed with regard to the portion of irreducible random movement and structured movement. It is shown how a quantitative analysis can be carried out by using computational mechanics. The stochastic matrix for both dynamics are reported. Latency introduces new states in the finite state machine description of the system in both dimensions, allowing for a full nearest neighbor coordination in the two dimensional case. Complexity analysis is used to characterize the movement, independently of the set of control parameters, making it suitable for the discussion of other random walk models. The complexity map of the system dynamics is reported for the two dimensional case.
Interval-walking training for the treatment of type 2 diabetes: a randomized, controlled trial
DEFF Research Database (Denmark)
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......: Subjects with type 2 diabetes were randomized to a control (n = 8), CWT (n = 12), or IWT 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. CWT performed all training at moderate intensity, whereas IWT...
Integrated photonic 3D waveguide arrays for quantum random walks on a circle
Linjordet, Trond
2010-01-01
Quantum random walks (QRWs) can be used to perform both quantum simulations and quantum algorithms. In order to exploit this potential, quantum walks on different types of graphs must be physically implemented. To this end this we design, model and experimentally fabricate, using the femtosecond laser direct-write technique, a 3D tubular waveguide array within glass to implement a photonic quantum walk on a circle. The boundary conditions of a QRW on a circle naturally suggests a 3D waveguide implementation - allowing much simpler device design than what could be achieved using a 2D waveguide architecture. We show that, in some cases, three-dimensional photonic circuits can be more suited to the simulation of complex quantum phenomena.
Mitran, T. L.; Melchert, O.; Hartmann, A. K.
2013-12-01
The main characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here the disorder allows for negative edge weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter ρ that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. The random walks are “greedy” in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight (associated with a net gain of “energy” for the walker). Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of ρ for different bias strengths B is put under scrutiny. Upon tuning ρ, the probability to find such a feasible lattice walk increases from zero to 1. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point ρc, resulting from numerically exact and “static” simulations in terms of the NWP model, can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems.
Random walks across the sea: the origin of rogue waves?
Birkholz, Simon; Veselić, Ivan; Demircan, Ayhan; Steinmeyer, Günter
2015-01-01
Ocean rogue waves are large and suddenly appearing surface gravity waves, which may cause severe damage to ships and other maritime structures. Despite years of research, the exact origin of rogue waves is still disputed. Linear interference of waves with random phase has often been cited as one possible explanation, but apparently does not satisfactorily explain the probability of extreme events in the ocean. Other explanations therefore suggested a decisive role of a nonlinearity in the system. Here we show that linear interference of a finite and variable number of waves may very well explain the heavy tail in the wave height distribution. Our model can explain all prototypical ocean rogue waves reported so far, including the "three sisters" as well as rogue holes. We further suggest nonlinear time series analysis for estimation of the characteristic number of interfering waves for a given sea state. If ocean dynamics is ruled by interference of less than ten waves, rogue waves cannot appear as a matter of...
Limit distributions of random walks on stochastic matrices
Indian Academy of Sciences (India)
Santanu Chakraborty; Arunava Mukherjea
2014-11-01
Problems similar to Ann. Prob. 22 (1994) 424–430 and J. Appl. Prob. 23 (1986) 1019–1024 are considered here. The limit distribution of the sequence $X_{n}X_{n−1}\\ldots X_{1}$, where $(X_{n})_{n≥ 1}$ is a sequence of i.i.d. 2 × 2 stochastic matrices with each $X_{n}$ distributed as , is identified here in a number of discrete situations. A general method is presented and it covers the cases when the random components $C_{n}$ and $D_{n}$ (not necessarily independent), $(C_{n}, D_{n})$ being the first column of $X_{n}$, have the same (or different) Bernoulli distributions. Thus $(C_{n}, D_{n})$ is valued in $\\{0, r\\}^{2}$, where is a positive real number. If for a given positive real , with $0 < r ≤ \\frac{1}{2}$, $r^{-1}C_{n}$ and $r^{-1}D_{n}$ are each Bernoulli with parameters $p_{1}$ and $p_{2}$ respectively, $0 < p_{1}$, $p_{2} < 1$ (which means $C_{n}\\sim p_{1}_{\\{r\\}} + (1 - p_{1})_{\\{0\\}}$ and $D_{n} \\sim p_{2}_{\\{r\\}} + (1 - p_{2})_{\\{0\\}}$), then it is well known that the weak limit of the sequence $^{n}$ exists whose support is contained in the set of all 2 × 2 rank one stochastic matrices. We show that $S()$, the support of , consists of the end points of a countable number of disjoint open intervals and we have calculated the -measure of each such point. To the best of our knowledge, these results are new.
DEFF Research Database (Denmark)
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....
Tadayon, M; Abedi, P; Farshadbakht, F
2016-08-01
Objective Sleep disturbances are one of the most common psycho-physiological issues among postmenopausal women. This study was designed to evaluate the impact of walking with a pedometer on the sleep quality of postmenopausal Iranian women. Methods This randomized, controlled trial was conducted on 112 women who were randomly assigned to two groups. The women in the intervention group (n = 56) were asked to walk with a pedometer each day for 12 weeks and to increase their walking distance by 500 steps per week. A sociodemographic instrument and the Pittsburgh Sleep Quality Index were used to collect data. Sleep quality was measured at baseline, 4, 8, and 12 weeks after intervention. The control group (n = 56) did not receive any intervention. Results After 12 weeks, subjective sleep quality, sleep latency, sleep duration, habitual sleep efficiency, sleep disturbances, use of sleeping medication, and daytime dysfunction improved to a significantly greater extent in the intervention group than in the control group (p sleep quality score was significantly higher in the intervention group than in the control group (0.64 vs. 0.98, p = 0.001). Conclusion This study showed that walking with a pedometer is an easy and cost-effective way to improve the quality of sleep among postmenopausal women. Use of this method in public health centers is recommended. PMID:26757356
Central limit theorem for biased random walk on multi-type Galton-Watson trees
Dembo, Amir
2010-01-01
Let T be a rooted multi-type Galton-Watson (MGW) tree of finitely many types with at least one offspring at each vertex, and an offspring distribution with exponential tails. The lambda-biased random walk (X_t, t>=0) on T is the nearest-neighbor random walk which, when at a vertex v with d(v) offspring, moves closer to the root with probability lambda/(lambda+d(v)), and to each of the offspring with probability 1/(lambda+d(v)). This walk is recurrent for lambda >= rho and transient for 0 <= lambda < rho, with rho the Perron-Frobenius eigenvalue for the (assumed) irreducible matrix of expected offspring numbers. We prove the following quenched CLT for the critical value lambda = rho: for almost every T, the process |X_{floor(nt)}|/sqrt{n} converges in law as n tends to infinity to a deterministic positive multiple of a reflected Brownian motion. Following the approach of Peres and Zeitouni (2008) for Galton-Watson trees, our proof is based on a new explicit description of a reversing measure for the walk...
Rodr, S
1995-01-01
We present a real space renormalization-group map for probabilities of random walks on a hierarchical lattice. From this, we study the asymptotic behavior of the end-to-end distance of a weakly self- avoiding random walk (SARW) that penalizes the (self-)intersection of two random walks in dimension four on the hierarchical lattice.
Random walks in Rindler spacetime and string theory at the tip of the cigar
International Nuclear Information System (INIS)
In this paper, we discuss Rindler space string thermodynamics from a thermal scalar point of view as an explicit example of the results obtained in http://dx.doi.org/10.1007/JHEP02(2014)127. We discuss the critical behavior of the string gas and interpret this as a random walk near the black hole horizon. Combining field theory arguments with the random walk path integral picture, we realize (at genus one) the picture put forward by Susskind of a long string surrounding black hole horizons. We find that thermodynamics is dominated by a long string living at string-scale distance from the horizon whose redshifted temperature is the Rindler or Hawking temperature. We provide further evidence of the recent proposal for string theory at the tip of the cigar by comparing with the flat space orbifold approach to Rindler thermodynamics. We discuss all types of closed strings (bosonic, type II and heterotic strings)
On Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment
Institute of Scientific and Technical Information of China (English)
CHANG Zhe; CAO Xiao-Feng; GUAN Cheng-Bo; DENG Zong-Wei; HUANG Chao-Guang; YANG Chun-Bin; LI Xin
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 fl, to decrease by 1 with probability f2, or remain unchanged with probability 1-f1-f2. 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.
Observing random walks of atoms in buffer gas through resonant light absorption
Aoki, Kenichiro; Mitsui, Takahisa
2016-07-01
Using resonant light absorption, random-walk motions of rubidium atoms in nitrogen buffer gas are observed directly. The transmitted light intensity through atomic vapor is measured, and its spectrum is obtained, down to orders of magnitude below the shot-noise level to detect fluctuations caused by atomic motions. To understand the measured spectra, the spectrum for atoms performing random walks in a Gaussian light beam is computed, and its analytical form is obtained. The spectrum has 1 /f2 (f is frequency) behavior at higher frequencies, crossing over to a different, but well-defined, behavior at lower frequencies. The properties of this theoretical spectrum agree excellently with the measured spectrum. This understanding also enables us to obtain the diffusion constant, the photon cross section of atoms in buffer gas, and the atomic number density from a single spectral measurement. We further discuss other possible applications of our experimental method and analysis.
Directory of Open Access Journals (Sweden)
Anita Sharma
2011-01-01
Full Text Available Blinking statistics of quantum dot has attracted much attraction in recent years. Various experiments were conducted and various theories have been given to explain this phenomenon. However, the problem is not yet resolved. The weak temperature dependence of the power law parameters have complicated the phenomena. We have simulated the blinking statistics of quantum dot based on the random walk model. We have shown that three-dimensional biased Levy random walk of electrons, the bias being the Columbic interaction between electrons and ionized atoms can explain the observed experimental results. We have simulated the blinking properties of quantum dots in a broad temperature range (10-300 K. The distributions exhibit power law behavior for a wide range of temperature, but the power law parameter increases marginally with temperature. The trend of change is independent of the size of the quantum dots as confirmed from the simulation.
French, O. E.
2009-06-01
A random walk model with a negative binomially fluctuating number of steps is considered in the case where the mean of the number fluctuations, \\bar{N} , is finite. The asymptotic behaviour of the resultant statistics in the large \\bar{N} limit is derived and shown to give the K distribution. The equivalence of this model to the hitherto unrelated doubly stochastic representation of the K distribution is also demonstrated. The convergence to the K distribution of the probability density function generated by a random walk with a finite mean number of steps is examined along with the moments, and the non-Gaussian statistics are shown to be a direct result of discreteness and bunching effects.
Observing random walks of atoms in buffer gas through resonant light absorption
Aoki, Kenichiro
2016-01-01
Using resonant light absorption, random walk motions of rubidium atoms in nitrogen buffer gas are observed directly. The transmitted light intensity through atomic vapor is measured and its spectrum is obtained, down to orders of magnitude below the shot noise level to detect fluctuations caused by atomic motions. To understand the measured spectra, the spectrum for atoms performing random walks in a gaussian light beam is computed and its analytical form is obtained. The spectrum has $1/f^2$ ($f$: frequency) behavior at higher frequencies, crossing over to a different, but well defined behavior at lower frequencies. The properties of this theoretical spectrum agree excellently with the measured spectrum. This understanding also enables us to obtain the diffusion constant, the photon cross section of atoms in buffer gas and the atomic number density, from a single spectral measurement. We further discuss other possible applications of our experimental method and analysis.
Stationary Probability and First-Passage Time of Biased Random Walk
Li, Jing-Wen; Tang, Shen-Li; Xu, Xin-Ping
2016-09-01
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. Our study sheds useful insights into the biased random-walk process. Supported by the National Natural Science Foundation of China under Grant No. 11205110, Shanghai Key Laboratory of Intelligent Information Processing (IIPL-2011-009), and Innovative Training Program for College Students under Grant No. 2015xj070
Institute of Scientific and Technical Information of China (English)
CHI Bing; LI Hong; FANG Dong
2007-01-01
Plume concentration prediction is one of the main contents of radioactive consequence assessment for early emergency response to nuclear accidents. Random characteristics of atmospheric diffusion itself was described, a random walk model of atmospheric diffusion (Random Walk) was introduced and compared with the Lagrangian puff model (RIMPUFF) in the nuclear emergency decision support system (RODOS) developed by the European Community for verification. The results show the concentrations calculated by the two models are quite close except that the plume area calculated by Random Walk is a little smaller than that by RIMPUFF. The random walk model for atmospheric diffusion can simulate the atmospheric diffusion in case of nuclear accidents, and provide more actual information for early emergency and consequence assessment as one of the atmospheric diffusion module of the nuclear emergency decision support system.
Englert, G. W.
1971-01-01
A model of the random walk is formulated to allow a simple computing procedure to replace the difficult problem of solution of the Fokker-Planck equation. The step sizes and probabilities of taking steps in the various directions are expressed in terms of Fokker-Planck coefficients. Application is made to many particle systems with Coulomb interactions. The relaxation of a highly peaked velocity distribution of particles to equilibrium conditions is illustrated.
Papáček, Š.; Matonoha, C. (Ctirad); Štumbauer, V.; Štys, D.
2012-01-01
The paper deals with photosynthetic microorganism growth modelling and simulation in a distributed parameter system. Main result concerns the development and comparison of two modelling frameworks for photo-bioreactor modelling. The first ”classical" approach is based on PDE (reaction-turbulent diffusion system) and finite difference method. The alternative approach is based on random walk model of transport by turbulent diffusion. The complications residing in modelling of multi-scale transp...
Recurrence rates and hitting-time distributions for random walks on the line
Pene, Francoise; Zweimüller, Roland
2010-01-01
We consider random walks on the line given by a sequence of independent identically distributed jumps belonging to the strict domain of attraction of a stable distribution, and first determine the almost sure exponential divergence rate, as r goes to zero, of the return time to (-r,r). We then refine this result by establishing a limit theorem for the hitting-time distributions of (x-r,x+r) with arbitrary real x.
Merom, Dafna; Grunseit, Anne; Eramudugolla, Ranmalee; Jefferis, Barbara; McNeill, Jade; Anstey, Kaarin J
2016-01-01
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 randomized controlled trial a...
α-TRANSIENCE AND α-RECURRENCE FOR RANDOM WALKS AND L(E)VY PROCESSES
Institute of Scientific and Technical Information of China (English)
ZHANG HUIZENG; ZHAO MINZHI; YING JIANGANG
2005-01-01
The authors investigate the α-transience and α-recurrence for random walks and Levy processes by means of the associated moment generating function, give a dichotomy theorem for not one-sided processes and prove that the process X is quasisymmetric if and only if X is not α-recurrent for all α＜ 0 which gives a probabilistic explanation of quasi-symmetry, a concept originated from C. J. Stone.
Waddling Random Walk: Fast and Accurate Sampling of Motif Statistics in Large Graphs
Han, Guyue; Sethu, Harish
2016-01-01
The relative frequency of small subgraphs within a large graph, such as one representing an online social network, is of high interest to sociologists, computer scientists and marketeers alike. However, the computation of these network motif statistics via naive enumeration is infeasible for either its prohibitive computational costs or access restrictions on the full graph data. Methods to estimate the motif statistics based on random walks by sampling only a small fraction of the subgraphs ...
The random walk of an electrostatic field using parallel infinite charged planes
Aldana, Rodrigo; Alcala, Jose Vidal; Gonzalez, Gabriel
2015-01-01
We show that it is possible to generate a random walk with an electrostatic field by means of several parallel infinite charged planes in which the surface charge distribution could be either $\\pm\\sigma$. We formulate the problem of this stochastic process by using a rate equation for the most probable value for the electrostatic field subject to the appropriate transition probabilities according to the electrostatic boundary conditions. Our model gives rise to a stochastic law when the charg...
Random Walk Based Segmentation for the Prostate on 3D Transrectal Ultrasound Images
Ma, Ling; Guo, Rongrong; Tian, Zhiqiang; Venkataraman, Rajesh; Sarkar, Saradwata; Liu, Xiabi; Nieh, Peter T.; Master, Viraj V.; Schuster, David M.; Fei, Baowei
2016-01-01
This paper proposes a new semi-automatic segmentation method for the prostate on 3D transrectal ultrasound images (TRUS) by combining the region and classification information. We use a random walk algorithm to express the region information efficiently and flexibly because it can avoid segmentation leakage and shrinking bias. We further use the decision tree as the classifier to distinguish the prostate from the non-prostate tissue because of its fast speed and superior performance, especially for a binary classification problem. Our segmentation algorithm is initialized with the user roughly marking the prostate and non-prostate points on the mid-gland slice which are fitted into an ellipse for obtaining more points. Based on these fitted seed points, we run the random walk algorithm to segment the prostate on the mid-gland slice. The segmented contour and the information from the decision tree classification are combined to determine the initial seed points for the other slices. The random walk algorithm is then used to segment the prostate on the adjacent slice. We propagate the process until all slices are segmented. The segmentation method was tested in 32 3D transrectal ultrasound images. Manual segmentation by a radiologist serves as the gold standard for the validation. The experimental results show that the proposed method achieved a Dice similarity coefficient of 91.37±0.05%. The segmentation method can be applied to 3D ultrasound-guided prostate biopsy and other applications.
The adaptive dynamic community detection algorithm based on the non-homogeneous random walking
Xin, Yu; Xie, Zhi-Qiang; Yang, Jing
2016-05-01
With the changing of the habit and custom, people's social activity tends to be changeable. It is required to have a community evolution analyzing method to mine the dynamic information in social network. For that, we design the random walking possibility function and the topology gain function to calculate the global influence matrix of the nodes. By the analysis of the global influence matrix, the clustering directions of the nodes can be obtained, thus the NRW (Non-Homogeneous Random Walk) method for detecting the static overlapping communities can be established. We design the ANRW (Adaptive Non-Homogeneous Random Walk) method via adapting the nodes impacted by the dynamic events based on the NRW. The ANRW combines the local community detection with dynamic adaptive adjustment to decrease the computational cost for ANRW. Furthermore, the ANRW treats the node as the calculating unity, thus the running manner of the ANRW is suitable to the parallel computing, which could meet the requirement of large dataset mining. Finally, by the experiment analysis, the efficiency of ANRW on dynamic community detection is verified.
Drug-target interaction prediction by random walk on the heterogeneous network.
Chen, Xing; Liu, Ming-Xi; Yan, Gui-Ying
2012-07-01
Predicting potential drug-target interactions from heterogeneous biological data is critical not only for better understanding of the various interactions and biological processes, but also for the development of novel drugs and the improvement of human medicines. In this paper, the method of Network-based Random Walk with Restart on the Heterogeneous network (NRWRH) is developed to predict potential drug-target interactions on a large scale under the hypothesis that similar drugs often target similar target proteins and the framework of Random Walk. Compared with traditional supervised or semi-supervised methods, NRWRH makes full use of the tool of the network for data integration to predict drug-target associations. It integrates three different networks (protein-protein similarity network, drug-drug similarity network, and known drug-target interaction networks) into a heterogeneous network by known drug-target interactions and implements the random walk on this heterogeneous network. When applied to four classes of important drug-target interactions including enzymes, ion channels, GPCRs and nuclear receptors, NRWRH significantly improves previous methods in terms of cross-validation and potential drug-target interaction prediction. Excellent performance enables us to suggest a number of new potential drug-target interactions for drug development.
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…
Solvable continuous-time random walk model of the motion of tracer particles through porous media.
Fouxon, Itzhak; Holzner, Markus
2016-08-01
We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)PLEEE81539-375510.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ, length l, and velocity v. We solve our model with independent l and v. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ. Universality of tracer diffusion in the porous medium is considered. PMID:27627271
Symmetry in stochasticity: Random walk models of large-scale structure
Indian Academy of Sciences (India)
Ravi K Sheth
2011-07-01
This paper describes the insights gained from the excursion set approach, in which various questions about the phenomenology of large-scale structure formation can be mapped to problems associated with the ﬁrst crossing distribution of appropriately deﬁned barriers by random walks. Much of this is summarized in R K Sheth, AIP Conf. Proc. 1132, 158 (2009). So only a summary is given here, and instead a few new excursion set related ideas and results which are not published elsewhere are presented. One is a generalization of the formation time distribution to the case in which formation corresponds to the time when half the mass was ﬁrst assembled in pieces, each of which was at least 1/ times the ﬁnal mass, and where ≥ 2; another is an analysis of the ﬁrst crossing distribution of the Ornstein–Uhlenbeck process. The ﬁrst derives from the mirror-image symmetry argument for random walks which Chandrasekhar described so elegantly in 1943; the second corrects a misuse of this argument. Finally, some discussion of the correlated steps and correlated walks assumptions associated with the excursion set approach, and the relation between these and peaks theory are also included. These are problems in which Chandra’s mirror-image symmetry is broken.
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.
Weak convergence of stochastic integrals driven by continuous-time random walks
Burr, Meredith N
2011-01-01
Brownian motion is a well-known model for normal diffusion, but not all physical phenomena behave according to a Brownian motion. Many phenomena exhibit irregular diffusive behavior, called anomalous diffusion. Examples of anomalous diffusion have been observed in physics, hydrology, biology, and finance, among many other fields. Continuous-time random walks (CTRWs), introduced by Montroll and Weiss, serve as models for anomalous diffusion. CTRWs generalize the usual random walk model by allowing random waiting times between successive random jumps. Under certain conditions on the jumps and waiting times, scaled CTRWs can be shown to converge in distribution to a limit process M(t) in the cadlag space D[0,infinity) with the Skorohod J_1 or M_1 topology. An interesting question is whether stochastic integrals driven by the scaled CTRWs X^n(t) converge in distribution to a stochastic integral driven by the CTRW limit process M(t). We prove weak convergence of the stochastic integrals driven by CTRWs for certain...
A model for a correlated random walk based on the ordered extension of pseudopodia.
Directory of Open Access Journals (Sweden)
Peter J M Van Haastert
Full Text Available Cell migration in the absence of external cues is well described by a correlated random walk. Most single cells move by extending protrusions called pseudopodia. To deduce how cells walk, we have analyzed the formation of pseudopodia by Dictyostelium cells. We have observed that the formation of pseudopodia is highly ordered with two types of pseudopodia: First, de novo formation of pseudopodia at random positions on the cell body, and therefore in random directions. Second, pseudopod splitting near the tip of the current pseudopod in alternating right/left directions, leading to a persistent zig-zag trajectory. Here we analyzed the probability frequency distributions of the angles between pseudopodia and used this information to design a stochastic model for cell movement. Monte Carlo simulations show that the critical elements are the ratio of persistent splitting pseudopodia relative to random de novo pseudopodia, the Left/Right alternation, the angle between pseudopodia and the variance of this angle. Experiments confirm predictions of the model, showing reduced persistence in mutants that are defective in pseudopod splitting and in mutants with an irregular cell surface.
A New Type of Limit Theorems for the One-Dimensional Quantum Random Walk
Konno, N
2002-01-01
In this paper we consider the one-dimensional quantum random walk X^{\\phi}_n at time n starting from initial qubit state \\phi determined by 2 \\times 2 unitary matrix U. We give a combinatorial expression for the characteristic function of X^{\\phi}_n. The expression clarifies the dependence of it on components of unitary matrix U and initial qubit state \\phi. As a consequence of the above results, we present a new type of limit theorems for the Hadamard walk. In contrast with the de Moivre-Laplace limit theorem, our symmetric case implies that X^{\\phi}_n/n \\Rightarrow Z^{\\phi} where Z^{\\phi} has a density 1 / \\pi (1-x^2) \\sqrt{1-2x^2} for x \\in (- \\sqrt{2}/2, \\sqrt{2}/2). Moreover we discuss some known simulation results based on our limit theorems.
