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
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.
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.
Dynamics on Multilayered Hyperbranched Fractals Through Continuous Time Random Walks
Volta, Antonio; Galiceanu, Mircea; Jurjiu, Aurel; Gallo, Tommaso; Gualandri, Luciano
We introduce a new method to generate three-dimensional structures, with mixed topologies. We focus on Multilayered Regular Hyperbranched Fractals (MRHF), three-dimensional networks constructed as a set of identical generalized Vicsek fractals, known as Regular Hyperbranched Fractals (RHF), layered on top of each other. Every node of any layer is directly connected only to copies of itself from nearest-neighbor layers. We found out that also for MRHF the eigenvalue spectrum of the connectivity matrix is determined through a semi-analytical method, which gives the opportunity to analyze very large structures. This fact allows us to study in detail the crossover effects of two basic topologies: linear, corresponding to the way we connect the layers and fractal due to the layers' topology. From the wealth of applications which depends on the eigenvalue spectrum we choose the return-to-the-origin probability. The results show the expected short-time and long-time behaviors. In the intermediate time domain we obtained two different power-law exponents: the first one is given by the combination linear-RHF, while the second one is peculiar either of a single RHF or of a single linear chain.
Bardou, F.
There exist important stochastic physical processes involving infinite mean waiting times. The mean divergence has dramatic consequences on the process dynamics. Fractal time random walks, a diffusion process, and subrecoil laser cooling, a concentration process, are two such processes that look qualitatively dissimilar. Yet, a unifying treatment of these two processes, which is the topic of this pedagogic paper, can be developed by combining renewal theory with the generalized central limit theorem. This approach enables to derive without technical difficulties the key physical properties and it emphasizes the role of the behaviour of sums with infinite means.
Random walks on random Koch curves
Energy Technology Data Exchange (ETDEWEB)
Seeger, S; Hoffmann, K H [Institut fuer Physik, Technische Universitaet, D-09107 Chemnitz (Germany); Essex, C [Department of Applied Mathematics, University of Western Ontario, London, ON N6A 5B7 (Canada)
2009-06-05
Diffusion processes in porous materials are often modeled as random walks on fractals. In order to capture the randomness of the materials random fractals are employed, which no longer show the deterministic self-similarity of regular fractals. Finding a continuum differential equation describing the diffusion on such fractals has been a long-standing goal, and we address the question of whether the concepts developed for regular fractals are still applicable. We use the random Koch curve as a convenient example as it provides certain technical advantages by its separation of time and space features. While some of the concepts developed for regular fractals can be used unaltered, others have to be modified. Based on the concept of fibers, we introduce ensemble-averaged density functions which produce a differentiable estimate of probability explicitly and compare it to random walk data.
Template-Directed Copolymerization, Random Walks along Disordered Tracks, and Fractals
Gaspard, Pierre
2016-12-01
In biology, template-directed copolymerization is the fundamental mechanism responsible for the synthesis of DNA, RNA, and proteins. More than 50 years have passed since the discovery of DNA structure and its role in coding genetic information. Yet, the kinetics and thermodynamics of information processing in DNA replication, transcription, and translation remain poorly understood. Challenging issues are the facts that DNA or RNA sequences constitute disordered media for the motion of polymerases or ribosomes while errors occur in copying the template. Here, it is shown that these issues can be addressed and sequence heterogeneity effects can be quantitatively understood within a framework revealing universal aspects of information processing at the molecular scale. In steady growth regimes, the local velocities of polymerases or ribosomes along the template are distributed as the continuous or fractal invariant set of a so-called iterated function system, which determines the copying error probabilities. The growth may become sublinear in time with a scaling exponent that can also be deduced from the iterated function system.
Odagaki, Takashi; Kasuya, Keisuke
2017-09-01
Using the Monte Carlo simulation, we investigate a memory-impaired self-avoiding walk on a square lattice in which a random walker marks each of sites visited with a given probability p and makes a random walk avoiding the marked sites. Namely, p = 0 and p = 1 correspond to the simple random walk and the self-avoiding walk, respectively. When p> 0, there is a finite probability that the walker is trapped. We show that the trap time distribution can well be fitted by Stacy's Weibull distribution b(a/b){a+1}/{b}[Γ({a+1}/{b})]-1x^a\\exp(-a/bx^b)} where a and b are fitting parameters depending on p. We also find that the mean trap time diverges at p = 0 as p- α with α = 1.89. In order to produce sufficient number of long walks, we exploit the pivot algorithm and obtain the mean square displacement and its Flory exponent ν(p) as functions of p. We find that the exponent determined for 1000 step walks interpolates both limits ν(0) for the simple random walk and ν(1) for the self-avoiding walk as [ ν(p) - ν(0) ] / [ ν(1) - ν(0) ] = pβ with β = 0.388 when p ≪ 0.1 and β = 0.0822 when p ≫ 0.1. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Directory of Open Access Journals (Sweden)
Shi Zhan
2011-03-01
Full Text Available These notes provide an elementary and self-contained introduction to branching random walks. Section 1 gives a brief overview of Galton–Watson trees, whereas Section 2 presents the classical law of large numbers for branching random walks. These two short sections are not exactly indispensable, but they introduce the idea of using size-biased trees, thus giving motivations and an avant-goût to the main part, Section 3, where branching random walks are studied from a deeper point of view, and are connected to the model of directed polymers on a tree. Tree-related random processes form a rich and exciting research subject. These notes cover only special topics. For a general account, we refer to the St-Flour lecture notes of Peres [47] and to the forthcoming book of Lyons and Peres [42], as well as to Duquesne and Le Gall [23] and Le Gall [37] for continuous random trees.
Random walks in a random environment
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the 'quenched' and the 'averaged' case. Keywords. Large deviations; random walks in a random environment. 1. Introduction. A random walk on Zd is a stochastic ...
Fractional random walk lattice dynamics
Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.
2017-02-01
We analyze time-discrete and time-continuous ‘fractional’ random walks on undirected regular networks with special focus on cubic periodic lattices in n = 1, 2, 3,.. dimensions. The fractional random walk dynamics is governed by a master equation involving fractional powers of Laplacian matrices {{L}\\fracα{2}}} where α =2 recovers the normal walk. First we demonstrate that the interval 0<α ≤slant 2 is admissible for the fractional random walk. We derive analytical expressions for the transition matrix of the fractional random walk and closely related the average return probabilities. We further obtain the fundamental matrix {{Z}(α )} , and the mean relaxation time (Kemeny constant) for the fractional random walk. The representation for the fundamental matrix {{Z}(α )} relates fractional random walks with normal random walks. We show that the matrix elements of the transition matrix of the fractional random walk exihibit for large cubic n-dimensional lattices a power law decay of an n-dimensional infinite space Riesz fractional derivative type indicating emergence of Lévy flights. As a further footprint of Lévy flights in the n-dimensional space, the transition matrix and return probabilities of the fractional random walk are dominated for large times t by slowly relaxing long-wave modes leading to a characteristic {{t}-\\frac{n{α}} -decay. It can be concluded that, due to long range moves of fractional random walk, a small world property is emerging increasing the efficiency to explore the lattice when instead of a normal random walk a fractional random walk is chosen.
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.
Evertsz, Carl Joseph Gabriel
1989-01-01
Laplacian Fractals are physical models for the fractal properties encountered in a selected group of natural phenomena. The basis models in this class are the Dialectric Breakdown Model and the closely related Diffusion- Limited Aggregration model and Laplacian Random Walks. A full mathematical
Fractal fluctuations in spatiotemporal variables when walking on a self-paced treadmill.
Choi, Jin-Seung; Kang, Dong-Won; Seo, Jeong-Woo; Tack, Gye-Rae
2017-12-08
This study investigated the fractal dynamic properties of stride time (ST), stride length (SL) and stride speed (SS) during walking on a self-paced treadmill (STM) in which the belt speed is automatically controlled by the walking speed. Twelve healthy young subjects participated in the study. The subjects walked at their preferred walking speed under four conditions: STM, STM with a metronome (STM+met), fixed-speed (conventional) treadmill (FTM), and FTM with a metronome (FTM+met). To compare the fractal dynamics between conditions, the mean, variability, and fractal dynamics of ST, SL, and SS were compared. Moreover, the relationship among the variables was examined under each walking condition using three types of surrogates. The mean values of all variables did not differ between the two treadmills, and the variability of all variables was generally larger for STM than for FTM. The use of a metronome resulted in a decrease in variability in ST and SS for all conditions. The fractal dynamic characteristics of SS were maintained with STM, in contrast to FTM, and only the fractal dynamic characteristics of ST disappeared when using a metronome. In addition, the fractal dynamic patterns of the cross-correlated surrogate results were identical to those of all variables for the two treadmills. In terms of the fractal dynamic properties, STM walking was generally closer to overground walking than FTM walking. Although further research is needed, the present results will be useful in research on gait fractal dynamics and rehabilitation. Copyright © 2017 Elsevier Ltd. All rights reserved.
Walking on fractals: diffusion and self-avoiding walks on percolation clusters
Blavatska, Viktoria; Janke, Wolfhard
2008-01-01
We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in space dimensions d=2, 3, 4. Our analysis yields estimates of universal exponents, governing the scaling laws for configurational properties of RWs and SAWs.
Ergodicity of Random Walks on Random DFA
Balle, Borja
2013-01-01
Given a DFA we consider the random walk that starts at the initial state and at each time step moves to a new state by taking a random transition from the current state. This paper shows that for typical DFA this random walk induces an ergodic Markov chain. The notion of typical DFA is formalized by showing that ergodicity holds with high probability when a DFA is sampled uniformly at random from the set of all automata with a fixed number of states. We also show the same result applies to DF...
Composite continuous time random walks
Hilfer, Rudolf
2017-12-01
Random walks in composite continuous time are introduced. Composite time flow is the product of translational time flow and fractional time flow [see Chem. Phys. 84, 399 (2002)]. The continuum limit of composite continuous time random walks gives a diffusion equation where the infinitesimal generator of time flow is the sum of a first order and a fractional time derivative. The latter is specified as a generalized Riemann-Liouville derivative. Generalized and binomial Mittag-Leffler functions are found as the exact results for waiting time density and mean square displacement.
Random walks in a random environment
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 114; Issue 4. Random Walks in a Random Environment. S R S Varadhan. Invited Articles Volume 114 Issue ... Author Affiliations. S R S Varadhan1. Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, NY 10012, USA ...
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Random walks, random fields, and disordered systems
Černý, Jiří; Kotecký, Roman
2015-01-01
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a mod...
Quantum random walks with history dependence
Flitney, Adrian P.; Abbott, Derek; Johnson, Neil F.
2003-01-01
We introduce a multi-coin discrete quantum random walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying the history dependence. By mixing the biased random walk with an unbiased one, the direction of the bias can be reversed leading to a new quantum version of Parrondo's paradox.
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.
Quantum walks induced by Dirichlet random walks on infinite trees
Higuchi, Yusuke; Segawa, Etsuo
2018-02-01
We consider the Grover walk on infinite trees from the viewpoint of spectral analysis. From the previous work, infinite regular trees provide localization. In this paper, we give the complete characterization of the eigenspace of this Grover walk, which involves localization of its behavior and recovers the previous work. Our result suggests that the Grover walk on infinite trees may be regarded as a limit of the quantum walk induced by the isotropic random walk with the Dirichlet boundary condition at the n-th depth rather than one with the Neumann boundary condition.
Moisture diffusivity in structure of random fractal fiber bed
Energy Technology Data Exchange (ETDEWEB)
Zhu, Fanglong, E-mail: zhufanglong_168@163.com [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); The Chinese People' s Armed Police Forces Academy, Langfan City (China); Zhou, Yu; Feng, Qianqian [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); Xia, Dehong [School of Mechanical Engineering, University of Science and Technology, Beijing (China)
2013-11-08
A theoretical expression related to effective moisture diffusivity to random fiber bed is derived by using fractal theory and considering both parallel and perpendicular channels to diffusion flow direction. In this Letter, macroporous structure of hydrophobic nonwoven material is investigated, and Knudsen diffusion and surface diffusion are neglected. The effective moisture diffusivity predicted by the present fractal model are compared with water vapor transfer rate (WVTR) experiment data and calculated values obtained from other theoretical models. This verifies the validity of the present fractal diffusivity of fibrous structural beds.
A discrete random walk on the hypercube
Zhang, Jingyuan; Xiang, Yonghong; Sun, Weigang
2018-03-01
In this paper, we study the scaling for mean first-passage time (MFPT) of random walks on the hypercube and obtain a closed-form formula for the MFPT over all node pairs. We also determine the exponent of scaling efficiency characterizing the random walks and compare it with those of the existing networks. Finally we study the random walks on the hypercube with a located trap and provide a solution of the Kirchhoff index of the hypercube.
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.
Persistent random walk with exclusion
Galanti, Marta; Fanelli, Duccio; Piazza, Francesco
2013-11-01
Modelling the propagation of a pulse in a dense milieu poses fundamental challenges at the theoretical and applied levels. To this aim, in this paper we generalize the telegraph equation to non-ideal conditions by extending the concept of persistent random walk to account for spatial exclusion effects. This is achieved by introducing an explicit constraint in the hopping rates, that weights the occupancy of the target sites. We derive the mean-field equations, which display nonlinear terms that are important at high density. We compute the evolution of the mean square displacement (MSD) for pulses belonging to a specific class of spatially symmetric initial conditions. The MSD still displays a transition from ballistic to diffusive behaviour. We derive an analytical formula for the effective velocity of the ballistic stage, which is shown to depend in a nontrivial fashion upon both the density (area) and the shape of the initial pulse. After a density-dependent crossover time, nonlinear terms become negligible and normal diffusive behaviour is recovered at long times.
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
Quantum random walks circuits with photonic waveguides
Peruzzo, Alberto; Matthews, Jonathan; Politi, Alberto; Lobino, Mirko; Zhou, Xiao-Qi; Thompson, Mark G.; O'Brien, Jeremy; Matsuda, Nobuyuki; Ismail, N.; Worhoff, Kerstin; Bromberg, Yaron; Lahini, Yoav; Silberberg, Yaron
2010-01-01
Arrays of 21 evanescently coupled waveguides are fabricated to implement quantum random walks and a generalised form of two-photon non-classical interference, which observed via two photon correlation.
Continuous Time Random Walk and Migration-Proliferation Dichotomy of Brain Cancer
Iomin, A.
A theory of fractional kinetics of glial cancer cells is presented. A role of the migration-proliferation dichotomy in the fractional cancer cell dynamics in the outer-invasive zone is discussed and explained in the framework of a continuous time random walk. The main suggested model is based on a construction of a 3D comb model, where the migration-proliferation dichotomy becomes naturally apparent and the outer-invasive zone of glioma cancer is considered as a fractal composite with a fractal dimension Dfr < 3.
Sunspot random walk and 22-year variation
Love, Jeffrey J.; Rigler, E. Joshua
2012-01-01
We examine two stochastic models for consistency with observed long-term secular trends in sunspot number and a faint, but semi-persistent, 22-yr signal: (1) a null hypothesis, a simple one-parameter random-walk model of sunspot-number cycle-to-cycle change, and, (2) an alternative hypothesis, a two-parameter random-walk model with an imposed 22-yr alternating amplitude. The observed secular trend in sunspots, seen from solar cycle 5 to 23, would not be an unlikely result of the accumulation of multiple random-walk steps. Statistical tests show that a 22-yr signal can be resolved in historical sunspot data; that is, the probability is low that it would be realized from random data. On the other hand, the 22-yr signal has a small amplitude compared to random variation, and so it has a relatively small effect on sunspot predictions. Many published predictions for cycle 24 sunspots fall within the dispersion of previous cycle-to-cycle sunspot differences. The probability is low that the Sun will, with the accumulation of random steps over the next few cycles, walk down to a Dalton-like minimum. Our models support published interpretations of sunspot secular variation and 22-yr variation resulting from cycle-to-cycle accumulation of dynamo-generated magnetic energy.
Random Field Ising Models: Fractal Interfaces and their Implications
Bupathy, A.; Kumar, M.; Banerjee, V.; Puri, S.
2017-10-01
We use a computationally efficient graph-cut (GC) method to obtain exact ground-states of the d = 3 random field Ising model (RFIM) on simple cubic (SC), bodycentered cubic (BCC) and face-centered cubic (FCC) lattices with Gaussian, Uniform and Bimodal distributions for the disorder Δ. At small-r, the correlation function C(r; Δ) shows a cusp singularity characterised by a non-integer roughness exponent α signifying rough fractal interfaces with dimension d f = d – α. In the paramagnetic phase (Δ > Δ c ), α ≃ 0:5 for all lattice and disorder types. In the ferromagnetic phase (Δ Fractal interfaces have important implications on growth and relaxation.
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...... that represent a quantification of how a term contributes to its context. Evaluation on two TREC collections and 350 topics shows that the random walk-based term weights perform at least comparably to the traditional tf-idf term weighting, while they outperform it when the distance between co-occurring terms...
Random walk centrality for temporal networks
Rocha, Luis E. C.; Masuda, Naoki
2014-06-01
Nodes can be ranked according to their relative importance within a network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based on random walks, for example the PageRank, have focused on static structures. However, several realistic networks are indeed dynamic, meaning that their structure changes in time. In this paper, we propose a centrality measure for temporal networks based on random walks under periodic boundary conditions that we call TempoRank. It is known that, in static networks, the stationary density of the random walk is proportional to the degree or the strength of a node. In contrast, we find that, in temporal networks, the stationary density is proportional to the in-strength of the so-called effective network, a weighted and directed network explicitly constructed from the original sequence of transition matrices. The stationary density also depends on the sojourn probability q, which regulates the tendency of the walker to stay in the node, and on the temporal resolution of the data. We apply our method to human interaction networks and show that although it is important for a node to be connected to another node with many random walkers (one of the principles of the PageRank) at the right moment, this effect is negligible in practice when the time order of link activation is included.
Exploring complex networks through random walks.
Costa, Luciano da Fontoura; Travieso, Gonzalo
2007-01-01
Most real complex networks--such as protein interactions, social contacts, and the Internet--are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key issue to investigate and characterize how effectively the nodes and edges of such networks can be covered by different strategies. At the same time, it is critically important to infer how well can topological measurements such as the average node degree and average clustering coefficient be estimated during such network explorations. The present article addresses these problems by considering random, Barabási-Albert (BA), and geographical network models with varying connectivity explored by three types of random walks: traditional, preferential to untracked edges, and preferential to unvisited nodes. A series of relevant results are obtained, including the fact that networks of the three studied models with the same size and average node degree allow similar node and edge coverage efficiency, the identification of linear scaling with the size of the network of the random walk step at which a given percentage of the nodes/edges is covered, and the critical result that the estimation of the averaged node degree and clustering coefficient by random walks on BA networks often leads to heavily biased results. Many are the theoretical and practical implications of such results.
Pollen Grains, Random Walks and Einstein
Indian Academy of Sciences (India)
wnian motion show us how the most profound physics and mathematics can emerge from simple, direct obser- vation of natural phenomena. Ideas related to Brownian motion and random walks appear today in mathematics, all the natural sciences, engineering, linguistics, finance, economics, and even the social sciences.
Pollen Grains, Random Walks and Einstein
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 10; Issue 12. Pollen Grains, Random Walks and Einstein. Sriram Ramaswamy. Volume 10 Issue 12 December 2005 pp 106-124. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/010/12/0106-0124 ...
Pollen Grains, Random Walks and Einstein
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 5; Issue 3. Pollen Grains, Random Walks and Einstein. Sriram Ramaswamy. General Article Volume 5 Issue 3 March 2000 pp 16-34. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/005/03/0016-0034 ...
Brownian Motion Problem: Random Walk and Beyond
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 10; Issue 8. Brownian Motion Problem: Random Walk and Beyond. Shama Sharma Vishwamittar. General Article Volume 10 Issue 8 August 2005 pp 49-66. Fulltext. Click here to view fulltext PDF. Permanent link:
RANDOM WALK HYPOTHESIS IN FINANCIAL MARKETS
Directory of Open Access Journals (Sweden)
Nicolae-Marius JULA
2017-05-01
Full Text Available Random walk hypothesis states that the stock market prices do not follow a predictable trajectory, but are simply random. If you are trying to predict a random set of data, one should test for randomness, because, despite the power and complexity of the used models, the results cannot be trustworthy. There are several methods for testing these hypotheses and the use of computational power provided by the R environment makes the work of the researcher easier and with a cost-effective approach. The increasing power of computing and the continuous development of econometric tests should give the potential investors new tools in selecting commodities and investing in efficient markets.
Open quantum random walk in terms of quantum Bernoulli noise
Wang, Caishi; Wang, Ce; Ren, Suling; Tang, Yuling
2018-03-01
In this paper, we introduce an open quantum random walk, which we call the QBN-based open walk, by means of quantum Bernoulli noise, and study its properties from a random walk point of view. We prove that, with the localized ground state as its initial state, the QBN-based open walk has the same limit probability distribution as the classical random walk. We also show that the probability distributions of the QBN-based open walk include those of the unitary quantum walk recently introduced by Wang and Ye (Quantum Inf Process 15:1897-1908, 2016) as a special case.
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.
Malicet, Dominique
2017-09-01
In this paper, we study random walks {g_n=f_{n-1}\\ldots f_0} on the group Homeo (S 1) of the homeomorphisms of the circle, where the homeomorphisms f k are chosen randomly, independently, with respect to a same probability measure {ν} . We prove that under the only condition that there is no probability measure invariant by {ν} -almost every homeomorphism, the random walk almost surely contracts small intervals. It generalizes what has been known on this subject until now, since various conditions on {ν} were imposed in order to get the phenomenon of contractions. Moreover, we obtain the surprising fact that the rate of contraction is exponential, even in the lack of assumptions of smoothness on the f k 's. We deduce various dynamical consequences on the random walk (g n ): finiteness of ergodic stationary measures, distribution of the trajectories, asymptotic law of the evaluations, etc. The proof of the main result is based on a modification of the Ávila-Viana's invariance principle, working for continuous cocycles on a space fibred in circles.