Excursions and local limit theorems for Bessel-like random walks
Alexander, Kenneth S
2009-01-01
We consider reflecting random walks on the nonnegative integers with drift of order 1/x at height x. We establish explicit asymptotics for various probabilities associated to such walks, including the distribution of the hitting time of 0 and first return time to 0, and the probability of being at a given height k at time n (uniformly in a large range of k.) In particular, for drift of form -\\delta/2x + o(1/x) with \\delta > -1, we show that the probability of a first return to 0 at time n is asymptotically n^{-c}\\phi(n), where c = (3+\\delta)/2 and \\phi is a slowly varying function given explicitly in terms of the o(1/x) terms.
Powder Mixing Simulation Using Random Walk Model in Eco-material Preparation
Institute of Scientific and Technical Information of China (English)
ZHANG Ji-ru; HU Zai-liang; LIU Zu-de
2004-01-01
The eco-material composition is not well-distributed in preparation. The eco-material samples were taken for computer image analysis, and its particle numbers and appearance parameters were measured. Based on the mechanism of connective mixing and diffusion, the particles distribution was simulated by a computer using the random walk with Levy flight. The results show that the eco-material microstructure simulated by a computer has an idealized porous structure. The particles distribution has a cluster characteristic that changes with the different size and number of particles in Levy flight trajectory. Each cluster consists of a collection of clusters and shows a structure of self-similar cluster,hence presents a well-defined fractal property. The results obtained from SEM observation are in good agreement with the numerical simulations, and show that the convective mixing presents in the Levy flight walk.
Quantitative characterisation of an engineering write-up using random walk analysis
Directory of Open Access Journals (Sweden)
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
An Adaptive K-random Walks Method for Peer-to-Peer Networks
Directory of Open Access Journals (Sweden)
Mahdi Ghorbani
2013-05-01
Full Text Available Designing an intelligent search method in peer-to-peer networks will significantly affect efficiency of the network taking into account sending a search query to nodes which have more probably stored the desired object. Machine learning techniques such as learning automaton can be used as an appropriate tool for this purpose. This paper tries to present a search method based on the learning automaton for the peer-to-peer networks, in which each node is selected according to values stored in its memory for sending the search queries rather than being selected randomly. The probable values are stored in tables and they indicate history of the node in previous searches for finding the desired object. For evaluation, simulation is used to demonstrate that the proposed algorithm outperforms K-random walk method which randomly sends the search queries to the nodes.
Lyapunov Exponents for Branching Processes in a Random Environment: The Effect of Information
Hautphenne, Sophie; Latouche, Guy
2016-04-01
We consider multitype branching processes evolving in a Markovian random environment. To determine whether or not the branching process becomes extinct almost surely is akin to computing the maximal Lyapunov exponent of a sequence of random matrices, which is a notoriously difficult problem. We define Markov chains associated to the branching process, and we construct bounds for the Lyapunov exponent. The bounds are obtained by adding or by removing information: to add information results in a lower bound, to remove information results in an upper bound, and we show that adding less information improves the lower bound. We give a few illustrative examples and we observe that the upper bound is generally more accurate than the lower bounds.
Convergence Rates for Loop-Erased Random Walk and other Loewner Curves
Viklund, Fredrik Johansson
2012-01-01
We estimate convergence rates for curves generated by the Loewner equation under the basic assumption that a convergence rate for the driving terms is known. An important tool is the "tip structure modulus", a geometric measure of regularity for Loewner curves in the capacity parameterization which is analogous to Warschawski's structure modulus, and is closely related to annuli crossings. The main application we have in mind is that of a random discrete-model curve approaching a Schramm-Loewner evolution (SLE) curve in the lattice size scaling limit. We carry out the approach in the case of loop-erased random walk in a simply connected domain. Under some mild assumptions of boundary regularity we obtain an explicit power-law rate for the convergence of the loop-erased random walk path towards the radial SLE(2) path in the supremum norm, the curves being parameterized by capacity. On the deterministic side we show that the tip structure modulus gives a sufficient geometric condition for a Loewner curve to be ...
Böinghoff, Christian; Kersting, Götz
2012-01-01
Intermediately subcritical branching processes in random environment are at the borderline between two subcritical regimes and exhibit a particularly rich behavior. In this paper, we prove a functional limit theorem for these processes. It is discussed together with two other recently proved limit theorems for the intermediately subcritical case and illustrated by several computer simulations.
On importance sampling with mixtures for random walks with heavy tails
Hult, Henrik
2009-01-01
Importance sampling algorithms for heavy-tailed random walks are considered. Using a specification with algorithms based on mixtures of the original distribution with some other distribution, sufficient conditions for obtaining bounded relative error are presented. It is proved that mixture algorithms of this kind can achieve asymptotically optimal relative error. Some examples of mixture algorithms are presented, including mixture algorithms using a scaling of the original distribution, and the bounds of the relative errors are calculated. The algorithms are evaluated numerically in a simple setting.
Strong approximation of Black--Scholes theory based on simple random walks
Nika, Zsolt; Szabados, Tamás
2014-01-01
A basic model in financial mathematics was introduced by Black, Scholes and Merton in 1973 (BSM model). A classical discrete approximation in distribution is the binomial model given by Cox, Ross and Rubinstein in 1979 (CRR model). The BSM and the CRR models have been used for example to price European call and put options. Our aim in this work is to give a strong (almost sure, pathwise) discrete approximation of the BSM model using a suitable nested sequence of simple, symmetric random walks...
The volume and time comparison principle and transition probability estimates for random walks
Telcs, András
2003-01-01
This paper presents necessary and sufficient conditions for on- and off-diagonal transition probability estimates for random walks on weighted graphs. On the integer lattice and on may fractal type graphs both the volume of a ball and the mean exit time from a ball are independent of the center, uniform in space. Here the upper estimate is given without such restriction and two-sided estimate is given if the mean exit time is independent of the center but the volume is not.
Localization on 4 sites for Vertex-reinforced random walks on $\\mathbb Z$
Basdevant, Anne-Laure; Singh, Arvind
2012-01-01
We characterize non-decreasing weight functions for which the associated one-dimensional vertex reinforced random walk (VRRW) localizes on 4 sites. A phase transition appears for weights of order $n\\log \\log n$: for weights growing faster than this rate, the VRRW localizes almost surely on at most 4 sites whereas for weights growing slower, the VRRW cannot localize on less than 5 sites. When $w$ is of order $n\\log \\log n$, the VRRW localizes almost surely on either 4 or 5 sites, both events happening with positive probability.
Elliptic equation for random walks. Application to transport in microporous media
DEFF Research Database (Denmark)
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 account the distribution of the residence times of molecules ill pores. The new elliptic diffusion equation is strictly derived by the operator approach. A criterion showing where the new equation should be applied instead of the standard diffusion equation is obtained. Boundary conditions are studied...
Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets
Emerson, Nathaniel D.
2006-01-01
We consider the harmonic measure on a disconnected polynomial Julia set in terms of Brownian motion. We show that the harmonic measure of any connected component of such a Julia set is zero. Associated to the polynomial is a combinatorial model, the tree with dynamics. We define a measure on the tree, which is a combinatorial version on harmonic measure. We show that this measure is isomorphic to the harmonic measure on the Julia set. The measure induces a random walk on the tree, which is is...
Random walk in degree space and the time-dependent Watts-Strogatz model
Grande, H L Casa; 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 form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.
Directory of Open Access Journals (Sweden)
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
Energy Technology Data Exchange (ETDEWEB)
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
Bottlenecks, burstiness, and fat tails regulate mixing times of non-Poissonian random walks
Delvenne, Jean-Charles; Rocha, Luis E C
2013-01-01
We focus on general continuous-time random walks on networks and find that the mixing time, i.e. the relaxation time for the random process to reach stationarity, is determined by a combination of three factors: the spectral gap, associated to bottlenecks in the underlying topology, burstiness, related to the second moment of the waiting time distribution, and the characteristic time of its exponential tail, which is an indicator of the tail `fatness'. We show theoretically that a strong modular structure dampens the importance of burstiness, and empirically that either of the three factors may be dominant in real-life data. These results provide a theoretical framework for the modeling of diffusion on temporal networks representing human interactions, often characterized by non-Poissonian contact patterns.
Two-step memory within Continuous Time Random Walk. Description of double-action market dynamics
Gubiec, Tomasz
2013-01-01
By means of a novel version of the Continuous-Time Random Walk (CTRW) model with memory, we describe, for instance, the stochastic process of a single share price on a double-auction market within the high frequency time scale. The memory present in the model is understood as dependence between successive share price jumps, while waiting times between price changes are considered as i.i.d. random variables. The range of this memory is defined herein by dependence between three successive jumps of the process. This dependence is motivated both empirically, by analysis of empirical two-point histograms, and theoretically, by analysis of the bid-ask bounce mechanism containing some delay. Our model turns out to be analytically solvable, which enables us a direct comparison of its predictions with empirical counterparts, for instance, with so significant and commonly used quantity as velocity autocorrelation function. This work strongly extends the capabilities of the CTRW formalism.
Effective-medium approximation for lattice random walks with long-range jumps
Thiel, Felix; Sokolov, Igor M.
2016-07-01
We consider the random walk on a lattice with random transition rates and arbitrarily long-range jumps. We employ Bruggeman's effective-medium approximation (EMA) to find the disorder-averaged (coarse-grained) dynamics. The EMA procedure replaces the disordered system with a cleverly guessed reference system in a self-consistent manner. We give necessary conditions on the reference system and discuss possible physical mechanisms of anomalous diffusion. In the case of a power-law scaling between transition rates and distance, lattice variants of Lévy-flights emerge as the effective medium, and the problem is solved analytically, bearing the effective anomalous diffusivity. Finally, we discuss several example distributions and demonstrate very good agreement with numerical simulations.
Counting the corners of a random walk and its application to traffic flow
International Nuclear Information System (INIS)
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)
Local and global survival for nonhomogeneous random walk systems on Z
Bertacchi, Daniela; Zucca, Fabio
2012-01-01
We study an interacting random walk system on Z where at time 0 there is an active particle at 0 and one inactive particle on each site $n \\ge 1$. Particles become active when hit by another active particle. Once activated perform an asymmetric nearest neighbour random walk which depends only on the starting location of the particle. We give conditions for global survival, local survival and infinite activation both in the case where all particles are immortal and in the case where particles have geometrically distributed lifespan (with parameter depending on the starting location of the particle). In particular, in the immortal case, we prove a 0-1 law for the probability of local survival when all particles drift to the right. Besides that, we give sufficient conditions for local survival or local extinction when all particles drift to the left. In the mortal case, we provide sufficient conditions for global survival, local survival and local extinction. Analysis of explicit examples is provided.
A random walk simulation of scalar mixing in flows through submerged vegeta-tions
Institute of Scientific and Technical Information of China (English)
梁东方
2014-01-01
The scalar transport phenomena in vertical two-dimensional flows are studied using the random walk method. The establi-shed Lagrangian model is first applied to study the idealized longitudinal dispersion in open channels, before being used to investi-gate the scalar mixing characteristics of the flows through submerged vegetations. The longitudinal dispersion coefficients of the fully-developed boundary layer flows, with and without vegetations, are calculated based on the positions of the particles. A conve-nient way of incorporating the effects of vegetations is proposed, where all the flow parameters are regarded to be continually distri-buted over the depth. The simulation results show high accuracy of the developed random walk method, and indicate that the new method of accounting for the vegetation effects is appropriate for all the test cases considered. The predicted longitudinal dispersion coefficients agree well with the measurements. The merit of the new method is highlighted by its simplicity and efficiency in com-parison with the conventional method that assumes the discontinuous distribution of the flow parameters over the depth.
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 F(ν) equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in F(ν) is inferred. The Laplacian operator in F(ν) is constructed. This allows us to map physical problems on fractals into the corresponding problems in F(ν). In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.
Transverse momentum spectra of the produced hadrons at SPS energy and a random walk model
Indian Academy of Sciences (India)
Bedangadas Mohanty
2014-05-01
The transverse momentum spectra of the produced hadrons have been compared to a model, which is based on the assumption that a nucleus–nucleus collision is a superposition of isotropically decaying thermal sources at a given freeze-out temperature. The freeze-out temperature in nucleus–nucleus collisions is fixed from the inverse slope of the transverse momentum spectra of hadrons in nucleon–nucleon collision. The successive collisions in the nuclear reaction lead to gain in transverse momentum, as the nucleons propagate in the nucleus following a random walk pattern. The average transverse rapidity shift per collision is determined from the nucleon–nucleus collision data. Using this information, we obtain parameter-free result for the transverse momentum distribution of produced hadrons in nucleus–nucleus collisions. It is observed that such a model is able to explain the transverse mass spectra of the produced pions at SPS energies. However, it fails to satisfactorily explain the transverse mass spectra of kaons and protons. This indicates the presence of collective effect which cannot be accounted for, by the initial state collision broadening of transverse momentum of produced hadrons, the basis of random walk model.
A lattice-model representation of continuous-time random walks
Energy Technology Data Exchange (ETDEWEB)
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.
A Random-Walk Based Privacy-Preserving Access Control for Online Social Networks
Directory of Open Access Journals (Sweden)
You-sheng Zhou
2016-02-01
Full Text Available Online social networks are popularized with people to connect friends, share resources etc. Meanwhile, the online social networks always suffer the problem of privacy exposure. The existing methods to prevent exposure are to enforce access control provided by the social network providers or social network users. However, those enforcements are impractical since one of essential goal of social network application is to share updates freely and instantly. To better the security and availability in social network applications, a novel random walking based access control of social network is proposed in this paper. Unlike using explicit attribute based match in the existing schemes, the results from random walking are employed to securely compute L1 distance between two social network users in the presented scheme, which not only avoids the leakage of private attributes, but also enables each social network user to define access control policy independently. The experimental results show that the proposed scheme can facilitate the access control for online social network.
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 F(ν) equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in F(ν) is inferred. The Laplacian operator in F(ν) is constructed. This allows us to map physical problems on fractals into the corresponding problems in F(ν). In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted. PMID:26764671
Institute of Scientific and Technical Information of China (English)
Zhang Jing-Yuan; Sun Wei-Gang; Chen Guan-Rong
2012-01-01
In this paper,we study the scaling for the mean first-passage time (MFPT) of the random walks on a generalized Koch network with a trap.Through the network construction,where the initial state is transformed from a triangle to a polygon,we obtain the exact scaling for the MFPT.We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order.In addition,we determine the exponents of scaling efficiency characterizing the random walks.Our results are the generalizations of those derived for the Koch network,which shed light on the analysis of random walks over various fractal networks.
Derrida's Generalized Random Energy models; 4, Continuous state branching and coalescents
Bovier, A
2003-01-01
In this paper we conclude our analysis of Derrida's Generalized Random Energy Models (GREM) by identifying the thermodynamic limit with a one-parameter family of probability measures related to a continuous state branching process introduced by Neveu. Using a construction introduced by Bertoin and Le Gall in terms of a coherent family of subordinators related to Neveu's branching process, we show how the Gibbs geometry of the limiting Gibbs measure is given in terms of the genealogy of this process via a deterministic time-change. This construction is fully universal in that all different models (characterized by the covariance of the underlying Gaussian process) differ only through that time change, which in turn is expressed in terms of Parisi's overlap distribution. The proof uses strongly the Ghirlanda-Guerra identities that impose the structure of Neveu's process as the only possible asymptotic random mechanism.
March, N. H.; Moreno, A. J.
2016-06-01
The critical exponent ν for randomly branched polymers with dimensionality d equal to 3, is known exactly as 1/2. Here, we invoke an already available string theory model to predict the remaining static critical exponents. Utilizing results of Hsu et al. (Comput Phys Commun. 2005;169:114-116), results are added for d = 8. Experiment plus simulation would now be important to confirm, or if necessary to refine, the proposed values.
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.
DEFF Research Database (Denmark)
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...
Collapse transition of a hydrophobic self-avoiding random walk in a coarse-grained model solvent
Gaudreault, Mathieu; Viñals, Jorge
2009-08-01
In order to study solvation effects on protein folding, we analyze the collapse transition of a self-avoiding random walk composed of hydrophobic segments that is embedded in a lattice model of a solvent. As expected, hydrophobic interactions lead to an attractive potential of mean force among chain segments. As a consequence, the random walk in solvent undergoes a collapse transition at a higher temperature than in its absence. Chain collapse is accompanied by the formation of a region depleted of solvent around the chain. In our simulation, the depleted region at collapse is as large as our computational domain.
A random walk evolution model of wireless sensor networks and virus spreading
International Nuclear Information System (INIS)
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)
RecRWR: A Recursive Random Walk Method for Improved Identification of Diseases
Directory of Open Access Journals (Sweden)
Joel Perdiz Arrais
2015-01-01
Full Text Available High-throughput methods such as next-generation sequencing or DNA microarrays lack precision, as they return hundreds of genes for a single disease profile. Several computational methods applied to physical interaction of protein networks have been successfully used in identification of the best disease candidates for each expression profile. An open problem for these methods is the ability to combine and take advantage of the wealth of biomedical data publicly available. We propose an enhanced method to improve selection of the best disease targets for a multilayer biomedical network that integrates PPI data annotated with stable knowledge from OMIM diseases and GO biological processes. We present a comprehensive validation that demonstrates the advantage of the proposed approach, Recursive Random Walk with Restarts (RecRWR. The obtained results outline the superiority of the proposed approach, RecRWR, in identifying disease candidates, especially with high levels of biological noise and benefiting from all data available.
Diffusion Limits of the Random Walk Metropolis Algorithm in High Dimensions
Mattingly, Jonathan C; Stuart, Andrew M
2010-01-01
Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have only been proved for target measures with a product structure, severely limiting their applicability. The purpose of this paper is to study diffusion limits for a class of naturally occuring high dimensional measures, found from the approximation of measures on a Hilbert space which are absolutely continuous with respect to a Gaussian reference measure. The diffusion limit of a random walk Metropolis algorithm to an infinite dimensional Hilbert space valued SDE (or SPDE) is proved, facilitating understanding of the computational complexity of the algorithm.
On the temporal order of first-passage times in one-dimensional lattice random walks
Sanders, J. B.; Temme, N. M.
2005-10-01
A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing modified Bessel functions of the first kind. By using several transformations, simpler integrals are obtained from which for two and three particles asymptotic approximations are derived for large values of the parameters. Expressions of the probability for n particles are also derived.I returned and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all. George Orwell, Politics and the English Language, Selected Essays, Penguin Books, 1957. (The citation is from Ecclesiastes 9:11.)
Note: Network random walk model of two-state protein folding: Test of the theory
Berezhkovskii, Alexander M.; Murphy, Ronan D.; Buchete, Nicolae-Viorel
2013-01-01
We study two-state protein folding in the framework of a toy model of protein dynamics. This model has an important advantage: it allows for an analytical solution for the sum of folding and unfolding rate constants [A. M. Berezhkovskii, F. Tofoleanu, and N.-V. Buchete, J. Chem. Theory Comput. 7, 2370 (2011), 10.1021/ct200281d] and hence for the reactive flux at equilibrium. We use the model to test the Kramers-type formula for the reactive flux, which was derived assuming that the protein dynamics is described by a Markov random walk on a network of complex connectivity [A. Berezhkovskii, G. Hummer, and A. Szabo, J. Chem. Phys. 130, 205102 (2009), 10.1063/1.3139063]. It is shown that the Kramers-type formula leads to the same result for the reactive flux as the sum of the rate constants.
Exact Statistics of Record Increments of Random Walks and Lévy Flights.
Godrèche, Claude; Majumdar, Satya N; Schehr, Grégory
2016-07-01
We study the statistics of increments in record values in a time series {x_{0}=0,x_{1},x_{2},…,x_{n}} generated by the positions of a random walk (discrete time, continuous space) of duration n steps. For arbitrary jump length distribution, including Lévy flights, we show that the distribution of the record increment becomes stationary, i.e., independent of n for large n, and compute it explicitly for a wide class of jump distributions. In addition, we compute exactly the probability Q(n) that the record increments decrease monotonically up to step n. Remarkably, Q(n) is universal (i.e., independent of the jump distribution) for each n, decaying as Q(n)∼A/sqrt[n] for large n, with a universal amplitude A=e/sqrt[π]=1.53362…. PMID:27419552
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.
Continuous time random walk: Galilei invariance and relation for the nth moment
Sau Fa, Kwok
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.
Fuzzy overlapping community detection based on local random walk and multidimensional scaling
Wang, Wenjun; Liu, Dong; Liu, Xiao; Pan, Lin
2013-12-01
A fuzzy overlapping community is an important kind of overlapping community in which each node belongs to each community to different extents. It exists in many real networks but how to identify a fuzzy overlapping community is still a challenging task. In this work, the concept of local random walk and a new distance metric are introduced. Based on the new distance measurement, the dissimilarity index between each node of a network is calculated firstly. Then in order to keep the original node distance as much as possible, the network structure is mapped into low-dimensional space by the multidimensional scaling (MDS). Finally, the fuzzy c-means clustering is employed to find fuzzy communities in a network. The experimental results show that the proposed algorithm is effective and efficient to identify the fuzzy overlapping communities in both artificial networks and real-world networks.
Guha Roy, Abhijit; Conjeti, Sailesh; Carlier, Stéphane G; Dutta, Pranab K; Kastrati, Adnan; Laine, Andrew F; Navab, Nassir; Katouzian, Amin; Sheet, Debdoot
2016-03-01
Intravascular imaging using ultrasound or optical coherence tomography (OCT) is predominantly used to adjunct clinical information in interventional cardiology. OCT provides high-resolution images for detailed investigation of atherosclerosis-induced thickening of the lumen wall resulting in arterial blockage and triggering acute coronary events. However, the stochastic uncertainty of speckles limits effective visual investigation over large volume of pullback data, and clinicians are challenged by their inability to investigate subtle variations in the lumen topology associated with plaque vulnerability and onset of necrosis. This paper presents a lumen segmentation method using OCT imaging physics-based graph representation of signals and random walks image segmentation approaches. The edge weights in the graph are assigned incorporating OCT signal attenuation physics models. Optical backscattering maxima is tracked along each A-scan of OCT and is subsequently refined using global graylevel statistics and used for initializing seeds for the random walks image segmentation. Accuracy of lumen versus tunica segmentation has been measured on 15 in vitro and 6 in vivo pullbacks, each with 150-200 frames using 1) Cohen's kappa coefficient (0.9786 ±0.0061) measured with respect to cardiologist's annotation and 2) divergence of histogram of the segments computed with Kullback-Leibler (5.17 ±2.39) and Bhattacharya measures (0.56 ±0.28). High segmentation accuracy and consistency substantiates the characteristics of this method to reliably segment lumen across pullbacks in the presence of vulnerability cues and necrotic pool and has a deterministic finite time-complexity. This paper in general also illustrates the development of methods and framework for tissue classification and segmentation incorporating cues of tissue-energy interaction physics in imaging. PMID:25700476
Conditional limit theorems for intermediately subcritical branching processes in random environment
Afanasyev, Valeriy; Kersting, Götz; Vatutin, Vladimir
2011-01-01
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition appears. In this paper we study the intermediately subcritical case, which constitutes the borderline within this phase transition. We study the asymptotic behavior of the survival probability. Next the size of the population and the shape of the random environment conditioned on non-extinction is examined. Finally we show that conditioned on non-extinction periods of small and large population sizes alternate. This kind of 'bottleneck' behavior appears under the annealed approach only in the intermediately subcritical case.
Shirai, Tomoyuki
2003-01-01
For a certain class of reversible random walks possibly with drift on an abelian covering graph of a finite graph, using the technique of twisted transition operator, we obtain the asymptotic behavior of the $n$-step transition probability $p_n(x,y)$ as $n \\to \\infty$ and give an expression of the constant which appears in the asymptotics.
Bang, Dae-Hyouk; Son, Young-Lan
2016-01-01
[Purpose] To investigate the effects of intensive aerobic exercise on respiratory capacity and walking ability in chronic stroke patients. [Subjects and Methods] The subjects were randomly assigned to an experimental group (n=6) or a control group (n=6). Patients in the experimental group received intensive aerobic exercise for 30 minutes and traditional physical therapy once a day, five days a week, for four weeks. The control group received aerobic exercise for 30 minutes and traditional physical therapy for 30 minutes a day, five days a week, for four weeks. [Results] After the intervention, both groups showed significant improvements in the forced vital capacity, forced expiratory volume in one second, 10-meter walking test, and six-minute walking test over the baseline results. The comparison of the two groups after the intervention revealed that the experimental group showed more significant improvements in the forced vital capacity, forced expiratory volume in one second, and six-minute walking test. There was no significant difference in saturation pulse oximetry oxygen and 10-meter walking test between the groups. [Conclusion] The results of this study suggest that intensive aerobic exercise has a positive effect on respiratory capacity and walking endurance in patients with chronic stroke.
Testing the imprint of non-standard cosmologies on void profiles using Monte Carlo random walks
Achitouv, Ixandra
2016-01-01
Using a Monte Carlo random walks of a log-normal distribution, we show how to qualitatively study void properties for non-standard cosmologies. We apply this method to an f(R) modified gravity model and recover the N-body simulation results of (Achitouv et al. 2016) for the void profiles and their deviation from GR. This method can potentially be extended to study other properties of the large scale structures such as the abundance of voids or overdense environments. We also introduce a new way to identify voids in the cosmic web, using only a few measurements of the density fluctuations around random positions. This algorithm allows to select voids with specific profiles and radii. As a consequence, we can target classes of voids with higher differences between f(R) and standard gravity void profiles. Finally we apply our void criteria to galaxy mock catalogues and discuss how the flexibility of our void finder can be used to reduce systematics errors when probing the growth rate in the galaxy-void correlati...
Revisiting random walks in fractal media: on the occurrence of time discrete scale invariance.
Bab, M A; Fabricius, G; Albano, Ezequiel V
2008-01-28
This paper addresses the kinetic behavior of random walks in fractal media. We perform extensive numerical simulations of both single and annihilating random walkers on several Sierpinski carpets, in order to study the time behavior of three observables: the average number of distinct sites visited by a single walker, the mean-square displacement from the origin, and the density of annihilating random walkers. We found that the time behavior of those observables is given by a power law modulated by soft logarithmic-periodic oscillations. We conjecture that logarithmic-periodic oscillations are a manifestation of a time domain discrete scale iNvariance (DSI) that occurs as a consequence of the spatial DSI of the substrate. Our conjecture implies that the logarithmic periods of oscillations in space and time domains are linked by a dynamic exponent z, through z=log(tau)/log(b(1)), where tau and b(1) are the fundamental scaling ratios of the DSI symmetry in the time and space domains, respectively. We use this relationship in order to compute z for different observables and fractals. Furthermore, we check the values obtained with independent measurements provided by the power-law behavior of the mean-square displacement with time [R(2)(t) proportional variant t(2/z)]. The very good agreement obtained between both computations of the z exponent gives strong support to the idea of an intimate interplay between spatial and time symmetry properties that we expect will have a quite general scope. We expect that the application of the outlined concepts in the field of dynamic processes in fractal media will stimulate further research.
Financial Data Analysis by means of Coupled Continuous-Time Random Walk in Rachev-Rűschendorf Model
Jurlewicz, A.; Wyłomańska, A.; Żebrowski, P.
2008-09-01
We adapt the continuous-time random walk formalism to describe asset price evolution. We expand the idea proposed by Rachev and Rűschendorf who analyzed the binomial pricing model in the discrete time with randomization of the number of price changes. As a result, in the framework of the proposed model we obtain a mixture of the Gaussian and a generalized arcsine laws as the limiting distribution of log-returns. Moreover, we derive an European-call-option price that is an extension of the Black-Scholes formula. We apply the obtained theoretical results to model actual financial data and try to show that the continuous-time random walk offers alternative tools to deal with several complex issues of financial markets.
Are the Variability Properties of the Kepler AGN Light Curves Consistent with a Damped Random Walk?
Kasliwal, Vishal P; Richards, Gordon T
2015-01-01
We test the consistency of active galactic nuclei (AGN) optical flux variability with the \\textit{damped random walk} (DRW) model. Our sample consists of 20 multi-quarter \\textit{Kepler} AGN light curves including both Type 1 and 2 Seyferts, radio-loud and -quiet AGN, quasars, and blazars. \\textit{Kepler} observations of AGN light curves offer a unique insight into the variability properties of AGN light curves because of the very rapid ($11.6-28.6$ min) and highly uniform rest-frame sampling combined with a photometric precision of $1$ part in $10^{5}$ over a period of 3.5 yr. We categorize the light curves of all 20 objects based on visual similarities and find that the light curves fall into 5 broad categories. We measure the first order structure function of these light curves and model the observed light curve with a general broken power-law PSD characterized by a short-timescale power-law index $\\gamma$ and turnover timescale $\\tau$. We find that less than half the objects are consistent with a DRW and ...
Continuous-time random walk for open systems: fluctuation theorems and counting statistics.
Esposito, Massimiliano; Lindenberg, Katja
2008-05-01
We consider continuous-time random walks (CTRW) for open systems that exchange energy and matter with multiple reservoirs. Each waiting time distribution (WTD) for times between steps is characterized by a positive parameter alpha , which is set to alpha=1 if it decays at least as fast as t{-2} at long times and therefore has a finite first moment. A WTD with alpha<1 decays as t{-alpha-1} . A fluctuation theorem for the trajectory quantity R , defined as the logarithm of the ratio of the probability of a trajectory and the probability of the time reversed trajectory, holds for any CTRW. However, R can be identified as a trajectory entropy change only if the WTDs have alpha=1 and satisfy separability (also called "direction time independence"). For nonseparable WTDs with alpha=1 , R can only be identified as a trajectory entropy change at long times, and a fluctuation theorem for the entropy change then only holds at long times. For WTDs with 0
Open Quantum Random Walks: Ergodicity, Hitting Times, Gambler's Ruin and Potential Theory
Lardizabal, Carlos F.; Souza, Rafael R.
2016-09-01
In this work we study certain aspects of open quantum random walks (OQRWs), a class of quantum channels described by Attal et al. (J Stat Phys 147: 832-852, 2012). As a first objective we consider processes which are nonhomogeneous in time, i.e., at each time step, a possibly distinct evolution kernel. Inspired by a spectral technique described by Saloff-Coste and Zúñiga (Stoch Proc Appl 117: 961-979, 2007), we define a notion of ergodicity for finite nonhomogeneous quantum Markov chains and describe a criterion for ergodicity of such objects in terms of singular values. As a second objective, and based on a quantum trajectory approach, we study a notion of hitting time for OQRWs and we see that many constructions are variations of well-known classical probability results, with the density matrix degree of freedom on each site giving rise to systems which are seen to be nonclassical. In this way we are able to examine open quantum versions of the gambler's ruin, birth-and-death chain and a basic theorem on potential theory.
Biased random walk in spatially embedded networks with total cost constraint
Niu, Rui-Wu; Pan, Gui-Jun
2016-11-01
We investigate random walk with a bias toward a target node in spatially embedded networks with total cost restriction introduced by Li et al. (2010). Precisely, The network is built from a two-dimension regular lattice to be improved by adding long-range shortcuts with probability P(rij) ∼rij-α, where rij is the Manhattan distance between sites i and j, and α is a variable exponent, the total length of the long-range connections is restricted. Bias is represented as a probability p of the packet or particle to travel at every hop toward the node which has the smallest Manhattan distance to the target node. By studying the mean first passage time (MFPT) for different exponent log , we find that the best transportation condition is obtained with an exponent α = d + 1(d = 2) for all p. The special phenomena can be possibly explained by the theory of information entropy, we find that when α = d + 1(d = 2), the spatial network with total cost restriction becomes an optimal network which has a maximum information entropy. In addition, the scaling of the MFPT with the size of the network is also investigated, and finds that the scaling of the MFPT with L follows a linear distribution for all p > 0.
Path statistics, memory, and coarse-graining of continuous-time random walks on networks
Manhart, Michael; Kion-Crosby, Willow; Morozov, Alexandre V.
2015-12-01
Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs.
Convex Hulls of Multiple Random Walks: A Large-Deviation Study
Dewenter, Timo; Hartmann, Alexander K; Majumdar, Satya N
2016-01-01
We study the polygons governing the convex hull of a point set created by the steps of $n$ independent two-dimensional random walkers. Each such walk consists of $T$ discrete time steps, where $x$ and $y$ increments are i.i.d. Gaussian. We analyze area $A$ and perimeter $L$ of the convex hulls. We obtain probability densities for these two quantities over a large range of the support by using a large-deviation approach allowing us to study densities below $10^{-900}$. We find that the densities exhibit a universal scaling behavior as a function of $A/T$ and $L/\\sqrt{T}$, respectively. As in the case of one walker ($n=1$), the densities follow Gaussian distributions for $L$ and $\\sqrt{A}$, respectively. We also obtained the rate functions for the area and perimeter, rescaled with the scaling behavior of their maximum possible values, and found limiting functions for $T \\rightarrow \\infty$, revealing that the densities follow the large-deviation principle. These rate functions can be described by a power law fo...
A general "bang-bang" principle for predicting the maximum of a random walk
Allaart, Pieter C
2009-01-01
Let $(B_t)_{0\\leq t\\leq T}$ be either a Bernoulli random walk or a Brownian motion with drift, and let $M_t:=\\max\\{B_s: 0\\leq s\\leq t\\}$, $0\\leq t\\leq T$. This paper solves the general optimal prediction problem \\sup_{0\\leq\\tau\\leq T}\\sE[f(M_T-B_\\tau)], where the supremum is over all stopping times $\\tau$ adapted to the natural filtration of $(B_t)$, and $f$ is a nonincreasing convex function. The optimal stopping time $\\tau^*$ is shown to be of "bang-bang" type: $\\tau^*\\equiv 0$ if the drift of the underlying process $(B_t)$ is negative, and $\\tau^*\\equiv T$ is the drift is positive. This result generalizes recent findings by S. Yam, S. Yung and W. Zhou [{\\em J. Appl. Probab.} {\\bf 46} (2009), 651--668] and J. Du Toit and G. Peskir [{\\em Ann. Appl. Probab.} {\\bf 19} (2009), 983--1014], and provides additional mathematical justification for the dictum in finance that one should sell bad stocks immediately, but keep good ones as long as possible.
State-independent importance sampling for random walks with regularly varying increments
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Karthyek R. A. Murthy
2015-03-01
Full Text Available We develop importance sampling based efficient simulation techniques for three commonly encountered rare event probabilities associated with random walks having i.i.d. regularly varying increments; namely, 1 the large deviation probabilities, 2 the level crossing probabilities, and 3 the level crossing probabilities within a regenerative cycle. Exponential twisting based state-independent methods, which are effective in efficiently estimating these probabilities for light-tailed increments are not applicable when the increments are heavy-tailed. To address the latter case, more complex and elegant state-dependent efficient simulation algorithms have been developed in the literature over the last few years. We propose that by suitably decomposing these rare event probabilities into a dominant and further residual components, simpler state-independent importance sampling algorithms can be devised for each component resulting in composite unbiased estimators with desirable efficiency properties. When the increments have infinite variance, there is an added complexity in estimating the level crossing probabilities as even the well known zero-variance measures have an infinite expected termination time. We adapt our algorithms so that this expectation is finite while the estimators remain strongly efficient. Numerically, the proposed estimators perform at least as well, and sometimes substantially better than the existing state-dependent estimators in the literature.
Continuous time random walk analysis of solute transport in fractured porous media
Energy Technology Data Exchange (ETDEWEB)
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.
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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.
Random Walks in Anderson's Garden: A Journey from Cuprates to Cooper Pair Insulators and Beyond
Baskaran, G
2016-01-01
Anderson's Garden is a drawing presented to Philip W. Anderson on the eve of his 60th birthday celebration, in 1983. This cartoon (Fig. 1), whose author is unknown, succinctly depicts some of Anderson's pre-1983 works, as a blooming garden. As an avid reader of Anderson's papers, random walk in Anderson's garden had become a part of my routine since graduate school days. This was of immense help and prepared me for a wonderful collaboration with the gardener himself, on the resonating valence bond (RVB) theory of High Tc cuprates and quantum spin liquids, at Princeton. The result was bountiful - the first (RVB mean field) theory for i) quantum spin liquids, ii) emergent fermi surfaces in Mott insulators and iii) superconductivity in doped Mott insulators. Beyond mean field theory - i) emergent gauge fields, ii) Ginzbuerg Landau theory with RVB gauge fields, iii) prediction of superconducting dome, iv) an early identification and study of a non-fermi liquid normal state of cuprates and so on. Here I narrate th...
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.
Pattern formation on networks with reactions: A continuous-time random-walk approach
Angstmann, C. N.; Donnelly, I. C.; Henry, B. I.
2013-03-01
We derive the generalized master equation for reaction-diffusion on networks from an underlying stochastic process, the continuous time random walk (CTRW). The nontrivial incorporation of the reaction process into the CTRW is achieved by splitting the derivation into two stages. The reactions are treated as birth-death processes and the first stage of the derivation is at the single particle level, taking into account the death process, while the second stage considers an ensemble of these particles including the birth process. Using this model we have investigated different types of pattern formation across the vertices on a range of networks. Importantly, the CTRW defines the Laplacian operator on the network in a non-ad hoc manner and the pattern formation depends on the structure of this Laplacian. Here we focus attention on CTRWs with exponential waiting times for two cases: one in which the rate parameter is constant for all vertices and the other where the rate parameter is proportional to the vertex degree. This results in nonsymmetric and symmetric CTRW Laplacians, respectively. In the case of symmetric Laplacians, pattern formation follows from the Turing instability. However in nonsymmetric Laplacians, pattern formation may be possible with or without a Turing instability.
Path statistics, memory, and coarse-graining of continuous-time random walks on networks.
Manhart, Michael; Kion-Crosby, Willow; Morozov, Alexandre V
2015-12-01
Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs.
Magnetic Field Line Random Walk in Isotropic Turbulence with Varying Mean Field
Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.; Rowlands, G.; Vyas, S.
2016-08-01
In astrophysical plasmas, the magnetic field line random walk (FLRW) plays an important role in guiding particle transport. The FLRW behavior is scaled by the Kubo number R=(b/{B}0)({{\\ell }}\\parallel /{{\\ell }}\\perp ) for rms magnetic fluctuation b, large-scale mean field {{\\boldsymbol{B}}}0, and coherence scales parallel ({{\\ell }}\\parallel ) and perpendicular ({{\\ell }}\\perp ) to {{\\boldsymbol{B}}}0. Here we use a nonperturbative analytic framework based on Corrsin’s hypothesis, together with direct computer simulations, to examine the R-scaling of the FLRW for varying B 0 with finite b and isotropic fluctuations with {{\\ell }}\\parallel /{{\\ell }}\\perp =1, instead of the well-studied route of varying {{\\ell }}\\parallel /{{\\ell }}\\perp for b \\ll {B}0. The FLRW for isotropic magnetic fluctuations is also of astrophysical interest regarding transport processes in the interstellar medium. With a mean field, fluctuations may have variance anisotropy, so we consider limiting cases of isotropic variance and transverse variance (with b z = 0). We obtain analytic theories, and closed-form solutions for extreme cases. Padé approximants are provided to interpolate all versions of theory and simulations to any B 0. We demonstrate that, for isotropic turbulence, Corrsin-based theories generally work well, and with increasing R there is a transition from quasilinear to Bohm diffusion. This holds even with b z = 0, when different routes to R\\to ∞ are mathematically equivalent; in contrast with previous studies, we find that a Corrsin-based theory with random ballistic decorrelation works well even up to R = 400, where the effects of trapping are barely perceptible in simulation results.
MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD
International Nuclear Information System (INIS)
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B 0)(ℓ∥/ℓ ) for rms magnetic fluctuation b, large-scale mean field B 0, and parallel and perpendicular coherence scales ℓ∥ and ℓ , respectively. Here we examine the FLRW when R → ∞ by taking B 0 → 0 for finite bz (fluctuation component along B 0), which differs from the well-studied route with bz = 0 or bz << B 0 as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B 0 = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k –1 or k –2 moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B 0 → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality
MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD
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Sonsrettee, W.; Ruffolo, D.; Snodin, A. P.; Wongpan, P. [Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400 (Thailand); Subedi, P.; Matthaeus, W. H. [Bartol Research Institute, University of Delaware, Newark, DE 19716 (United States); Chuychai, P., E-mail: bturbulence@gmail.com, E-mail: david.ruf@mahidol.ac.th, E-mail: andrew.snodin@gmail.com, E-mail: pat.wongpan@postgrad.otago.ac.nz, E-mail: piyanate@gmail.com, E-mail: prasub@udel.edu, E-mail: whm@udel.edu [Thailand Center of Excellence in Physics, CHE, Ministry of Education, Bangkok 10400 (Thailand)
2015-01-01
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B {sub 0})(ℓ{sub ∥}/ℓ ) for rms magnetic fluctuation b, large-scale mean field B {sub 0}, and parallel and perpendicular coherence scales ℓ{sub ∥} and ℓ , respectively. Here we examine the FLRW when R → ∞ by taking B {sub 0} → 0 for finite b{sub z} (fluctuation component along B {sub 0}), which differs from the well-studied route with b{sub z} = 0 or b{sub z} << B {sub 0} as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B {sub 0} = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k {sup –1} or k {sup –2} moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B {sub 0} → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.
Magnetic Field Line Random Walk in Isotropic Turbulence with Zero Mean Field
Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.
2015-01-01
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B 0)(l∥/l) for rms magnetic fluctuation b, large-scale mean field B 0, and parallel and perpendicular coherence scales l∥ and l, respectively. Here we examine the FLRW when R → ∞ by taking B 0 → 0 for finite bz (fluctuation component along B 0), which differs from the well-studied route with bz = 0 or bz Lt B 0 as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B 0 = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k -1 or k -2 moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B 0 → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.
Terçariol, César Augusto Sangaletti; Martinez, Alexandre Souto
2008-09-01
Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2 , as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N1) is just n=e=2.72... while in the mu=2 case, the mean number n of visited points grows proportionally to N;{12} . Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones. PMID:18850997
A non-Levy random walk in chacma baboons: what does it mean?
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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.
Multifractality and thermodynamics on financial markets - Continuous-Time Random Walk approach
International Nuclear Information System (INIS)
We thoroughly study the thermodynamic properties of the anomalous multifractal structure of random interevent (or intertransaction) times for futures contracts by using Continuous-Time Random Walk (CTRW) formalism of Montroll-Weiss, as well as Scher and Lax. Although the approach is quite general (and can be applied to any inter-human communication having nontrivial priority) we consider it in the context of the financial market where heterogeneous agent activities can occur within a wide spectrum of time scales. We found as the main, general consequence that within this extended formalism the scaling power-dependent partition function, Z(q), diverges for any negative scaling powers q (which justify the name anomalous), while for the positive ones it possesses scaling with exponent τ(q) which is a non-analytic (singular) function of q. In the definition of the partition function we used the pausing-time distribution as the central one, which has the form of a convolution (or superstatistics used, e.g., for the description of turbulence as well as a speculative market). Its integral kernel is given by the stretched exponential distribution (often used in disordered systems). This is an intermediate one between the exponential distribution assumed in the original version of the CTRW formalism (for description of the transient photocurrent measured in amorphous glossy material) and the Gaussian one sometimes used in this context (e.g. for discussion of hydrogen in amorphous metals and for aging effects in glasses). A more refined but heuristic analytical prediction was also considered. We argue that this superstatistics defines a kind of non-geometric random multiplicative cascadic process (while the geometric one was used, e.g., in the fully developed turbulence) which says how the investor activities are spreading among different scales ruled by fluctuations. As the most important result we found (by using the saddle-point approximation) the third- and higher
Step angles to reduce the north-finding error caused by rate random walk with fiber optic gyroscope.
Wang, Qin; Xie, Jun; Yang, Chuanchuan; He, Changhong; Wang, Xinyue; Wang, Ziyu
2015-10-20
We study the relationship between the step angles and the accuracy of north finding with fiber optic gyroscopes. A north-finding method with optimized step angles is proposed to reduce the errors caused by rate random walk (RRW). Based on this method, the errors caused by both angle random walk and RRW are reduced by increasing the number of positions. For when the number of positions is even, we proposed a north-finding method with symmetric step angles that can reduce the error caused by RRW and is not affected by the azimuth angles. Experimental results show that, compared with the traditional north-finding method, the proposed methods with the optimized step angles and the symmetric step angles can reduce the north-finding errors by 67.5% and 62.5%, respectively. The method with symmetric step angles is not affected by the azimuth angles and can offer consistent high accuracy for any azimuth angles.
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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
Intravitreal Triamcinolone for Acute Branch Retinal Vein Occlusion: a Randomized Clinical Trial
Directory of Open Access Journals (Sweden)
Alireza Ramezani
2011-01-01
Full Text Available Purpose: To evaluate the therapeutic effect of intravitreal triamcinolone (IVT injection for recent branch retinal vein occlusion (BRVO. Methods: In a randomized controlled clinical trial, 30 phakic eyes with recent (less than 10 weeks′ duration BRVO were assigned to two groups. The treatment group (16 eyes received 4 mg IVT and the control group (14 eyes received subconjunctival sham injections. Changes in visual acuity (VA were the main outcome measure. Results: VA and central macular thickness (CMT changes were not significantly different between the study groups at any time point. Within group analysis showed significant VA improvement from baseline in the IVT group up to three months (P 0.05. Significant reduction in CMT was noticed only in the treatment group (‑172 ± 202 μm, P = 0.029 and at 4 months. Ocular hypertension occurred in 4 (25% and 2 (14.3% eyes in the IVT and control groups, respectively. Conclusion: A single IVT injection had a non-significant beneficial effect on VA and CMT in acute BRVO as compared to the natural history of the condition. The 3-month deferred treatment protocol advocated by the Branch Vein Occlusion Study Group may be a safer option than IVT injection considering its potential side effects.
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.
Identifying co-targets to fight drug resistance based on a random walk model
Directory of Open Access Journals (Sweden)
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.