Quantum random walks and their convergence to Evans–Hudson ...
Indian Academy of Sciences (India)
Quantum dynamical semigroup; Evans–Hudson flow; quantum random walk. 1. Introduction. The aim of this article is to investigate convergence of random walks on von Neumann algebra to Evans–Hudson flows. Here the random walks and Evans–Hudson flows are gene- ralizations of classical Markov chains and Markov ...
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.
Interface mobility from interface random walk
Trautt, Zachary; Upmanyu, Moneesh; Karma, Alain
2007-03-01
Computational studies aimed at extracting interface mobilities require driving forces orders of magnitude higher than those occurring experimentally. We present a computational methodology that extracts the absolute interface mobility in the zero driving force limit by monitoring the one-dimensional random walk of the mean interface position along the interface normal. The method exploits a fluctuation-dissipation relation similar to the Stokes-Einstein relation, which relates the diffusion coefficient of this Brownian-like random walk to the interface mobility. Atomic-scale simulations of grain boundaries in model crystalline systems validate the theoretical predictions, and also highlight the profound effect of impurities. The generality of this technique combined with its inherent spatial-temporal efficiency should allow computational studies to effectively complement experiments in understanding interface kinetics in diverse material systems.
Random walk centrality in interconnected multilayer networks
Solé-Ribalta, Albert; Gómez, Sergio; Arenas, Alex
2015-01-01
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) influential 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.
Localization transition of biased random walks on random networks.
Sood, Vishal; Grassberger, Peter
2007-08-31
We study random walks on large random graphs that are biased towards a randomly chosen but fixed target node. We show that a critical bias strength bc exists such that most walks find the target within a finite time when b > bc. For b infinity before hitting the target. The phase transition at b=bc is a critical point in the sense that quantities such as the return probability P(t) show power laws, but finite-size behavior is complex and does not obey the usual finite-size scaling ansatz. By extending rigorous results for biased walks on Galton-Watson trees, we give the exact analytical value for bc and verify it by large scale simulations.
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.
A random walk model to evaluate autism
Moura, T. R. S.; Fulco, U. L.; Albuquerque, E. L.
2018-02-01
A common test administered during neurological examination in children is the analysis of their social communication and interaction across multiple contexts, including repetitive patterns of behavior. Poor performance may be associated with neurological conditions characterized by impairments in executive function, such as the so-called pervasive developmental disorders (PDDs), a particular condition of the autism spectrum disorders (ASDs). Inspired in these diagnosis tools, mainly those related to repetitive movements and behaviors, we studied here how the diffusion regimes of two discrete-time random walkers, mimicking the lack of social interaction and restricted interests developed for children with PDDs, are affected. Our model, which is based on the so-called elephant random walk (ERW) approach, consider that one of the random walker can learn and imitate the microscopic behavior of the other with probability f (1 - f otherwise). The diffusion regimes, measured by the Hurst exponent (H), is then obtained, whose changes may indicate a different degree of autism.
Hermann, Philipp; Mrkvička, Tomáš; Mattfeldt, Torsten; Minárová, Mária; Helisová, Kateřina; Nicolis, Orietta; Wartner, Fabian; Stehlík, Milan
2015-08-15
Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper. Copyright © 2015 John Wiley & Sons, Ltd.
Maximal-entropy random walk unifies centrality measures
Ochab, J. K.
2012-12-01
This paper compares a number of centrality measures and several (dis-)similarity matrices with which they can be defined. These matrices, which are used among others in community detection methods, represent quantities connected to enumeration of paths on a graph and to random walks. Relationships between some of these matrices are derived in the paper. These relationships are inherited by the centrality measures. They include measures based on the principal eigenvector of the adjacency matrix, path enumeration, as well as on the stationary state, stochastic matrix, or mean first-passage times of a random walk. As the random walk defining the centrality measure can be arbitrarily chosen, we pay particular attention to the maximal-entropy random walk, which serves as a very distinct alternative to the ordinary (diffusive) random walk used in network analysis. The various importance measures, defined both with the use of ordinary random walk and the maximal-entropy random walk, are compared numerically on a set of benchmark graphs with varying mixing parameter and are grouped with the use of the agglomerative clustering technique. It is shown that centrality measures defined with the two different random walks cluster into two separate groups. In particular, the group of centrality measures defined by the maximal-entropy random walk does not cluster with any other measures on change of graphs’ parameters, and members of this group produce mutually closer results than members of the group defined by the ordinary random walk.
Maximal-entropy random walk unifies centrality measures.
Ochab, J K
2012-12-01
This paper compares a number of centrality measures and several (dis-)similarity matrices with which they can be defined. These matrices, which are used among others in community detection methods, represent quantities connected to enumeration of paths on a graph and to random walks. Relationships between some of these matrices are derived in the paper. These relationships are inherited by the centrality measures. They include measures based on the principal eigenvector of the adjacency matrix, path enumeration, as well as on the stationary state, stochastic matrix, or mean first-passage times of a random walk. As the random walk defining the centrality measure can be arbitrarily chosen, we pay particular attention to the maximal-entropy random walk, which serves as a very distinct alternative to the ordinary (diffusive) random walk used in network analysis. The various importance measures, defined both with the use of ordinary random walk and the maximal-entropy random walk, are compared numerically on a set of benchmark graphs with varying mixing parameter and are grouped with the use of the agglomerative clustering technique. It is shown that centrality measures defined with the two different random walks cluster into two separate groups. In particular, the group of centrality measures defined by the maximal-entropy random walk does not cluster with any other measures on change of graphs' parameters, and members of this group produce mutually closer results than members of the group defined by the ordinary random walk.
Molecular motors: thermodynamics and the random walk.
Thomas, N; Imafuku, Y; Tawada, K
2001-10-22
The biochemical cycle of a molecular motor provides the essential link between its thermodynamics and kinetics. The thermodynamics of the cycle determine the motor's ability to perform mechanical work, whilst the kinetics of the cycle govern its stochastic behaviour. We concentrate here on tightly coupled, processive molecular motors, such as kinesin and myosin V, which hydrolyse one molecule of ATP per forward step. Thermodynamics require that, when such a motor pulls against a constant load f, the ratio of the forward and backward products of the rate constants for its cycle is exp [-(DeltaG + u(0)f)/kT], where -DeltaG is the free energy available from ATP hydrolysis and u(0) is the motor's step size. A hypothetical one-state motor can therefore act as a chemically driven ratchet executing a biased random walk. Treating this random walk as a diffusion problem, we calculate the forward velocity v and the diffusion coefficient D and we find that its randomness parameter r is determined solely by thermodynamics. However, real molecular motors pass through several states at each attachment site. They satisfy a modified diffusion equation that follows directly from the rate equations for the biochemical cycle and their effective diffusion coefficient is reduced to D-v(2)tau, where tau is the time-constant for the motor to reach the steady state. Hence, the randomness of multistate motors is reduced compared with the one-state case and can be used for determining tau. Our analysis therefore demonstrates the intimate relationship between the biochemical cycle, the force-velocity relation and the random motion of molecular motors.
The subtle nature of financial random walks.
Bouchaud, Jean-Philippe
2005-06-01
We first review the most important "stylized facts" of financial time series, that turn out to be, to a large extent, universal. We then recall how the multifractal random walk of Bacry, Muzy, and Delour generalizes the standard model of financial price changes and accounts in an elegant way for many of their empirical properties. In a second part, we provide empirical evidence for a very subtle compensation mechanism that underlies the random nature of price changes. This compensation drives the market close to a critical point, that may explain the sensitivity of financial markets to small perturbations, and their propensity to enter bubbles and crashes. We argue that the resulting unpredictability of price changes is very far from the neoclassical view that markets are informationally efficient.
The subtle nature of financial random walks
Bouchaud, Jean-Philippe
2005-06-01
We first review the most important "stylized facts" of financial time series, that turn out to be, to a large extent, universal. We then recall how the multifractal random walk of Bacry, Muzy, and Delour generalizes the standard model of financial price changes and accounts in an elegant way for many of their empirical properties. In a second part, we provide empirical evidence for a very subtle compensation mechanism that underlies the random nature of price changes. This compensation drives the market close to a critical point, that may explain the sensitivity of financial markets to small perturbations, and their propensity to enter bubbles and crashes. We argue that the resulting unpredictability of price changes is very far from the neoclassical view that markets are informationally efficient.
The Not-so-Random Drunkard's Walk
Ehrhardt, George
2013-01-01
This dataset contains the results of a quasi-experiment, testing Karl Pearson's "drunkard's walk" analogy for an abstract random walk. Inspired by the alternate hypothesis that drunkards stumble to the side of their dominant hand, it includes data on intoxicated test subjects walking a 10' line. Variables include: the…
Continuous-time random-walk model of transport in variably saturated heterogeneous porous media.
Zoia, Andrea; Néel, Marie-Christine; Cortis, Andrea
2010-03-01
We propose a unified physical framework for transport in variably saturated porous media. This approach allows fluid flow and solute migration to be treated as ensemble averages of fluid and solute particles, respectively. We consider the cases of homogeneous and heterogeneous porous materials. Within a fractal mobile-immobile continuous time random-walk framework, the heterogeneity will be characterized by algebraically decaying particle retention times. We derive the corresponding (nonlinear) continuum-limit partial differential equations and we compare their solutions to Monte Carlo simulation results. The proposed methodology is fairly general and can be used to track fluid and solutes particles trajectories for a variety of initial and boundary conditions.
Discriminative parameter estimation for random walks segmentation.
Baudin, Pierre-Yves; Goodman, Danny; Kumrnar, Puneet; Azzabou, Noura; Carlier, Pierre G; Paragios, Nikos; Kumar, M Pawan
2013-01-01
The Random Walks (RW) algorithm is one of the most efficient and easy-to-use probabilistic segmentation methods. By combining contrast terms with prior terms, it provides accurate segmentations of medical images in a fully automated manner. However, one of the main drawbacks of using the RW algorithm is that its parameters have to be hand-tuned. we propose a novel discriminative learning framework that estimates the parameters using a training dataset. The main challenge we face is that the training samples are not fully supervised. Specifically, they provide a hard segmentation of the images, instead of a probabilistic segmentation. We overcome this challenge by treating the optimal probabilistic segmentation that is compatible with the given hard segmentation as a latent variable. This allows us to employ the latent support vector machine formulation for parameter estimation. We show that our approach significantly outperforms the baseline methods on a challenging dataset consisting of real clinical 3D MRI volumes of skeletal muscles.
Heterogeneous continuous-time random walks
Grebenkov, Denis S.; Tupikina, Liubov
2018-01-01
We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.
Continuous time persistent random walk: a review and some generalizations
Masoliver, Jaume; Lindenberg, Katja
2017-06-01
We review some extensions of the continuous time random walk first introduced by Elliott Montroll and George Weiss more than 50 years ago [E.W. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965)], extensions that embrace multistate walks and, in particular, the persistent random walk. We generalize these extensions to include fractional random walks and derive the associated master equation, namely, the fractional telegrapher's equation. We dedicate this review to our joint work with George H. Weiss (1930-2017). It saddens us greatly to report the recent death of George Weiss, a scientific giant and at the same time a lovely and humble man.
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
Quantum random walks and their convergence to Evans–Hudson ...
Indian Academy of Sciences (India)
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 ...
Branching random walks with displacements coming from a power law
Indian Academy of Sciences (India)
Parthanil Roy Joint work with Ayan Bhattacharya and Rajat Subhra Hazra
2015-07-04
Branching random walks with displacements coming from a power law. Parthanil Roy. Joint work with Ayan Bhattacharya and Rajat Subhra Hazra. Indian Statistical Institute. July 04, 2015. Parthanil Roy (I.S.I.). Branching random walk. July 04, 2015. 1 / 14 ...
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.
Girold, Sébastien; Rousseau, Jérome; Le Gal, Magalie; Coudeyre, Emmanuel; Le Henaff, Jacqueline
2017-07-01
With Nordic walking, or walking with poles, one can travel a greater distance and at a higher rate than with walking without poles, but whether the activity is beneficial for patients with cardiovascular disease is unknown. This randomized controlled trial was undertaken to determine whether Nordic walking was more effective than walking without poles on walk distance to support rehabilitation training for patients with acute coronary syndrome (ACS) and peripheral arterial occlusive disease (PAOD). Patients were recruited in a private specialized rehabilitation centre for cardiovascular diseases. The entire protocol, including patient recruitment, took place over 2 months, from September to October 2013. We divided patients into 2 groups: Nordic Walking Group (NWG, n=21) and Walking Group without poles (WG, n=21). All patients followed the same program over 4 weeks, except for the walk performed with or without poles. The main outcome was walk distance on the 6-min walk test. Secondary outcomes were maximum heart rate during exercise and walk distance and power output on a treadmill stress test. We included 42 patients (35 men; mean age 57.2±11 years and BMI 26.5±4.5kg/m 2 ). At the end of the training period, both groups showed improved walk distance on the 6-min walk test and treatment stress test as well as power on the treadmill stress test (Pwalk distance than the WG (Pwalking training appeared more efficient than training without poles for increasing walk distance on the 6-min walk test for patients with ACS and PAOD. Copyright © 2017. Published by Elsevier Masson SAS.
Zero Range Process and Multi-Dimensional Random Walks
Bogoliubov, Nicolay M.; Malyshev, Cyril
2017-07-01
The special limit of the totally asymmetric zero range process of the low-dimensional non-equilibrium statistical mechanics described by the non-Hermitian Hamiltonian is considered. The calculation of the conditional probabilities of the model are based on the algebraic Bethe ansatz approach. We demonstrate that the conditional probabilities may be considered as the generating functions of the random multi-dimensional lattice walks bounded by a hyperplane. This type of walks we call the walks over the multi-dimensional simplicial lattices. The answers for the conditional probability and for the number of random walks in the multi-dimensional simplicial lattice are expressed through the symmetric functions.
Efficient sampling of complex network with modified random walk strategies
Xie, Yunya; Chang, Shuhua; Zhang, Zhipeng; Zhang, Mi; Yang, Lei
2018-02-01
We present two novel random walk strategies, choosing seed node (CSN) random walk and no-retracing (NR) random walk. Different from the classical random walk sampling, the CSN and NR strategies focus on the influences of the seed node choice and path overlap, respectively. Three random walk samplings are applied in the Erdös-Rényi (ER), Barabási-Albert (BA), Watts-Strogatz (WS), and the weighted USAir networks, respectively. Then, the major properties of sampled subnets, such as sampling efficiency, degree distributions, average degree and average clustering coefficient, are studied. The similar conclusions can be reached with these three random walk strategies. Firstly, the networks with small scales and simple structures are conducive to the sampling. Secondly, the average degree and the average clustering coefficient of the sampled subnet tend to the corresponding values of original networks with limited steps. And thirdly, all the degree distributions of the subnets are slightly biased to the high degree side. However, the NR strategy performs better for the average clustering coefficient of the subnet. In the real weighted USAir networks, some obvious characters like the larger clustering coefficient and the fluctuation of degree distribution are reproduced well by these random walk strategies.
Bisht, Konark; Klumpp, Stefan; Banerjee, Varsha; Marathe, Rahul
2017-11-01
A human pathogen, Neisseria gonorrhoeae (NG), moves on surfaces by attaching and retracting polymeric structures called Type IV pili. The tug-of-war between the pili results in a two-dimensional stochastic motion called twitching motility. In this paper, with the help of real-time NG trajectories, we develop coarse-grained models for their description. The fractal properties of these trajectories are determined and their influence on first passage time and formation of bacterial microcolonies is studied. Our main observations are as follows: (i) NG performs a fast ballistic walk on small time scales and a slow diffusive walk over long time scales with a long crossover region; (ii) there exists a characteristic persistent length lp*, which yields the fastest growth of bacterial aggregates or biofilms. Our simulations reveal that lp*˜L0.6 , where L ×L is the surface on which the bacteria move; (iii) the morphologies have distinct fractal characteristics as a consequence of the ballistic and diffusive motion of the constituting bacteria.
Conditioned one-way simple random walk and representation theory
Lecouvey, Cédric; Lesigne, Emmanuel; Peigné, Marc
2012-01-01
32 pages; International audience; We call one-way simple random walk a random walk in the quadrant Z₊ⁿ whose increments belong to the canonical base. In relation with representation theory of Lie algebras and superalgebras, we describe the law of such a random walk conditioned to stay in a closed octant, a semi-open octant or other types of semi-groups. The combinatorial representation theory of these algebras allows us to describe a generalized Pitman transformation which realizes the condit...
Random fractal characters and length uncertainty of the continental ...
Indian Academy of Sciences (India)
The results show that the scaling region of the continental coastline of China is from 0.1 to 400 km. In the scaling region, the box-counting dimension and the divider dimension of the coastline are 1.2004 and. 1.0929, respectively. According to fractal theory, the divider dimension more accurately represents the irregularity of ...
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.
A random walk down Main Street
David Matthew Levinson
2016-01-01
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 emerge...
Record statistics of financial time series and geometric random walks
Sabir, Behlool; Santhanam, M. S.
2014-09-01
The study of record statistics of correlated series in physics, such as random walks, is gaining momentum, and several analytical results have been obtained in the past few years. In this work, we study the record statistics of correlated empirical data for which random walk models have relevance. We obtain results for the records statistics of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent α lying in the range 1.5≤α≤1.8. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that obtained from empirical stock data.
Eich, H-J; Mach, H; Werner, C; Hesse, S
2004-09-01
To evaluate the immediate and long-term effects of aerobic treadmill plus Bobath walking training in subacute stroke survivors compared with Bobath walking training alone. Randomized controlled trial. Rehabilitation unit. Fifty patients, first-time supratentorial stroke, stroke interval less than six weeks, Barthel Index (0-100) from 50 to 80, able to walk a minimum distance of 12 m with either intermittent help or stand-by while walking, cardiovascular stable, minimum 50 W in the bicycle ergometry, randomly allocated to two groups, A and B. Group A 30 min of treadmill training, harness secured and minimally supported according to patients' needs, and 30 min of physiotherapy, every workday for six weeks, speed and inclination of the treadmill were adjusted to achieve a heart rate of HR: (Hrmax-HRrest)*0.6+HRrest; in group B 60 min of daily physiotherapy for six weeks. Primary outcome variables were the absolute improvement of walking velocity (m/s) and capacity (m), secondary were gross motor function including walking ability (score out of 13) and walking quality (score out of 41), blindly assessed before and after the intervention, and at follow-up three months later. Patients tolerated the aerobic training well with no side-effects, significantly greater improvement of walking velocity and capacity both at study end (p =0.001 versus p =0.002) and at follow-up (p Bobath walking training in moderately affected stroke patients was better than Bobath walking training alone with respect to the improvement of walking velocity and capacity. The treatment approach is recommended in patients meeting the inclusion criteria. A multicentre trial should follow to strengthen the evidence.
Convergence of a random walk method for the Burgers equation
Energy Technology Data Exchange (ETDEWEB)
Roberts, S.
1985-10-01
In this paper we consider a random walk algorithm for the solution of Burgers' equation. The algorithm uses the method of fractional steps. The non-linear advection term of the equation is solved by advecting ''fluid'' particles in a velocity field induced by the particles. The diffusion term of the equation is approximated by adding an appropriate random perturbation to the positions of the particles. Though the algorithm is inefficient as a method for solving Burgers' equation, it does model a similar method, the random vortex method, which has been used extensively to solve the incompressible Navier-Stokes equations. The purpose of this paper is to demonstrate the strong convergence of our random walk method and so provide a model for the proof of convergence for more complex random walk algorithms; for instance, the random vortex method without boundaries.
Superstatistical analysis and modelling of heterogeneous random walks
Metzner, Claus; Mark, Christoph; Steinwachs, Julian; Lautscham, Lena; Stadler, Franz; Fabry, Ben
2015-06-01
Stochastic time series are ubiquitous in nature. In particular, random walks with time-varying statistical properties are found in many scientific disciplines. Here we present a superstatistical approach to analyse and model such heterogeneous random walks. The time-dependent statistical parameters can be extracted from measured random walk trajectories with a Bayesian method of sequential inference. The distributions and correlations of these parameters reveal subtle features of the random process that are not captured by conventional measures, such as the mean-squared displacement or the step width distribution. We apply our new approach to migration trajectories of tumour cells in two and three dimensions, and demonstrate the superior ability of the superstatistical method to discriminate cell migration strategies in different environments. Finally, we show how the resulting insights can be used to design simple and meaningful models of the underlying random processes.
Random walks in the quarter-plane: invariant measures and performance bounds
Chen, Y.
2015-01-01
This monograph focuses on random walks in the quarter-plane. Such random walks are frequently used to model queueing systems and the invariant measure of a random walk is of major importance in studying the performance of these systems. In special cases the invariant measure of a random walk can be
Mardoukhi, Yousof; Jeon, Jae-Hyung; Metzler, Ralf
2015-11-28
We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T(-h) with h fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
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
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.
A generalized model via random walks for information filtering
Energy Technology Data Exchange (ETDEWEB)
Ren, Zhuo-Ming, E-mail: zhuomingren@gmail.com [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland); Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, ChongQing, 400714 (China); Kong, Yixiu [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland); Shang, Ming-Sheng, E-mail: msshang@cigit.ac.cn [Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, ChongQing, 400714 (China); Zhang, Yi-Cheng [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland)
2016-08-06
There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation. - Highlights: • We propose a generalized recommendation model employing the random walk dynamics. • The proposed model with single and hybrid of degree information is analyzed. • A strategy with the hybrid degree information improves precision of recommendation.
Fractal transit networks: Self-avoiding walks and Lévy flights
von Ferber, Christian; Holovatch, Yurij
2013-01-01
Using the data on the Berlin public transport network, the present study extends previous observations of fractality within public transport routes by showing that also the distribution of inter-station distances along routes displays non-trivial power law behaviour. This indicates that the routes may in part also be described as Lévy-flights. The latter property may result from the fact that the routes are planned to be adapted to the fluctuating demand densities throughout the served area. We also relate this to optimization properties of Lévy flights.
Prior knowledge, random walks and human skeletal muscle segmentation.
Baudin, P Y; Azzabou, N; Carlier, P G; Paragios, Nikos
2012-01-01
In this paper, we propose a novel approach for segmenting the skeletal muscles in MRI automatically. In order to deal with the absence of contrast between the different muscle classes, we proposed a principled mathematical formulation that integrates prior knowledge with a random walks graph-based formulation. Prior knowledge is represented using a statistical shape atlas that once coupled with the random walks segmentation leads to an efficient iterative linear optimization system. We reveal the potential of our approach on a challenging set of real clinical data.
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
Navigation by anomalous random walks on complex networks.
Weng, Tongfeng; Zhang, Jie; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan
2016-11-23
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks.
Mindful Walking in Psychologically Distressed Individuals: A Randomized Controlled Trial
Directory of Open Access Journals (Sweden)
M. Teut
2013-01-01
Full Text Available Background. The aim of this randomized, controlled study was to investigate the effectiveness of a mindful walking program in patients with high levels of perceived psychological distress. Methods. Participants aged between 18 and 65 years with moderate to high levels of perceived psychological distress were randomized to 8 sessions of mindful walking in 4 weeks (each 40 minutes walking, 10 minutes mindful walking, 10 minutes discussion or to no study intervention (waiting group. Primary outcome parameter was the difference to baseline on Cohen’s Perceived Stress Scale (CPSS after 4 weeks between intervention and control. Results. Seventy-four participants were randomized in the study; 36 (32 female, 52.3 ± 8.6 years were allocated to the intervention and 38 (35 female, 49.5 ± 8.8 years to the control group. Adjusted CPSS differences after 4 weeks were −8.8 [95% CI: −10.8; −6.8] (mean 24.2 [22.2; 26.2] in the intervention group and −1.0 [−2.9; 0.9] (mean 32.0 [30.1; 33.9] in the control group, resulting in a highly significant group difference (. Conclusion. Patients participating in a mindful walking program showed reduced psychological stress symptoms and improved quality of life compared to no study intervention. Further studies should include an active treatment group and a long-term follow-up.
Mindful walking in psychologically distressed individuals: a randomized controlled trial.
Teut, M; Roesner, E J; Ortiz, M; Reese, F; Binting, S; Roll, S; Fischer, H F; Michalsen, A; Willich, S N; Brinkhaus, B
2013-01-01
Background. The aim of this randomized, controlled study was to investigate the effectiveness of a mindful walking program in patients with high levels of perceived psychological distress. Methods. Participants aged between 18 and 65 years with moderate to high levels of perceived psychological distress were randomized to 8 sessions of mindful walking in 4 weeks (each 40 minutes walking, 10 minutes mindful walking, 10 minutes discussion) or to no study intervention (waiting group). Primary outcome parameter was the difference to baseline on Cohen's Perceived Stress Scale (CPSS) after 4 weeks between intervention and control. Results. Seventy-four participants were randomized in the study; 36 (32 female, 52.3 ± 8.6 years) were allocated to the intervention and 38 (35 female, 49.5 ± 8.8 years) to the control group. Adjusted CPSS differences after 4 weeks were -8.8 [95% CI: -10.8; -6.8] (mean 24.2 [22.2; 26.2]) in the intervention group and -1.0 [-2.9; 0.9] (mean 32.0 [30.1; 33.9]) in the control group, resulting in a highly significant group difference (P mindful walking program showed reduced psychological stress symptoms and improved quality of life compared to no study intervention. Further studies should include an active treatment group and a long-term follow-up.
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...
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian ... TARUN KANTI GHOSH2. Inter-University Centre for Astronomy and Astrophysics, Ganeshkhind, Pune 411 007, India; Department of Physics, Indian Institute of Technology, Kanpur 208 016, India ...
Stability of reaction fronts in random walk simulations
Nagy, Noemi; Izsak, F.
A model of propagating reaction fronts is given for simple autocatalytic reactions and the stability of the propagating reaction fronts are studied in several numerical experiments. The corresponding random walk simulations - extending of a recent algorithm - make possible the simultaneous treatment
Simulating intrafraction prostate motion with a random walk model
Directory of Open Access Journals (Sweden)
Tobias Pommer, PhD
2017-07-01
Conclusions: Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during delivery of radiation therapy.
Random walk models of large-scale structure
Indian Academy of Sciences (India)
Abstract. This paper describes the insights gained from the excursion set approach, in which vari- ous 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 ...
Random walk and the Zimbabwe capital markets | Dhlakama ...
African Journals Online (AJOL)
JASSA: Journal of Applied Science in Southern Africa. Journal Home · ABOUT · Advanced Search · Current Issue · Archives · Journal Home > Vol 6, No 2 (2000) >. Log in or Register to get access to full text downloads. Username, Password, Remember me, or Register. Random walk and the Zimbabwe capital markets.
Atomic clocks and the continuous-time random-walk
Formichella, Valerio; Camparo, James; Tavella, Patrizia
2017-11-01
Atomic clocks play a fundamental role in many fields, most notably they generate Universal Coordinated Time and are at the heart of all global navigation satellite systems. Notwithstanding their excellent timekeeping performance, their output frequency does vary: it can display deterministic frequency drift; diverse continuous noise processes result in nonstationary clock noise (e.g., random-walk frequency noise, modelled as a Wiener process), and the clock frequency may display sudden changes (i.e., "jumps"). Typically, the clock's frequency instability is evaluated by the Allan or Hadamard variances, whose functional forms can identify the different operative noise processes. Here, we show that the Allan and Hadamard variances of a particular continuous-time random-walk, the compound Poisson process, have the same functional form as for a Wiener process with drift. The compound Poisson process, introduced as a model for observed frequency jumps, is an alternative to the Wiener process for modelling random walk frequency noise. This alternate model fits well the behavior of the rubidium clocks flying on GPS Block-IIR satellites. Further, starting from jump statistics, the model can be improved by considering a more general form of continuous-time random-walk, and this could bring new insights into the physics of atomic clocks.
Renewal theory for perturbed random walks and similar processes
Iksanov, Alexander
2016-01-01
This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration. Being of major importance in modern probability theory, both theoretical and applied, these objects have been used to model various phenomena in the natural sciences as well as in insurance and finance. The book also presents the many significant results and efficient techniques and methods that have been worked out in the last decade. The first chapter is devoted to perturbed random walks and discusses their asymptotic behavior and various functionals pertaining to them, including supremum and first-passage time. The second chapter examines perpetuities, presenting results on continuity of their distributions and the existence of moments, as well as weak convergence of divergent perpetuities. Focusing on random processes with immigration, the third chapter investigates the existence of moments, describes long-time behavior and discusses limit theorems, both with and without scaling. Chapters fou...
The McMillan Theorem for Colored Branching Processes and Dimensions of Random Fractals
Directory of Open Access Journals (Sweden)
Victor Bakhtin
2014-12-01
Full Text Available For the simplest colored branching process, we prove an analog to the McMillan theorem and calculate the Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In this setting, the role of Shannon’s entropy is played by the Kullback–Leibler divergence, and the Hausdorff dimensions are computed by means of the so-called Billingsley–Kullback entropy, defined in the paper.
Brach, Jennifer S; Lowry, Kristin; Perera, Subashan; Hornyak, Victoria; Wert, David; Studenski, Stephanie A; VanSwearingen, Jessie M
2015-03-01
To test the proposed mechanism of action of a task-specific motor learning intervention by examining its effect on measures of the motor control of gait. Single-blinded randomized clinical trial. University research laboratory. Adults (N=40) aged ≥65 years with gait speed >1.0m/s and impaired motor skill (figure-of-8 walk time >8s). The 2 interventions included a task-oriented motor learning and a standard exercise program; both interventions included strength training. Both lasted 12 weeks, with twice-weekly, 1-hour, physical therapist-supervised sessions. Two measures of the motor control of gait, gait variability and smoothness of walking, were assessed pre- and postintervention by assessors masked to the treatment arm. Of 40 randomized subjects, 38 completed the trial (mean age ± SD, 77.1±6.0y). The motor learning group improved more than the standard group in double-support time variability (.13m/s vs .05m/s; adjusted difference [AD]=.006, P=.03). Smoothness of walking in the anteroposterior direction improved more in the motor learning than standard group for all conditions (usual: AD=.53, P=.05; narrow: AD=.56, P=.01; dual task: AD=.57, P=.04). Smoothness of walking in the vertical direction also improved more in the motor learning than standard group for the narrow-path (AD=.71, P=.01) and dual-task (AD=.89, P=.01) conditions. Among older adults with subclinical walking difficulty, there is initial evidence that task-oriented motor learning exercise results in gains in the motor control of walking, while standard exercise does not. Task-oriented motor learning exercise is a promising intervention for improving timing and coordination deficits related to mobility difficulties in older adults, and needs to be evaluated in a definitive larger trial. Copyright © 2015 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.
Movements of molecular motors: Ratchets, random walks and traffic phenomena
Klumpp, Stefan; Nieuwenhuizen, Theo M.; Lipowsky, Reinhard
2005-10-01
Processive molecular motors which drive the traffic of organelles in cells move in a directed way along cytoskeletal filaments. On large time scales, they perform motor walks, i.e., peculiar random walks which arise from the repeated unbinding from and rebinding to filaments. Unbound motors perform Brownian motion in the surrounding fluid. In addition, the traffic of molecular motors exhibits many cooperative phenomena. In particular, it faces similar problems as the traffic on streets such as the occurrence of traffic jams and the coordination of (two-way) traffic. These issues are studied here theoretically using lattice models.
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.
Ada, Louise; Dean, Catherine M; Morris, Meg E; Simpson, Judy M; Katrak, Pesi
2010-06-01
The main objective of this randomized trial was to determine whether treadmill walking with body weight support was effective at establishing independent walking more often and earlier than current physiotherapy intervention for nonambulatory stroke patients. A randomized trial with concealed allocation, blinded assessment, and intention-to-treat analysis was conducted. One hundred twenty-six stroke patients who were unable to walk were recruited and randomly allocated to an experimental or a control group within 4 weeks of stroke. The experimental group undertook up to 30 minutes per day of treadmill walking with body weight support via an overhead harness whereas the control group undertook up to 30 minutes of overground walking. The primary outcome was the proportion of participants achieving independent walking within 6 months. Kaplan-Meier estimates of the proportion of experimental participants who achieved independent walking were 37% compared with 26% of the control group at 1 month, 66% compared with 55% at 2 months, and 71% compared with 60% at 6 months (P=0.13). The experimental group walked 2 weeks earlier, with a median time to independent walking of 5 weeks compared to 7 weeks for the control group. In addition, 14% (95% CI, -1-28) more of the experimental group were discharged home. Treadmill walking with body weight support is feasible, safe, and tends to result in more people walking independently and earlier after stroke. Trial Registration- ClinicalTrial.gov (NCT00167531).
Fractal generator for efficient production of random planar patterns and symbols in digital mapping
Chen, Qiyu; Liu, Gang; Ma, Xiaogang; Li, Xinchuan; He, Zhenwen
2017-08-01
In digital cartography, the automatic generation of random planar patterns and symbols is still an ongoing challenge. Those patterns and symbols of randomness have randomly variated configurations and boundaries, and their generating algorithms are constrained by the shape features, cartographic standards and many other conditions. The fractal geometry offers favorable solutions to simulate random boundaries and patterns. In the work presented in this paper, we used both fractal theory and random Iterated Function Systems (IFS) to develop a method for the automatic generation of random planar patterns and symbols. The marshland and the trough cross-bedding patterns were used as two case studies for the implementation of the method. We first analyzed the morphological characteristics of those two planar patterns. Then we designed algorithms and implementation schemes addressing the features of each pattern. Finally, we ran the algorithms to generate the patterns and symbols, and compared them with the requirements of a few digital cartographic standards. The method presented in this paper has already been deployed in a digital mapping system for practical uses. The flexibility of the method also allows it to be reused and/or adapted in various software platforms for digital mapping.
Solving Schroedinger's equation using random walks
Aspuru-Guzik, Alan
Exact and almost exact solutions for energies and properties of atoms and molecules can be obtained by quantum Monte Carlo (QMC) methods. This thesis is composed of different contributions to various QMC methodologies, as well as applications to electronic excitations of biological systems. We propose a wave function optimization functional that is robust regarding the presence of outliers. Our work, and subsequent applications by others, has shown the convergence properties and robustness of the absolute deviation (AD) functional as compared to the variance functional (VF). We apply the method to atoms from the second row of the periodic table, as well as third-row transition metal atoms, including an all-electron calculation of Sc. In all cases, the AD functional converges faster than the VF. Soft effective core potentials (ECPs) with no divergence at the origin are constructed and validated for second- an third-row atoms of the periodic table. The ECPs we developed have been used by others in several successful studies. As an application of the DMC approach to biochemical problems, we studied the electronic excitations of free-base porphyrin and obtained results in excellent agreement with experiment. These findings validate the use of the DMC approach for these kinds of systems. A study of the role of spheroidene in the photo-protection mechanism of Rhodobacter sphaeroides is described. At the time of writing, calculations for the estimation of excitation energies for the bacteriochlorophyll and spheroidene molecules as well as storage of the random walkers for future prediction of the excitation energy transfer rate are being performed. To date, the calculations mentioned above are the largest all-electron studies on molecules. For the computation of these systems, a sparse linear-scaling DMC algorithm was developed. This algorithm provides a speedup of at least a factor of ten over previously published methods. The method is validated on systems up to 390
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.
Statistical Modeling of Robotic Random Walks on Different Terrain
Naylor, Austin; Kinnaman, Laura
Issues of public safety, especially with crowd dynamics and pedestrian movement, have been modeled by physicists using methods from statistical mechanics over the last few years. Complex decision making of humans moving on different terrains can be modeled using random walks (RW) and correlated random walks (CRW). The effect of different terrains, such as a constant increasing slope, on RW and CRW was explored. LEGO robots were programmed to make RW and CRW with uniform step sizes. Level ground tests demonstrated that the robots had the expected step size distribution and correlation angles (for CRW). The mean square displacement was calculated for each RW and CRW on different terrains and matched expected trends. The step size distribution was determined to change based on the terrain; theoretical predictions for the step size distribution were made for various simple terrains. It's Dr. Laura Kinnaman, not sure where to put the Prefix.
Continuous Time Random Walks with memory and financial distributions
Montero, Miquel; Masoliver, Jaume
2017-11-01
We study financial distributions from the perspective of Continuous Time Random Walks with memory. We review some of our previous developments and apply them to financial problems. We also present some new models with memory that can be useful in characterizing tendency effects which are inherent in most markets. We also briefly study the effect on return distributions of fractional behaviors in the distribution of pausing times between successive transactions.
Governing equations and solutions of anomalous random walk limits.
Meerschaert, Mark M; Benson, David A; Scheffler, Hans-Peter; Becker-Kern, Peter
2002-12-01
Continuous time random walks model anomalous diffusion. Coupling allows the magnitude of particle jumps to depend on the waiting time between jumps. Governing equations for the long-time scaling limits of these models are found to have fractional powers of coupled space and time differential operators. Explicit solutions and scaling properties are presented for these equations, which can be used to model flow in porous media and other physical systems.
Maximal-entropy random walk unifies centrality measures
Ochab, J. K.
2012-01-01
In this paper analogies between different (dis)similarity matrices are derived. These matrices, which are connected to path enumeration and random walks, are used in community detection methods or in computation of centrality measures for complex networks. The focus is on a number of known centrality measures, which inherit the connections established for similarity matrices. These measures are based on the principal eigenvector of the adjacency matrix, path enumeration, as well as on the sta...
Fractional telegrapher's equation from fractional persistent random walks
Masoliver, Jaume, 1951-
2016-01-01
We generalize the telegrapher's equation to allow for anomalous transport. We derive the space-time fractional telegrapher's equation using the formalism of the persistent random walk in continuous time. We also obtain the characteristic function of the space-time fractional process and study some particular cases and asymptotic approximations. Similarly to the ordinary telegrapher's equation, the time-fractional equation also presents distinct behaviors for different time scales. Specificall...
Non-linear continuous time random walk models★
Stage, Helena; Fedotov, Sergei
2017-11-01
A standard assumption of continuous time random walk (CTRW) processes is that there are no interactions between the random walkers, such that we obtain the celebrated linear fractional equation either for the probability density function of the walker at a certain position and time, or the mean number of walkers. The question arises how one can extend this equation to the non-linear case, where the random walkers interact. The aim of this work is to take into account this interaction under a mean-field approximation where the statistical properties of the random walker depend on the mean number of walkers. The implementation of these non-linear effects within the CTRW integral equations or fractional equations poses difficulties, leading to the alternative methodology we present in this work. We are concerned with non-linear effects which may either inhibit anomalous effects or induce them where they otherwise would not arise. Inhibition of these effects corresponds to a decrease in the waiting times of the random walkers, be this due to overcrowding, competition between walkers or an inherent carrying capacity of the system. Conversely, induced anomalous effects present longer waiting times and are consistent with symbiotic, collaborative or social walkers, or indirect pinpointing of favourable regions by their attractiveness. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Ant-inspired density estimation via random walks.
Musco, Cameron; Su, Hsin-Hao; Lynch, Nancy A
2017-10-03
Many ant species use distributed population density estimation in applications ranging from quorum sensing, to task allocation, to appraisal of enemy colony strength. It has been shown that ants estimate local population density by tracking encounter rates: The higher the density, the more often the ants bump into each other. We study distributed density estimation from a theoretical perspective. We prove that a group of anonymous agents randomly walking on a grid are able to estimate their density within a small multiplicative error in few steps by measuring their rates of encounter with other agents. Despite dependencies inherent in the fact that nearby agents may collide repeatedly (and, worse, cannot recognize when this happens), our bound nearly matches what would be required to estimate density by independently sampling grid locations. From a biological perspective, our work helps shed light on how ants and other social insects can obtain relatively accurate density estimates via encounter rates. From a technical perspective, our analysis provides tools for understanding complex dependencies in the collision probabilities of multiple random walks. We bound the strength of these dependencies using local mixing properties of the underlying graph. Our results extend beyond the grid to more general graphs, and we discuss applications to size estimation for social networks, density estimation for robot swarms, and random walk-based sampling for sensor networks.
Lamb's problem on random mass density fields with fractal and Hurst effects.
Nishawala, V V; Ostoja-Starzewski, M; Leamy, M J; Porcu, E
2016-12-01
This paper reports on a generalization of Lamb's problem to a linear elastic, infinite half-space with random fields (RFs) of mass density, subject to a normal line load. Both, uncorrelated and correlated (with fractal and Hurst characteristics) RFs without any weak noise restrictions, are proposed. Cellular automata (CA) is used to simulate the wave propagation. CA is a local computational method which, for rectangular discretization of spatial domain, is equivalent to applying the finite difference method to the governing equations of classical elasticity. We first evaluate the response of CA to an uncorrelated mass density field, more commonly known as white-noise, of varying coarseness as compared to CA's node density. We then evaluate the response of CA to multiscale mass density RFs of Cauchy and Dagum type; these fields are unique in that they are able to model and decouple the field's fractal dimension and Hurst parameter. We focus on stochastic imperfection sensitivity; we determine to what extent the fractal or the Hurst parameter is a significant factor in altering the solution to the planar stochastic Lamb's problem by evaluating the coefficient of variation of the response when compared with the coefficient of variation of the RF.
Social aggregation in pea aphids: experiment and random walk modeling.
Directory of Open Access Journals (Sweden)
Christa Nilsen
Full Text Available From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid's nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control.
A Novel Algorithm of Quantum Random Walk in Server Traffic Control and Task Scheduling
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.
Realistic simulation of breast mass appearance using random walk
Rashidnasab, Alaleh; Elangovan, Premkumar; Dance, David R.; Young, Kenneth C.; Yip, Mary; Diaz, Oliver; Wells, Kevin
2012-03-01
The aim of the present work was to develop a method for simulating breast lesions in digital mammographic images. Based on the visual appearance of real masses, three dimensional masses were created using a 3D random walk method where the choice of parameters (number of walks and number of steps) enables one to control the appearance of the simulated structure. This work is the first occasion that the random walk results have been combined with a model of digital mammographic imaging systems. This model takes into account appropriate physical image acquisition processes representing a particular digital X-ray mammography system. The X-ray spectrum, local glandularity above the insertion site and scatter were all taken account during the insertion procedure. A preliminary observer study was used to validate the realism of the masses. Seven expert readers each viewed 60 full field mammograms and rated the realism of the masses they contained. Half of the images contained real, histologically-confirmed masses, and half contained simulated lesions. The ROC analysis of the study (average AUC of 0.58+/-0.06) suggests that, on the average, there is evidence that the radiologists could distinguish, somewhat, between real and simulated masses.
Sau Fa, Kwok
2017-03-01
Recently, fractal and generalized Fokker-Planck equations have been the subject of considerable interest. In this work, the fractal and generalized Fokker-Planck equations connected with the Langevin equation and continuous time random walk model are considered. Descriptions and applications of these models to the fixed samples of the mouse brain using magnetic resonance imaging (MRI) are discussed.
Non-random walks in monkeys and humans
Boyer, Denis; Crofoot, Margaret C.; Walsh, Peter D.
2012-01-01
Principles of self-organization play an increasingly central role in models of human activity. Notably, individual human displacements exhibit strongly recurrent patterns that are characterized by scaling laws and can be mechanistically modelled as self-attracting walks. Recurrence is not, however, unique to human displacements. Here we report that the mobility patterns of wild capuchin monkeys are not random walks, and they exhibit recurrence properties similar to those of cell phone users, suggesting spatial cognition mechanisms shared with humans. We also show that the highly uneven visitation patterns within monkey home ranges are not entirely self-generated but are forced by spatio-temporal habitat heterogeneities. If models of human mobility are to become useful tools for predictive purposes, they will need to consider the interaction between memory and environmental heterogeneities. PMID:22031731
Conditioned random walks and interaction-driven condensation
Szavits-Nossan, Juraj; Evans, Martin R.; Majumdar, Satya N.