Systematic Angle Random Walk Estimation of the Constant Rate Biased Ring Laser Gyro
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Guohu Feng
2013-02-01
Full Text Available An actual account of the angle random walk (ARW coefficients of gyros in the constant rate biased rate ring laser gyro (RLG inertial navigation system (INS is very important in practical engineering applications. However, no reported experimental work has dealt with the issue of characterizing the ARW of the constant rate biased RLG in the INS. To avoid the need for high cost precise calibration tables and complex measuring set-ups, the objective of this study is to present a cost-effective experimental approach to characterize the ARW of the gyros in the constant rate biased RLG INS. In the system, turntable dynamics and other external noises would inevitably contaminate the measured RLG data, leading to the question of isolation of such disturbances. A practical observation model of the gyros in the constant rate biased RLG INS was discussed, and an experimental method based on the fast orthogonal search (FOS for the practical observation model to separate ARW error from the RLG measured data was proposed. Validity of the FOS-based method was checked by estimating the ARW coefficients of the mechanically dithered RLG under stationary and turntable rotation conditions. By utilizing the FOS-based method, the average ARW coefficient of the constant rate biased RLG in the postulate system is estimated. The experimental results show that the FOS-based method can achieve high denoising ability. This method estimate the ARW coefficients of the constant rate biased RLG in the postulate system accurately. The FOS-based method does not need precise calibration table with high cost and complex measuring set-up, and Statistical results of the tests will provide us references in engineering application of the constant rate biased RLG INS.
A Web-Based Intervention to Encourage Walking (StepWise): Pilot Randomized Controlled Trial
Hargreaves, Elaine Anne; Mutrie, Nanette; Fleming, Jade Dallas
2016-01-01
Background Despite Internet-based interventions that incorporate pedometers with appropriate goal-setting processes and other theoretically-based behavior change strategies being proposed as a means of increasing walking behavior, few have incorporated all of these key features or assessed maintenance of behavior change. Objective The objective of our study was to investigate the effect of a 12-week pedometer step goal walking program individually tailored to baseline step counts, combined wi...
Avena, L; Redig, F
2009-01-01
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 proved a law of large numbers for dynamic random environments satisfying a space-time mixing property called cone-mixing. If an attractive spin-flip system has a finite average coupling time at the origin for two copies starting from the all-occupied and the all-vacant configuration, respectively, then it is cone-mixing. In the present paper we prove a large deviation principle for the empirical speed of the random walk, both quenched and annealed, and exhibit some properties of the associated rate functions. Under an exponential space-time mixing condition for the spin-flip system, which is stronger than cone-mixing, the two rate functions have a unique zero, i.e., the slow-down phenomenon known to be possible in ...
3rd Workshop on Branching Processes and their Applications
González, Miguel; Gutiérrez, Cristina; Martínez, Rodrigo; Minuesa, Carmen; Molina, Manuel; Mota, Manuel; Ramos, Alfonso; WBPA15
2016-01-01
This volume gathers papers originally presented at the 3rd Workshop on Branching Processes and their Applications (WBPA15), which was held from 7 to 10 April 2015 in Badajoz, Spain (http://branching.unex.es/wbpa15/index.htm). The papers address a broad range of theoretical and practical aspects of branching process theory. Further, they amply demonstrate that the theoretical research in this area remains vital and topical, as well as the relevance of branching concepts in the development of theoretical approaches to solving new problems in applied fields such as Epidemiology, Biology, Genetics, and, of course, Population Dynamics. The topics covered can broadly be classified into the following areas: 1. Coalescent Branching Processes 2. Branching Random Walks 3. Population Growth Models in Varying and Random Environments 4. Size/Density/Resource-Dependent Branching Models 5. Age-Dependent Branching Models 6. Special Branching Models 7. Applications in Epidemiology 8. Applications in Biology and Genetics Offer...
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Leal Alejo
2006-11-01
Full Text Available Abstract Background Whole-body vibration (WBV is a new type of exercise that has been increasingly tested for the ability to prevent bone fractures and osteoporosis in frail people. There are two currently marketed vibrating plates: a the whole plate oscillates up and down; b reciprocating vertical displacements on the left and right side of a fulcrum, increasing the lateral accelerations. A few studies have shown recently the effectiveness of the up-and-down plate for increasing Bone Mineral Density (BMD and balance; but the effectiveness of the reciprocating plate technique remains mainly unknown. The aim was to compare the effects of WBV using a reciprocating platform at frequencies lower than 20 Hz and a walking-based exercise programme on BMD and balance in post-menopausal women. Methods Twenty-eight physically untrained post-menopausal women were assigned at random to a WBV group or a Walking group. Both experimental programmes consisted of 3 sessions per week for 8 months. Each vibratory session included 6 bouts of 1 min (12.6 Hz in frequency and 3 cm in amplitude with 60° of knee flexion with 1 min rest between bouts. Each walking session was 55 minutes of walking and 5 minutes of stretching. Hip and lumbar BMD (g·cm-2 were measured using dual-energy X-ray absorptiometry and balance was assessed by the blind flamingo test. ANOVA for repeated measurements was adjusted by baseline data, weight and age. Results After 8 months, BMD at the femoral neck in the WBV group was increased by 4.3% (P = 0.011 compared to the Walking group. In contrast, the BMD at the lumbar spine was unaltered in both groups. Balance was improved in the WBV group (29% but not in the Walking group. Conclusion The 8-month course of vibratory exercise using a reciprocating plate is feasible and is more effective than walking to improve two major determinants of bone fractures: hip BMD and balance.
Yilmaz, Atilla
2009-01-01
We consider the quenched and averaged (or annealed) large deviation rate functions $I_q$ and $I_a$ for space-time and (the usual) space-only RWRE on $\\mathbb{Z}^d$. By Jensen's inequality, $I_a\\leq I_q$. In the space-time case, when $d\\geq3+1$, $I_q$ and $I_a$ are known to be equal on an open set containing the typical velocity $\\xi_o$. When $d=1+1$, we prove that $I_q$ and $I_a$ are equal only at $\\xi_o$. Similarly, when $d=2+1$, we show that $I_a
Effects of nordic walking and exercise in type 2 diabetes mellitus: a randomized controlled trial
DEFF Research Database (Denmark)
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...
Nuzhnaya, Tatyana; Bakic, Predrag; Kontos, Despina; Megalooikonomou, Vasileios; Ling, Haibin
2012-02-01
This work is a part of our ongoing study aimed at understanding a relation between the topology of anatomical branching structures with the underlying image texture. Morphological variability of the breast ductal network is associated with subsequent development of abnormalities in patients with nipple discharge such as papilloma, breast cancer and atypia. In this work, we investigate complex dependence among ductal components to perform segmentation, the first step for analyzing topology of ductal lobes. Our automated framework is based on incorporating a conditional random field with texture descriptors of skewness, coarseness, contrast, energy and fractal dimension. These features are selected to capture the architectural variability of the enhanced ducts by encoding spatial variations between pixel patches in galactographic image. The segmentation algorithm was applied to a dataset of 20 x-ray galactograms obtained at the Hospital of the University of Pennsylvania. We compared the performance of the proposed approach with fully and semi automated segmentation algorithms based on neural network classification, fuzzy-connectedness, vesselness filter and graph cuts. Global consistency error and confusion matrix analysis were used as accuracy measurements. For the proposed approach, the true positive rate was higher and the false negative rate was significantly lower compared to other fully automated methods. This indicates that segmentation based on CRF incorporated with texture descriptors has potential to efficiently support the analysis of complex topology of the ducts and aid in development of realistic breast anatomy phantoms.
Directory of Open Access Journals (Sweden)
Michael Yvonne L
2009-07-01
Full Text Available Abstract Background Using data from the SHAPE trial, a randomized 6-month neighborhood-based intervention designed to increase walking activity among older adults, this study identified and analyzed social-ecological factors mediating and moderating changes in walking activity. Methods Three potential mediators (social cohesion, walking efficacy, and perception of neighborhood problems and minutes of brisk walking were assessed at baseline, 3-months, and 6-months. One moderator, neighborhood walkability, was assessed using an administrative GIS database. The mediating effect of change in process variables on change in brisk walking was tested using a product-of-coefficients test, and we evaluated the moderating effect of neighborhood walkability on change in brisk walking by testing the significance of the interaction between walkability and intervention status. Results Only one of the hypothesized mediators, walking efficacy, explained the intervention effect (product of the coefficients (95% CI = 8.72 (2.53, 15.56. Contrary to hypotheses, perceived neighborhood problems appeared to suppress the intervention effects (product of the coefficients (95% CI = -2.48, -5.6, -0.22. Neighborhood walkability did not moderate the intervention effect. Conclusion Walking efficacy may be an important mediator of lay-lead walking interventions for sedentary older adults. Social-ecologic theory-based analyses can support clinical interventions to elucidate the mediators and moderators responsible for producing intervention effects.
Feyyaz Zeren; Filiz Konuk
2013-01-01
In this study, the random walk hypothesis for emerging markets has been tested. First of all,Harvey et. al. (2008) linearity test was made in this study where different time intervals were handled. ADF (1979) unit root test was made to the linear series in order to test the efficiency of the market based on the results of the linearity test and in stock exchanges in India and Russia where Brazil and China stock markets are not efficient, it was concluded that the efficient market hypothesis i...
Ellery, Adam J.; Baker, Ruth E.; Simpson, Matthew J.
2016-10-01
Migration of cells and molecules in vivo is affected by interactions with obstacles. These interactions can include crowding effects, as well as adhesion/repulsion between the motile cell/molecule and the obstacles. Here we present an analytical framework that can be used to separately quantify the roles of crowding and adhesion/repulsion using a lattice-based random walk model. Our method leads to an exact calculation of the long time Fickian diffusivity, and avoids the need for computationally expensive stochastic simulations.
First-passage times in multi-scale random walks: the impact of movement scales on search efficiency
Campos, Daniel; Bartumeus, Frederic; Raposo, E. P.; Méndez, Vicenç
2015-01-01
An efficient searcher needs to balance properly the tradeoff between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free L\\'evy search strategies. Here we study multi-scale random walks as an approximation to the scale- free case and derive the exact expressions for their mean-first passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the asymm...
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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
Energy Technology Data Exchange (ETDEWEB)
Aslangul, C.; Bouchaud, J.; Georges, A.; Pottier, N.; Saint-James, D. (Universite Paris VII (France))
1989-04-01
The authors present new exact results for a one-dimensional asymmetric disordered hopping model. The lattice is taken infinite from the start and they do not resort to the periodization scheme used by Derrida. An explicit resummation allows for the calculation of the velocity V and the diffusion constant D (which are found to coincide with those given by Derrida) and for demonstrating that V is indeed a self-averaging quantity; the same property is established for D in the limiting case of a directed walk.
Dafna eMerom; Anne eGrunseit; Ranmalee eEramudugolla; Barbarra eJefferis; Jade eMcneil; Anstey, Kaarin J
2016-01-01
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-d...
Analysis of diffusion and trapping efficiency for random walks on non-fractal scale-free trees
Peng, Junhao; Xiong, Jian; Xu, Guoai
2014-08-01
In this paper, the discrete random walks on the recursive non-fractal scale-free trees (NFSFT) are studied, and a kind of method to calculate the analytic solutions of the mean first-passage time (MFPT) for any pair of nodes, the mean trapping time (MTT) for any target node and mean diffusing time (MDT) for any starting node are proposed. Furthermore, we compare the trapping efficiency and diffusion efficiency between any two nodes of NFSFT by using the MTT and the MDT as the measures of trapping efficiency and diffusion efficiency respectively, and find the best (or worst) trapping sites and the best (or worst) diffusion sites. The results show that the two hubs of NFSFT are not only the best trapping site but also the worst diffusion site, and that the nodes which are the farthest nodes from the two hubs are not only the worst trapping sites but also the best diffusion sites. Furthermore, we find that the ratio between the maximum and minimum of MTT grows logarithmically with network order, but the ratio between the maximum and minimum of MDT is almost equal to 1. The results imply that the trap's position has great effect on the trapping efficiency, but the position of starting node has little effect on diffusion efficiency. Finally, the simulation for random walks on NFSFT is done, and it is consistent with the derived results.
Lafitte-Godillon, Pauline; Tran, Viet Chi
2012-01-01
In this paper, we study a distylous flower population in which self-reproduction is not permitted. Individuals are diploid, and two alleles, A and a, can be found at the considered locus S. Pollen and ovules of flowers with the same genotype at locus S cannot mate. This prevents the pollen of a given flower to fecundate its stigmates. Only genotypes AA and Aa can be maintained in the population, so that the latter can be described by a random walk in the positive quadrant whose components are the number of individuals of each genotype. This random walk is not homogeneous and its transitions depend on the location of the process. We are interested in the computation of the extinction probabilities, where extinction happens when one of the axis is reached by the process. These extinction probabilities, which depend on the initial condition, satisfy a doubly-indexed recurrence equation that cannot be solved directly. We consider the associated generating function and show that it satisfies a partial differential...
Exact two-point resistance, and the simple random walk on the complete graph minus N edges
Energy Technology Data Exchange (ETDEWEB)
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.
Asymptotic Behavior for Random Walks in Time-Random Environment on Z1%直线上时间随机环境下随机游动的渐近性质
Institute of Scientific and Technical Information of China (English)
胡学平; 祝东进
2008-01-01
In this paper,we give a general model of random walks in time-random environment in any countable space.Moreover,when the environment is independently identically distributed,a recurrence-transience criterion and the law of large numbers are derived in the nearest-neighbor case on Z1.At last,under regularity conditions,we prove that the RWIRE {Xn} on Z1 satisfies a central limit theorem,which is similar to the corresponding results in the case of classical random walks.
Horvath, Illes; Veto, Balint
2010-01-01
The problems considered in the present paper have their roots in two different cultures. The 'true' (or myopic) self-avoiding walk model (TSAW) was introduced in the physics literature by Amit, Parisi and Peliti. This is a nearest neighbor non-Markovian random walk in Z^d which prefers to jump to those neighbors which were less visited in the past. The self-repelling Brownian polymer model (SRBP), initiated in the probabilistic literature by Durrett and Rogers (independently of the physics community), is the continuous space-time counterpart: a diffusion in R^d pushed by the negative gradient of the (mollified) occupation time measure of the process. In both cases, similar long memory effects are caused by a pathwise self-repellency of the trajectories due to a push by the negative gradient of (softened) local time. We investigate the asymptotic behaviour of TSAW and SRBP in the non-recurrent dimensions. First, we identify a natural stationary (in time) and ergodic distribution of the environment (the local t...
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.
Asymptotic Feynman-Kac formulae for large symmetrised systems of random walks
Adams, Stefan; Dorlas, Tony
2006-01-01
We study large deviations principles for $ N $ random processes on the lattice $ \\Z^d $ with finite time horizon $ [0,\\beta] $ under a symmetrised measure where all initial and terminal points are uniformly given by a random permutation. That is, given a permutation $ \\sigma $ of $ N $ elements and a vector $ (x_1,...,x_N) $ of $ N $ initial points we let the random processes terminate in the points $ (x_{\\sigma(1)},...,x_{\\sigma(N)}) $ and then sum over all possible permutations and initial ...
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.
Li, Xingfeng; Tian, Jie; Wang, Xiaoxiang; Dai, Jianping; Ai, Lin
2004-04-01
The aim of this study was to assess the validation of the local density random walk (LDRW) function to correct the delayed and dispersed arterial input function (AIF) data derived from dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI). Instead of using the gamma-variate function to smooth and extrapolate the AIF curves, we suggested a method which was based on diffusion with drift approach. Forty-seven AIF curves from ten patients were segmented to test the effectiveness of the proposed method. The results of the comparisons with the gamma-variate function showed that the LDRW distribution function may provide a new means for more accurate correction of AIF curves.
Douglas-Kazakov on the road to superfluidity: from random walks to black holes
Gorsky, Alexander; Nechaev, Sergei
2016-01-01
Inspired by the connection between $(1+1)D$ "vicious walks" (VW) and 2D YM theory, we consider different incarnations of large-$N$ Douglas-Kazakov (DK) phase transition in stochastic processes and in gauge field theories focusing at its physical interpretations. We generalize the connection between VW and YM, and study the influence of initial and final out-of-equilibrium distributions of walkers on the DK phase transition, as well as describe the effect of $\\theta$-term in related stochastic processes. We consider the Jack stochastic process involving Calogero-type interaction between walkers and find the dependence of the transition point on the coupling constant. Using the relation between large-$N$ 2D $q$-YM and extremal black hole (BH) with large-$N$ magnetic charge, we conjecture the physical interpretation of the DK phase transitions in the 4D extremal charged black holes and its relation to Brownian branes. Utilizing the interpretation of superfluidity as the specific response on the external gravipho...
Hladky, Paul W.
2007-01-01
Random-climb models enable undergraduate chemistry students to visualize polymer molecules, quantify their configurational properties, and relate molecular structure to a variety of physical properties. The model could serve as an introduction to more elaborate models of polymer molecules and could help in learning topics such as lattice models of…
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…
Uffelen, J.G.Z. van; Chin A Paw, M.J.M.; Hopman-Rock, M.; Mechelen, W. van
2007-01-01
Objectives: To examine the effect of walking and vitamin B supplementation on quality-of-life (QoL) in community-dwelling adults with mild cognitive impairment. Methods: One year, double-blind, placebo-controlled trial. Participants were randomized to: (1) twice-weekly, group-based, moderate-intensi
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
Directory of Open Access Journals (Sweden)
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.
On the gap and time interval between the first two maxima of long continuous time random walks
Mounaix, Philippe; Schehr, Grégory; Majumdar, Satya N.
2016-01-01
We consider a one-dimensional continuous time random walk (CTRW) on a fixed time interval T where at each time step the walker waits a random time τ, before performing a jump drawn from a symmetric continuous probability distribution function (PDF) f(η ) , of Lévy index 0μ /2 ). We investigate the joint PDF of the gap g between the first two highest positions of the CTRW and the time t separating these two maxima. We show that this PDF reaches a stationary limiting joint distribution p(g, t) in the limit of long CTRW, T\\to ∞ . Our exact analytical results show a very rich behavior of this joint PDF in the (γ,μ ) plane, which we study in great detail. Our main results are verified by numerical simulations. This work provides a non trivial extension to CTRWs of the recent study in the discrete time setting by Majumdar et al (2014 J. Stat. Mech. P09013).
Price Formation Modelling by Continuous-Time Random Walk: An Empirical Study
Directory of Open Access Journals (Sweden)
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.
Jannique G Z van Uffelen; Chin A Paw, Marijke J. M.; Hopman-Rock, Marijke; van Mechelen, Willem
2007-01-01
Objectives To examine the effect of walking and vitamin B supplementation on quality-of-life (QoL) in community-dwelling adults with mild cognitive impairment. Methods One year, double-blind, placebo-controlled trial. Participants were randomized to: (1) twice-weekly, group-based, moderate-intensity walking program (n = 77) or a light-intensity placebo activity program (n = 75); and (2) daily vitamin B pills containing 5 mg folic acid, 0.4 mg B12, 50 mg B6 (n = 78) or placebo pills (n = 74). ...
Peighambari, Mohammadmehdi; Sanati, Hamidreza; Hadjikarimi, Majid; Zahedmehr, Ali; Shakerian, Farshad; Firouzi, Ata; Kiani, Reza; Sadeghipour, Parham; Kzaemi Asl, Siamak
2016-01-01
Background: There is a paucity of data regarding the role of side branch (SB) predilation during the provisional stenting of bifurcation lesions. Objectives: The present study aimed to assess the effects of SB predilation on the outcomes of true bifurcation interventions. Patients and Methods: Sixty patients with true bifurcation lesions according to the Medina classification were included in the study and randomly assigned to receive SB predilation before stenting the main branch (n = 30) or no predilation as the control group (n = 30). Results: There was a trend toward the higher occurrence of dissection in the predilated ostial lesions of the SB compared to the non-predilated group (16.7% vs. 0, P = 0.07). Performance of the SB predilation was not associated with improved flow of the SB or fewer degrees of ostial stenosis after stenting the main branch, the need to rewire, rewiring time, or the rate of use of the final kissing balloon dilation and double stents procedures. Conclusions: Routine predilation of the SB in provisional stenting of true bifurcation lesions seems to be ineffective and might be associated with some undesirable consequences. Still, there are some complex ostial lesions of the SB which could benefit from predilation. PMID:26949691
Random walks, diffusion limited aggregation in a wedge, and average conformal maps.
Sander, Leonard M; Somfai, Ellák
2005-06-01
We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that a different, but related, ensemble average, that of the conformal maps associated with random clusters, yields a nontrivial shape which is also not far from the Saffman-Taylor finger. However, we have previously demonstrated that the same average of DLA in a channel geometry is not the Saffman-Taylor finger. This casts doubt on the idea that the average of noisy diffusion-limited growth is governed by a simple transcription of noise-free results. PMID:16035911
Molecular motion in cell membranes: Analytic study of fence-hindered random walks
Kenkre, V. M.; Giuggioli, L.; Kalay, Z.
2008-05-01
A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G -protein coupled μ -opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.
Molecular motion in cell membranes: analytic study of fence-hindered random walks
Kenkre, V M; Kalay, Z
2008-01-01
A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G-protein coupled mu-opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.
Random walks based multi-image segmentation: Quasiconvexity results and GPU-based solutions.
Collins, Maxwell D; Xu, Jia; Grady, Leo; Singh, Vikas
2012-01-01
We recast the Cosegmentation problem using Random Walker (RW) segmentation as the core segmentation algorithm, rather than the traditional MRF approach adopted in the literature so far. Our formulation is similar to previous approaches in the sense that it also permits Cosegmentation constraints (which impose consistency between the extracted objects from ≥ 2 images) using a nonparametric model. However, several previous nonparametric cosegmentation methods have the serious limitation that they require adding one auxiliary node (or variable) for every pair of pixels that are similar (which effectively limits such methods to describing only those objects that have high entropy appearance models). In contrast, our proposed model completely eliminates this restrictive dependence -the resulting improvements are quite significant. Our model further allows an optimization scheme exploiting quasiconvexity for model-based segmentation with no dependence on the scale of the segmented foreground. Finally, we show that the optimization can be expressed in terms of linear algebra operations on sparse matrices which are easily mapped to GPU architecture. We provide a highly specialized CUDA library for Cosegmentation exploiting this special structure, and report experimental results showing these advantages.
Effect of 60Co-gamma radiation on the random walk error of interferometric fiber optic gyroscopes
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Two 60Co-gamma radiation experiments were launched to explore the radiation effect on optical components and interferometric fiber optic gyroscope （IFOG）. In optical components radiation experiment, the result showed that polarization-maintaining （PM） fiber coil loss was the most affected parameter in all the RWC （random walk coefficient） related parameters, compared with the weak sensitivity of other components parameters. In the IFOG radiation experiment, the RWC performance degradation was found to be almost due to an increase of the PM fiber attenuation. Based on the experiment result, a RWC prediction model in radiation, which is obtained by embedding PM fiber loss expression into the RWC model, was built following a power law of dose and dose rate. An IFOG RWC in space radiation environment was predicted from radiation dose and dose rate by the RWC prediction model. This RWC value calculated from test data is fully accorded to the RWC value predicted from radiation dose.
Records for the number of distinct sites visited by a random walk on the fully-connected lattice
Turban, L
2016-01-01
We consider a random walk on the fully-connected lattice with $N$ sites and study the time evolution of the number of distinct sites $s$ visited by the walker on a subset with $n$ sites. A record value $v$ is obtained for $s$ at a record time $t$ when the walker visits a site of the subset for the first time. The record time $t$ is a partial covering time when $v
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.
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.
Swank, C. M.; Petukhov, A. K.; Golub, R.
2016-06-01
The behavior of a spin undergoing Larmor precession in the presence of fluctuating fields is of interest to workers in many fields. The fluctuating fields cause frequency shifts and relaxation which are related to their power spectrum, which can be determined by taking the Fourier transform of the auto-correlation functions of the field fluctuations. Recently we have shown how to calculate these correlation functions for all values of mean-free path (ballistic to diffusive motion) in finite bounded regions by using the model of persistent continuous time random walks (CTRW) for particles subject to scattering by fixed (frozen) scattering centers so that the speed of the moving particles is not changed by the collisions. In this work we show how scattering with energy exchange from an ensemble of scatterers in thermal equilibrium can be incorporated into the CTRW. We present results for 1, 2, and 3 dimensions. The results agree for all these cases contrary to the previously studied "frozen" models. Our results for the velocity autocorrelation function show a long-time tail (˜t-1 /2 ), which we also obtain from conventional diffusion theory, with the same power, independent of dimensionality. Our results are valid for any Markovian scattering kernel as well as for any kernel based on a scattering cross section ˜1 /v .
Onoma, D P; Ruan, S; Thureau, S; Nkhali, L; Modzelewski, R; Monnehan, G A; Vera, P; Gardin, I
2014-12-01
A segmentation algorithm based on the random walk (RW) method, called 3D-LARW, has been developed to delineate small tumors or tumors with a heterogeneous distribution of FDG on PET images. Based on the original algorithm of RW [1], we propose an improved approach using new parameters depending on the Euclidean distance between two adjacent voxels instead of a fixed one and integrating probability densities of labels into the system of linear equations used in the RW. These improvements were evaluated and compared with the original RW method, a thresholding with a fixed value (40% of the maximum in the lesion), an adaptive thresholding algorithm on uniform spheres filled with FDG and FLAB method, on simulated heterogeneous spheres and on clinical data (14 patients). On these three different data, 3D-LARW has shown better segmentation results than the original RW algorithm and the three other methods. As expected, these improvements are more pronounced for the segmentation of small or tumors having heterogeneous FDG uptake.
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
Institute of Scientific and Technical Information of China (English)
WU An-Cai; XU Xin-Jian; WU Zhi-Xi; WANG Ying-Hai
2007-01-01
We investigate the dynamics of random walks on weighted networks. Assuming that the edge weight and the node strength are used as local information by a random walker. Two kinds of walks, weight-dependent walk and strength-dependent walk, are studied. Exact expressions for stationary distribution and average return time are derived and confirmed by computer simulations. The distribution of average return time and the mean-square that a weight-dependent walker can arrive at a new territory more easily than a strength-dependent one.
Zhang, Zhongzhi; Sheng, Yibin
2015-01-01
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-neighb...
Cortis, Andrea; Harter, Thomas; Hou, Lingling; Atwill, E. Robert; Packman, Aaron I.; Green, Peter G.
2006-12-01
Complex transport behavior other than advection-dispersion, simple retardation, and first-order removal has been observed in many biocolloid transport experiments in porous media. Such nonideal transport behavior is particularly evident in the late time elution of biocolloids at low concentrations. Here we present a series of saturated column experiments that were designed to measure the breakthrough and long-term elution of Cryptosporidium parvum in medium sand for a few thousand pore volumes after the initial source of oocysts was removed. For a wide range of ionic strengths, I, we consistently observe slower-than-Fickian, power law tailing. The slope of the tail is flatter for higher I. At very high ionic strength the slope decays to a rate slower than t-1. To explain this behavior, we propose a new filtration model based on the continuous time random walk (CTRW) theory. Our theory upscales heterogeneities at both the pore-scale geometry of the flow field and the grain surface physicochemical properties that affect biocolloid attachment and detachment. Pore-scale heterogeneities in fluid flow are shown to control the breakthrough of a conservative tracer but are shown to have negligible effect on oocyst transport. In our experiments, C. parvum transport is dominated by the effects of physicochemical heterogeneities. The CTRW model provides a parsimonious theory of nonreactive and reactive transport. The CTRW filtration process is controlled by three parameters, Λ, β, and c, which are related to the overall breakthrough retardation (R = 1 + Λ), the slope of the power law tail (β), and the transition to a slower than t-1 decay (c).
SOME LIMIT PROPERTIES OF LOCAL TIME FOR RANDOM WALK%随机游动局部时的某些极限性质
Institute of Scientific and Technical Information of China (English)
闻继威; 严云良
2006-01-01
Let X,X1,X2,...be i.i.d.random variables with EX2+δ0).Consider a one-dimensional random walk S={Sn}n≥0,starting from S0=0.Let ξk]=x}.A strong approximation of ξ*(n) by the local time for Wiener process is presented and the limsup-type and liminf-type laws of iterated logarithm of the maximum local time ξ*(n) are obtained.Furthermore,the precise asymptotics in the law of iterated logarithm of ξ*(n) is proved.
Liu, Baoshun; Zhao, Xiujian
2014-10-28
The continuous time random walk (CTRW) simulation was used to study the photocatalytic kinetics of nanocrystalline (nc)-TiO2 assemblies in this research. nc-TiO2 assemblies, such as nc-TiO2 porous films and nc-TiO2 hierarchical structures, are now widely used in photocatalysis. The nc-TiO2 assemblies have quasi-disordered networks consisting of many tiny nanoparticles, so the charge transport within them can be studied by CTRW simulation. We considered the experimental facts that the holes can be quickly trapped and transferred to organic species just after photogeneration, and the electrons transfer to O2 slowly and accumulate in the conduction band of TiO2, which is believed to be the rate-limiting process of the photocatalysis under low light intensity and low organic concentration. Due to the existence of numerous traps, the electron transport within the nc-TiO2 assemblies follows a multi-trapping (MT) mechanism, which significantly limits the electron diffusion speed. The electrons need to undergo several steps of MT transport before transferring to oxygen, so it is highly important that the electron transport in nc-TiO2 networks is determined for standard photocatalytic reactions. Based on the MT transport model, the transient decays of photocurrents during the photocatalytic oxidation of formic acid were studied by CTRW simulation, and are in good accordance with experiments. The steady state photocatalysis was also simulated. The effects of organic concentration, light intensity, temperature, and nc-TiO2 crystallinity on the photocatalytic kinetics were investigated, and were also consistent with the experimental results. Due to the agreement between the simulation and the experiments for both the transient and the steady state photocatalysis, the MT charge transport should be an important mechanism that controls the kinetics of recombination and photocatalysis in nc-TiO2 assemblies. Also, our research provides a new methodology to study the photocatalytic
Liu, Baoshun; Zhao, Xiujian
2014-10-28
The continuous time random walk (CTRW) simulation was used to study the photocatalytic kinetics of nanocrystalline (nc)-TiO2 assemblies in this research. nc-TiO2 assemblies, such as nc-TiO2 porous films and nc-TiO2 hierarchical structures, are now widely used in photocatalysis. The nc-TiO2 assemblies have quasi-disordered networks consisting of many tiny nanoparticles, so the charge transport within them can be studied by CTRW simulation. We considered the experimental facts that the holes can be quickly trapped and transferred to organic species just after photogeneration, and the electrons transfer to O2 slowly and accumulate in the conduction band of TiO2, which is believed to be the rate-limiting process of the photocatalysis under low light intensity and low organic concentration. Due to the existence of numerous traps, the electron transport within the nc-TiO2 assemblies follows a multi-trapping (MT) mechanism, which significantly limits the electron diffusion speed. The electrons need to undergo several steps of MT transport before transferring to oxygen, so it is highly important that the electron transport in nc-TiO2 networks is determined for standard photocatalytic reactions. Based on the MT transport model, the transient decays of photocurrents during the photocatalytic oxidation of formic acid were studied by CTRW simulation, and are in good accordance with experiments. The steady state photocatalysis was also simulated. The effects of organic concentration, light intensity, temperature, and nc-TiO2 crystallinity on the photocatalytic kinetics were investigated, and were also consistent with the experimental results. Due to the agreement between the simulation and the experiments for both the transient and the steady state photocatalysis, the MT charge transport should be an important mechanism that controls the kinetics of recombination and photocatalysis in nc-TiO2 assemblies. Also, our research provides a new methodology to study the photocatalytic
Huang, Ran
2016-10-01
An inhomogeneous random recursive lattice is constructed from the multi-branched Husimi square lattice. The number of repeating units connected on one vertex is randomly set to be 2 or 3 with a fixed ratio P2 or P3 with P2 +P3 = 1. The lattice is designed to describe complex thermodynamic systems with variable coordinating neighbors, e.g. the asymmetric range around the surface of a bulk system. Classical ferromagnetic spin-1 Ising model is solved on the lattice to achieve an annealed solution via the local exact calculation technique. The model exhibits distinct spontaneous magnetization similar to the deterministic system, with however rigorous thermal fluctuations and significant singularities on the entropy behavior around the critical temperature, indicating a complex superheating frustration in the cross-dimensional range induced by the stochasticity. The critical temperature was found to be exponentially correlated to the structural ratio P with the coefficient fitted as 0.53187, while the ground state energy presents linear correlation to P, implying a well-defined average property according to the structural ratio.
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DePaul Vincent G
2011-10-01
Full Text Available Abstract Background Although task-oriented training has been shown to improve walking outcomes after stroke, it is not yet clear whether one task-oriented approach is superior to another. The purpose of this study is to compare the effectiveness of the Motor Learning Walking Program (MLWP, a varied overground walking task program consistent with key motor learning principles, to body-weight-supported treadmill training (BWSTT in community-dwelling, ambulatory, adults within 1 year of stroke. Methods/Design A parallel, randomized controlled trial with stratification by baseline gait speed will be conducted. Allocation will be controlled by a central randomization service and participants will be allocated to the two active intervention groups (1:1 using a permuted block randomization process. Seventy participants will be assigned to one of two 15-session training programs. In MLWP, one physiotherapist will supervise practice of various overground walking tasks. Instructions, feedback, and guidance will be provided in a manner that facilitates self-evaluation and problem solving. In BWSTT, training will emphasize repetition of the normal gait cycle while supported over a treadmill, assisted by up to three physiotherapists. Outcomes will be assessed by a blinded assessor at baseline, post-intervention and at 2-month follow-up. The primary outcome will be post-intervention comfortable gait speed. Secondary outcomes include fast gait speed, walking endurance, balance self-efficacy, participation in community mobility, health-related quality of life, and goal attainment. Groups will be compared using analysis of covariance with baseline gait speed strata as the single covariate. Intention-to-treat analysis will be used. Discussion In order to direct clinicians, patients, and other health decision-makers, there is a need for a head-to-head comparison of different approaches to active, task-related walking training after stroke. We hypothesize that
Michas, Georgios; Vallianatos, Filippos; Karakostas, Vassilios; Papadimitriou, Eleftheria; Sammonds, Peter
2014-05-01
Efpalion aftershock sequence occurred in January 2010, when an M=5.5 earthquake was followed four days later by another strong event (M=5.4) and numerous aftershocks (Karakostas et al., 2012). This activity interrupted a 15 years period of low to moderate earthquake occurrence in Corinth rift, where the last major event was the 1995 Aigion earthquake (M=6.2). Coulomb stress analysis performed in previous studies (Karakostas et al., 2012; Sokos et al., 2012; Ganas et al., 2013) indicated that the second major event and most of the aftershocks were triggered due to stress transfer. The aftershocks production rate decays as a power-law with time according to the modified Omori law (Utsu et al., 1995) with an exponent larger than one for the first four days, while after the occurrence of the second strong event the exponent turns to unity. We consider the earthquake sequence as a point process in time and space and study its spatiotemporal evolution considering a Continuous Time Random Walk (CTRW) model with a joint probability density function of inter-event times and jumps between the successive earthquakes (Metzler and Klafter, 2000). Jump length distribution exhibits finite variance, whereas inter-event times scale as a q-generalized gamma distribution (Michas et al., 2013) with a long power-law tail. These properties are indicative of a subdiffusive process in terms of CTRW. Additionally, the mean square displacement of aftershocks is constant with time after the occurrence of the first event, while it changes to a power-law with exponent close to 0.15 after the second major event, illustrating a slow diffusive process. During the first four days aftershocks cluster around the epicentral area of the second major event, while after that and taking as a reference the second event, the aftershock zone is migrating slowly with time to the west near the epicentral area of the first event. This process is much slower from what would be expected from normal diffusion, a
Directory of Open Access Journals (Sweden)
PAŞCA LUCIAN
2015-04-01
Full Text Available This paper attempts to test the efficiency of the Romanian Capital Market by assessing some basic statistical properties of prices for the ten most liquid stocks listed on the Bucharest Stock Exchange. More specifically, by testing if stock price series exhibit a random walk-like behaviour. For robustness of the results, two unit root tests—the Augmented Dickey-Fuller and the Kwiatkowski-Phillips-Schmidt-Shin—are used to measure stationarity for both prices and returns, and determine if price dynamics is determined by an order one integrated process (a proxy for the random walk. Further Lo and MacKinley‘s Variance Ratio Test is applied to study if the variance of returns is a linear time-dependent function (a well-known property of a random variable. The analysis is done for a period between 15 October 1997, or the listing date on the stock exchange, respectively, and 10 April 2013, for both daily and weekly observations. Furthermore, to take into account the distortive effects of the financial turmoil from 2007-2009 on market efficiency, a separate analysis has been conducted for two sub-periods, pre- and post-recession, respectively.
基于Mean Shift和随机游走的图像分割算法%Image Segmentation Algorithm Based on Mean Shift and Random Walk
Institute of Scientific and Technical Information of China (English)
穆克; 程伟; 褚俊霞
2012-01-01
An improved random walk algorithm was proposed herein.First,Mean Shift algorithm was adopted to preprocess the image,which was partitioned into a series of homogeneous areas,so that the homogeneous areas were taken as nodes to walk at random,with noise inhibited while reducing the number of nodes.Second,PMD was used to define the weight between regions.Thirdly,seeds were improved to have added the auxiliary seeds,and the auxiliary and signed seeds were used to walk random,with region merging realized.The final image segmentation was reached.Experimental results expatiates that the proposed method highlights the segmentation accuracy.%提出了一种改进的随机游走算法。首先,采用Mean Shift算法对图像进行预处理,将图像划分成一些同质区域,用同质区域作为节点进行随机游走,在降低节点数的同时也抑制了噪声对分割的影响;其次,利用马氏距离定义区域之间的权值;对种子点进行了改进,增加了辅助种子点,利用辅助种子点和用户标记的种子点进行随机游走,实现同质区域的合并,实现图像的最终分割。实验结果表明,该算法提高了图像分割的精度。
Wu, Li-Ling; Wang, Kuo-Ming; Liao, Po-I; Kao, Yu-Hsiu; Huang, Yi-Ching
2015-10-01
Over 73% of hi-tech industry employees in Taiwan lack regular exercise. They are exposed to a highly variable and stressful work environment for extended periods of time, and may subsequently experience depression, detrimental to workers' physiological and mental health. In this cross-sectional survey, the authors explored the effect of an 8-week brisk walking program on the fatigue of employees in the hi-tech industry. The participants, from a hi-tech company in northern Taiwan, were randomly assigned to an experimental group (EG; 41 subjects, Mage = 33.34 ± 6.40) or control group (CG; 45 subjects, Mage = 29.40 ± 3.60). Following the 8-week brisk walking program, the EG showed significantly lower scores for subjective fatigue, working motivation, attention, and overall fatigue. The authors confirmed that the 8-week outdoor brisk walking program significantly improved the level of fatigue among employees of the hi-tech industry. The finding serves as an important reference for health authorities in Taiwan and provides awareness of workplace health promotion in the hi-tech industry. PMID:26194655
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Stanley Sai-Chuen Hui
2015-01-01
Full Text Available Tai Chi and walking are both moderate-intensity physical activity (PA that can be easily practiced in daily life. The objective of the study was to determine the effects of these two PAs on weight loss, metabolic syndrome parameters, and bone mineral density (BMD in Chinese adults. We randomized 374 middle-aged subjects (45.8 ± 5.3 years into 12-week training (45 minutes per day, 5 days per week of Tai Chi (n=124 or self-paced walking (n=121 or control group (n=129. On average, Tai Chi and walking groups lost 0.50 and 0.76 kg of body weight and 0.47 and 0.59 kg of fat mass after intervention, respectively. The between-group difference of waist circumference (WC and fasting blood glucose (FBG was −3.7 cm and −0.18 mmol/L for Tai Chi versus control and −4.1 cm and −0.22 mmol/L for walking versus control. No significant differences were observed regarding lean mass, blood pressure, triglycerides, total cholesterol, high-density and low-density lipoprotein cholesterol, and BMD compared to control. Change in lean mass, not fat mass or total weight loss, was significantly correlated to the change in BMD. Our results suggest that both of these two PAs can produce moderate weight loss and significantly improve the WC and FBG in Hong Kong Chinese adults, with no additional effects on BMD.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process Xn =-μ+∞∑j=-∞ψn-jεj, where {ε, εn; -∞＜ n ＜ +∞}is a sequence of independent, identically distributed random variables with zero mean, μ＞0 is a constant and the coefficients {ψi;-∞＜ i ＜∞} satisfy 0 ＜∞∑j=-∞|jψj| ＜∞. Under the conditions that the distribution function of |ε| has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{supn≥0(-nμ+∞∑j=-∞εjβnj) ＞ x}is discussed. Then the result is applied to ultimate ruin probability.
The distribution of first hitting times of random walks on Erd\\H{o}s-R\\'enyi networks
Tishby, Ido; Biham, Ofer; Katzav, Eytan
2016-01-01
We present analytical results for the distribution of first hitting times of random walkers on Erd\\H{o}s-R\\'enyi networks. Starting from a random initial node, a random walker hops randomly between adjacent nodes on the network until it hits a node which it has already visited before. At this point, the path is terminated. The path length $d$, pursued by the random walker from the initial node up to its termination is called the first hitting time or the first intersection length. Using recur...
Directory of Open Access Journals (Sweden)
Fortlage Laurie A
2007-11-01
Full Text Available 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 step counts and 2 structured goals targeting bout steps defined as walking that lasts for 10 minutes or longer at a pace of at least 60 steps per minute. We sought to determine which goal-setting strategy was more effective at increasing bout steps. Participants were sedentary adults with type 2 diabetes. All participants: wore enhanced pedometers with embedded USB ports; uploaded detailed, time-stamped step-count data to a website called Stepping Up to Health; and received automated step-count feedback, automatically calculated goals, and tailored motivational messages throughout the six-week intervention. Only the automated goal calculations and step-count feedback differed between the two groups. The primary outcome of interest was increase in steps taken during the previously defined bouts of walking (lasting at least 10 minutes or longer at a pace of at least 60 steps per minute between baseline and end of the intervention. Results Thirty-five participants were randomized and 30 (86% completed the pilot study. Both groups significantly increased bout steps, but there was no statistically significant difference between groups. Among study completers, bout steps increased by 1921 ± 2729 steps a day. Those who received lifestyle goals were more satisfied with the intervention (p = 0.006 and wore the pedometer more often (p Conclusion In this six-week intervention, Lifestyle Goals group participants achieved increases in bout steps comparable to the
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Derya Kahraman
2005-01-01
Full Text Available Random walk model is one of the models that are used to test weak-form efficiency. If changes in stock prices follow a random walk model, the price changes will not have serial correlation. In this study, the Istanbul Stock Exchange 100 Index closing price changes for one, five, nine, and sixteen day differencing intervals for 1.1.1996-27.10.2004 period and three non-overlapping sub periods are tested for serial correlation. Since the results verify that the Istanbul Stock Exchange 100 Index does not follow a random walk model during any of the periods tested, investors may be able to profit from some carefully designed trading rules.
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Yutaka Morishima
Full Text Available Due to the reduced physical activity of patients who have undergone total hip arthroplasty (THA, there are no home-based exercise training regimens for preventing muscle atrophy and aerobic capacity impairment in these patients. We examined whether interval walking training (IWT could prevented these issues. Twenty-eight female patients (∼60 years of age who had undergone THA more than 2 months prior were randomly divided into IWT (n = 14 and control (CNT, n = 14 groups. The IWT subjects trained at a target of 60 min of fast walking at >70% peak aerobic capacity for walking (VO₂peak per wk for 12 wk, while those in the CNT maintained their previous sedentary life during the same period. We measured the energy expenditure of the daily physical activity, except during sleeping and bathing, every minute and every day during the intervention. We also measured the isometric knee extension (FEXT and flexion (FFLX forces, VO₂peak, and anaerobic threshold during the graded cycling exercise (VO₂AT before and after the intervention. All subjects, except for one in IWT, completed the protocol. FFLX increased by 23% on the operated side (P = 0.003 and 14% on the non-operated side of IWT (P = 0.006, while it only increased on the operated side of CNT (P = 0.03. The VO₂peak and VO₂AT in IWT increased by 8% (P = 0.08 and 13% (P = 0.002, respectively, and these changes were significantly higher in the IWT than in CNT group (both, P<0.05. In conclusion, IWT might be an effective home-based training regimen for preventing the muscle atrophy from reduced daily physical activity in THA patients.UMIN-CTR UMIN000013172.
Derya Kahraman; Mehmet Erkan
2005-01-01
Random walk model is one of the models that are used to test weak-form efficiency. If changes in stock prices follow a random walk model, the price changes will not have serial correlation. In this study, the Istanbul Stock Exchange 100 Index closing price changes for one, five, nine, and sixteen day differencing intervals for 1.1.1996-27.10.2004 period and three non-overlapping sub periods are tested for serial correlation. Since the results verify that the Istanbul Stock Exchange 100 Index ...
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P.D.Gujrati
2002-01-01
Full Text Available Theoretical evidence is presented in this review that architectural aspects can play an important role, not only in the bulk but also in confined geometries by using our recursive lattice theory, which is equally applicable to fixed architectures (regularly branched polymers, stars, dendrimers, brushes, linear chains, etc. and variable architectures, i.e. randomly branched structures. Linear chains possess an inversion symmetry (IS of a magnetic system (see text, whose presence or absence determines the bulk phase diagram. Fixed architectures possess the IS and yield a standard bulk phase diagram in which there exists a theta point at which two critical lines C and C' meet and the second virial coefficient A2 vanishes. The critical line C appears only for infinitely large polymers, and an order parameter is identified for this criticality. The critical line C' exists for polymers of all sizes and represents phase separation criticality. Variable architectures, which do not possess the IS, give rise to a topologically different phase diagram with no theta point in general. In confined regions next to surfaces, it is not the IS but branching and monodispersity, which becomes important in the surface regions. We show that branching plays no important role for polydisperse systems, but become important for monodisperse systems. Stars and linear chains behave differently near a surface.
... safety reasons, especially on uneven ground. See a physical therapist for exercise therapy and walking retraining. For a ... the right position for standing and walking. A physical therapist can supply these and provide exercise therapy, if ...