2017-01-01
We consider a discrete-time continuous-space random walk under the constraints that the number of returns to the origin (local time) and the total area under the walk are fixed. We first compute the joint probability of an excursion having area a and returning to the origin for the first time after time τ. We then show how condensation occurs when the total area constraint is increased: an excursion containing a finite fraction of the area emerges. Finally we show how the phenomena generalises previously studied cases of condensation induced by several constraints and how it is related to interaction-driven condensation which allows us to explain the phenomenon in the framework of large deviation theory.
History dependent quantum random walks as quantum lattice gas automata
Energy Technology Data Exchange (ETDEWEB)
Shakeel, Asif, E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu; Love, Peter J., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu [Department of Physics, Haverford College, Haverford, Pennsylvania 19041 (United States); Meyer, David A., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu [Department of Mathematics, University of California/San Diego, La Jolla, California 92093-0112 (United States)
2014-12-15
Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the history information arise naturally as geometrical degrees of freedom on the lattice.
Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry
Mayer, Volker; Skorulski, Bartlomiej
2011-01-01
The theory of random dynamical systems originated from stochastic differential equations. It is intended to provide a framework and techniques to describe and analyze the evolution of dynamical systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic syst...
Clustered continuous-time random walks: diffusion and relaxation consequences.
Weron, Karina; Stanislavsky, Aleksander; Jurlewicz, Agnieszka; Meerschaert, Mark M; Scheffler, Hans-Peter
2012-06-08
We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies.
Long-Range Navigation on Complex Networks using L\\'evy Random Walks
Riascos, A. P.; Mateos, José L.
2012-01-01
We introduce a strategy of navigation in undirected networks, including regular, random, and complex networks, that is inspired by L\\'evy random walks, generalizing previous navigation rules. We obtained exact expressions for the stationary probability distribution, the occupation probability, the mean first passage time, and the average time to reach a node on the network. We found that the long-range navigation using the L\\'evy random walk strategy, compared with the normal random walk stra...
First Passage Time for Random Walks in Heterogeneous Networks
Hwang, S.; Lee, D.-S.; Kahng, B.
2012-08-01
The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous networks, is not yet fully understood. Here, we study, both analytically and numerically, the scaling behavior of the FPT distribution to a given target node, averaged over all starting nodes. We find that random walks arrive quickly at a local hub, and therefore, the FPT distribution shows a crossover with respect to time from fast decay behavior (induced from the attractive effect to the hub) to slow decay behavior (caused by the exploring of the entire system). Moreover, the mean FPT is independent of the degree of the target node in the case of compact exploration. These theoretical results justify the necessity of using a random jump protocol (empirically used in search engines) and provide guidelines for designing an effective network to make information quickly accessible.
Aging Renewal Theory and Application to Random Walks
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Johannes H. P. Schulz
2014-02-01
Full Text Available We discuss a renewal process in which successive events are separated by scale-free waiting time periods. Among other ubiquitous long-time properties, this process exhibits aging: events counted initially in a time interval [0,t] statistically strongly differ from those observed at later times [t_{a},t_{a}+t]. The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. In complex, disordered media, processes with scale-free waiting times play a particularly prominent role. We set up a unified analytical foundation for such anomalous dynamics by discussing in detail the distribution of the aging renewal process. We analyze its half-discrete, half-continuous nature and study its aging time evolution. These results are readily used to discuss a scale-free anomalous diffusion process, the continuous-time random walk. By this, we not only shed light on the profound origins of its characteristic features, such as weak ergodicity breaking, along the way, we also add an extended discussion on aging effects. In particular, we find that the aging behavior of time and ensemble averages is conceptually very distinct, but their time scaling is identical at high ages. Finally, we show how more complex motion models are readily constructed on the basis of aging renewal dynamics.
How fast does a random walk cover a torus?
Grassberger, Peter
2017-07-01
We present high statistics simulation data for the average time that a random walk needs to cover completely a two-dimensional torus of size L ×L . They confirm the mathematical prediction that ˜(LlnL ) 2 for large L , but the prefactor seems to deviate significantly from the supposedly exact result 4 /π derived by Dembo et al. [Ann. Math. 160, 433 (2004), 10.4007/annals.2004.160.433], if the most straightforward extrapolation is used. On the other hand, we find that this scaling does hold for the time TN (t )=1(L ) at which the average number of yet unvisited sites is 1, as also predicted previously. This might suggest (wrongly) that and TN (t )=1(L ) scale differently, although the distribution of rescaled cover times becomes sharp in the limit L →∞ . But our results can be reconciled with those of Dembo et al. by a very slow and nonmonotonic convergence of /(LlnL ) 2 , as had been indeed proven by Belius et al. [Probab. Theory Relat. Fields 167, 461 (2017), 10.1007/s00440-015-0689-6] for Brownian walks, and was conjectured by them to hold also for lattice walks.
KNOTS AND RANDOM WALKS IN VIBRATED GRANULAR CHAINS
Energy Technology Data Exchange (ETDEWEB)
E. BEN-NAIM; ET AL
2000-08-01
The authors study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with the theoretical values.
From quenched disorder to continuous time random walk
Burov, Stanislav
2017-11-01
This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation, t →t /Λ1 /α , for a transient process in the subdiffusive regime is sufficient for asymptotic mapping. An exact form of the constant Λ1 /α is established. A disorder averaged position probability density function for a quenched trap model is obtained, and analytic expressions for the diffusion coefficient and drift are provided.
Nonparametric resampling of random walks for spectral network clustering
Fallani, Fabrizio De Vico; Nicosia, Vincenzo; Latora, Vito; Chavez, Mario
2014-01-01
Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to replicate structural features of complex networks based on the non-parametric resampling of the transition matrix associated with an unbiased random walk on the graph. We test this bootstrapping technique on synthetic and real-world modular networks and we show that the ensemble of replicates obtained through resampling can be used to improve the performance of standard spectral algorithms for community detection.
Cochlea Segmentation using Iterated Random Walks with Shape Prior
DEFF Research Database (Denmark)
Ruiz Pujadas, Esmeralda; Kjer, Hans Martin; Vera, Sergio
2016-01-01
Cochlear implants can restore hearing to deaf or partially deaf patients. In order to plan the intervention, a model from high resolution μCT images is to be built from accurate cochlea segmentations and then, adapted to a patient-specific model. Thus, a precise segmentation is required to build...... such a model. We propose a new framework for segmentation of μCT cochlear images using random walks where a region term is combined with a distance shape prior weighted by a confidence map to adjust its influence according to the strength of the image contour. Then, the region term can take advantage...
Fractional telegrapher's equation from fractional persistent random walks.
Masoliver, Jaume
2016-05-01
We generalize the telegrapher's equation to allow for anomalous transport. We derive the space-time fractional telegrapher's equation using the formalism of the persistent random walk in continuous time. We also obtain the characteristic function of the space-time fractional process and study some particular cases and asymptotic approximations. Similarly to the ordinary telegrapher's equation, the time-fractional equation also presents distinct behaviors for different time scales. Specifically, transitions between different subdiffusive regimes or from superdiffusion to subdiffusion are shown by the fractional equation as time progresses.
Nonparametric resampling of random walks for spectral network clustering.
De Vico Fallani, Fabrizio; Nicosia, Vincenzo; Latora, Vito; Chavez, Mario
2014-01-01
Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to replicate structural features of complex networks based on the non-parametric resampling of the transition matrix associated with an unbiased random walk on the graph. We test this bootstrapping technique on synthetic and real-world modular networks and we show that the ensemble of replicates obtained through resampling can be used to improve the performance of standard spectral algorithms for community detection.
Fractional telegrapher's equation from fractional persistent random walks
Masoliver, Jaume
2016-05-01
We generalize the telegrapher's equation to allow for anomalous transport. We derive the space-time fractional telegrapher's equation using the formalism of the persistent random walk in continuous time. We also obtain the characteristic function of the space-time fractional process and study some particular cases and asymptotic approximations. Similarly to the ordinary telegrapher's equation, the time-fractional equation also presents distinct behaviors for different time scales. Specifically, transitions between different subdiffusive regimes or from superdiffusion to subdiffusion are shown by the fractional equation as time progresses.
: The origins of the random walk model in financial theory
Walter, Christian
2013-01-01
Ce texte constitue le chapitre 2 de l'ouvrage Le modèle de marche au hasard en finance, de Christian Walter, à paraître chez Economica, collection " Audit, assurance, actuariat ", en juin 2013. Il est publié ici avec l'accord de l'éditeur.; Three main concerns pave the way for the birth of the random walk model in financial theory: an ethical issue with Jules Regnault (1834-1894), a scientific issue with Louis Bachelier (1870-1946) and a pratical issue with Alfred Cowles (1891-1984). Three to...
Anomalous diffusion in correlated continuous time random walks
Energy Technology Data Exchange (ETDEWEB)
Tejedor, Vincent; Metzler, Ralf, E-mail: metz@ph.tum.d [Physics Department T30 g, Technical University of Munich, 85747 Garching (Germany)
2010-02-26
We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with the mean squared displacement (r{sup 2}(t)) {approx_equal} t{sup 2/3}. Long-ranged correlations of the waiting times with a power-law exponent alpha (0 < alpha <= 2) give rise to subdiffusion of the form (r{sup 2}(t)) {approx_equal} t{sup {alpha}/(1+{alpha})}. In contrast, correlations in the jump lengths are shown to produce superdiffusion. We show that in both cases weak ergodicity breaking occurs. Our results are in excellent agreement with simulations. (fast track communication)
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.
The effect of vertical scaling on the estimation of the fractal dimension of randomly rough surfaces
Schouwenaars, Rafael; Jacobo, Víctor H.; Ortiz, Armando
2017-12-01
Fractal analysis of randomly rough surface is an interesting tool to establish relationships between surface geometry and properties. Nonetheless, the observation that different methods to determine the fractal dimension D yield different results has raised questions about its physical meaning. This work shows that such variations are caused by the mathematical details of the methods used, particularly by the effect of vertical scaling. For the triangular prism method (TPM), applied to fractional Brownian motion, the effect of vertical scaling on the numerical estimation of D can be addressed through analytic calculations. The analytic approach was compared to simulations of surface topography obtained by the random midpoint algorithm (RMA) using TPM, box count method (BCM), differential box count (DBC) and detrended fluctuation analysis (DFA). The effect of scaling for TPM is considerable and coincides with the mathematical predictions. BCM and DBC show no effect of scaling but provide poor estimates at high D. A small effect was found for DFA. It is concluded that TPM provides a precise estimate of D which is independent of vertical scaling for infinite image resolution. At finite resolutions, the estimation error on D can be minimised by choosing an optimal vertical scaling factor.
Record statistics of a strongly correlated time series: random walks and Lévy flights
Godrèche, Claude; Majumdar, Satya N.; Schehr, Grégory
2017-08-01
We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few years, it was indeed realized that random walks are a very useful ‘laboratory’ to test the effects of correlations on the record statistics. We start with the simple one-dimensional random walk with symmetric jumps (both continuous and discrete) and discuss in detail the statistics of the number of records, as well as of the ages of the records, i.e. the lapses of time between two successive record breaking events. Then we review the results that were obtained for a wide variety of random walk models, including random walks with a linear drift, continuous time random walks, constrained random walks (like the random walk bridge) and the case of multiple independent random walkers. Finally, we discuss further observables related to records, like the record increments, as well as some questions raised by physical applications of record statistics, like the effects of measurement error and noise.
Walk dimension for light in complex disordered media
Savo, Romolo; Burresi, Matteo; Svensson, Tomas; Vynck, Kevin; Wiersma, Diederik S.
2014-08-01
Transport in complex systems is characterized by a fractal dimension—the walk dimension—that indicates the diffusive or anomalous nature of the underlying random walk process. Here we report on the experimental retrieval of this key quantity, using light waves propagating in disordered media. The approach is based on measurements of the time-resolved transmission, in particular on how the lifetime scales with sample size. We show that this allows one to retrieve the walk dimension and apply the concept to samples with varying degree of fractal heterogeneity. In addition, the method provides the first experimental demonstration of anomalous light dynamics in a random medium.
The Random Walk Model Based on Bipartite Network
Directory of Open Access Journals (Sweden)
Zhang Man-Dun
2016-01-01
Full Text Available With the continuing development of the electronic commerce and growth of network information, there is a growing possibility for citizens to be confused by the information. Though the traditional technology of information retrieval have the ability to relieve the overload of information in some extent, it can not offer a targeted personality service based on user’s interests and activities. In this context, the recommendation algorithm arose. In this paper, on the basis of conventional recommendation, we studied the scheme of random walk based on bipartite network and the application of it. We put forward a similarity measurement based on implicit feedback. In this method, a uneven character vector is imported(the weight of item in the system. We put forward a improved random walk pattern which make use of partial or incomplete neighbor information to create recommendation information. In the end, there is an experiment in the real data set, the recommendation accuracy and practicality are improved. We promise the reality of the result of the experiment
Do MENA stock market returns follow a random walk process?
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.
An explicit semantic relatedness measure based on random walk
Directory of Open Access Journals (Sweden)
HU Sihui
2016-10-01
Full Text Available The semantic relatedness calculation of open domain knowledge network is a significant issue.In this paper,pheromone strategy is drawn from the thought of ant colony algorithm and is integrated into the random walk which is taken as the basic framework of calculating the semantic relatedness degree.The pheromone distribution is taken as a criterion of determining the tightness degree of semantic relatedness.A method of calculating semantic relatedness degree based on random walk is proposed and the exploration process of calculating the semantic relatedness degree is presented in a dominant way.The method mainly contains Path Select Model(PSM and Semantic Relatedness Computing Model(SRCM.PSM is used to simulate the path selection of ants and pheromone release.SRCM is used to calculate the semantic relatedness by utilizing the information returned by ants.The result indicates that the method could complete semantic relatedness calculation in linear complexity and extend the feasible strategy of semantic relatedness calculation.
A Random Walk Approach to Query Informative Constraints for Clustering.
Abin, Ahmad Ali
2017-08-09
This paper presents a random walk approach to the problem of querying informative constraints for clustering. The proposed method is based on the properties of the commute time, that is the expected time taken for a random walk to travel between two nodes and return, on the adjacency graph of data. Commute time has the nice property of that, the more short paths connect two given nodes in a graph, the more similar those nodes are. Since computing the commute time takes the Laplacian eigenspectrum into account, we use this property in a recursive fashion to query informative constraints for clustering. At each recursion, the proposed method constructs the adjacency graph of data and utilizes the spectral properties of the commute time matrix to bipartition the adjacency graph. Thereafter, the proposed method benefits from the commute times distance on graph to query informative constraints between partitions. This process iterates for each partition until the stop condition becomes true. Experiments on real-world data show the efficiency of the proposed method for constraints selection.
Predicting genetic interactions with random walks on biological networks
Directory of Open Access Journals (Sweden)
Singh Ambuj K
2009-01-01
Full Text Available Abstract Background Several studies have demonstrated that synthetic lethal genetic interactions between gene mutations provide an indication of functional redundancy between molecular complexes and pathways. These observations help explain the finding that organisms are able to tolerate single gene deletions for a large majority of genes. For example, system-wide gene knockout/knockdown studies in S. cerevisiae and C. elegans revealed non-viable phenotypes for a mere 18% and 10% of the genome, respectively. It has been postulated that the low percentage of essential genes reflects the extensive amount of genetic buffering that occurs within genomes. Consistent with this hypothesis, systematic double-knockout screens in S. cerevisiae and C. elegans show that, on average, 0.5% of tested gene pairs are synthetic sick or synthetic lethal. While knowledge of synthetic lethal interactions provides valuable insight into molecular functionality, testing all combinations of gene pairs represents a daunting task for molecular biologists, as the combinatorial nature of these relationships imposes a large experimental burden. Still, the task of mapping pairwise interactions between genes is essential to discovering functional relationships between molecular complexes and pathways, as they form the basis of genetic robustness. Towards the goal of alleviating the experimental workload, computational techniques that accurately predict genetic interactions can potentially aid in targeting the most likely candidate interactions. Building on previous studies that analyzed properties of network topology to predict genetic interactions, we apply random walks on biological networks to accurately predict pairwise genetic interactions. Furthermore, we incorporate all published non-interactions into our algorithm for measuring the topological relatedness between two genes. We apply our method to S. cerevisiae and C. elegans datasets and, using a decision tree
Random walks on activity-driven networks with attractiveness
Alessandretti, Laura; Sun, Kaiyuan; Baronchelli, Andrea; Perra, Nicola
2017-05-01
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously distributed. Here, we present a time-varying network model where each node and the dynamical formation of ties are characterized by these two features. We study how these properties affect random-walk processes unfolding on the network when the time scales describing the process and the network evolution are comparable. We derive analytical solutions for the stationary state and the mean first-passage time of the process, and we study cases informed by empirical observations of social networks. Our work shows that previously disregarded properties of real social systems, such as heterogeneous distributions of activity and attractiveness as well as the correlations between them, substantially affect the dynamical process unfolding on the network.
Integrodifferential diffusion equation for continuous-time random walk.
Fa, Kwok Sau; Wang, K G
2010-01-01
In this paper, we present an integrodifferential diffusion equation for continuous-time random walk that is valid for a generic waiting time probability density function. Using this equation, we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential and a combination of power law and generalized Mittag-Leffler function. We show that for the case of the exponential waiting time probability density function, a normal diffusion is generated and the probability density function is Gaussian distribution. In the case of the combination of a power law and generalized Mittag-Leffler waiting probability density function, we obtain the subdiffusive behavior for all the time regions from small to large times and probability density function is non-Gaussian distribution.
A martingale approach for the elephant random walk
Bercu, Bernard
2018-01-01
The purpose of this paper is to establish, via a martingale approach, some refinements on the asymptotic behavior of the one-dimensional elephant random walk (ERW). The asymptotic behavior of the ERW mainly depends on a memory parameter p which lies between zero and one. This behavior is totally different in the diffusive regime 0 ≤slant p <3/4 , the critical regime p=3/4 , and the superdiffusive regime 3/4. In the diffusive and critical regimes, we establish some new results on the almost sure asymptotic behavior of the ERW, such as the quadratic strong law and the law of the iterated logarithm. In the superdiffusive regime, we provide the first rigorous mathematical proof that the limiting distribution of the ERW is not Gaussian.
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.
Maps of random walks on complex networks reveal community structure.
Rosvall, Martin; Bergstrom, Carl T
2008-01-29
To comprehend the multipartite organization of large-scale biological and social systems, we introduce an information theoretic approach that reveals community structure in weighted and directed networks. We use the probability flow of random walks on a network as a proxy for information flows in the real system and decompose the network into modules by compressing a description of the probability flow. The result is a map that both simplifies and highlights the regularities in the structure and their relationships. We illustrate the method by making a map of scientific communication as captured in the citation patterns of >6,000 journals. We discover a multicentric organization with fields that vary dramatically in size and degree of integration into the network of science. Along the backbone of the network-including physics, chemistry, molecular biology, and medicine-information flows bidirectionally, but the map reveals a directional pattern of citation from the applied fields to the basic sciences.
Scaling Limit of Symmetric Random Walk in High-Contrast Periodic Environment
Piatnitski, A.; Zhizhina, E.
2017-09-01
The paper deals with the asymptotic properties of a symmetric random walk in a high contrast periodic medium in Z^d , d≥1 . From the existing homogenization results it follows that under diffusive scaling the limit behaviour of this random walk need not be Markovian. The goal of this work is to show that if in addition to the coordinate of the random walk in Z^d we introduce an extra variable that characterizes the position of the random walk inside the period then the limit dynamics of this two-component process is Markov. We describe the limit process and observe that the components of the limit process are coupled. We also prove the convergence in the path space for the said random walk.
Scaling Limit of Symmetric Random Walk in High-Contrast Periodic Environment
Piatnitski, A.; Zhizhina, E.
2017-11-01
The paper deals with the asymptotic properties of a symmetric random walk in a high contrast periodic medium in Z^d, d≥1. From the existing homogenization results it follows that under diffusive scaling the limit behaviour of this random walk need not be Markovian. The goal of this work is to show that if in addition to the coordinate of the random walk in Z^d we introduce an extra variable that characterizes the position of the random walk inside the period then the limit dynamics of this two-component process is Markov. We describe the limit process and observe that the components of the limit process are coupled. We also prove the convergence in the path space for the said random walk.
Subordinated diffusion and continuous time random walk asymptotics.
Dybiec, Bartłomiej; Gudowska-Nowak, Ewa
2010-12-01
Anomalous transport is usually described either by models of continuous time random walks (CTRWs) or, otherwise, by fractional Fokker-Planck equations (FFPEs). The asymptotic relation between properly scaled CTRW and fractional diffusion process has been worked out via various approaches widely discussed in literature. Here, we focus on a correspondence between CTRWs and time and space fractional diffusion equation stemming from two different methods aimed to accurately approximate anomalous diffusion processes. One of them is the Monte Carlo simulation of uncoupled CTRW with a Lévy α-stable distribution of jumps in space and a one-parameter Mittag-Leffler distribution of waiting times. The other is based on a discretized form of a subordinated Langevin equation in which the physical time defined via the number of subsequent steps of motion is itself a random variable. Both approaches are tested for their numerical performance and verified with known analytical solutions for the Green function of a space-time fractional diffusion equation. The comparison demonstrates a trade off between precision of constructed solutions and computational costs. The method based on the subordinated Langevin equation leads to a higher accuracy of results, while the CTRW framework with a Mittag-Leffler distribution of waiting times provides efficiently an approximate fundamental solution to the FFPE and converges to the probability density function of the subordinated process in a long-time limit. © 2010 American Institute of Physics.
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.
Ranking competitors using degree-neutralized random walks.
Directory of Open Access Journals (Sweden)
Seungkyu Shin
Full Text Available 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.
Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.