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Alan D Dangour
2011-04-01
Full Text Available BACKGROUND: Ageing is associated with increased risk of poor health and functional decline. Uncertainties about the health-related benefits of nutrition and physical activity for older people have precluded their widespread implementation. We investigated the effectiveness and cost-effectiveness of a national nutritional supplementation program and/or a physical activity intervention among older people in Chile. METHODS AND FINDINGS: We conducted a cluster randomized factorial trial among low to middle socioeconomic status adults aged 65-67.9 years living in Santiago, Chile. We randomized 28 clusters (health centers into the study and recruited 2,799 individuals in 2005 (~100 per cluster. The interventions were a daily micronutrient-rich nutritional supplement, or two 1-hour physical activity classes per week, or both interventions, or neither, for 24 months. The primary outcomes, assessed blind to allocation, were incidence of pneumonia over 24 months, and physical function assessed by walking capacity 24 months after enrollment. Adherence was good for the nutritional supplement (~75%, and moderate for the physical activity intervention (~43%. Over 24 months the incidence rate of pneumonia did not differ between intervention and control clusters (32.5 versus 32.6 per 1,000 person years respectively; risk ratio = 1.00; 95% confidence interval 0.61-1.63; p = 0.99. In intention-to-treat analysis, after 24 months there was a significant difference in walking capacity between the intervention and control clusters (mean difference 33.8 meters; 95% confidence interval 13.9-53.8; p = 0.001. The overall cost of the physical activity intervention over 24 months was US$164/participant; equivalent to US$4.84/extra meter walked. The number of falls and fractures was balanced across physical activity intervention arms and no serious adverse events were reported for either intervention. CONCLUSIONS: Chile's nutritional supplementation program for
The distribution of first hitting times of random walks on Erd\\H{o}s-R\\'enyi networks
Tishby, Ido; Katzav, Eytan
2016-01-01
We present analytical results for the distribution of first hitting times of random walkers on Erd\\H{o}s-R\\'enyi networks. Starting from a random initial node, a random walker hops randomly between adjacent nodes on the network until it hits a node which it has already visited before. At this point, the path is terminated. The path length $d$, pursued by the random walker from the initial node up to its termination is called the first hitting time or the first intersection length. Using recursion equations, we obtain analytical results for the tail distribution of the path lengths, $P(d>\\ell)$. The results are found to be in excellent agreement with simulations. It turns out that the distribution $P(d>\\ell)$ follows a product of an exponential distribution and a Rayleigh distribution. We also obtain expressions for the mean, median and standard deviation of this distribution in terms of the network size and its mean degree. It is found that the first hitting time is much shorter than the last hitting time of ...
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D. Merom
2015-01-01
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.
International Nuclear Information System (INIS)
It is well known that bioturbation can contribute significantly to the vertical transport of fallout radionuclides in grassland soils. To examine this effect also for a forest soil, activity-depth profiles of Chernobyl-derived 134Cs from a limed plot (soil, hapludalf under spruce) with a high abundance of earthworms (Lumbricus rubellus) in the Olu horizon (thickness=3.5 cm) were evaluated and compared with the corresponding depth profiles from an adjacent control plot. For this purpose, a random-walk based transport model was developed, which considers (1) the presence of an initial activity-depth distribution, (2) the deposition history of radiocesium at the soil surface, (3) individual diffusion/dispersion coefficients and convection rates for the different soil horizons, and (4) mixing by bioturbation within one soil horizon. With this model, the observed 134Cs-depth distribution at the control site (no bioturbation) and at the limed site could be simulated quite satisfactorily. It is shown that the observed, substantial long-term enrichment of 134Cs in the bioturbation horizon can be modeled by an exceptionally effective diffusion process, combined with a partial reflection of the randomly moving particles at the two borders of the bioturbation zone. The present model predicts significantly longer residence times of radiocesium in the organic soil layer of the forest soil than obtained from a first-order compartment model, which does not consider bioturbation explicitly
随机环境中受控分枝过程的稳定性%STABILITY OF CONTROLLED BRANCHING CHAINS IN RANDOM ENVIRONMENT
Institute of Scientific and Technical Information of China (English)
王伟刚; 胡迪鹤
2009-01-01
本文研究了控制函数独立同分布,并且第n代的繁殖情况取决于环境的随机环境中分枝过程.给出了该模型稳定的充分条件,当环境平稳遍历时,得到了过程几乎处处灭绝的充分条件.%We consider controlled branching chains in random environments, that the controlled functions are i.i.d. random variables and the reproduction of an individual in the n-th season depends on the environments. Some results on process stability are shown. The extinction probabilities are given when environments are stationary and ergodic.
深市股票价格波动的随机游走模型%The Random Walk Model of Shenzhen Stock Market Price' Fluctuation
Institute of Scientific and Technical Information of China (English)
杨美丽
2012-01-01
Using the random walk model, this paper made research on the fluctuation of Shenzhen stork market prices. It shows the stock prices follow the random walk process and the market has weak efficiency. While the external impact on stock market will disappear slowly, the effects will be lasting and has " leverage effect". There is not any breakpoint in the stock price sequence since opening. Compared with the previous researches, this reflects the relationship between the long-term fluctuations and short--term fluctuations on stock price. Therefore, government should further standardize market operation, promote information circulation, keep robust stock market policies to better promote the development of Chinese stock market and the operation of macroeconomic. And we should notice the lasting external impact when stud- ying the stock market prices" fluctuation during a specific period.%采用随机游走模型,对深市股票价格波动进行研究。结果表明,深市股票价格波动服从随机游走,市场弱有效;虽外部冲击对股市的影响会逐渐消散,但其影响是持久的,且存在＂杠杆效应＂;自开市以来,股价波动不存在断点。对比前人研究,本研究认为,这恰恰反映了股价的长期波动与短期波动间的关系。即,长期中,股市作为现货市场的一种反映,遵循价值规律;而短期内,由于政策的变动,市场信息的不对称和投资者的跟风、从众等心理,股市频繁剧烈震荡,偏离其长期趋势。由此,政府应进一步规范市场运作,促进信息流通,保持股市政策的稳健性;研究者进行股市分析时,也须先排除分析时段前外部冲击的持续性影响。
Physical implementation of quantum walks
Manouchehri, Kia
2013-01-01
Given the extensive application of random walks in virtually every science related discipline, we may be at the threshold of yet another problem solving paradigm with the advent of quantum walks. Over the past decade, quantum walks have been explored for their non-intuitive dynamics, which may hold the key to radically new quantum algorithms. This growing interest has been paralleled by a flurry of research into how one can implement quantum walks in laboratories. This book presents numerous proposals as well as actual experiments for such a physical realization, underpinned by a wide range of
Random Walk Investigation in Indian Market with special reference to S&P Nifty – Fifty Stocks.
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Tamilselvan M Manickam
2015-10-01
Full Text Available The competence of a financial system is entirely depending upon the stock market efficiency. The gradual growth of equity investor’s participation is inevitable to enrich the overall growth of emerging economies.Hence the necessity is felt to provide an empirical support to the investing community. For the purpose, this study attempts to examine the weak-form efficiency of Indian stock market – National Stock Exchange (NSE. The study has used the daily closing price of the Nifty fiftystocks from 3rdJanuary 2011 to 24thApril 2015. To test the weak form efficiency both parametric and non-parametric tests called Autocorrelation, Augmented Dicky Fuller test, and Runs Test were performed. The study reveals that 39 stocks of NSE-Nifty Fifty are found to be weak form inefficient, so that the investors can formulate trading strategies to gain abnormal returns. The Index and 10 stocks are found to be weak form efficient during the study period since the price series found to be autocorrelation existence.Key words: Time Series - Auto Correlation – Unit Root Test – Random Walk– Stationary – National Stock Exchange
Ellery, Adam J.; Baker, Ruth E.; Simpson, Matthew J.
2016-05-01
The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motion of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations.
International Nuclear Information System (INIS)
Despite the widespread acceptance of the relevance of the nodes of one-body electronic wave functions (atomic or molecular orbitals) in determining chemical properties, relatively little is known about the corresponding nodes of many-body wave functions. As an alternative to mapping the nodal surfaces present in the ground states of many-electron systems, we have focused instead on the structural domains implied by these surfaces. In the spirit of Monte Carlo techniques, the nodal hypervolumes of a series of atomic N-body Hartree--Fock level electronic wave functions have been mapped using a random-walk simulation in 3N dimensional configuration space. The basic structural elements of the domain of atomic or molecular wave functions are identified as nodal regions (continuous volumes of the same sign) and permutational cells (identical building blocks). Our algorithm determines both the relationships among nodal regions or cells (topology) as well as the geometric properties within each structural domain. Our results indicate that ground-state Hartree--Fock wave functions generally consist of four equivalent nodal regions (two positive and two negative), each constructed from one or more permutational cells. We have developed an operational method to distinguish otherwise identical permutational cells. The limitations and most probable sources of error associated with this numerical method are discussed as are directions for future research
Turban, L
2016-01-01
The probability distribution of the number $s$ of distinct sites visited up to time $t$ by a random walk on the fully-connected lattice with $N$ sites is first obtained by solving the eigenvalue problem associated with the discrete master equation. Then, using generating function techniques, we compute the joint probability distribution of $s$ and $r$, where $r$ is the number of sites visited only once up to time $t$. Mean values, variances and covariance are deduced from the generating functions and their finite-size-scaling behaviour is studied. Introducing properly centered and scaled variables $u$ and $v$ for $r$ and $s$ and working in the scaling limit ($t\\to\\infty$, $N\\to\\infty$ with $w=t/N$ fixed) the joint probability density of $u$ and $v$ is shown to be a bivariate Gaussian density. It follows that the fluctuations of $r$ and $s$ around their mean values in a finite-size system are Gaussian in the scaling limit. The same type of finite-size scaling is expected to hold on periodic lattices above the ...
Quantum Walks on the Hypercube
Moore, Cristopher; Moore, Cristopher; Russell, Alexander
2001-01-01
Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the n-dimensional hypercube, one in discrete time and one in continuous time. In both cases we show that the quantum walk mixes in (\\pi/4)n steps, faster than the O(n log n) steps required by the classical walk. In the continuous-time case, the probability distribution is {\\em exactly} uniform at this time. More importantly, these walks expose several subtleties in the definition of mixing time for quantum walks. Even though the continuous-time walk has an O(n) instantaneous mixing time at which it is precisely uniform, it never approaches the uniform distribution when the stopping time is chosen randomly as in [AharonovAKV2001]. Our analysis treats interference between terms of different phase more carefully than is necessary for the walk on the cycle; previous general bounds p...
Institute of Scientific and Technical Information of China (English)
何昌保; 马秀丽; 余长明
2016-01-01
For dual source CT image with contrast media,due to heart soft tissue density and contrast media uneven distribution result in the CT value of heart tissues uneven and boundary fuzzy,taking a single image segmentation algorithm is too difficult to obtain satisfactory results,so morphological reconstruction and random walks hybrid method is proposed in this paper.Firstly,we used morphological reconstruction operation on image smoothing filtering, which makes the heart cavity gray information convergence and gray level differences with the surrounding tissue and get the left atrium area with the fuzzy boundary;Then the random walks algorithm sets the seed points for each region of the image,and gives the weight of each side,and takes the weight of the edge as the transfer probability.For each unlabeled point is calculated from the point of first arrival probability of seed points.Finally,according to the first hit probability to choose the maximum that a class as belonging to the class,attribute of the unlabeled points and finally get the accurate left atrial.%针对在传统的CT介入式治疗过程中，胸腔中软组织较多软组织的厚度和注射的造影剂在心脏中呈现的不均匀分布，导致在采用CT成像的图像中胸腔内部各组织之间存在边界模糊或者确实等状况，本文提出一种采用形态重构和随机行走相结合的分割方法。首先利用形态学开闭运算对图像进行化简，并使得心脏 CT腔体边界分离，进而使得各个组织组织分离，再结合Random walks算法。从而使得不需要标记太多种子点的情况下提高了分割的速度和准确性，实验证明该方法能够达到预期的目标。
DEFF Research Database (Denmark)
Hartvigsen, Jan; Morsø, Lars; Bendix, Tom;
2010-01-01
BACKGROUND: Active approaches including both specific and unspecific exercise are probably the most widely recommended treatment for patients with chronic low back pain but it is not known exactly which types of exercise provide the most benefit. Nordic Walking - power walking using ski poles...
ON MARKOV CHAINS IN SPACE-TIME RANDOM ENVIRONMENTS
Institute of Scientific and Technical Information of China (English)
Hu Dihe; Hu Xiaoyu
2009-01-01
In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with Abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Ф and a random Markov kernel (RMK) p(γ). In Section 3, the authors establish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov branching chain in space-time random environment.
International Nuclear Information System (INIS)
Multiscale features of transport processes in fractured porous media make numerical modeling a difficult task, both in conceptualization and computation. Modeling the mass transfer through the fracture-matrix interface is one of the critical issues in the simulation of transport in a fractured porous medium. Because conventional dual-continuum-based numerical methods are unable to capture the transient features of the diffusion depth into the matrix (unless they assume a passive matrix medium), such methods will overestimate the transport of tracers through the fractures, especially for the cases with large fracture spacing, resulting in artificial early breakthroughs. We have developed a new method for calculating the particle-transfer probability that can capture the transient features of diffusion depth into the matrix within the framework of the dual-continuum random-walk particle method (RWPM) by introducing a new concept of activity range of a particle within the matrix. Unlike the multiple-continuum approach, the new dual-continuum RWPM does not require using additional grid blocks to represent the matrix. It does not assume a passive matrix medium and can be applied to the cases where global water flow exists in both continua. The new method has been verified against analytical solutions for transport in the fracture-matrix systems with various fracture spacing. The calculations of the breakthrough curves of radionuclides from a potential repository to the water table in Yucca Mountain demonstrate the effectiveness of the new method for simulating 3-D, mountain-scale transport in a heterogeneous, fractured porous medium under variably saturated conditions
Rahbaralam, Maryam; Fernàndez-Garcia, Daniel; Sanchez-Vila, Xavier
2015-12-01
Random walk particle tracking methods are a computationally efficient family of methods to solve reactive transport problems. While the number of particles in most realistic applications is in the order of 106-109, the number of reactive molecules even in diluted systems might be in the order of fractions of the Avogadro number. Thus, each particle actually represents a group of potentially reactive molecules. The use of a low number of particles may result not only in loss of accuracy, but also may lead to an improper reproduction of the mixing process, limited by diffusion. Recent works have used this effect as a proxy to model incomplete mixing in porous media. In this work, we propose using a Kernel Density Estimation (KDE) of the concentrations that allows getting the expected results for a well-mixed solution with a limited number of particles. The idea consists of treating each particle as a sample drawn from the pool of molecules that it represents; this way, the actual location of a tracked particle is seen as a sample drawn from the density function of the location of molecules represented by that given particle, rigorously represented by a kernel density function. The probability of reaction can be obtained by combining the kernels associated to two potentially reactive particles. We demonstrate that the observed deviation in the reaction vs time curves in numerical experiments reported in the literature could be attributed to the statistical method used to reconstruct concentrations (fixed particle support) from discrete particle distributions, and not to the occurrence of true incomplete mixing. We further explore the evolution of the kernel size with time, linking it to the diffusion process. Our results show that KDEs are powerful tools to improve computational efficiency and robustness in reactive transport simulations, and indicates that incomplete mixing in diluted systems should be modeled based on alternative mechanistic models and not on a
Directory of Open Access Journals (Sweden)
Rosane Garcia Collevatti
2015-08-01
Full Text Available Understanding the dispersal routes of Neotropical savanna tree species is an essential step to unravel the effects of past climate change on genetic patterns, species distribution and population demography. Here we reconstruct the demographic history and dispersal dynamics of the Neotropical savanna tree species Tabebuia aurea to understand the effects of Quaternary climate change on its current spatial patterns of genetic diversity. We sampled 285 individuals from 21 populations throughout Brazilian savannas and sequenced all individuals for three chloroplast intergenic spacers and ITS nrDNA. We analyzed data using a multi-model inference framework by coupling the relaxed random walk model, ecological niche modeling (ENM and statistical phylogeography. The most recent common ancestor of T. aurea lineages dated from ~4.0 ± 2.5 Ma. Tabebuia aurea lineages cyclically dispersed from the West towards the Central-West Brazil, and from the Southeast towards the East and Northeast Brazil, following the paleodistribution dynamics shown by the ENMs through the last glacial cycle. A historical refugium through time may have allowed dispersal of lineages among populations of Central Brazil, overlapping with population expansion during interglacial periods and the diversification of new lineages. Range and population expansion through the Quaternary were, respectively, the most frequent prediction from ENMs and the most likely demographic scenario from coalescent simulations. Consistent phylogeographic patterns among multiple modeling inferences indicate a promising approach, allowing us to understand how cyclical climate changes through the Quaternary drove complex population dynamics and the current patterns of species distribution and genetic diversity.
Agutter, P S; Wheatley, D N
2000-11-01
For many years, it has been believed that diffusion is the principle motive force for distributing molecules within the cell. Yet, our current information about the cell makes this improbable. Furthermore, the argument that limitations responsible for the relative constancy of cell size--which seldom varies by more than a factor of 2, whereas organisms can vary in mass by up to 10(24)--are based on the limits of diffusion is questionable. This essay seeks to develop an alternative explanation based on transport of molecules along structural elements in the cytoplasm and nucleus. This mechanism can better account for cell size constancy, in light of modern biological knowledge of the complex microstructure of the cell, than simple diffusion.
Quantum walks and search algorithms
Portugal, Renato
2013-01-01
This book addresses an interesting area of quantum computation called quantum walks, which play an important role in building quantum algorithms, in particular search algorithms. Quantum walks are the quantum analogue of classical random walks. It is known that quantum computers have great power for searching unsorted databases. This power extends to many kinds of searches, particularly to the problem of finding a specific location in a spatial layout, which can be modeled by a graph. The goal is to find a specific node knowing that the particle uses the edges to jump from one node to the next. This book is self-contained with main topics that include: Grover's algorithm, describing its geometrical interpretation and evolution by means of the spectral decomposition of the evolution operater Analytical solutions of quantum walks on important graphs like line, cycles, two-dimensional lattices, and hypercubes using Fourier transforms Quantum walks on generic graphs, describing methods to calculate the limiting d...
Muñoz-Cobo, José; Chiva, Sergio; El Aziz Essa, Mohamed; Mendes, Santos
2012-08-01
Two phase flow experiments with different superficial velocities of gas and water were performed in a vertical upward isothermal cocurrent air-water flow column with conditions ranging from bubbly flow, with very low void fraction, to transition flow with some cap and slug bubbles and void fractions around 25%. The superficial velocities of the liquid and the gas phases were varied from 0.5 to 3 m/s and from 0 to 0.6 m/s, respectively. Also to check the effect of changing the surface tension on the previous experiments small amounts of 1-butanol were added to the water. These amounts range from 9 to 75 ppm and change the surface tension. This study is interesting because in real cases the surface tension of the water diminishes with temperature, and with this kind of experiments we can study indirectly the effect of changing the temperature on the void fraction distribution. The following axial and radial distributions were measured in all these experiments: void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter and turbulence intensity. The range of values of the gas superficial velocities in these experiments covered the range from bubbly flow to the transition to cap/slug flow. Also with transition flow conditions we distinguish two groups of bubbles in the experiments, the small spherical bubbles and the cap/slug bubbles. Special interest was devoted to the transition region from bubbly to cap/slug flow; the goal was to understand the physical phenomena that take place during this transition A set of numerical simulations of some of these experiments for bubbly flow conditions has been performed by coupling a Lagrangian code, that tracks the three dimensional motion of the individual bubbles in cylindrical coordinates inside the field of the carrier liquid, to an Eulerian model that computes the magnitudes of continuous phase and to a 3D random walk model that takes on account the fluctuation in the velocity field of the
Moy, Marilyn L; Martinez, Carlos H; Kadri, Reema; Roman, Pia; Holleman, Robert G; Kim, Hyungjin Myra; Nguyen, Huong Q; Cohen, Miriam D; Goodrich, David E; Giardino, Nicholas D
2016-01-01
Background Regular physical activity (PA) is recommended for persons with chronic obstructive pulmonary disease (COPD). Interventions that promote PA and sustain long-term adherence to PA are needed. Objective We examined the effects of an Internet-mediated, pedometer-based walking intervention, called Taking Healthy Steps, at 12 months. Methods Veterans with COPD (N=239) were randomized in a 2:1 ratio to the intervention or wait-list control. During the first 4 months, participants in the intervention group were instructed to wear the pedometer every day, upload daily step counts at least once a week, and were provided access to a website with four key components: individualized goal setting, iterative feedback, educational and motivational content, and an online community forum. The subsequent 8-month maintenance phase was the same except that participants no longer received new educational content. Participants randomized to the wait-list control group were instructed to wear the pedometer, but they did not receive step-count goals or instructions to increase PA. The primary outcome was health-related quality of life (HRQL) assessed by the St George’s Respiratory Questionnaire Total Score (SGRQ-TS); the secondary outcome was daily step count. Linear mixed-effect models assessed the effect of intervention over time. One participant was excluded from the analysis because he was an outlier. Within the intervention group, we assessed pedometer adherence and website engagement by examining percent of days with valid step-count data, number of log-ins to the website each month, use of the online community forum, and responses to a structured survey. Results Participants were 93.7% male (223/238) with a mean age of 67 (SD 9) years. At 12 months, there were no significant between-group differences in SGRQ-TS or daily step count. Between-group difference in daily step count was maximal and statistically significant at month 4 (P<.001), but approached zero in months 8
Volkers, Karin M.; Scherder, Erik J. A.