Rhea, Christopher K; Kiefer, Adam W; D'Andrea, Susan E; Warren, William H; Aaron, Roy K
2014-08-01
Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA α in the baseline condition was 0.77±0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA α=0.87±0.06) and to the random metronome (DFA α=0.61±0.10) (both p<.05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon. Copyright © 2014 Elsevier B.V. All rights reserved.
Saccadic Tracking with Random Walk (brownian Motion) Stimuli.
Horner, Douglas Gordon
This study was designed to evaluate the saccadic system's response to continuously presented random walk (Brownian motion) stimuli. Our goals were: (1) to examine how closely timed consecutive saccades interact; and (2) to estimate the response modification time for the new position of the stimulus to give an estimate of integration and decision delays. Horizontal eye movements resulting from rapid continuous random target movements were recorded. Step amplitudes of 1.5 and 3.0 degrees were alternated between single- and rapid double-step movements every 200 to 400 msec. From these random multiple stimulus step sequences, saccadic responses to single 3.0 degree step stimuli were collected for subjects to evaluate interactions of consecutive saccades. The results showed that: (1) subjects are capable of making independent goal directed saccades with intersaccadic intervals as short as 50 msec, and (2) subjects had individual biases in the direction of the successive saccades. The main interaction between saccades was related to the spatial error of the preceding saccade combining with the new stimulus step to yield the new error signal for the next saccade. The magnitude of the new retinal error signal was reflected in the latency of the following saccade. To evaluate the decision period of the saccadic system, the single-step responses were used as templates to assess the modification times for staircase, pulse under -return and pulse over-return double-step stimuli. The responses were organized by whether consecutive saccades continued in the same direction or in the opposite direction. The results on the modification times indicate saccadic responses are directed to the new stimulus 85 to 90 msec after the new position of the stimulus. This modification time was independent of stimuli and preferred direction of responses. The 85-90 msec modification delay is used to estimate the time interval needed to program the next saccade.
Comets, F
2003-01-01
We consider a one-dimensional random walk in random environment in the Sinai's regime. Our main result is that logarithms of the transition probabilities, after a suitable rescaling, converge in distribution as time tends to infinity, to some functional of the Brownian motion. We compute the law of this functional when the initial and final points agree. Also, among other things, we estimate the probability of being at time~$t$ at distance at least $z$ from the initial position, when $z$ is larger than $\\ln^2 t$, but still of logarithmic order in time.
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...... of maximum milking speed. Wood curve did not provide a good fit to the data set. Quadratic random regressions gave better predictions compared with the random walk model. However random walk model does not need to be evaluated for different orders of regression coefficients. In addition with the Kalman...... filter applications: random walk model could give online prediction of breeding values. Hence without waiting for whole lactation records, genetic evaluation could be made when the daily or monthly data is available...
Random Walk Particle Tracking For Multiphase Heat Transfer
Lattanzi, Aaron; Yin, Xiaolong; Hrenya, Christine
2017-11-01
As computing capabilities have advanced, direct numerical simulation (DNS) has become a highly effective tool for quantitatively predicting the heat transfer within multiphase flows. Here we utilize a hybrid DNS framework that couples the lattice Boltzmann method (LBM) to the random walk particle tracking (RWPT) algorithm. The main challenge of such a hybrid is that discontinuous fields pose a significant challenge to the RWPT framework and special attention must be given to the handling of interfaces. We derive a method for addressing discontinuities in the diffusivity field, arising at the interface between two phases. Analytical means are utilized to develop an interfacial tracer balance and modify the RWPT algorithm. By expanding the modulus of the stochastic (diffusive) step and only allowing a subset of the tracers within the high diffusivity medium to undergo a diffusive step, the correct equilibrium state can be restored (globally homogeneous tracer distribution). The new RWPT algorithm is implemented within the SUSP3D code and verified against a variety of systems: effective diffusivity of a static gas-solids mixture, hot sphere in unbounded diffusion, cooling sphere in unbounded diffusion, and uniform flow past a hot sphere.
Ordering of random walks: the leader and the laggard
Energy Technology Data Exchange (ETDEWEB)
Ben-Avraham, D [Department of Physics, Clarkson University, Potsdam, NY 13699-5820, USA (United States); Johnson, B M [Department of Physics, Clarkson University, Potsdam, NY 13699-5820, USA (United States); Monaco, C A [Department of Physics, Clarkson University, Potsdam, NY 13699-5820, USA (United States); Krapivsky, P L [Center for BioDynamics, Center for Polymer Studies, and Department of Physics, Boston University, Boston, MA 02215, USA (United States); Redner, S [Center for BioDynamics, Center for Polymer Studies, and Department of Physics, Boston University, Boston, MA 02215, USA (United States)
2003-02-21
We investigate two complementary problems related to maintaining the relative positions of N random walks on the line: (i) the leader problem, that is, the probability L{sub N}(t) that the leftmost particle remains the leftmost as a function of time and (ii) the laggard problem, the probability R{sub N}(t) that the rightmost particle never becomes the leftmost. We map these ordering problems onto an equivalent (N - 1)-dimensional electrostatic problem. From this construction we obtain a very accurate estimate for L{sub N}(t) for N = 4, the first case that is not exactly solvable: L{sub 4}(t) {proportional_to} t{sup -{beta}{sub 4}}, with {beta}{sub 4} = 0.91342(8). The probability of being the laggard also decays algebraically, R{sub N}(t) {proportional_to} t{sup -{gamma}{sub N}}; we derive {gamma}{sub 2} = 1/2, {gamma}{sub 3} = 3/8, and argue that {gamma}{sub N} {yields} N{sup -1} ln N as N {yields} {infinity}.
Peer-to-Peer Topology Formation Using Random Walk
Kwong, Kin-Wah; Tsang, Danny H. K.
Peer-to-Peer (P2P) systems such as live video streaming and content sharing are usually composed of a huge number of users with heterogeneous capacities. As a result, designing a distributed algorithm to form such a giant-scale topology in a heterogeneous environment is a challenging question because, on the one hand, the algorithm should exploit the heterogeneity of users' capacities to achieve load-balancing and, on the other hand, the overhead of the algorithm should be kept as low as possible. To meet such requirements, we introduce a very simple protocol for building heterogeneous unstructured P2P networks. The basic idea behind our protocol is to exploit a simple, distributed nature of random walk sampling to assist the peers in selecting their suitable neighbors in terms of capacity and connectivity to achieve load-balancing. To gain more insights into our proposed protocol, we also develop a detailed analysis to investigate our protocol under any heterogeneous P2P environment. The analytical results are validated by the simulations. The ultimate goal of this chapter is to stimulate further research to explore the fundamental issues in heterogeneous P2P networks.
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.
Positive polynomials, convex integral polytopes, and a random walk problem
Handelman, David E
1987-01-01
Emanating from the theory of C*-algebras and actions of tori theoren, the problems discussed here are outgrowths of random walk problems on lattices. An AGL (d,Z)-invariant (which is a partially ordered commutative algebra) is obtained for lattice polytopes (compact convex polytopes in Euclidean space whose vertices lie in Zd), and certain algebraic properties of the algebra are related to geometric properties of the polytope. There are also strong connections with convex analysis, Choquet theory, and reflection groups. This book serves as both an introduction to and a research monograph on the many interconnections between these topics, that arise out of questions of the following type: Let f be a (Laurent) polynomial in several real variables, and let P be a (Laurent) polynomial with only positive coefficients; decide under what circumstances there exists an integer n such that Pnf itself also has only positive coefficients. It is intended to reach and be of interest to a general mathematical audience as we...
Electron avalanche structure determined by random walk theory
Englert, G. W.
1973-01-01
A self-consistent avalanche solution which accounts for collective long range Coulomb interactions as well as short range elastic and inelastic collisions between electrons and background atoms is made possible by a random walk technique. Results show that the electric field patterns in the early formation stages of avalanches in helium are close to those obtained from theory based on constant transport coefficients. Regions of maximum and minimum induced electrostatic potential phi are located on the axis of symmetry and within the volume covered by the electron swarm. As formation time continues, however, the region of minimum phi moves to slightly higher radii and the electric field between the extrema becomes somewhat erratic. In the intermediate formation periods the avalanche growth is slightly retarded by the high concentration of ions in the tail which oppose the external electric field. Eventually the formation of ions and electrons in the localized regions of high field strength more than offset this effect causing a very abrupt increase in avalanche growth.
Random walks with long-range steps generated by functions of Laplacian matrices
Riascos, A. P.; Michelitsch, T. M.; Collet, B. A.; Nowakowski, A. F.; Nicolleau, F. C. G. A
2017-01-01
In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information in the Laplacian matrix, that describes the connections of a network, to a dynamics determined by functions of this matrix. The resulting processes is non-local allowing transitions of the random walker from one node to nodes beyond its nearest neighbors. I...
Kapadia, Naaz; Masani, Kei; Catharine Craven, B; Giangregorio, Lora M; Hitzig, Sander L; Richards, Kieva; Popovic, Milos R
2014-09-01
Multi-channel surface functional electrical stimulation (FES) for walking has been used to improve voluntary walking and balance in individuals with spinal cord injury (SCI). To investigate short- and long-term benefits of 16 weeks of thrice-weekly FES-assisted walking program, while ambulating on a body weight support treadmill and harness system, versus a non-FES exercise program, on improvements in gait and balance in individuals with chronic incomplete traumatic SCI, in a randomized controlled trial design. Individuals with traumatic and chronic (≥18 months) motor incomplete SCI (level C2 to T12, American Spinal Cord Injury Association Impairment Scale C or D) were recruited from an outpatient SCI rehabilitation hospital, and randomized to FES-assisted walking therapy (intervention group) or aerobic and resistance training program (control group). Outcomes were assessed at baseline, and after 4, 6, and 12 months. Gait, balance, spasticity, and functional measures were collected. Spinal cord independence measure (SCIM) mobility sub-score improved over time in the intervention group compared with the control group (baseline/12 months: 17.27/21.33 vs. 19.09/17.36, respectively). On all other outcome measures the intervention and control groups had similar improvements. Irrespective of group allocation walking speed, endurance, and balance during ambulation all improved upon completion of therapy, and majority of participants retained these gains at long-term follow-ups. Task-oriented training improves walking ability in individuals with incomplete SCI, even in the chronic stage. Further randomized controlled trials, involving a large number of participants are needed, to verify if FES-assisted treadmill training is superior to aerobic and strength training.
DEFF Research Database (Denmark)
Visser, Andre
2008-01-01
The movement of plankton, either by turbulent mixing or their own inherent motility, can be simulated in a Lagrangian framework as a random walk. Validation of random walk simulations is essential. There is a continuum of mathematically valid stochastic integration schemes upon which random walk ...
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
2017-02-09
Feb 9, 2017 ... We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplica- tive approaches have been compared.
Movement and Man at the end of the Random Walks
Sacripanti, Attilio
2008-01-01
In this paper, it is presented the well known aspect of non linearity of internal human body structures. Similarity on the basis of the Fractional Brownian Motion from the static ones, as the geometrical fractals like the Intestine and placenta linings, Airways in lungs, Arterial system in kidneys and so on. To the kinematics ones, as the temporal fractals like Heart beat sequences, Electroencephalograms, Respiratory tidal volumes, DNA sequences mapping and so on. But this internal well known knowledge is astonishing extendible from the internal, through the Brownian basis of the muscular contraction, to the macroscopic external human movements, like the orthostatic equilibrium, gait, running training, judo contest and soccer, basketball, football or water polo games, by means of the ubiquitous continuous presence; the Brownian Dynamics.
Walking adaptability therapy after stroke: study protocol for a randomized controlled trial.
Timmermans, Celine; Roerdink, Melvyn; van Ooijen, Marielle W; Meskers, Carel G; Janssen, Thomas W; Beek, Peter J
2016-08-26
Walking in everyday life requires the ability to adapt walking to the environment. This adaptability is often impaired after stroke, and this might contribute to the increased fall risk after stroke. To improve safe community ambulation, walking adaptability training might be beneficial after stroke. This study is designed to compare the effects of two interventions for improving walking speed and walking adaptability: treadmill-based C-Mill therapy (therapy with augmented reality) and the overground FALLS program (a conventional therapy program). We hypothesize that C-Mill therapy will result in better outcomes than the FALLS program, owing to its expected greater amount of walking practice. This is a single-center parallel group randomized controlled trial with pre-intervention, post-intervention, retention, and follow-up tests. Forty persons after stroke (≥3 months) with deficits in walking or balance will be included. Participants will be randomly allocated to either C-Mill therapy or the overground FALLS program for 5 weeks. Both interventions will incorporate practice of walking adaptability and will be matched in terms of frequency, duration, and therapist attention. Walking speed, as determined by the 10 Meter Walking Test, will be the primary outcome measure. Secondary outcome measures will pertain to walking adaptability (10 Meter Walking Test with context or cognitive dual-task and Interactive Walkway assessments). Furthermore, commonly used clinical measures to determine walking ability (Timed Up-and-Go test), walking independence (Functional Ambulation Category), balance (Berg Balance Scale), and balance confidence (Activities-specific Balance Confidence scale) will be used, as well as a complementary set of walking-related assessments. The amount of walking practice (the number of steps taken per session) will be registered using the treadmill's inbuilt step counter (C-Mill therapy) and video recordings (FALLS program). This process measure will
Fractals and Hidden Symmetries in DNA
Directory of Open Access Journals (Sweden)
Carlo Cattani
2010-01-01
complex representation, together with the corresponding walks on DNA; in particular, it is shown that DNA walks are fractals. Finally, by using the wavelet analysis, the existence of symmetries is proven.
Movie Recommendation using Random Walks over the Contextual Graph
DEFF Research Database (Denmark)
Bogers, Toine
Recommender systems have become an essential tool in fighting information overload. However, the majority of recommendation algorithms focus only on using ratings information, while disregarding information about the context of the recommendation process. We present ContextWalk, a recommendation...
Covering Ground: Movement Patterns and Random Walk Behavior in Aquilonastra anomala Sea Stars.
Lohmann, Amanda C; Evangelista, Dennis; Waldrop, Lindsay D; Mah, Christopher L; Hedrick, Tyson L
2016-10-01
The paths animals take while moving through their environments affect their likelihood of encountering food and other resources; thus, models of foraging behavior abound. To collect movement data appropriate for comparison with these models, we used time-lapse photography to track movements of a small, hardy, and easy-to-obtain organism, Aquilonastra anomala sea stars. We recorded the sea stars in a tank over many hours, with and without a food cue. With food present, they covered less distance, as predicted by theory; this strategy would allow them to remain near food. We then compared the paths of the sea stars to three common models of animal movement: Brownian motion, Lévy walks, and correlated random walks; we found that the sea stars' movements most closely resembled a correlated random walk. Additionally, we compared the search performance of models of Brownian motion, a Lévy walk, and a correlated random walk to that of a model based on the sea stars' movements. We found that the behavior of the modeled sea star walk was similar to that of the modeled correlated random walk and the Brownian motion model, but that the sea star walk was slightly more likely than the other walks to find targets at intermediate distances. While organisms are unlikely to follow an idealized random walk in all details, our data suggest that comparing the effectiveness of an organism's paths to those from theory can give insight into the organism's actual movement strategy. Finally, automated optical tracking of invertebrates proved feasible, and A. anomala was revealed to be a tractable, 2D-movement study system.
Mathematical conversations multicolor problems, problems in the theory of numbers, and random walks
Dynkin, E B
2006-01-01
Comprises Multicolor Problems, dealing with map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; Random Walks, addressing basic problems in probability theory. 1963 edition.
Long-range navigation on complex networks using Lévy random walks
Riascos, A. P.; Mateos, José L.
2012-11-01
We introduce a strategy of navigation in undirected networks, including regular, random, and complex networks, that is inspired by Lévy random walks, generalizing previous navigation rules. We obtained exact expressions for the stationary probability distribution, the occupation probability, the mean first passage time, and the average time to reach a node on the network. We found that the long-range navigation using the Lévy random walk strategy, compared with the normal random walk strategy, is more efficient at reducing the time to cover the network. The dynamical effect of using the Lévy walk strategy is to transform a large-world network into a small world. Our exact results provide a general framework that connects two important fields: Lévy navigation strategies and dynamics on complex networks.
Random walks exhibiting anomalous diffusion: elephants, urns and the limits of normality
Kearney, Michael J.; Martin, Richard J.
2018-01-01
A random walk model is presented which exhibits a transition from standard to anomalous diffusion as a parameter is varied. The model is a variant on the elephant random walk and differs in respect of the treatment of the initial state, which in the present work consists of a given number N of fixed steps. This also links the elephant random walk to other types of history dependent random walk. As well as being amenable to direct analysis, the model is shown to be asymptotically equivalent to a non-linear urn process. This provides fresh insights into the limiting form of the distribution of the walker’s position at large times. Although the distribution is intrinsically non-Gaussian in the anomalous diffusion regime, it gradually reverts to normal form when N is large under quite general conditions.
Ovchinnikov, M. N.
2017-09-01
The fundamental solutions of the diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences between fundamental solutions, flows and concentration gradients were studied. The new modified non-local diffusion equation of the telegrapher type with correction function is suggested. It contains only microparameters of the random walk problem.
Random Walks and Market Efficiency: Evidence from International Real Estate Markets
Robert T. Kleiman; Payne, James E.; Anandi P. Sahu
2002-01-01
This study performs tests of the random walk hypothesis for international commercial real estate markets utilizing stock market indices of real estate share prices for three geographical regions: Europe, Asia and North America. The augmented Dickey-Fuller and Phillips-Perron unit root tests and Cochrane variance ratio test find that each of these markets (as well as associated broader stock markets) exhibits random walk behavior. Moreover, a non-parametric runs test provides support for weak-...
Energy Technology Data Exchange (ETDEWEB)
Conte, Elio [Department of Pharmacology and Human Physiology and Tires, Center for Innovative Technologies for Signal Detection and Processing, University of Bari (Italy); School of Advanced International Studies on Theoretical and Nonlinear Methodologies-Bari (Italy)], E-mail: elio.conte@fastwebnet.it; Khrennikov, Andrei [International Center for Mathematical Modelling in Physics and Cognitive Sciences, M.S.I., University of Vaexjoe, S-35195 (Sweden); Federici, Antonio [Department of Pharmacology and Human Physiology and Tires, Center for Innovative Technologies for Signal Detection and Processing, University of Bari (Italy); Zbilut, Joseph P. [Department of Molecular Biophysics and Physiology, Rush University Medical Center, 1653W Congress, Chicago, IL 60612 (United States)
2009-09-15
We develop a new method for analysis of fundamental brain waves as recorded by the EEG. To this purpose we introduce a Fractal Variance Function that is based on the calculation of the variogram. The method is completed by using Random Matrix Theory. Some examples are given. We also discuss the link of such formulation with H. Weiss and V. Weiss golden ratio found in the brain, and with El Naschie fractal Cantorian space-time theory.
Esbenshade, Donald H., Jr.
1991-01-01
Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)
Directory of Open Access Journals (Sweden)
WU Hao
2017-05-01
Full Text Available The differences in the satellite orbit and signal quality of global navigation satellite positioning system, resulting in the complexity of random walk noise in GNSS time series, has become a bottleneck problem in applying GNSS technology to the high precision deformation monitoring industry. For the complex characteristics of random walk noise, small magnitude, low frequency and low sensitivity, an improved semisoft threshold algorithm is presented. Then it forms a unified system of semisoft threshold function, so as to improve the adaptability of conventional semisoft threshold for random walk noise. In order to verify and evaluate the effect of improved semisoft threshold algorithm, MATLAB platform is used to generate a linear trend, periodic and random walk noise of the GNSS time series, a total of 1700 epochs. The results show that the improved semisoft threshold method is better than the classical method, and has better performance in the SNR and root mean square error. The evaluation results show that the morphological character has been performanced high consistency between the noise reduced by improved method with random walk noise. Further from the view of quantitative point, the evaluation results of spectral index analysis verify the applicability of the improved method for random walk noise.
Patching, Geoffrey R.; Rahm, Johan; Jansson, Märit; Johansson, Maria
2017-01-01
Accurate assessment of people’s preferences for different outdoor lighting applications is increasingly considered important in the development of new urban environments. Here a new method of random environmental walking is proposed to complement current methods of assessing urban lighting applications, such as self-report questionnaires. The procedure involves participants repeatedly walking between different lighting applications by random selection of a lighting application and preferred choice or by random selection of a lighting application alone. In this manner, participants are exposed to all lighting applications of interest more than once and participants’ preferences for the different lighting applications are reflected in the number of times they walk to each lighting application. On the basis of an initial simulation study, to explore the feasibility of this approach, a comprehensive field test was undertaken. The field test included random environmental walking and collection of participants’ subjective ratings of perceived pleasantness (PP), perceived quality, perceived strength, and perceived flicker of four lighting applications. The results indicate that random environmental walking can reveal participants’ preferences for different lighting applications that, in the present study, conformed to participants’ ratings of PP and perceived quality of the lighting applications. As a complement to subjectively stated environmental preferences, random environmental walking has the potential to expose behavioral preferences for different lighting applications. PMID:28337163
On a random walk with memory and its relation with Markovian processes
Energy Technology Data Exchange (ETDEWEB)
Turban, Loic, E-mail: turban@lpm.u-nancy.f [Groupe de Physique Statistique, Departement Physique de la Matiere et des Materiaux, Institut Jean Lamour (Laboratoire associe au CNRS UMR 7198), CNRS-Nancy Universite-UPV Metz, BP 70239, F-54506 Vandoeuvre les Nancy Cedex (France)
2010-07-16
We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and leads to a non-diffusive walk. The time evolution of the displacement is given by an equivalent Markovian dynamical process. The probability density for the position of the walker is the same at any time as for a random walk with shrinking steps, although the two-time correlation functions are quite different.
Persistent fluctuations in stride intervals under fractal auditory stimulation.
Marmelat, Vivien; Torre, Kjerstin; Beek, Peter J; Daffertshofer, Andreas
2014-01-01
Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.
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.
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...
Human mammary epithelial cells exhibit a bimodal correlated random walk pattern.
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Alka A Potdar
2010-03-01
Full Text Available Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells that exist in multi-cellular organisms (humans follow a bimodal correlated random walk (BCRW.Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation.Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.
Fractal physiology and the fractional calculus: a perspective
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Bruce J West
2010-10-01
Full Text Available This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. We review the allometric aggregation approach to the processing of physiologic time series as a way of determining the fractal character of the underlying phenomena. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. Fractional operators acting on fractal functions yield fractal functions, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine. Allometric control incorporates long-time memory, inverse power-law (IPL correlations, and long-range interactions in complex phenomena as manifest by IPL distributions. We hypothesize that allometric control, rather than homeostatic control, maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can be described using the fractional calculus to capture the dynamics of complex physiologic networks. This hypothesis is supported by a number of physiologic time series data.
Generalized Mittag-Leffler relaxation: clustering-jump continuous-time random walk approach.
Jurlewicz, Agnieszka; Weron, Karina; Teuerle, Marek
2008-07-01
A stochastic generalization of renormalization-group transformation for continuous-time random walk processes is proposed. The renormalization consists in replacing the jump events from a randomly sized cluster by a single renormalized (i.e., overall) jump. The clustering of the jumps, followed by the corresponding transformation of the interjump time intervals, yields a new class of coupled continuous-time random walks which, applied to modeling of relaxation, lead to the general power-law properties usually fitted with the empirical Havriliak-Negami function.
Baxter, Susan V; Hale, Leigh A; Stebbings, Simon; Gray, Andrew R; Smith, Catherine M; Treharne, Gareth J
2016-03-01
Exercise has been recognized as important in the management of rheumatoid arthritis (RA). Walking is a low-cost and low-impact activity, requiring little supervision. It requires no specialist training, is suited to a variety of environments and is inherently a clinically meaningful measure of independence. The aim of the present study was to determine whether a designed walking programme for people with RA successfully facilitated regular physical activity in participants, without detriment to pain levels. Thirty-three people with RA were recruited from Dunedin Hospital rheumatology outpatient clinics and enrolled in a walking randomized controlled trial (RCT) feasibility study. Participants were randomly allocated to the walking intervention (n = 11) or control (n = 22) groups. Control participants received a nutrition education session, and the walking intervention group received instructions on a walking route with three loops, to be completed 3-4 times per week. The walking route shape was designed so that the length of the walk could be tailored by participants. Both groups were assessed at baseline and six weeks later. The primary outcome measures were feasibility, acceptability and safety. The principal secondary outcome was change in walking speed after the intervention. Additional outcome measures were a step-up test, activity limitations (on the Health Assessment Questionnaire), global well-being (on the European Quality of Life Questionnaire), self-efficacy for managing arthritis symptoms, self-efficacy for physical activity, daily pedometer readings and a daily visual analogue scale for pain. Participants successfully completed the walk for the suggested frequency, indicating feasibility and acceptability. There were no reported adverse effects of participation and the walking intervention group did not have higher daily pain levels than the control group, indicating safety. The walking intervention group showed a pattern of improvements in
Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications
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Zhongtuan Zheng
2017-01-01
Full Text Available This paper investigates, both theoretically and numerically, preferential random walks (PRW on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW. Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.
Miller, B.; Blin, A. H.; Dworzecka, M.; Griffin, J. J.
1984-08-01
The correspondence between a random walk process, comprising discrete steps on the integer values of ( N, Z) and the Markovian discrete master equation which it uniquely specifies is reviewed. Differences between the random walk distribution calculated at integral values of the step count q and that of its Markovian master equation at corresponding values of the (continuous) time parameter ( are studied for a certain soluble two-dimensional example. The mean values of N and Z calculated from the random walk and Markovian master equation agree precisely. The second and higher moments which are also linear in the distribution function agree in leading order. But in this case, the N, Z correlation width vanishes identically for the master equation, and is finite in general for the random walk, while the widths of the distributions (which are bilinear in the distribution function) may differ even in leading order. The relevance of these differences to data measured against some independent variable (e.g. total kinetic energy loss in a heavyion collision), which is in fact uniquely related neither to q nor to t, is discussed. Since both random walk and master equations are currently used to analyze the phenomenology of nuclear heavy-ion collisions, the fact that they offer different predictions, and that depending upon the physical circumstances either (or neither) may be the correct description, recommends the development of a more rational basis for choosing between them.
Fractal physiology and the fractional calculus: a perspective.
West, Bruce J
2010-01-01
This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a
Chaos, Periodic Chaos, and the Random- Walk Problem
Kozak, John J.; Musho, Matthew K.; Hatlee, Michael D.
1982-12-01
The authors have studied whether numerically generated sequences from the logistic parabola fb(x)=4bx(1-x) with b, x∈[0,1], for values of b, above the Feigenbaum critical value b∞, are truly chaotic or whether they are periodic but with exceedingly large periods and very long transients. Using the logistic parabola the authors calculate via Monte Carlo simulation the average walk length for trapping on a one-dimensional lattice with a centrosymmetric trap. Comparison with exact results suggests that the only "truly chaotic" sequence is the one for which b=1.
Kim, Chang-Yong; Lee, Jung-Sun; Kim, Hyeong-Dong
2017-02-01
The purposes of the present study were to compare the effects of backward and lateral walking training and to identify whether additional backward or lateral walking training would be more effective in increasing the walking function of poststroke patients. Fifty-one subjects with hemiplegic stroke were randomly allocated to 3 groups, each containing 17 subjects: the control group, the backward walking training group, and the lateral walking training group. The walking abilities of each group were assessed using a 10-m walk test and the GAITRite system for spatiotemporal gait. The results show that there were significantly greater posttest increases in gait velocity (F = -12.09, P = 0.02) and stride length (F = -11.50, P = 0.02), decreases in the values of the 10-m walk test (F = -7.10, P = 0.03) (P training group compared with those in the other 2 groups. These findings demonstrate that asymmetric gait patterns in poststroke patients could be improved by receiving additional lateral walking training therapy rather than backward walking training. Complete the self-assessment activity and evaluation online at http://www.physiatry.org/JournalCME CME OBJECTIVES: Upon completion of this article, the reader should be able to: (1) understand the potential benefits of backward walking (BW) and lateral walking (LW) training on improving muscle strength and gait; (2) appreciate the potential value of backward and lateral walking gait training in the treatment of hemiplegic stroke patients; and (3) appropriately incorporate backward and lateral walking gait training into the treatment plan of hemiplegic stroke patients. Advanced ACCREDITATION: The Association of Academic Physiatrists is accredited by the Accreditation Council for Continuing Medical Education to provide continuing medical education for physicians.The Association of Academic Physiatrists designates this activity for a maximum of 1.5 AMA PRA Category 1 Credit(s)™. Physicians should only claim credit
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...
Evolution of the concentration PDF in random environments modeled by global random walk
Suciu, Nicolae; Vamos, Calin; Attinger, Sabine; Knabner, Peter
2013-04-01
The evolution of the probability density function (PDF) of concentrations of chemical species transported in random environments is often modeled by ensembles of notional particles. The particles move in physical space along stochastic-Lagrangian trajectories governed by Ito equations, with drift coefficients given by the local values of the resolved velocity field and diffusion coefficients obtained by stochastic or space-filtering upscaling procedures. A general model for the sub-grid mixing also can be formulated as a system of Ito equations solving for trajectories in the composition space. The PDF is finally estimated by the number of particles in space-concentration control volumes. In spite of their efficiency, Lagrangian approaches suffer from two severe limitations. Since the particle trajectories are constructed sequentially, the demanded computing resources increase linearly with the number of particles. Moreover, the need to gather particles at the center of computational cells to perform the mixing step and to estimate statistical parameters, as well as the interpolation of various terms to particle positions, inevitably produce numerical diffusion in either particle-mesh or grid-free particle methods. To overcome these limitations, we introduce a global random walk method to solve the system of Ito equations in physical and composition spaces, which models the evolution of the random concentration's PDF. The algorithm consists of a superposition on a regular lattice of many weak Euler schemes for the set of Ito equations. Since all particles starting from a site of the space-concentration lattice are spread in a single numerical procedure, one obtains PDF estimates at the lattice sites at computational costs comparable with those for solving the system of Ito equations associated to a single particle. The new method avoids the limitations concerning the number of particles in Lagrangian approaches, completely removes the numerical diffusion, and
High Dimensional Spectral Graph Theory and Non-backtracking Random Walks on Graphs
Kempton, Mark
This thesis has two primary areas of focus. First we study connection graphs, which are weighted graphs in which each edge is associated with a d-dimensional rotation matrix for some fixed dimension d, in addition to a scalar weight. Second, we study non-backtracking random walks on graphs, which are random walks with the additional constraint that they cannot return to the immediately previous state at any given step. Our work in connection graphs is centered on the notion of consistency, that is, the product of rotations moving from one vertex to another is independent of the path taken, and a generalization called epsilon-consistency. We present higher dimensional versions of the combinatorial Laplacian matrix and normalized Laplacian matrix from spectral graph theory, and give results characterizing the consistency of a connection graph in terms of the spectra of these matrices. We generalize several tools from classical spectral graph theory, such as PageRank and effective resistance, to apply to connection graphs. We use these tools to give algorithms for sparsification, clustering, and noise reduction on connection graphs. In non-backtracking random walks, we address the question raised by Alon et. al. concerning how the mixing rate of a non-backtracking random walk to its stationary distribution compares to the mixing rate for an ordinary random walk. Alon et. al. address this question for regular graphs. We take a different approach, and use a generalization of Ihara's Theorem to give a new proof of Alon's result for regular graphs, and to extend the result to biregular graphs. Finally, we give a non-backtracking version of Polya's Random Walk Theorem for 2-dimensional grids.
Randomized Controlled Theory-Based, E-Mail-Mediated Walking Intervention.
Richards, Elizabeth A; Ogata, Niwako; Cheng, Ching-Wei
2017-02-01
The purpose of this study was to evaluate the ability of two concurrent randomized controlled interventions based on social cognitive theory to increase walking. A second purpose was to compare the efficacy of the intervention between two distinct groups: dog owners and non-dog owners. Adult dog owners ( n = 40) and non-dog owners ( n = 65) were randomized into control or intervention groups. Intervention groups received bi-weekly emails for first 4 weeks and then weekly email for the next 8 weeks targeting self-efficacy, social support, goal setting, and benefits/barriers to walking. Dog owner messages focused on dog walking while non-dog owners received general walking messages. Control groups received a 1-time email reviewing current physical activity guidelines. At 6 months, both intervention groups reported greater increases in walking and maintained these increases at 12 months. The greatest increases were seen in the dog owner intervention group. In conclusion, dog owners accumulated more walking, which may be attributed to the dog-owner relationship.
Random walk of motor planning in task-irrelevant dimensions
van Beers, R.J.; Brenner, E.; Smeets, J.B.J.
2013-01-01
The movements that we make are variable. It is well established that at least a part of this variability is caused by noise in central motor planning. Here, we studied how the random effects of planning noise translate into changes in motor planning. Are the random effects independently added to a
Random time averaged diffusivities for Lévy walks
Froemberg, D.; Barkai, E.
2013-07-01
We investigate a Lévy walk alternating between velocities ±v0 with opposite sign. The sojourn time probability distribution at large times is a power law lacking its mean or second moment. The first case corresponds to a ballistic regime where the ensemble averaged mean squared displacement (MSD) at large times is ⟨x2⟩ ∝ t2, the latter to enhanced diffusion with ⟨x2⟩ ∝ tν, 1 function and the time averaged MSD are calculated. In the ballistic case, the deviations of the time averaged MSD from a purely ballistic behavior are shown to be distributed according to a Mittag-Leffler density function. In the enhanced diffusion regime, the fluctuations of the time averages MSD vanish at large times, yet very slowly. In both cases we quantify the discrepancy between the time averaged and ensemble averaged MSDs.
Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki
2017-12-01
We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2} ). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3} ) and the level sets of the Gaussian free field ({d≥ 3} ). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.
A comparison of orthoses in the treatment of idiopathic toe walking: A randomized controlled trial.
Herrin, Kinsey; Geil, Mark
2016-04-01
Orthotic treatment of idiopathic toe walking is complicated by the lack of a known etiology. This study compared control of toe walking using an articulated ankle-foot orthosis versus a rigid carbon fiber footplate attached to a foot orthosis. Ascertain differences between two orthoses in the control of idiopathic toe walking. Randomized controlled trial. A total of 18 children with idiopathic toe walking were randomized to either the ankle-foot orthosis or foot orthosis treatment group in a Parallel Randomized Controlled Trial with no blinding. Prior to and after 6 weeks of treatment, participants completed three-dimensional gait assessment and the L-test of Functional Mobility. Parents completed a satisfaction survey and a subset of the Orthotic and Prosthetic User Survey after treatment. Nine participants were analyzed in each group. Both groups showed significant improvement in kinematics versus baseline with orthoses; however, when the orthoses were removed, the ankle-foot orthosis group did not immediately sustain this improvement, while the foot orthosis group did. Parents preferred the foot orthosis for donning and appearance. The ankle-foot orthosis controls idiopathic toe walking, but subjects may revert to earlier patterns following treatment. The foot orthosis does not control idiopathic toe walking as well but is less restrictive and more accepted by children and their parents, with similar out-of-brace effects. This study suggests that sequential orthotic treatment for children with idiopathic toe walking (ITW) may be beneficial. Initial treatment could include a less restrictive orthosis like a foot orthosis (FO); if this is unsuccessful within a set time frame, then the patient may require a more restrictive form of treatment such as an ankle-foot orthosis (AFO). © The International Society for Prosthetics and Orthotics 2015.
Seeing shapes in seemingly random spatial patterns: Fractal analysis of Rorschach inkblots
Taylor, R. P.; Martin, T. P.; Montgomery, R. D.; Smith, J. H.; Micolich, A. P.; Boydston, C.; Scannell, B. C.; Fairbanks, M. S.; Spehar, B.
2017-01-01
Rorschach inkblots have had a striking impact on the worlds of art and science because of the remarkable variety of associations with recognizable and namable objects they induce. Originally adopted as a projective psychological tool to probe mental health, psychologists and artists have more recently interpreted the variety of induced images simply as a signature of the observers’ creativity. Here we analyze the relationship between the spatial scaling parameters of the inkblot patterns and the number of induced associations, and suggest that the perceived images are induced by the fractal characteristics of the blot edges. We discuss how this relationship explains the frequent observation of images in natural scenery. PMID:28196082
DEFF Research Database (Denmark)
Bruun Jensen, Casper
2007-01-01
. Instead, I outline a fractal approach to the study of space, society, and infrastructure. A fractal orientation requires a number of related conceptual reorientations. It has implications for thinking about scale and perspective, and (sociotechnical) relations, and for considering the role of the social...... and a fractal social theory....
Directory of Open Access Journals (Sweden)
Choon Sen Seah
2017-12-01
Full Text Available Microarray technology has become one of the elementary tools for researchers to study the genome of organisms. As the complexity and heterogeneity of cancer is being increasingly appreciated through genomic analysis, cancerous classification is an emerging important trend. Significant directed random walk is proposed as one of the cancerous classification approach which have higher sensitivity of risk gene prediction and higher accuracy of cancer classification. In this paper, the methodology and material used for the experiment are presented. Tuning parameter selection method and weight as parameter are applied in proposed approach. Gene expression dataset is used as the input datasets while pathway dataset is used to build a directed graph, as reference datasets, to complete the bias process in random walk approach. In addition, we demonstrate that our approach can improve sensitive predictions with higher accuracy and biological meaningful classification result. Comparison result takes place between significant directed random walk and directed random walk to show the improvement in term of sensitivity of prediction and accuracy of cancer classification.
The Hidden Flow Structure and Metric Space of Network Embedding Algorithms Based on Random Walks.
Gu, Weiwei; Gong, Li; Lou, Xiaodan; Zhang, Jiang
2017-10-13
Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a network, such as the clustering and linking prediction but also learns the latent vector representation of the nodes which provides theoretical support for a variety of applications, such as visualization, link prediction, node classification, and recommendation. As the latest progress of the research, several algorithms based on random walks have been devised. Although those algorithms have drawn much attention for their high scores in learning efficiency and accuracy, there is still a lack of theoretical explanation, and the transparency of those algorithms has been doubted. Here, we propose an approach based on the open-flow network model to reveal the underlying flow structure and its hidden metric space of different random walk strategies on networks. We show that the essence of embedding based on random walks is the latent metric structure defined on the open-flow network. This not only deepens our understanding of random- walk-based embedding algorithms but also helps in finding new potential applications in network embedding.
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...
One-dimensional random walk of nanosized liquid Pb inclusions on dislocations in Al
DEFF Research Database (Denmark)
Johnson, E.; Levinsen, M.T.; Steenstrup, S.
2004-01-01
to and perpendicular to the dislocations respectively. Movements parallel to the dislocation lines display properties of partially confined one-dimensional random walks where smaller inclusions can be seen to move over distances that are many times their own sizes. In contrast, the trajectories perpendicular...
Estimating filtration coefficients for straining from percolation and random walk theories
DEFF Research Database (Denmark)
Yuan, Hao; Shapiro, Alexander; You, Zhenjiang
2012-01-01
the experimentally observed power law dependencies of filtration coefficients and large penetration depths of particles. Such a capture mechanism is realized in a 2D pore network model with periodical boundaries with the random walk of particles on the percolation lattice. Geometries of infinite and finite clusters...
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 and the...
Do exchange rates follow random walks? A variance ratio test of the ...
African Journals Online (AJOL)
However, emerging markets in sub-Saharan Africa have received little attention in this regard. This study applies Lo and MacKinlay's (1988) conventional variance ... Both types of variance ratio tests reject the random-walk hypothesis over the data span. The implication is that technical and fundamental analysis can help ...
Replacement and zig-zag products, Cayley graphs and Lamplighter random walk
Directory of Open Access Journals (Sweden)
Alfredo Donno
2013-03-01
Full Text Available We investigate two constructions - the replacement and the zig-zag product of graphs - describing several fascinating connections with Combinatorics, via the notion of expander graph, Group Theory, via the notion of semidirect product and Cayley graph, andwith Markov chains, via the Lamplighter random walk. Many examples are provided.
Chen, Y.; Boucherie, Richardus J.; Goseling, Jasper
2016-01-01
We consider homogeneous random walks in the quarter-plane. The necessary conditions which characterize random walks of which the invariant measure is a sum of geometric terms are provided in Chen et al. (arXiv:1304.3316, 2013, Probab Eng Informational Sci 29(02):233–251, 2015). Based on these
Necessary conditions for the invariant measure of a random walk to be a sum of geometric terms
Chen, Y.; Boucherie, Richardus J.; Goseling, Jasper
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as an infinite sum of geometric terms. We present necessary conditions for the invariant measure of a random walk to be a sum of geometric terms. We
Elavsky, Steriani; McAuley, Edward
2007-01-01
To examine the effects of walking and yoga on multidimensional self-esteem and roles played by self-efficacy, body composition, and physical activity (PA) in changes in esteem. Four-month randomized controlled exercise trial with three arms: walking, yoga, and control. Previously low-active middle-aged women (n=164; M age = 49.9; SD = 3.6). Structured and supervised walking program meeting three times per week for I hour and supervised yoga program meeting twice per week for 90 minutes. Body composition, fitness assessment, and battery of psychologic measures. Panel analysis within a structural equation modeling framework using Mplus 3.0. The walking and yoga interventions failed to enhance global or physical self-esteem but improved subdomain esteem relative to physical condition and strength (for walking) and body attractiveness (for both walking and yoga). Over time the effects of PA, self-efficacy, and body fat on changes in physical self-esteem and global esteem were mediated by changes in physical condition and body attractiveness subdomain esteem. Women reporting greater levels of self-efficacy and PA with lower body fat also reported greater enhancements in subdomain esteem. These results provide support for the hierarchic and multidimensional nature of self-esteem and indicate that middle-aged women may enhance certain aspects of physical self-esteem by participating in PA.
Comer, Christine M; Johnson, Mark I; Marchant, Paul R; Redmond, Anthony C; Bird, Howard A; Conaghan, Philip G
2010-01-01
Comer CM, Johnson MI, Marchant PR, Redmond AC, Bird HA, Conaghan PG. The effectiveness of walking stick use for neurogenic claudication: results from a randomized trial and the effects on walking tolerance and posture. To determine the immediate effects of using a stick on walking tolerance and on the potential explanatory variable of posture, and to provide a preliminary evaluation of the effects of daily walking stick use on symptoms and function for people with neurogenic claudication. A 2-phase study of neurogenic claudication patients comprising a randomized trial of 2 weeks of home use of a walking stick and a crossover study comparing walking tolerance and posture with and without a walking stick. A primary care-based musculoskeletal service. Patients aged 50 years or older with neurogenic claudication symptoms (N=46; 24 women, 22 men, mean age=71.26y) were recruited. Walking stick. Phase 1 of the trial used the Zurich Claudication Questionnaire symptom severity and physical function scores to measure outcome. The total walking distance during a shuttle walking test and the mean lumbar spinal posture (measured by using electronic goniometry) were used as the primary outcome measurements in the second phase. Forty of the participants completed phase 1 of the trial, and 40 completed phase 2. No significant differences in symptom severity or physical function were shown in score improvements for walking stick users (stick user scores - control scores) in the 2-week trial (95% confidence interval [CI], -.24 to .28 and -.10 to .26, respectively). In the second phase of the trial, the ratio of the shuttle walking distance with a stick to without a stick showed no significance (95% CI, .959-1.096) between the groups. Furthermore, the use of a walking stick did not systematically promote spinal flexion; no significant difference was shown for mean lumbar spinal flexion for stick use versus no stick (95% CI, .351 degrees -.836 degrees ). The prescription of a walking
On the genealogy of branching random walks and of directed polymers
Derrida, Bernard; Mottishaw, Peter
2016-08-01
It is well known that the mean-field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite-size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks.
Fractal frontiers of bursts and cracks in a fiber bundle model of creep rupture.