2011-01-01
Background: Physical activity has proven to be beneficial for physical functioning, cognition, depression, anxiety, rest-activity rhythm, quality of life (QoL), activities of daily living (ADL) and pain in older people. The aim of this study is to investigate the effect of walking regularly on physi
Recursive Branching Simulated Annealing Algorithm
Bolcar, Matthew; Smith, J. Scott; Aronstein, David
2012-01-01
This innovation is a variation of a simulated-annealing optimization algorithm that uses a recursive-branching structure to parallelize the search of a parameter space for the globally optimal solution to an objective. The algorithm has been demonstrated to be more effective at searching a parameter space than traditional simulated-annealing methods for a particular problem of interest, and it can readily be applied to a wide variety of optimization problems, including those with a parameter space having both discrete-value parameters (combinatorial) and continuous-variable parameters. It can take the place of a conventional simulated- annealing, Monte-Carlo, or random- walk algorithm. In a conventional simulated-annealing (SA) algorithm, a starting configuration is randomly selected within the parameter space. The algorithm randomly selects another configuration from the parameter space and evaluates the objective function for that configuration. If the objective function value is better than the previous value, the new configuration is adopted as the new point of interest in the parameter space. If the objective function value is worse than the previous value, the new configuration may be adopted, with a probability determined by a temperature parameter, used in analogy to annealing in metals. As the optimization continues, the region of the parameter space from which new configurations can be selected shrinks, and in conjunction with lowering the annealing temperature (and thus lowering the probability for adopting configurations in parameter space with worse objective functions), the algorithm can converge on the globally optimal configuration. The Recursive Branching Simulated Annealing (RBSA) algorithm shares some features with the SA algorithm, notably including the basic principles that a starting configuration is randomly selected from within the parameter space, the algorithm tests other configurations with the goal of finding the globally optimal
Directory of Open Access Journals (Sweden)
Eggenberger P
2015-10-01
Full Text Available Patrick Eggenberger,1 Nathan Theill,2,3 Stefan Holenstein,1 Vera Schumacher,4,5 Eling D de Bruin1,6,7 1Department of Health Sciences and Technology, Institute of Human Movement Sciences and Sport, ETH Zurich, 2Division of Psychiatry Research, 3Center for Gerontology, 4Department of Gerontopsychology and Gerontology, 5University Research Priority Program “Dynamics of Healthy Aging”, University of Zurich, Zurich, Switzerland; 6Department of Epidemiology, CAPHRI School for Public Health and Primary Care, 7Centre for Evidence Based Physiotherapy, Maastricht University, Maastricht, the Netherlands Background: About one-third of people older than 65 years fall at least once a year. Physical exercise has been previously demonstrated to improve gait, enhance physical fitness, and prevent falls. Nonetheless, the addition of cognitive training components may potentially increase these effects, since cognitive impairment is related to gait irregularities and fall risk. We hypothesized that simultaneous cognitive–physical training would lead to greater improvements in dual-task (DT gait compared to exclusive physical training.Methods: Elderly persons older than 70 years and without cognitive impairment were randomly assigned to the following groups: 1 virtual reality video game dancing (DANCE, 2 treadmill walking with simultaneous verbal memory training (MEMORY, or 3 treadmill walking (PHYS. Each program was complemented with strength and balance exercises. Two 1-hour training sessions per week over 6 months were applied. Gait variables, functional fitness (Short Physical Performance Battery, 6-minute walk, and fall frequencies were assessed at baseline, after 3 months and 6 months, and at 1-year follow-up. Multiple regression analyses with planned comparisons were carried out.Results: Eighty-nine participants were randomized to three groups initially; 71 completed the training and 47 were available at 1-year follow-up. DANCE/MEMORY showed a
Institute of Scientific and Technical Information of China (English)
王汉兴; 赵飞; 卢金余
2006-01-01
In this paper, we investigate Galton-Watson branching processes in random environments. In the case where the environmental process is a Markov chain which is positive recurrent or has a transition matrix Q (θ,α) such that supθ Q (θ,α)> 0 for some α, we prove that the model has the asymptotic behavior being similar to that of Galton-Watson branching processes. In other case where the environments are non-stationary independent, the sufficient conditions are obtained for certain extinction and uncertain extinction for the model.
Directory of Open Access Journals (Sweden)
Howatson Glyn
2012-07-01
Full Text Available Abstract Background It is well documented that exercise-induced muscle damage (EIMD decreases muscle function and causes soreness and discomfort. Branched-chain amino acid (BCAA supplementation has been shown to increase protein synthesis and decrease muscle protein breakdown, however, the effects of BCAAs on recovery from damaging resistance training are unclear. Therefore, the aim of this study was to examine the effects of a BCAA supplementation on markers of muscle damage elicited via a sport specific bout of damaging exercise in trained volunteers. Methods Twelve males (mean ± SD age, 23 ± 2 y; stature, 178.3 ± 3.6 cm and body mass, 79.6 ± 8.4 kg were randomly assigned to a supplement (n = 6 or placebo (n = 6 group. The damaging exercise consisted of 100 consecutive drop-jumps. Creatine kinase (CK, maximal voluntary contraction (MVC, muscle soreness (DOMS, vertical jump (VJ, thigh circumference (TC and calf circumference (CC were measured as markers of muscle damage. All variables were measured immediately before the damaging exercise and at 24, 48, 72 and 96 h post-exercise. Results A significant time effect was seen for all variables. There were significant group effects showing a reduction in CK efflux and muscle soreness in the BCAA group compared to the placebo (P Conclusion The present study has shown that BCAA administered before and following damaging resistance exercise reduces indices of muscle damage and accelerates recovery in resistance-trained males. It seems likely that BCAA provided greater bioavailablity of substrate to improve protein synthesis and thereby the extent of secondary muscle damage associated with strenuous resistance exercise. Clinical Trial Registration Number: NCT01529281.
Kocur, Piotr; Wiernicka, Marzena; Wilski, Maciej; Kaminska, Ewa; Furmaniuk, Lech; Maslowska, Marta Flis; Lewandowski, Jacek
2015-12-01
[Purpose] To assess the effect of 12-weeks Nordic walking training on gait parameters and some elements of postural control. [Subjects and Methods] Sixty-seven women aged 65 to 74 years were enrolled in this study. The subjects were divided into a Nordic Walking group (12 weeks of Nordic walking training, 3 times a week for 75 minutes) and a control group. In both study groups, a set of functional tests were conducted at the beginning and at the end of the study: the Forward Reach Test (FRT) and the Upward Reach Test (URT) on a stabilometric platform, and the analysis of gait parameters on a treadmill. [Results] The NW group showed improvements in: the range of reach in the FRT test and the URT test in compared to the control group. The length of the gait cycle and gait cycle frequency also showed changes in the NW group compared to the control group. [Conclusion] A 12-week NW training program had a positive impact on selected gait parameters and may improve the postural control of women aged over 65 according to the results selected functional tests.
Cellular telephone use during free-living walking significantly reduces average walking speed
Jacob E. Barkley; Lepp, Andrew
2016-01-01
Background Cellular telephone (cell phone) use decreases walking speed in controlled laboratory experiments and there is an inverse relationship between free-living walking speed and heart failure risk. The purpose of this study was to examine the impact of cell phone use on walking speed in a free-living environment. Methods Subjects (n = 1142) were randomly observed walking on a 50 m University campus walkway. The time it took each subject to walk 50 m was recorded and subjects were coded i...
随机环境中分枝过程的暂留性与灭绝概率的性质%Some Properties of Branching Processes in Random Environments
Institute of Scientific and Technical Information of China (English)
胡杨利; 杨向群
2012-01-01
从随机环境中分枝过程是随机环境中马氏链入手,讨论了随机环境中分枝过程状态的暂留性、常返性以及灭绝概率的性质.%Based on the fact that branching processes in random environments are Markovian chains in random environments, transience and recurrence of the states are discussed and some properties of the extinction probability are obtained.
Institute of Scientific and Technical Information of China (English)
刘洪毓
2002-01-01
Many people dislike walking to the bank and standing in long lines. They are dissatisfied with their bank's limited hours, too. They want to do some banking at night, and on weekends. For such people, their problems may soon be over.
One dimensional quantum walk with unitary noise
Shapira, D; Bracken, A J; Hackett, M; Shapira, Daniel; Biham, Ofer; Hackett, Michelle
2003-01-01
The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution Pt(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t) ~ t, unlike the classical random walk for which sigma(t) ~ sqrt{t}. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be T ~ alpha^(-2) where alpha is the standard deviation of the noise.
Institute of Scientific and Technical Information of China (English)
信怀义
2016-01-01
Web topics are noisy.Users can boost the topic by two ways when they browsing the Internet - add related web pages into the topic and delete unrelated contents from the topic,this process is called web topic boosting.In this paper,we proposed a heterogeneous graph based random walk model to simulate web topic boosting.In this model,heterogeneous graph simulates relationships among web contents and random walk simulates the behavior of web browsing.The random walking produces a probability ranking of objects to a given noisy topic,buy which we can de-termine the boosted topic.The results demonstrate that our model simulates web topic boosting process correctly and completely.In addition,the user studies also demonstrate the effectiveness of this model.%网络话题充满噪声,用户在浏览网络的过程中,逐步添加关联性高的网页到话题中,并从话题中删除关联性低的网页,从而形成纯净话题,这就是话题优化的过程.基于此,本文提出一种基于异质图随机游走的模型来模拟用户优化话题的过程,异质图模拟网络内容的关联性,而随机游走模拟用户浏览网络的过程.对于一个网络话题,该模型能够计算出所有网页属于该话题的概率,根据概率分布就能够判断真正属于该话题的网页,从而模拟网络话题优化的过程.仿真结果证实,本文提出的模型可以准确、完整的模拟话题的优化.而通过用户对优化结果的主观评价,同样证实了模型的有效性.
Maximum of the Characteristic Polynomial of Random Unitary Matrices
Arguin, Louis-Pierre; Belius, David; Bourgade, Paul
2016-09-01
It was recently conjectured by Fyodorov, Hiary and Keating that the maximum of the characteristic polynomial on the unit circle of a {N× N} random unitary matrix sampled from the Haar measure grows like {CN/(log N)^{3/4}} for some random variable C. In this paper, we verify the leading order of this conjecture, that is, we prove that with high probability the maximum lies in the range {[N^{1 - ɛ},N^{1 + ɛ}]} , for arbitrarily small ɛ. The method is based on identifying an approximate branching random walk in the Fourier decomposition of the characteristic polynomial, and uses techniques developed to describe the extremes of branching random walks and of other log-correlated random fields. A key technical input is the asymptotic analysis of Toeplitz determinants with dimension-dependent symbols. The original argument for these asymptotics followed the general idea that the statistical mechanics of 1/f-noise random energy models is governed by a freezing transition. We also prove the conjectured freezing of the free energy for random unitary matrices.
DeepWalk: Online Learning of Social Representations
Perozzi, Bryan; Al-Rfou, Rami; Skiena, Steven
2014-01-01
We present DeepWalk, a novel approach for learning latent representations of vertices in a network. These latent representations encode social relations in a continuous vector space, which is easily exploited by statistical models. DeepWalk generalizes recent advancements in language modeling and unsupervised feature learning (or deep learning) from sequences of words to graphs. DeepWalk uses local information obtained from truncated random walks to learn latent representations by treating wa...
Institute of Scientific and Technical Information of China (English)
许健才; 张良均; 余燕团
2016-01-01
在图像分割中，针对 FCM 算法存在聚类数目需要预先给定、收敛速度慢等缺点，本文把快速模糊 C 均值聚类算法和随机游走算法相结合，具体方法为先采用快速模糊 C 均值聚类算法对图像进行预分割，以便获得聚类中心的位置，然后将该中心作为随机游走的种子点，再进行图像分割，实验结果得到了较为满意的预期效果，证明该方法是可行的。本文的研究为快速 FCM 实现自适应性和开发图形图像预处理系统提供了技术支持与理论依据。%As far as image segmentation, the defeat of the number of clusters for FCM algorithm is reeded to be improued. In this paper, the fast fuzzy C-means clustering and random walk algorithm are combined to solve the problem of image segmentation. Firstly, the fast FCM for image pre-segmentation to obtain the number of clusters and cluster central location as the seed points of random walk firstly. Then, for image segmentation, experimental results show that this method is feasible, and get a more satisfactory desired purpose. Results of this study achieve self-adaptive and fast FCM develop graphical image preprocessing system provides technical support and theoretical basis.
Willey, David
2010-01-01
This article gives a brief history of fire-walking and then deals with the physics behind fire-walking. The author has performed approximately 50 fire-walks, took the data for the world's hottest fire-walk and was, at one time, a world record holder for the longest fire-walk (www.dwilley.com/HDATLTW/Record_Making_Firewalks.html). He currently…
Chen, I-Fan; Wu, Huey-June; Chen, Chung-Yu; Chou, Kuei-Ming; Chang, Chen-Kang
2016-01-01
Background The decline in cognitive performance has been shown after fatiguing exercise. Branched-chain amino acids (BCAA) have been suggested to alleviate exercise-induced central fatigue. Arginine and citrulline could remove the excess NH3 accumulation accompanied with BCAA supplementation by increasing nitric oxide biosynthesis and/or urea cycle. The purpose of this study is to investigate the effect of the combined supplementation of BCAA, arginine, and citrulline on central fatigue after...
Efficient quantum walk on a quantum processor
Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L.; Wang, Jingbo B.; Matthews, Jonathan C. F.
2016-05-01
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor.
Walk modularity and community structure in networks
Mehrle, David; Harkin, Anthony
2014-01-01
Modularity maximization has been one of the most widely used approaches in the last decade for discovering community structure in networks of practical interest in biology, computing, social science, statistical mechanics, and more. Modularity is a quality function that measures the difference between the number of edges found within clusters minus the number of edges one would statistically expect to find based on random chance. We present a natural generalization of modularity based on the difference between the actual and expected number of walks within clusters, which we call walk-modularity. Walk-modularity can be expressed in matrix form, and community detection can be performed by finding leading eigenvectors of the walk-modularity matrix. We demonstrate community detection on both synthetic and real-world networks and find that walk-modularity maximization returns significantly improved results compared to traditional modularity maximization.
Efficient quantum walk on a quantum processor.
Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L; Wang, Jingbo B; Matthews, Jonathan C F
2016-01-01
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor. PMID:27146471
Non-Markovian decoherent quantum walks
Institute of Scientific and Technical Information of China (English)
Xue Peng; Zhang Yong-Sheng
2013-01-01
Quantum walks act in obviously different ways from their classical counterparts,but decoherence will lessen and close this gap between them.To understand this process,it is necessary to investigate the evolution of quantum walks under different decoherence situations.In this article,we study a non-Markovian decoherent quantum walk on a line.In a short time regime,the behavior of the walk deviates from both ideal quantum walks and classical random walks.The position variance as a measure of the quantum walk collapses and revives for a short time,and tends to have a linear relation with time.That is,the walker's behavior shows a diffusive spread over a long time limit,which is caused by non-Markovian dephasing affecting the quantum correlations between the quantum walker and his coin.We also study both quantum discord and measurement-induced disturbance as measures of the quantum correlations,and observe both collapse and revival in the short time regime,and the tendency to be zero in the long time limit.Therefore,quantum walks with non-Markovian decoherence tend to have diffusive spreading behavior over long time limits,while in the short time regime they oscillate between ballistic and diffusive spreading behavior,and the quantum correlation collapses and revives due to the memory effect.
Mason, Nick
2007-01-01
A generation ago, it was part of growing up for all kids when they biked or walked to school. But in the last 30 years, heavier traffic, wider roads and more dangerous intersections have made it riskier for students walking or pedaling. Today, fewer than 15 percent of kids bike or walk to school compared with more than 50 percent in 1969. In the…
Intra-limb coordination while walking is affected by cognitive load and walking speed.
Ghanavati, Tabassom; Salavati, Mahyar; Karimi, Noureddin; Negahban, Hossein; Ebrahimi Takamjani, Ismail; Mehravar, Mohammad; Hessam, Masumeh
2014-07-18
Knowledge about intra-limb coordination (ILC) during challenging walking conditions provides insight into the adaptability of central nervous system (CNS) for controlling human gait. We assessed the effects of cognitive load and speed on the pattern and variability of the ILC in young people during walking. Thirty healthy young people (19 female and 11 male) participated in this study. They were asked to perform 9 walking trials on a treadmill, including walking at three paces (preferred, slower and faster) either without a cognitive task (single-task walking) or while subtracting 1׳s or 3׳s from a random three-digit number (simple and complex dual-task walking, respectively). Deviation phase (DP) and mean absolute relative phase (MARP) values-indicators of variability and phase dynamic of ILC, respectively-were calculated using the data collected by a motion capture system. We used a two-way repeated measure analysis of variance for statistical analysis. The results showed that cognitive load had a significant main effect on DP of right shank-foot and thigh-shank, left shank-foot and pelvis-thigh (peffect of walking speed was significant on DP of all segments in each side and MARP of both thigh-shank and pelvis-thigh segments (pcognitive load and walking speed was only significant for MARP values of left shank-foot and right pelvis-thigh (pcognitive load and speed could significantly affect the ILC and variability and phase dynamic during walking. PMID:24861632
International Nuclear Information System (INIS)
Monte Carlo continuous time random walk simulation is used to study the effects of confinement on electron transport, in porous TiO2. In this work, we have introduced a columnar structure instead of the thick layer of porous TiO2 used as anode in conventional dye solar cells. Our simulation results show that electron diffusion coefficient in the proposed columnar structure is significantly higher than the diffusion coefficient in the conventional structure. It is shown that electron diffusion in the columnar structure depends both on the cross section area of the columns and the porosity of the structure. Also, we demonstrate that such enhanced electron diffusion can be realized in the columnar photo-electrodes with a cross sectional area of ∼1 μm2 and porosity of 55%, by a simple and low cost fabrication process. Our results open up a promising approach to achieve solar cells with higher efficiencies by engineering the photo-electrode structure
小世界网络中随机游走谈判者之间的命名演化博弈%Naming game between mobile agents randomly walking in small-world networks
Institute of Scientific and Technical Information of China (English)
陈光平; 张志远; 郝加波; 陈小波
2015-01-01
A model of naming game between mobile agents in small⁃world networks is proposed. It is found that the mobile velocity play an important role in the convergence time by investigating the phenomenon that the agents make random walk while they are playing naming⁃game. The relations of different names,total names and success rate with mobile velocity are investigated in detail. All of these results may be contributed to understanding the collective behavior of mobile agents,and the emergence and maintain of cooperative game as well.%提出一个在小世界网络中，移动谈判者之间命名博弈（Naming Game）模型，研究谈判者在进行命名博弈的同时进行随机游走，发现移动快慢对收敛的时间有重要的影响；还研究了不同词汇数、总词汇数和谈判成功率与谈判者运动的关系。这些研究有助于更好理解移动参与者的群体行为特征，也有助于理解参与者的合作演化行为的产生和维持。
A Lamperti type representation of Continuous-State Branching Processes with Immigration
Caballero, Ma Emilia; Bravo, Gerónimo Uribe
2010-01-01
Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we extend the Lamperti representation of continuous-state branching processes to allow immigration. The representation is obtained by solving a random ordinary differential equation defined by a pair of independent L\\'evy processes. Stability of the solutions is studied and gives, in particular, limit theorems (of a type previously studied by Grimvall, Kawazu and Watanabe, and Li) and a simulation scheme for continuous-state branching processes with immigration. We further apply our stability analysis to extend Pitman's limit theorem concerning Galton-Watson processes conditioned on total population size to more general offspring laws.
Winding angles of long lattice walks
Hammer, Yosi; Kantor, Yacov
2016-07-01
We study the winding angles of random and self-avoiding walks (SAWs) on square and cubic lattices with number of steps N ranging up to 107. We show that the mean square winding angle of random walks converges to the theoretical form when N → ∞. For self-avoiding walks on the square lattice, we show that the ratio /2 converges slowly to the Gaussian value 3. For self-avoiding walks on the cubic lattice, we find that the ratio /2 exhibits non-monotonic dependence on N and reaches a maximum of 3.73(1) for N ≈ 104. We show that to a good approximation, the square winding angle of a self-avoiding walk on the cubic lattice can be obtained from the summation of the square change in the winding angles of lnN independent segments of the walk, where the ith segment contains 2i steps. We find that the square winding angle of the ith segment increases approximately as i0.5, which leads to an increase of the total square winding angle proportional to (lnN)1.5.
Mechanical properties of branched actin filaments
Razbin, Mohammadhosein; Benetatos, Panayotis; Zippelius, Annette
2015-01-01
Cells moving on a two dimensional substrate generate motion by polymerizing actin filament networks inside a flat membrane protrusion. New filaments are generated by branching off existing ones, giving rise to branched network structures. We investigate the force-extension relation of branched filaments, grafted on an elastic structure at one end and pushing with the free ends against the leading edge cell membrane. Single filaments are modeled as worm-like chains, whose thermal bending fluctuations are restricted by the leading edge cell membrane, resulting in an effective force. Branching can increase the stiffness considerably; however the effect depends on branch point position and filament orientation, being most pronounced for intermediate tilt angles and intermediate branch point positions. We describe filament networks without cross-linkers to focus on the effect of branching. We use randomly positioned branch points, as generated in the process of treadmilling, and orientation distributions as measur...
Escape rates for rotor walk in Z^d
Florescu, Laura; Ganguly, Shirshendu; Levine, Lionel; Peres, Yuval
2013-01-01
Rotor walk is a deterministic analogue of random walk. We study its recurrence and transience properties on Z^d for the initial configuration of all rotors aligned. If n particles in turn perform rotor walks starting from the origin, we show that the number that escape (i.e., never return to the origin) is of order n in dimensions d>=3, and of order n/log(n) in dimension 2.
Explicit expression of the counting generating function for Gessel's walk
Kurkova, Irina
2009-01-01
We consider the so-called Gessel's walk, that is the planar random walk that is confined to the first quadrant and that can move in unit steps to the West, North-East, East and South-West. For this walk we make explicit the generating function of the number of paths starting at $(0,0)$ and ending at $(i,j)$ in time $k$.
DEFF Research Database (Denmark)
Vestergaard, Maria Quvang Harck; Olesen, Mette; Helmer, Pernille Falborg
2014-01-01
; Frumkin 2002). The term ‘walkability’ focuses on how the physical structures in the urban environment can promote walking, and how this potentially eases issues of public health and liveability in our cities (Krizek et al. 2009). However, the study of walking should not be reduced merely to the ‘hardware...... factors like lifestyle and life situation should be addressed in order to understand ‘walkability’ fully. The challenge is to approach issues linked to the ‘more-than representational’ (Thrift 2007; Vannini 2012) act of walking and thereby understand pedestrian behaviour in general, but also...... the individual perception of walking. This chapter exemplifies shows how a ‘more-than representational’ dimension can be added to the act of walking and open up for a more value-based discussion of walking, in this chapter exemplified in the Danish context. The chapter provides seven different cases of how...
DEFF Research Database (Denmark)
Nilsson, Niels Chr.
Recent technological advances may soon bring immersive virtual reality (IVR) out of the laboratory and into the homes of consumers. This means that IVR systems will be deployed in settings where the physical interaction space is very limited in size. If users wish to navigate virtual environments...... on foot, these spatial constraints are problematic since they make real walking infeasible. Walking-in-Place (WIP) techniques constitute a convenient and inexpensive approach to facilitating walking within virtual environments. This thesis focuses on the factors influencing the degree of perceived...... naturalness of WIP locomotion; i.e., the degree to which the user’s experience of walking through a virtual environment using WIP locomotion is mistakable for the experience of real walking. I take the degree of correspondence between the sensorimotor loops of real walking and WIP locomotion as my point...
A characterisation of superposable random measures
Maillard, Pascal
2011-01-01
Let $Z$ be a point process on $\\R$ and $T_\\alpha Z$ its translation by $\\alpha\\in\\R$. Let $Z'$ be an independent copy of $Z$. We say that $Z$ is \\emph{superposable}, if $T_\\alpha Z + T_\\beta Z'$ and $Z$ are equal in law for every $\\alpha,\\beta\\in\\R$, such that $\\e^\\alpha + \\e^\\beta = 1.$ We prove a characterisation of superposable point processes in terms of decorated Poisson processes, which was conjectured by Brunet and Derrida [A branching random walk seen from the tip, 2010, \\url{http://arxiv.org/abs/1011.4864v1}]. We further prove a generalisation to random measures.