Danku, Zsuzsa; Kun, Ferenc; Herrmann, Hans J
2015-12-01
We investigate the geometrical structure of breaking bursts generated during the creep rupture of heterogeneous materials. Using a fiber bundle model with localized load sharing we show that bursts are compact geometrical objects; however, their external frontiers have a fractal structure which reflects their growth dynamics. The perimeter fractal dimension of bursts proved to have the universal value 1.25 independent of the external load and of the amount of disorder in the system. We conjecture that according to their geometrical features, breaking bursts fall in the universality class of loop-erased self-avoiding random walks with perimeter fractal dimension 5/4 similar to the avalanches of Abelian sand pile models. The fractal dimension of the growing crack front along which bursts occur proved to increase from 1 to 1.25 as bursts gradually cover the entire front.
Fractal gait patterns are retained after entrainment to a fractal stimulus.
Rhea, Christopher K; Kiefer, Adam W; Wittstein, Matthew W; Leonard, Kelsey B; MacPherson, Ryan P; Wright, W Geoffrey; Haran, F Jay
2014-01-01
Previous work has shown that fractal patterns in gait can be altered by entraining to a fractal stimulus. However, little is understood about how long those patterns are retained or which factors may influence stronger entrainment or retention. In experiment one, participants walked on a treadmill for 45 continuous minutes, which was separated into three phases. The first 15 minutes (pre-synchronization phase) consisted of walking without a fractal stimulus, the second 15 minutes consisted of walking while entraining to a fractal visual stimulus (synchronization phase), and the last 15 minutes (post-synchronization phase) consisted of walking without the stimulus to determine if the patterns adopted from the stimulus were retained. Fractal gait patterns were strengthened during the synchronization phase and were retained in the post-synchronization phase. In experiment two, similar methods were used to compare a continuous fractal stimulus to a discrete fractal stimulus to determine which stimulus type led to more persistent fractal gait patterns in the synchronization and post-synchronization (i.e., retention) phases. Both stimulus types led to equally persistent patterns in the synchronization phase, but only the discrete fractal stimulus led to retention of the patterns. The results add to the growing body of literature showing that fractal gait patterns can be manipulated in a predictable manner. Further, our results add to the literature by showing that the newly adopted gait patterns are retained for up to 15 minutes after entrainment and showed that a discrete visual stimulus is a better method to influence retention.
Ebrahim, S; Thompson, P W; Baskaran, V; Evans, K
1997-07-01
to evaluate the effects of brisk walking on bone mineral density in women who had suffered an upper limb fracture. randomized placebo-controlled trial. Assessments of bone mineral density were made before and at 1 and 2 years after intervention. Standardized and validated measures of physical capacity, self-rated health status and falls were used. district general hospital outpatient department. 165 women drawn from local accident and emergency departments with a history of fracture of an upper limb in the previous 2 years. Women were randomly allocated to intervention (self-paced brisk walking) or placebo (upper limb exercises) groups. both groups were seen at 3-monthly intervals to assess progress, measure physical capacity and maintain enthusiasm. The brisk-walking group were instructed to progressively increase the amount and speed of walking in a manner that suited them. The upper limb exercise placebo group were asked to carry out a series of exercises designed to improve flexibility and fine hand movements, appropriate for a past history of upper limb fracture. drop-outs from both intervention and placebo groups were substantial (41%), although there were no significant differences in bone mineral density, physical capacity or health status between drop-outs and participants. At 2 years, among those completing the trial, bone mineral density at the femoral neck had fallen in the placebo group to a greater extent than in the brisk-walking group [mean net difference between intervention and placebo groups 0.019 g/cm2, 95% confidence interval (CI) -0.0026 to +0.041 g/cm2, P = 0.056]. Lumbar spine bone mineral density had increased to a similar extent (+0.017 g/cm2) in both groups. The cumulative risk of falls was higher in the brisk-walking group (excess risk of 15 per 100 person-years, 95% CI 1.4-29 per 100 person-years, P risk or self-rated health status between intervention and placebo groups. the promotion of exercise through brisk-walking advice given by
Koschate, J; Drescher, U; Thieschäfer, L; Heine, O; Baum, K; Hoffmann, U
2016-12-01
This study aims to compare cardiorespiratory kinetics as a response to a standardised work rate protocol with pseudo-random binary sequences between cycling and walking in young healthy subjects. Muscular and pulmonary oxygen uptake (V̇O2) kinetics as well as heart rate kinetics were expected to be similar for walking and cycling. Cardiac data and V̇O2 of 23 healthy young subjects were measured in response to pseudo-random binary sequences. Kinetics were assessed applying time series analysis. Higher maxima of cross-correlation functions between work rate and the respective parameter indicate faster kinetics responses. Muscular V̇O2 kinetics were estimated from heart rate and pulmonary V̇O2 using a circulatory model. Muscular (walking vs. cycling [mean±SD in arbitrary units]: 0.40±0.08 vs. 0.41±0.08) and pulmonary V̇O2 kinetics (0.35±0.06 vs. 0.35±0.06) were not different, although the time courses of the cross-correlation functions of pulmonary V̇O2 showed unexpected biphasic responses. Heart rate kinetics (0.50±0.14 vs. 0.40±0.14; P=0.017) was faster for walking. Regarding the biphasic cross-correlation functions of pulmonary V̇O2 during walking, the assessment of muscular V̇O2 kinetics via pseudo-random binary sequences requires a circulatory model to account for cardio-dynamic distortions. Faster heart rate kinetics for walking should be considered by comparing results from cycle and treadmill ergometry. © Georg Thieme Verlag KG Stuttgart · New York.
Test of Random Walk Behavior in Karachi Stock Exchange
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.
Continuous-Time Random Walk with multi-step memory: an application to market dynamics
Gubiec, Tomasz; Kutner, Ryszard
2017-11-01
An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary number of successive jumps of the process while waiting times between jumps are considered as i.i.d. random variables. This dependence was established analyzing empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale. Then, it was justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model appeared exactly analytically solvable. Therefore, it enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus, the present research significantly extends capabilities of the CTRW formalism. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
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.
[CGM]). Resultater: Training adherence was high (89 + 4%), and training energy expenditure and mean intensity were comparable between training groups. Nine and four of the subjects reported “Improved Health” in the IWT and CWT group, respectively. VO2max increased 16.1 + 3.7% in the IWT group (P...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......: 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...
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
Stability, fairness and random walks in the bargaining problem
Kapeller, Jakob; Steinerberger, Stefan
2017-12-01
We study the classical bargaining problem and its two canonical solutions, (NASH and KALAI-SMORODINSKY), from a novel point of view: we ask for stability of the solution if both players are able distort the underlying bargaining process by reference to a third party (e.g. a court). By exploring the simplest case, where decisions of the third party are made randomly we obtain a stable solution, where players do not have any incentive to refer to such a third party. While neither the Nash nor the Kalai-Smorodinsky solution are able to ensure stability in case reference to a third party is possible, we found that the Kalai-Smorodinsky solution seems to always dominate the stable allocation which constitutes novel support in favor of the latter.
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....
Volchenkov, D.; Blanchard, Ph.
2007-02-01
Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an informationlike parameter which plays the role of an individual fingerprint of Genius loci. Global structural properties of a city can be characterized by the thermodynamic parameters calculated in the random walk problem.
Schauer, Michael; Mauritz, Karl-Heinz
2003-11-01
To demonstrate the effect of rhythmical auditory stimulation in a musical context for gait therapy in hemiparetic stroke patients, when the stimulation is played back measure by measure initiated by the patient's heel-strikes (musical motor feedback). Does this type of musical feedback improve walking more than a less specific gait therapy? The randomized controlled trial considered 23 registered stroke patients. Two groups were created by randomization: the control group received 15 sessions of conventional gait therapy and the test group received 15 therapy sessions with musical motor feedback. Inpatient rehabilitation hospital. Median post-stroke interval was 44 days and the patients were able to walk without technical aids with a speed of approximately 0.71 m/s. Gait velocity, step duration, gait symmetry, stride length and foot rollover path length (heel-on-toe-off distance). The test group showed more mean improvement than the control group: stride length increased by 18% versus 0%, symmetry deviation decreased by 58% versus 20%, walking speed increased by 27% versus 4% and rollover path length increased by 28% versus 11%. Musical motor feedback improves the stroke patient's walk in selected parameters more than conventional gait therapy. A fixed memory in the patient's mind about the song and its timing may stimulate the improvement of gait even without the presence of an external pacemaker.
Reflection principles for biased random walks and application to escape time distributions
Khantha, M.; Balakrishnan, V.
1985-12-01
We present a reflection principle for an arbitrary biased continuous time random walk (comprising both Markovian and non-Markovian processes) in the presence of a reflecting barrier on semi-infinite and finite chains. For biased walks in the presence of a reflecting barrier this principle (which cannot be derived from combinatorics) is completely different from its familiar form in the presence of an absorbing barrier. The result enables us to obtain closed-form solutions for the Laplace transform of the conditional probability for biased walks on finite chains for all three combinations of absorbing and reflecting barriers at the two ends. An important application of these solutions is the calculation of various first-passage-time and escape-time distributions. We obtain exact results for the characteristic functions of various kinds of escape time distributions for biased random walks on finite chains. For processes governed by a long-tailed event-time distribution we show that the mean time of escape from bounded regions diverges even in the presence of a bias—suggesting, in a sense, the absence of true long-range diffusion in such "frozen" processes.
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.
Directory of Open Access Journals (Sweden)
Carson eIngo
2015-03-01
Full Text Available In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusionthrough novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.
Random walks in Rindler spacetime and string theory at the tip of the cigar
Energy Technology Data Exchange (ETDEWEB)
Mertens, Thomas G.; Verschelde, Henri [Ghent University, Department of Physics and AstronomyKrijgslaan, 281-S9, 9000 Gent (Belgium); Zakharov, Valentin I. [ITEP, B. Cheremushkinskaya 25, Moscow, 117218 (Russian Federation); Max-Planck Institut für Physik, 80805 München (Germany); Moscow Inst Phys & Technol, Dolgoprudny, Moscow Region, 141700 (Russian Federation)
2014-03-20
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)
Ingo, Carson; Sui, Yi; Chen, Yufen; Parrish, Todd B; Webb, Andrew G; Ronen, Itamar
2015-03-01
In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.
Ingo, Carson; Sui, Yi; Chen, Yufen; Parrish, Todd; Webb, Andrew; Ronen, Itamar
2015-03-01
In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.
On properties of continuous-time random walks with non-Poissonian jump-times
Energy Technology Data Exchange (ETDEWEB)
Villarroel, Javier [Facultad de Ciencias, Universidad de Salamanca. Plaza Merced s/n, E-37008 Salamanca (Spain)], E-mail: javier@usal.es; Montero, Miquel [Departament de Fisica Fonamental, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona (Spain)], E-mail: miquel.montero@ub.edu
2009-10-15
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary time by recourse to renewal theory. The case of Erlang distributed times is analyzed in detail. Several concrete examples are considered.
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 randomized controlled trial a...
A random walk-based segmentation framework for 3D ultrasound images of the prostate.
Ma, Ling; Guo, Rongrong; Tian, Zhiqiang; Fei, Baowei
2017-10-01
Accurate segmentation of the prostate on ultrasound images has many applications in prostate cancer diagnosis and therapy. Transrectal ultrasound (TRUS) has been routinely used to guide prostate biopsy. This manuscript proposes a semiautomatic segmentation method for the prostate on three-dimensional (3D) TRUS images. The proposed segmentation method uses a context-classification-based random walk algorithm. Because context information reflects patient-specific characteristics and prostate changes in the adjacent slices, and classification information reflects population-based prior knowledge, we combine the context and classification information at the same time in order to define the applicable population and patient-specific knowledge so as to more accurately determine the seed points for the random walk algorithm. The method is initialized with the user drawing the prostate and non-prostate circles on the mid-gland slice and then automatically segments the prostate on other slices. To achieve reliable classification, we use a new adaptive k-means algorithm to cluster the training data and train multiple decision-tree classifiers. According to the patient-specific characteristics, the most suitable classifier is selected and combined with the context information in order to locate the seed points. By providing accuracy locations of the seed points, the random walk algorithm improves segmentation performance. We evaluate the proposed segmentation approach on a set of 3D TRUS volumes of prostate patients. The experimental results show that our method achieved a Dice similarity coefficient of 91.0% ± 1.6% as compared to manual segmentation by clinically experienced radiologist. The random walk-based segmentation framework, which combines patient-specific characteristics and population information, is effective for segmenting the prostate on ultrasound images. The segmentation method can have various applications in ultrasound-guided prostate procedures. © 2017
Imperatore, Pasquale; Iodice, Antonio; Riccio, Daniele
2017-12-27
A general, approximate perturbation method, able to provide closed-form expressions of scattering from a layered structure with an arbitrary number of rough interfaces, has been recently developed. Such a method provides a unique tool for the characterization of radar response patterns of natural rough multilayers. In order to show that, here, for the first time in a journal paper, we describe the application of the developed perturbation theory to fractal interfaces; we then employ the perturbative method solution to analyze the scattering from real-world layered structures of practical interest in remote sensing applications. We focus on the dependence of normalized radar cross section on geometrical and physical properties of the considered scenarios, and we choose two classes of natural stratifications: wet paleosoil covered by a low-loss dry sand layer and a sea-ice layer above water with dry snow cover. Results are in accordance with the experimental evidence available in the literature for the low-loss dry sand layer, and they may provide useful indications about the actual ability of remote sensing instruments to perform sub-surface sensing for different sensor and scene parameters.
Directory of Open Access Journals (Sweden)
Pasquale Imperatore
2017-12-01
Full Text Available A general, approximate perturbation method, able to provide closed-form expressions of scattering from a layered structure with an arbitrary number of rough interfaces, has been recently developed. Such a method provides a unique tool for the characterization of radar response patterns of natural rough multilayers. In order to show that, here, for the first time in a journal paper, we describe the application of the developed perturbation theory to fractal interfaces; we then employ the perturbative method solution to analyze the scattering from real-world layered structures of practical interest in remote sensing applications. We focus on the dependence of normalized radar cross section on geometrical and physical properties of the considered scenarios, and we choose two classes of natural stratifications: wet paleosoil covered by a low-loss dry sand layer and a sea-ice layer above water with dry snow cover. Results are in accordance with the experimental evidence available in the literature for the low-loss dry sand layer, and they may provide useful indications about the actual ability of remote sensing instruments to perform sub-surface sensing for different sensor and scene parameters.
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…
Directory of Open Access Journals (Sweden)
Zhuo Qi Lee
Full Text Available Biased random walk has been studied extensively over the past decade especially in the transport and communication networks communities. The mean first passage time (MFPT of a biased random walk is an important performance indicator in those domains. While the fundamental matrix approach gives precise solution to MFPT, the computation is expensive and the solution lacks interpretability. Other approaches based on the Mean Field Theory relate MFPT to the node degree alone. However, nodes with the same degree may have very different local weight distribution, which may result in vastly different MFPT. We derive an approximate bound to the MFPT of biased random walk with short relaxation time on complex network where the biases are controlled by arbitrarily assigned node weights. We show that the MFPT of a node in this general case is closely related to not only its node degree, but also its local weight distribution. The MFPTs obtained from computer simulations also agree with the new theoretical analysis. Our result enables fast estimation of MFPT, which is useful especially to differentiate between nodes that have very different local node weight distribution even though they share the same node degrees.
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.
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
Vamos, C; Vereecken, H
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.
Balakrishnan, V.; Kozak, John J.
2013-11-01
We present exact, analytic results for the mean time to trapping of a random walker on the class of deterministic Sierpinski graphs embedded in d≥2 Euclidean dimensions, when both nearest-neighbor (NN) and next-nearest-neighbor (NNN) jumps are included. Mean first-passage times are shown to be modified significantly as a consequence of the fact that NNN transitions connect fractals of two consecutive generations.
Fatemi, Omid; Panchanathan, Sethuraman
1997-01-01
Visual media processing is becoming increasingly important because of the wide variety of image and video based applications. Recently, several architectures have been reported in the literature to implement image and video processing algorithms. They range from programmable DSP processors to application specific integrated circuits (ASICs). DSPs have to be software programed to execute individual operations in image and video processing. However they are not suitable for real-time execution of highly compute intensive applications such as fractal block processing (FBP). On the other hand, dedicated architectures and ASICs are designed to implement specific functions. Since they are optimized for a specific task, they cannot be used in a wide variety of applications. In this paper, we propose a parallel and pipelined architecture called fractal engine to implement the operations in FBP. Fractal engine is simple, modular, scaleable and is optimized to execute both low level and mid level operations. We note that implementation of the basic operations by fractal engine enables efficient execution of a majority of visual computing tasks. These include spatial filtering, contrast enhancement, frequency domain operations, histogram calculation, geometric transforms, indexing, vector quantization, fractal block coding, motion estimation, etc. The individual modules of fractal engine have been implemented in VHDL (VHSIC hardware description language). We have chosen to demonstrate the real-time execution capability of fractal engine by mapping a fractal block coding (FBC) algorithm onto the proposed architecture.
Osler, Thomas J.
1999-01-01
Because fractal images are by nature very complex, it can be inspiring and instructive to create the code in the classroom and watch the fractal image evolve as the user slowly changes some important parameter or zooms in and out of the image. Uses programming language that permits the user to store and retrieve a graphics image as a disk file.…
Merom, Dafna; Grunseit, Anne; Eramudugolla, Ranmalee; Jefferis, Barbara; Mcneill, Jade; Anstey, Kaarin J
2016-01-01
A physically active lifestyle has the potential to prevent cognitive decline and dementia, yet the optimal type of physical activity/exercise remains unclear. Dance is of special interest as it complex sensorimotor rhythmic activity with additional cognitive, social, and affective dimensions. To determine whether dance benefits executive function more than walking, an activity that is simple and functional. Two-arm randomized controlled trial among community-dwelling older adults. The intervention group received 1 h of ballroom dancing twice weekly over 8 months (~69 sessions) in local community dance studios. The control group received a combination of a home walking program with a pedometer and optional biweekly group-based walking in local community park to facilitate socialization. Executive function tests: processing speed and task shift by the Trail Making Tests, response inhibition by the Stroop Color-Word Test, working memory by the Digit Span Backwards test, immediate and delayed verbal recall by the Rey Auditory Verbal Learning Test, and visuospatial recall by the Brief Visuospatial Memory Test (BVST). One hundred and fifteen adults (mean 69.5 years, SD 6.4) completed baseline and delayed baseline (3 weeks apart) before being randomized to either dance (n = 60) or walking (n = 55). Of those randomized, 79 (68%) completed the follow-up measurements (32 weeks from baseline). In the dance group only, "non-completers" had significantly lower baseline scores on all executive function tests than those who completed the full program. Intention-to-treat analyses showed no group effect. In a random effects model including participants who completed all measurements, adjusted for baseline score and covariates (age, education, estimated verbal intelligence, and community), a between-group effect in favor of dance was noted only for BVST total learning (Cohen's D Effect size 0.29, p = 0.07) and delayed recall (Cohen's D Effect size = 0
Yang, Mingliang; Li, Jianjun; Guan, Xinyu; Gao, Lianjun; Gao, Feng; Du, Liangjie; Zhao, Hongmei; Yang, Degang; Yu, Yan; Wang, Qimin; Wang, Rencheng; Ji, Linhong
2017-09-01
The high energy cost of paraplegic walking using a reciprocating gait orthosis (RGO) is attributed to limited hip motion and excessive upper limb loading for support. To address the limitation, we designed the hip energy storage walking orthosis (HESWO) which uses a spring assembly on the pelvic shell to store energy from the movements of the healthy upper limbs and flexion-extension of the lumbar spine and hip and returns this energy to lift the pelvis and lower limb to assist with the swing and stance components of a stride. Our aim was to evaluate gait and energy cost indices for the HESWO compared to the RGO in patients with paraplegia. The cross-over design was used in the pilot study. Twelve patients with a complete T4-L5 chronic spinal cord injury underwent gait training using the HESWO and RGO. Gait performance (continuous walking distance, as well as the maximum and comfortable walking speeds) and energy expenditure (at a walking speed of 3.3m/min on a treadmill) were measured at the end of the 4-week training session. Compared to the RGO, the HESWO increased continuous walking distance by 24.7% (Penergy expenditure by 13.9% (P<0.05). Our preliminary results provide support for the use of the HESWO as an alternative support for paraplegic walking. Copyright © 2017. Published by Elsevier B.V.
Chand, Sai; Dixit, Vinayak V
2018-01-04
The repercussions from congestion and accidents on major highways can have significant negative impacts on the economy and environment. It is a primary objective of transport authorities to minimize the likelihood of these phenomena taking place, to improve safety and overall network performance. In this study, we use the Hurst Exponent metric from Fractal Theory, as a congestion indicator for crash-rate modeling. We analyze one month of traffic speed data at several monitor sites along the M4 motorway in Sydney, Australia and assess congestion patterns with the Hurst Exponent of speed (Hspeed). Random Parameters and Latent Class Tobit models were estimated, to examine the effect of congestion on historical crash rates, while accounting for unobserved heterogeneity. Using a latent class modeling approach, the motorway sections were probabilistically classified into two segments, based on the presence of entry and exit ramps. This will allow transportation agencies to implement appropriate safety/traffic countermeasures when addressing accident hotspots or inadequately managed sections of motorway. Copyright © 2017 Elsevier Ltd. All rights reserved.
Souza, Marcelo Cardoso de; Jennings, Fábio; Morimoto, Hisa; Natour, Jamil
2016-09-17
The purpose was to evaluate the effectiveness of a progressive muscle strengthening program using a Swiss ball for AS patients. Sixty patients with AS were randomized into the intervention group (IG) or the control group (CG). Eight exercises were performed by the IG patients with free weights on a Swiss ball two times per week for 16 weeks. The evaluations were performed by a blinded evaluator at baseline and after 4, 8, 12 and 16 weeks using the following instruments: the one-repetition maximum test (1 RM), BASMI, BASFI, HAQ-S, SF-36, 6-minute walk test, Time Up and Go test, BASDAI, ASDAS, ESR and CRP dosage and Likert scale. There was a statistical difference between groups for: strength (1RM capacity) in the following exercises: abdominal, rowing, squat, triceps and reverse fly (pSwiss ball is effective for improving muscle strength and walking performance in patients with AS. Copyright © 2016. Published by Elsevier Editora Ltda.