Institute of Scientific and Technical Information of China (English)
金弟; 杨博; 刘杰; 刘大有; 何东晓
2012-01-01
网络簇结构是复杂网络最普遍和最重要的拓扑属性之一,网络聚类问题就是要找出给定网络中的所有类簇.有很多实际应用问题可被建模成网络聚类问题.尽管目前已有许多网络聚类方法被提出,但如何进一步提高聚类精度,特别是在没有先验知识(如网络簇个数)的情况下如何发现合理的网络簇结构,仍是一个未能很好解决的难题.针对该问题,在马尔可夫随机游走思想的启发下,从仿生角度出发提出一种全新的网络聚类算法——基于随机游走的蚁群算法RWACO.该算法将蚁群算法的框架作为RWACO的基本框架,对于每一代,以马尔可夫随机游走模型作为启发式规则；基于集成学习思想,将蚂蚁的局部解融合为全局解,并用其更新信息素矩阵.通过“强化簇内连接,弱化簇间连接”这一进化策略,使网络簇结构逐渐地呈现出来.实验结果表明,对一些典型的计算机生成网络和真实网络,该算法能够较准确地探测出网络的真实类簇数与一些有代表性的算法相比,具有较高的聚类精度.%Community structure is one of the most important topological properties in complex networks. The network clustering problem (NCP) refers to the detection of network community structures, and many practical problems can be modeled as NCPs. So far, lots of network clustering algorithms have been proposed. However, further improvements in the clustering accuracy, especially when discovering reasonable community structure without prior knowledge, still constitute an open problem. Building on Markov random walks, the paper addresses this problem with a novel ant colony optimization strategy, named as RWACO, which improves prior results on the NCPs and does not require knowledge of the number of communities present on a given network. The framework of ant colony optimization is taken as the basic framework in the RWACO algorithm. In each iteration, a Markov
Quantum Walks for Computer Scientists
Venegas-Andraca, Salvador
2008-01-01
Quantum computation, one of the latest joint ventures between physics and the theory of computation, is a scientific field whose main goals include the development of hardware and algorithms based on the quantum mechanical properties of those physical systems used to implement such algorithms. Solving difficult tasks (for example, the Satisfiability Problem and other NP-complete problems) requires the development of sophisticated algorithms, many of which employ stochastic processes as their mathematical basis. Discrete random walks are a popular choice among those stochastic processes. Inspir
Energy Technology Data Exchange (ETDEWEB)
Munoz-Cobo, Jose L., E-mail: jlcobos@iqn.upv.es [Instituto de Ingenieria Energetica, Universidad Politecnica de Valencia, Valencia (Spain); Chiva, Sergio [Department of Mechanical Engineering and Construction, Universitat Jaume I, Castellon (Spain); Essa, Mohamed Ali Abd El Aziz [Instituto de Ingenieria Energetica, Universidad Politecnica de Valencia, Valencia (Spain); Mendes, Santos [Facultad de Ingenieria Mecanica y Electrica, Universidad Autonoma de Nuevo Leon (Mexico)
2012-01-15
Highlights: Black-Right-Pointing-Pointer We have simulated bubbly flow in vertical pipes by coupling a Lagrangian model to an Eulerian one, and to a 3D random walk model. Black-Right-Pointing-Pointer A set of experiments in a vertical column with isothermal co-current two phase flow have been performed and used to validate the previous model. Black-Right-Pointing-Pointer We have investigated the influence of the turbulence induced by the bubbles on the results. Black-Right-Pointing-Pointer Comparison of experimental and computed results has been performed for different boundary conditions. - Abstract: A set of two phase flow experiments for different conditions ranging from bubbly flow to cap/slug flow have been performed under isothermal concurrent upward air-water flow conditions in a vertical column of 3 m height. Special attention in these experiments was devoted to the transition from bubbly to cap/slug flow. The interfacial velocity of the bubbles and the void fraction distribution was obtained using 2 and 4 sensors conductivity probes. Numerical simulations of these experiments for bubbly flow conditions were performed by coupling a Lagrangian code with an Eulerian one. The first one tracks the 3D motion of the individual bubbles in cylindrical coordinates (r, {phi}, z) inside the fluid field under the action of the following forces: buoyancy, drag, lift, wall lubrication. Also we have incorporated a 3D stochastic differential equation model to account for the random motion of the individual bubbles in the turbulent velocity field of the carrier liquid. Also we have considered the deformations undergone by the bubbles when they touch the walls of the pipe and are compressed until they rebound. The velocity and turbulence fields of the liquid phase were computed by solving the time dependent conservation equations in its Reynolds Averaged Transport Equation form (RANS). The turbulent kinetic energy k, and the dissipation rate {epsilon} transport equations
Exact asymptotics of the freezing transition of a logarithmically correlated random energy model
Webb, Christian
2011-01-01
We consider a logarithmically correlated random energy model, namely a model for directed polymers on a Cayley tree, which was introduced by Derrida and Spohn. We prove asymptotic properties of a generating function of the partition function of the model by studying a discrete time analogy of the KPP-equation - thus translating Bramson's work on the KPP-equation into a discrete time case. We also discuss connections to extreme value statistics of a branching random walk and a rescaled multiplicative cascade measure beyond the critical point.
Relativistic diffusion processes and random walk models
Dunkel, Jörn; Talkner, Peter; Hänggi, Peter
2006-01-01
The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (non-continuous) d...
A random walk through fractal dimensions
Kaye, Brian H
2008-01-01
Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science.From reviews of the first edition:''...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems.'' MRS Bulletin
A Random Walk: Stumbling across Connections
Wasserman, Nicholas H.
2015-01-01
Finding and designing tasks that allow for students to make connections among mathematical ideas is important for mathematics educators. One such task, which affords students the opportunity to make connections and engage with significant mathematical ideas through a variety of problem-solving approaches, is described in this article. Three…
Random walk of a "drunk company"
Semenov, A. G.
2016-05-01
We study the collective behavior of a system of Brownian agents each of which moves orienting itself to the group as a whole. This system is the simplest model of the motion of a "united drunk company." For such a system, we use the functional integration technique to calculate the probability of transition from one point to another and to determine the time dependence of the probability density to find a member of the "drunk company" near a given point. It turns out that the system exhibits an interesting collective behavior at large times and this behavior cannot be described by the simplest mean-field-type approximation. We also obtain an exact solution in the case where one of the agents is "sober" and moves along a given trajectory. The obtained results are used to discuss whether such systems can be described by different theoretical approaches.
Currow David C; Everett Bronwyn; Salamonson Yenna; Denniss Robert; Zecchin Robert; Newton Phillip J; Du Hui Y; Macdonald Peter S; Davidson Patricia M
2011-01-01
Abstract Background Chronic heart failure (CHF) is a chronic debilitating condition with economic consequences, mostly because of frequent hospitalisations. Physical activity and adequate self-management capacity are important risk reduction strategies in the management of CHF. The Home-Heart-Walk is a self-monitoring intervention. This model of intervention has adapted the 6-minute walk test as a home-based activity that is self-administered and can be used for monitoring physical functional...
Du, Hui Y; Newton, Phillip J.; Zecchin, Robert; Denniss, Robert; Salamonson, Yenna; Everett, Bronwyn; Currow, David C; Macdonald, Peter S; Davidson, Patricia M
2011-01-01
Background Chronic heart failure (CHF) is a chronic debilitating condition with economic consequences, mostly because of frequent hospitalisations. Physical activity and adequate self-management capacity are important risk reduction strategies in the management of CHF. The Home-Heart-Walk is a self-monitoring intervention. This model of intervention has adapted the 6-minute walk test as a home-based activity that is self-administered and can be used for monitoring physical functional capacity...
Centers for Disease Control (CDC) Podcasts
2012-07-31
This podcast is based on the August 2012 CDC Vital Signs report. While more adults are walking, only half get the recommended amount of physical activity. Listen to learn how communities, employers, and individuals may help increase walking. Created: 7/31/2012 by Centers for Disease Control and Prevention (CDC). Date Released: 8/7/2012.
Dertien, Edwin
2006-01-01
This paper describes the design and construction of Dribbel, a passivity-based walking robot. Dribbel has been designed and built at the Control Engineering group of the University of Twente. This paper focuses on the practical side: the design approach, construction, electronics, and software design. After a short introduction of dynamic walking, the design process, starting with simulation, is discussed.
Adaptive walks on correlated fitness landscapes with heterogeneous connectivities
International Nuclear Information System (INIS)
We propose a model for studying the statistical properties of adaptive walks on correlated fitness landscapes which are established in genotype spaces of complex structure. The fitness distribution on the genotype space follows either the bivariate Gaussian distribution or the bivariate exponential distribution. In both cases the degree of correlation of the fitness landscape can be tuned by using a single parameter. To perform the adaptive walks two distinct rules are applied: the random adaptation walk (RAW) and the gradient adaptation walk (GAW). While for the RAW the mean walk length, L-bar, is a monotonic increasing function of the connectivity of the genotype space, for the GAW L-bar is a one-humped function. The RAW produces longer adaptive walks compared to the GAW, though its performance is slightly poorer and thereby the local maxima reached by the GAW algorithm are usually closer to the global optimum of the fitness landscape
Kokshenev, V B
2004-01-01
The problem of biped locomotion at steady speeds is discussed through the Lagrangian formulation developed for velocity-dependent, body driving forces. Human walking on a level surface is analyzed in terms of the data on the resultant ground-reaction force and the external work. It is shown that the trajectory of the human center of mass is due to a superposition of its rectilinear motion with a given speed V and a backward rotation along a shortened hypocycloid. A stiff-to-compliant crossover between walking gaits is established at mid speeds, which separate slow walking from fast walking, limited by V_{\\max}=3.4 m/s. Key words: locomotion, bipedalism, human, biomechanics, walking.
Directory of Open Access Journals (Sweden)
Juliana M. Rodrigues-Baroni
2014-12-01
Full Text Available OBJECTIVE: To systematically review the available evidence on the efficacy of walking training associated with virtual reality-based training in patients with stroke. The specific questions were: Is walking training associated with virtual reality-based training effective in increasing walking speed after stroke? Is this type of intervention more effective in increasing walking speed, than non-virtual reality-based walking interventions? METHOD: A systematic review with meta-analysis of randomized clinical trials was conducted. Participants were adults with chronic stroke and the experimental intervention was walking training associated with virtual reality-based training to increase walking speed. The outcome data regarding walking speed were extracted from the eligible trials and were combined using a meta-analysis approach. RESULTS: Seven trials representing eight comparisons were included in this systematic review. Overall, the virtual reality-based training increased walking speed by 0.17 m/s (IC 95% 0.08 to 0.26, compared with placebo/nothing or non-walking interventions. In addition, the virtual reality-based training increased walking speed by 0.15 m/s (IC 95% 0.05 to 0.24, compared with non-virtual reality walking interventions. CONCLUSIONS: This review provided evidence that walking training associated with virtual reality-based training was effective in increasing walking speed after stroke, and resulted in better results than non-virtual reality interventions.
One-dimensional quantum walk with unitary noise
International Nuclear Information System (INIS)
The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution Pt(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, σ(t) scales as σ(t)∼t, unlike the classical random walk for which σ(t)∼√(t). It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be T∼α-2, where α is the standard deviation of the noise
Quantum walk coherences on a dynamical percolation graph
Elster, Fabian; Barkhofen, Sonja; Nitsche, Thomas; Novotný, Jaroslav; Gábris, Aurél; Jex, Igor; Silberhorn, Christine
2015-08-01
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In particular, quantum walks on percolation structures constitute an attractive platform for studying open system dynamics of random media. Here, we present an implementation of quantum walks differing from the previous experiments by achieving dynamical control of the underlying graph structure. We demonstrate the evolution of an optical time-multiplexed quantum walk over six double steps, revealing the intricate interplay between the internal and external degrees of freedom. The observation of clear non-Markovian signatures in the coin space testifies the high coherence of the implementation and the extraordinary degree of control of all system parameters. Our work is the proof-of-principle experiment of a quantum walk on a dynamical percolation graph, paving the way towards complex simulation of quantum transport in random media.
Derrida, Bernard; Meerson, Baruch; Sasorov, Pavel V
2016-04-01
Consider a one-dimensional branching Brownian motion and rescale the coordinate and time so that the rates of branching and diffusion are both equal to 1. If X_{1}(t) is the position of the rightmost particle of the branching Brownian motion at time t, the empirical velocity c of this rightmost particle is defined as c=X_{1}(t)/t. Using the Fisher-Kolmogorov-Petrovsky-Piscounov equation, we evaluate the probability distribution P(c,t) of this empirical velocity c in the long-time t limit for c>2. It is already known that, for a single seed particle, P(c,t)∼exp[-(c^{2}/4-1)t] up to a prefactor that can depend on c and t. Here we show how to determine this prefactor. The result can be easily generalized to the case of multiple seed particles and to branching random walks associated with other traveling-wave equations. PMID:27176286
Park, Seong Doo; Yu, Seong Hun
2015-01-01
[Purpose] This study examined Nordic walking as an exercise intervention for the elderly with depression. [Subjects] Twenty-four patients who were diagnosed with depression were randomly selected and divided into two groups, an experimental group which performed Nordic walking, and a control group, which performed normal walking. [Methods] Both groups practiced their respective walking exercise for 50 minutes per day, three times a week for eight weeks. To compare the effects of the intervent...
A Tag Ranking Method Based on HITS and Random Walk%一种基于HITS和随机跳转的网页标签排序方法
Institute of Scientific and Technical Information of China (English)
汪兆鹏; 胡侠; 倪宁; 王灿
2011-01-01
Web 2.0应用的兴起,推进了情报学科由"文献组织"向"知识组织"演化.网页标签作为重要的Web 2 0应用之一,已经成为大众组织知识的常用途径.然而,现有的标签排序方法难以有效满足知识组织的需求.本文在三核协同标签模型的基础上,充分考虑标签和用户、标签和标签、标签和文档之间的关系,提出了一种结合HITS和随机跳转的标签排序方法.该方法利用高质量标签和高质量用户之间的相互加强关系,根据标签之间的相似性来找出高质量相关标签,有效提高标签排序的质量.在Delicious数据集上的实验结果表明,该方法能较大提高标签排序的准确度.%With the rise of Web 2. 0 applications, a new trend in information science, namely the evolution from "organizing document" to "organizing knowledge" , is looming on the horizon. One of' important Web 2. 0 applications,social tag, is making this trend a reality by adding meaningful annotations to Web pages. However, existing tag ranking methods are not efficient in knowledge organization. To improve tag ranking performance , this paper proposes a new ranking algorithm by utilizing relationships among users, tags and Web documents in a tripartite collaborative tagging model. By combining HITS and random walk, we effectively exploit the mutual reinforcement between quality users and quality tags and retrieve related tags by measuring similarity between tags. Experimental results on Delicious dataset demonstrate the effectiveness of our algorithm.
Institute of Scientific and Technical Information of China (English)
刘方鑫; 何明; 刘光云; 康凯
2015-01-01
The energy of sensors is limited and the performance of Underwater Acoustic Sensor Networks(UASNs) descends by complex marine environment. These factors restrict promoting of application of UASNs into monitoring the marine environment and developing the marine resources. In order to solve the problems of the imbalance of data trans-mission load and low fault-tolerance of UASNs, the characterization of dynamic behaviors of data transmission of UASNs has been quantitatively curved. Some reasons of sensor nodes failure in complex marine environment have been analyzed. The evolution model of network based on cluster structure is established. A fault-tolerance mechanism of random walk is proposed. It would improve the fault-tolerance and extend the life cycle of UASNs. The simulation results verify the ratio-nality and validity of the model. The research results show that the mechanism can reveal the general characterization of dynamic behaviors and the law of the UASNs.%水下传感器节点能量有限、复杂海洋环境影响网络性能下降等因素,制约了水声传感器网络在海洋资源开发、海洋监测等方面的应用推广.为解决水声传感器网络的数据传输负载不均衡、容错能力低等问题,刻画水声传感器网络传播动力学特性,分析复杂海洋环境中传感器节点失效原因,建立了簇结构网络演化模型,提出了一种随机游走容错机制,以提高水声传感器网络容错性和延长其生命周期.仿真实验验证了该模型的合理性和有效性,实验结果表明该机制能揭示水下传感器网络中存在的普遍动力学特性和规律.
Institute of Scientific and Technical Information of China (English)
史丽萍; 唐书林; 刘强; 苑婧婷
2012-01-01
Considering the different perception ability for quality information by different customers, the paper argued "enthalpy" in physics, defined the fluctuation of customs' perception value caused by quality information as enthalpy change of quality information transmission, and that enthalpy change of quality information was the key indicator of describing quality evolution. The paper adopted random walk model to establish enthalpy change model of quality different times, further discovered the time and space of enthalpy change. Research results indicated that enthalpy change of quality information transmission obeyed Gaussian distribution, whose convergence was proportional to perception ability of quality information by customer. Positive enthalpy change could increase customer' s perception value, which would purchase desire; negative enthalpy change would cause "enthalpy black hole" of customer' s perception value, which would betoken the occurrence of quality crisis. Comparing the enthalpy and price of different times Could identify the development stage and affecting region of quality crisis, which would provide distinguishing basis for enterprise decision.%从顾客对质量信息的感知能力差异出发,本文认为质量信息的传递会导致顾客感知价值呈现波动性,因此引入物理学中"焓"的概念,将因质量信息引起顾客感知价值的波动定义为"质量信息传递的焓变",认为质量信息的焓变是描述质量演变的关键性指标.本文利用随机游走理论建立了质量信息传递的焓变模型来描述同一时间不同顾客、同一顾客不同时间的焓,发现焓变的时间和空间.研究结果表明质量信息传递的焓变服从高斯分布,其收敛性跟顾客对质量信息的感知能力成正比.正焓变会增加顾客感知价值,提升购买欲望;负焓变会使顾客感知价值出现"焓黑洞",预示着质量危机的发生.对比不同时刻的焓和价格可以识别出质量危机
基于随机游走的大容量固态硬盘磨损均衡算法%A Random-Walk Based Wear-Leveling Algorithm for Large-Capacity SSDs
Institute of Scientific and Technical Information of China (English)
赵鹏; 白石
2012-01-01
Large-capacity flash based SSD (Solid-state disk) has the potential to become the storage system alternative in the future. It has many advantages: non-volatility, low-power con-sumption and shock resistance and so on. However, reliability is still a critical problem when using NAND flash memory. Every block of NAND flash memory has a limited number of write/ erase cycles, after the limited number, the data that keep in the block become unreliable. Many wear-leveling algorithms have been proposed to solve the reliability problem. But with the capaci-ty of SSD increases, these algorithms always need more and more DRAM capacity. We propose a random-walk based wear-leveling algorithm for large-capacity SSD that can obviously reduce memory consumption (only 15. 6% DRAM space compared to BET algorithm) for storing wear-ing information and achieve the same performance compare with other algorithms.%基于闪存的大容量固态硬盘(SSD)能够在未来取代磁盘.它有很多优点,包括非易失性、低能耗、抗震性强等.然而,基于NAND闪存的存储块自身存在有限的擦除重写次数的问题一直影响着它的广泛应用.当闪存芯片达到擦除重写的限制次数后,存储块上的数据就会变得不可靠.目前研究者们已经提出了一些磨损均衡算法来解决这个问题.但当固态硬盘的存储容量不断增大后,这些算法需要越来越多的内存容量来保证运行.文中提出一种基于随机游走的磨损均衡算法来应用在大容量的固态硬盘上,该算法能够很大程度地减少内存消耗.实验表明所需内存容量仅为BET算法的15.6％,与此同时磨损均衡的性能并没有降低.
Gallesco, Christophe; Popov, Serguei; Vachkovskaia, Marina
2010-01-01
A spider consists of several, say $N$, particles. Particles can jump independently according to a random walk if the movement does not violate some given restriction rules. If the movement violates a rule it is not carried out. We consider random walk in random environment (RWRE) on $\\Z$ as underlying random walk. We suppose the environment $\\omega=(\\omega_x)_{x \\in \\Z}$ to be elliptic, with positive drift and nestling, so that there exists a unique positive constant $\\kappa$ such that $\\E[((1-\\omega_0)/\\omega_0)^{\\kappa}]=1$. The restriction rules are kept very general; we only assume transitivity and irreducibility of the spider. The main result is that the speed of a spider is positive if $\\kappa/N>1$ and null if $\\kappa/N<1$. In particular, if $\\kappa/N <1$ a spider has null speed but the speed of a (single) RWRE is positive.
Photonics walking up a human hair
Zeng, Hao; Parmeggiani, Camilla; Martella, Daniele; Wasylczyk, Piotr; Burresi, Matteo; Wiersma, Diederik S.
2016-03-01
While animals have access to sugars as energy source, this option is generally not available to artificial machines and robots. Energy delivery is thus the bottleneck for creating independent robots and machines, especially on micro- and nano- meter length scales. We have found a way to produce polymeric nano-structures with local control over the molecular alignment, which allowed us to solve the above issue. By using a combination of polymers, of which part is optically sensitive, we can create complex functional structures with nanometer accuracy, responsive to light. In particular, this allowed us to realize a structure that can move autonomously over surfaces (it can "walk") using the environmental light as its energy source. The robot is only 60 μm in total length, thereby smaller than any known terrestrial walking species, and it is capable of random, directional walking and rotating on different dry surfaces.
Locomotor sequence learning in visually guided walking
DEFF Research Database (Denmark)
Choi, Julia T; Jensen, Peter; Nielsen, Jens Bo
2016-01-01
to modify step length from one trial to the next. Our sequence learning paradigm is derived from the serial reaction-time (SRT) task that has been used in upper limb studies. Both random and ordered sequences of step lengths were used to measure sequence-specific and sequence non-specific learning during......Voluntary limb modifications must be integrated with basic walking patterns during visually guided walking. Here we tested whether voluntary gait modifications can become more automatic with practice. We challenged walking control by presenting visual stepping targets that instructed subjects...... of step lengths over 300 training steps. Younger children (age 6-10 years, N = 8) have lower baseline performance, but their magnitude and rate of sequence learning was the same compared to older children (11-16 years, N = 10) and healthy adults. In addition, learning capacity may be more limited...
Fast Scramblers, Democratic Walks and Information Fields
Magan, Javier M
2015-01-01
We study a family of weighted random walks on complete graphs. These `democratic walks' turn out to be explicitly solvable, and we find the hierarchy window for which the characteristic time scale saturates the so-called fast scrambling conjecture. We show that these democratic walks describe well the properties of information spreading in systems in which every degree of freedom interacts with every other degree of freedom, such as Matrix or infinite range models. The argument is based on the analysis of suitably defined `Information fields' ($\\mathcal{I}$), which are shown to evolve stochastically towards stationarity due to unitarity of the microscopic model. The model implies that in democratic systems, stabilization of one subsystem is equivalent to global scrambling. We use these results to study scrambling of infalling perturbations in black hole backgrounds, and argue that the near horizon running coupling constants are connected to entanglement evolution of single particle perturbations in democratic...
Quantum graph walks I: mapping to quantum walks
Higuchi, Yusuke; Konno, Norio; Sato, Iwao; Segawa, Etsuo
2012-01-01
We clarify that coined quantum walk is determined by only the choice of local quantum coins. To do so, we characterize coined quantum walks on graph by disjoint Euler circles with respect to symmetric arcs. In this paper, we introduce a new class of coined quantum walk by a special choice of quantum coins determined by corresponding quantum graph, called quantum graph walk. We show that a stationary state of quantum graph walk describes the eigenfunction of the quantum graph.
Biomechanical analysis of rollator walking
DEFF Research Database (Denmark)
Alkjaer, T; Larsen, Peter K; Pedersen, Gitte;
2006-01-01
The rollator is a very popular walking aid. However, knowledge about how a rollator affects the walking patterns is limited. Thus, the purpose of the study was to investigate the biomechanical effects of walking with and without a rollator on the walking pattern in healthy subjects....