Souza, Marcelo Cardoso de; Jennings, Fábio; Morimoto, Hisa; Natour, Jamil
The purpose was to evaluate the effectiveness of a progressive muscle strengthening program using a Swiss ball for AS patients. Sixty patients with AS were randomized into the intervention group (IG) or the control group (CG). Eight exercises were performed by the IG patients with free weights on a Swiss ball two times per week for 16 weeks. The evaluations were performed by a blinded evaluator at baseline and after 4, 8, 12 and 16 weeks using the following instruments: the one-repetition maximum test (1 RM), BASMI, BASFI, HAQ-S, SF-36, 6-minute walk test, time up and go test, BASDAI, ASDAS, ESR and CRP dosage and Likert scale. There was a statistical difference between groups for: strength (1 RM capacity) in the following exercises: abdominal, rowing, squat, triceps and reverse fly (pSwiss ball is effective for improving muscle strength and walking performance in patients with AS. Copyright © 2016 Elsevier Editora Ltda. All rights reserved.
Boyer, D.; Romo-Cruz, J. C. R.
2014-10-01
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random-walk model with long-range memory for which not only the mean-square displacement (MSD) but also the propagator can be obtained exactly in the asymptotic limit. The model consists of a random walker on a lattice, which, at a constant rate, stochastically relocates at a site occupied at some earlier time. This time in the past is chosen randomly according to a memory kernel, whose temporal decay can be varied via an exponent parameter. In the weakly non-Markovian regime, memory reduces the diffusion coefficient from the bare value. When the mean backward jump in time diverges, the diffusion coefficient vanishes and a transition to an anomalous subdiffusive regime occurs. Paradoxically, at the transition, the process is an anticorrelated Lévy flight. Although in the subdiffusive regime the model exhibits some features of the continuous time random walk with infinite mean waiting time, it belongs to another universality class. If memory is very long-ranged, a second transition takes place to a regime characterized by a logarithmic growth of the MSD with time. In this case the process is asymptotically Gaussian and effectively described as a scaled Brownian motion with a diffusion coefficient decaying as 1 /t .
Ma, Tianren; Xia, Zhengyou
2017-05-01
Currently, with the rapid development of information technology, the electronic media for social communication is becoming more and more popular. Discovery of communities is a very effective way to understand the properties of complex networks. However, traditional community detection algorithms consider the structural characteristics of a social organization only, with more information about nodes and edges wasted. In the meanwhile, these algorithms do not consider each node on its merits. Label propagation algorithm (LPA) is a near linear time algorithm which aims to find the community in the network. It attracts many scholars owing to its high efficiency. In recent years, there are more improved algorithms that were put forward based on LPA. In this paper, an improved LPA based on random walk and node importance (NILPA) is proposed. Firstly, a list of node importance is obtained through calculation. The nodes in the network are sorted in descending order of importance. On the basis of random walk, a matrix is constructed to measure the similarity of nodes and it avoids the random choice in the LPA. Secondly, a new metric IAS (importance and similarity) is calculated by node importance and similarity matrix, which we can use to avoid the random selection in the original LPA and improve the algorithm stability. Finally, a test in real-world and synthetic networks is given. The result shows that this algorithm has better performance than existing methods in finding community structure.
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.
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
Barnsley, Michael F
2012-01-01
""Difficult concepts are introduced in a clear fashion with excellent diagrams and graphs."" - Alan E. Wessel, Santa Clara University""The style of writing is technically excellent, informative, and entertaining."" - Robert McCartyThis new edition of a highly successful text constitutes one of the most influential books on fractal geometry. An exploration of the tools, methods, and theory of deterministic geometry, the treatment focuses on how fractal geometry can be used to model real objects in the physical world. Two sixteen-page full-color inserts contain fractal images, and a bonus CD of
Boyer, Denis; Solis-Salas, Citlali
2014-06-01
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where a random walker intermittently revisits previously visited sites according to a reinforced rule. The emergence of frequently visited locations generates very slow diffusion, logarithmic in time, whereas the walker probability density tends to a Gaussian. This scaling form does not emerge from the central limit theorem but from an unusual balance between random and long-range memory steps. In single trajectories, occupation patterns are heterogeneous and have a scale-free structure. The model exhibits good agreement with data of free-ranging capuchin monkeys.
Multiple random walks on complex networks: A harmonic law predicts search time
Weng, Tongfeng; Zhang, Jie; Small, Michael; Hui, Pan
2017-05-01
We investigate multiple random walks traversing independently and concurrently on complex networks and introduce the concept of mean first parallel passage time (MFPPT) to quantify their search efficiency. The mean first parallel passage time represents the expected time required to find a given target by one or some of the multiple walkers. We develop a general theory that allows us to calculate the MFPPT analytically. Interestingly, we find that the global MFPPT follows a harmonic law with respect to the global mean first passage times of the associated walkers. Remarkably, when the properties of multiple walkers are identical, the global MFPPT decays in a power law manner with an exponent of unity, irrespective of network structure. These findings are confirmed by numerical and theoretical results on various synthetic and real networks. The harmonic law reveals a universal principle governing multiple random walks on networks that uncovers the contribution and role of the combined walkers in a target search. Our paradigm is also applicable to a broad range of random search processes.
Rote, Aubrianne E; Klos, Lori A; Brondino, Michael J; Harley, Amy E; Swartz, Ann M
2015-06-16
Facebook may be a useful tool to provide a social support group to encourage increases in physical activity. This study examines the efficacy of a Facebook social support group to increase steps/day in young women. Female college freshmen (N = 63) were randomized to one of two 8-week interventions: a Facebook Social Support Group (n = 32) or a Standard Walking Intervention (n = 31). Participants in both groups received weekly step goals and tracked steps/day with a pedometer. Women in the Facebook Social Support Group were also enrolled in a Facebook group and asked to post information about their steps/day and provide feedback to one another. Women in both intervention arms significantly increased steps/day pre- to postintervention (F(8,425) = 94.43, P Social Support Group increased steps/day significantly more (F(1,138) = 11.34, P social support group to increase physical activity in young women. Women in the Facebook Social Support Group increased walking by approximately 1.5 miles/day more than women in the Standard Walking Intervention which, if maintained, could have a profound impact on their future health.
A stylistic classification of Russian-language texts based on the random walk model
Kramarenko, A. A.; Nekrasov, K. A.; Filimonov, V. V.; Zhivoderov, A. A.; Amieva, A. A.
2017-09-01
A formal approach to text analysis is suggested that is based on the random walk model. The frequencies and reciprocal positions of the vowel letters are matched up by a process of quasi-particle migration. Statistically significant difference in the migration parameters for the texts of different functional styles is found. Thus, a possibility of classification of texts using the suggested method is demonstrated. Five groups of the texts are singled out that can be distinguished from one another by the parameters of the quasi-particle migration process.
Energy Technology Data Exchange (ETDEWEB)
Calvo, I [Laboratorio Nacional de Fusion, Asociacion EURATOM-CIEMAT, E-28040 Madrid (Spain); Carreras, B A [BACV Solutions Inc., Oak Ridge, TN 37830 (United States); Sanchez, R [Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Milligen, B Ph van [Laboratorio Nacional de Fusion, Asociacion EURATOM-CIEMAT, E-28040 Madrid (Spain)
2007-11-09
In this paper, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out the fluid limit equation, formulated in terms of the periodic version of the fractional Riemann-Liouville operators, for which we provide explicit expressions. Finally, we compute the propagator in some simple cases. The analysis presented herein should be relevant when investigating anomalous transport phenomena in systems with periodic dimensions.
Energy Technology Data Exchange (ETDEWEB)
Calvo, Ivan [CIEMAT, Madrid; Carreras, Benjamin A [ORNL; Sanchez, Raul [ORNL; van Milligen, B. Ph. [Asociacion EURATOM-CIEMAT
2007-01-01
In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out the fluid limit equation, formulated in terms of the periodic version of the fractional Riemann-Liouville operators, for which we provide explicit expressions. Finally, we compute the propagator in some simple cases. The analysis presented herein should be relevant when investigating anomalous transport phenomena in systems with periodic dimensions.
Czech Academy of Sciences Publication Activity Database
Papáček, Š.; Matonoha, Ctirad; Štumbauer, V.; Štys, D.
2012-01-01
Roč. 82, č. 10 (2012), s. 2022-2032 ISSN 0378-4754. [Modelling 2009. IMACS Conference on Mathematical Modelling and Computational Methods in Applied Sciences and Engineering /4./. Rožnov pod Radhoštěm, 22.06.2009-26.06.2009] Grant - others:CENAKVA(CZ) CZ.1.05/2.1.00/01.0024; GA JU(CZ) 152//2010/Z Institutional research plan: CEZ:AV0Z10300504 Keywords : multiscale modelling * distributed parameter system * boundary value problem * random walk * photosynthetic factory Subject RIV: EI - Biotechnology ; Bionics Impact factor: 0.836, year: 2012
Fast Inbound Top-K Query for Random Walk with Restart
Zhang, Chao; Jiang, Shan; Chen, Yucheng; Sun, Yidan; Han, Jiawei
2015-01-01
Random walk with restart (RWR) is widely recognized as one of the most important node proximity measures for graphs, as it captures the holistic graph structure and is robust to noise in the graph. In this paper, we study a novel query based on the RWR measure, called the inbound top-k (Ink) query. Given a query node q and a number k, the Ink query aims at retrieving k nodes in the graph that have the largest weighted RWR scores to q. Ink queries can be highly useful for various applications ...
Exact Partition Function for the Random Walk of an Electrostatic Field
Directory of Open Access Journals (Sweden)
Gabriel González
2017-01-01
Full Text Available The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either ±σ is obtained. We find the electrostatic energy of the system and show that it can be analyzed through generalized Dyck paths. The relation between the electrostatic field and generalized Dyck paths allows us to sum overall possible electrostatic field configurations and is used for obtaining the partition function of the system. We illustrate our results with one example.
Tracking random walk of individual domain walls in cylindrical nanomagnets with resistance noise.
Singh, Amrita; Mukhopadhyay, Soumik; Ghosh, Arindam
2010-08-06
The stochasticity of domain-wall (DW) motion in magnetic nanowires has been probed by measuring slow fluctuations, or noise, in electrical resistance at small magnetic fields. By controlled injection of DWs into isolated cylindrical nanowires of nickel, we have been able to track the motion of the DWs between the electrical leads by discrete steps in the resistance. Closer inspection of the time dependence of noise reveals a diffusive random walk of the DWs with a universal kinetic exponent. Our experiments outline a method with which electrical resistance is able to detect the kinetic state of the DWs inside the nanowires, which can be useful in DW-based memory designs.
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...
Random walks with shape prior for cochlea segmentation in ex vivo μCT
DEFF Research Database (Denmark)
Ruiz Pujadas, Esmeralda; Kjer, Hans Martin; Piella, Gemma
2016-01-01
previously proposed the use of a high-resolution model built from μCT images and then adapted to patient-specific clinical CT scans. As the accuracy of the model is dependent on the precision of the original segmentation, it is extremely important to have accurate μCT segmentation algorithms. Methods We......(2):236–253, 2013) and constrained random walks (Li et al. in Advances in image and video technology. Springer, Berlin, pp 215–226, 2012). Our approach demonstrated higher accuracy results due to the probability density model constituted by the region term and shape prior information weighed by a confidence map...
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
Gao, Jianbo; Hu, Jing; Mao, Xiang; Perc, Matjaž
2012-01-01
Culturomics was recently introduced as the application of high-throughput data collection and analysis to the study of human culture. Here, we make use of these data by investigating fluctuations in yearly usage frequencies of specific words that describe social and natural phenomena, as derived from books that were published over the course of the past two centuries. We show that the determination of the Hurst parameter by means of fractal analysis provides fundamental insights into the nature of long-range correlations contained in the culturomic trajectories, and by doing so offers new interpretations as to what might be the main driving forces behind the examined phenomena. Quite remarkably, we find that social and natural phenomena are governed by fundamentally different processes. While natural phenomena have properties that are typical for processes with persistent long-range correlations, social phenomena are better described as non-stationary, on–off intermittent or Lévy walk processes. PMID:22337632
A continuous-time random-walk approach to the Cole-Davidson dielectric response of dipolar liquids
DEFF Research Database (Denmark)
Szabat, B.; Langner, K. M.; Klösgen-Buchkremer, Beate Maria
2004-01-01
We show how the Cole-Davidson relaxation response, characteristic of alcoholic systems, can be derived within the framework of the continuous-time random walk (CTRW). Using the random-variable formalism, we indicate that the high-frequency power law of dielectric spectra is determined by the heavy...
A continuous-time random-walk approach to the Cole-Davidson dielectric response of dipolar liquids
DEFF Research Database (Denmark)
Szabat, Bozena; Langner, Karol M.; Klösgen, Beate Maria
2005-01-01
We show how the Cole-Davidson relaxation response, characteristic of alcoholic systems, can be derived within the framework of the continuous-time random walk 4CTRW). Using the random-variable formalism, we indicate that the high-frequency power law of dielectric spectra is determined by the heavy...
Lv, Chao; Zheng, Lianqing; Yang, Wei
2012-01-28
Molecular dynamics sampling can be enhanced via the promoting of potential energy fluctuations, for instance, based on a Hamiltonian modified with the addition of a potential-energy-dependent biasing term. To overcome the diffusion sampling issue, which reveals the fact that enlargement of event-irrelevant energy fluctuations may abolish sampling efficiency, the essential energy space random walk (EESRW) approach was proposed earlier. To more effectively accelerate the sampling of solute conformations in aqueous environment, in the current work, we generalized the EESRW method to a two-dimension-EESRW (2D-EESRW) strategy. Specifically, the essential internal energy component of a focused region and the essential interaction energy component between the focused region and the environmental region are employed to define the two-dimensional essential energy space. This proposal is motivated by the general observation that in different conformational events, the two essential energy components have distinctive interplays. Model studies on the alanine dipeptide and the aspartate-arginine peptide demonstrate sampling improvement over the original one-dimension-EESRW strategy; with the same biasing level, the present generalization allows more effective acceleration of the sampling of conformational transitions in aqueous solution. The 2D-EESRW generalization is readily extended to higher dimension schemes and employed in more advanced enhanced-sampling schemes, such as the recent orthogonal space random walk method. © 2012 American Institute of Physics
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.
Personalized PageRank Clustering: A graph clustering algorithm based on random walks
A. Tabrizi, Shayan; Shakery, Azadeh; Asadpour, Masoud; Abbasi, Maziar; Tavallaie, Mohammad Ali
2013-11-01
Graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications. In addition, exponential growth of real-world graphs such as social networks, biological networks and electrical circuits demands clustering algorithms with nearly-linear time and space complexity. In this paper we propose Personalized PageRank Clustering (PPC) that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph. We combine random walks and modularity to precisely and efficiently reveal the clusters of a graph. PPC is a top-down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly-linear approaches that are mainly bottom-up. It also gives a hierarchy of clusters that is useful in many applications. PPC has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets. Furthermore, its top-down approach makes it a flexible solution for clustering problems with different requirements.
Wei, Kun; Zhong, Suchuan
2017-08-01
Phenomenologically inspired by dolphins' unihemispheric sleep, we introduce a minimal model for random walks with physiological memory. The physiological memory consists of long-term memory which includes unconscious implicit memory and conscious explicit memory, and working memory which serves as a multi-component system for integrating, manipulating and managing short-term storage. The model assumes that the sleeping state allows retrievals of episodic objects merely from the episodic buffer where these memory objects are invoked corresponding to the ambient objects and are thus object-oriented, together with intermittent but increasing use of implicit memory in which decisions are unconsciously picked up from historical time series. The process of memory decay and forgetting is constructed in the episodic buffer. The walker's risk attitude, as a product of physiological heuristics according to the performance of objected-oriented decisions, is imposed on implicit memory. The analytical results of unihemispheric random walks with the mixture of object-oriented and time-oriented memory, as well as the long-time behavior which tends to the use of implicit memory, are provided, indicating the common sense that a conservative risk attitude is inclinable to slow movement.
Size-dependent diffusion coefficient in a myopic random walk on a strip
Revathi, S.; Valsakumar, M. C.; Balakrishnan, V.; Weiss, G. H.
1992-07-01
We consider a random walk in discrete time ( n = 0, 1, 2, …) on a square lattice of finite width in the y-direction, i.e., {j, m | j ɛ Z, m = 1, 2, 3, …, N} . A myopic walker at ( j,1) or ( j, N) jumps with probability {1}/{3} to any of the available nearest-neighbor sites at the end of a time step. This couples the motions in the x- and y-directions, and leads to several interesting features, including a coefficient of diffusion in the x-direction that depends on the transverse size N of the strip. Explicit solutions for (and the lateral variance ) are given for small values of N. A closed-form expression is obtained for the (discrete Laplace) transform of for general N. The asymptotic behaviors of and are found, the corrections falling off exponentially with increasing n. The results obtained are generalized to a myopic random walk in d dimensions, and it is shown that the diffusion coefficient has an explicit geometry dependence involving the surface-to-volume ratio. This coefficient can therefore serve as a probe of the geometry of the structure on which diffusion takes place.
Martinez, David; Otegi, Arantxa; Soroa, Aitor; Agirre, Eneko
2014-10-01
Most of the information in Electronic Health Records (EHRs) is represented in free textual form. Practitioners searching EHRs need to phrase their queries carefully, as the record might use synonyms or other related words. In this paper we show that an automatic query expansion method based on the Unified Medicine Language System (UMLS) Metathesaurus improves the results of a robust baseline when searching EHRs. The method uses a graph representation of the lexical units, concepts and relations in the UMLS Metathesaurus. It is based on random walks over the graph, which start on the query terms. Random walks are a well-studied discipline in both Web and Knowledge Base datasets. Our experiments over the TREC Medical Record track show improvements in both the 2011 and 2012 datasets over a strong baseline. Our analysis shows that the success of our method is due to the automatic expansion of the query with extra terms, even when they are not directly related in the UMLS Metathesaurus. The terms added in the expansion go beyond simple synonyms, and also add other kinds of topically related terms. Expansion of queries using related terms in the UMLS Metathesaurus beyond synonymy is an effective way to overcome the gap between query and document vocabularies when searching for patient cohorts. Copyright © 2014 Elsevier Inc. All rights reserved.
Narrow log-periodic modulations in non-Markovian random walks
Diniz, R. M. B.; Cressoni, J. C.; da Silva, M. A. A.; Mariz, A. M.; de Araújo, J. M.
2017-12-01
What are the necessary ingredients for log-periodicity to appear in the dynamics of a random walk model? Can they be subtle enough to be overlooked? Previous studies suggest that long-range damaged memory and negative feedback together are necessary conditions for the emergence of log-periodic oscillations. The role of negative feedback would then be crucial, forcing the system to change direction. In this paper we show that small-amplitude log-periodic oscillations can emerge when the system is driven by positive feedback. Due to their very small amplitude, these oscillations can easily be mistaken for numerical finite-size effects. The models we use consist of discrete-time random walks with strong memory correlations where the decision process is taken from memory profiles based either on a binomial distribution or on a delta distribution. Anomalous superdiffusive behavior and log-periodic modulations are shown to arise in the large time limit for convenient choices of the models parameters.
BRWLDA: bi-random walks for predicting lncRNA-disease associations
Yu, Guoxian; Fu, Guangyuan; Lu, Chang; Ren, Yazhou; Wang, Jun
2017-01-01
Increasing efforts have been done to figure out the association between lncRNAs and complex diseases. Many computational models construct various lncRNA similarity networks, disease similarity networks, along with known lncRNA-disease associations to infer novel associations. However, most of them neglect the structural difference between lncRNAs network and diseases network, hierarchical relationships between diseases and pattern of newly discovered associations. In this study, we developed a model that performs Bi-Random Walks to predict novel LncRNA-Disease Associations (BRWLDA in short). This model utilizes multiple heterogeneous data to construct the lncRNA functional similarity network, and Disease Ontology to construct a disease network. It then constructs a directed bi-relational network based on these two networks and available lncRNAs-disease associations. Next, it applies bi-random walks on the network to predict potential associations. BRWLDA achieves reliable and better performance than other comparing methods not only on experiment verified associations, but also on the simulated experiments with masked associations. Case studies further demonstrate the feasibility of BRWLDA in identifying new lncRNA-disease associations. PMID:28947982
A Random Walk in the Park: An Individual-Based Null Model for Behavioral Thermoregulation.
Vickers, Mathew; Schwarzkopf, Lin
2016-04-01
Behavioral thermoregulators leverage environmental temperature to control their body temperature. Habitat thermal quality therefore dictates the difficulty and necessity of precise thermoregulation, and the quality of behavioral thermoregulation in turn impacts organism fitness via the thermal dependence of performance. Comparing the body temperature of a thermoregulator with a null (non-thermoregulating) model allows us to estimate habitat thermal quality and the effect of behavioral thermoregulation on body temperature. We define a null model for behavioral thermoregulation that is a random walk in a temporally and spatially explicit thermal landscape. Predicted body temperature is also integrated through time, so recent body temperature history, environmental temperature, and movement influence current body temperature; there is no particular reliance on an organism's equilibrium temperature. We develop a metric called thermal benefit that equates body temperature to thermally dependent performance as a proxy for fitness. We measure thermal quality of two distinct tropical habitats as a temporally dynamic distribution that is an ergodic property of many random walks, and we compare it with the thermal benefit of real lizards in both habitats. Our simple model focuses on transient body temperature; as such, using it we observe such subtleties as shifts in the thermoregulatory effort and investment of lizards throughout the day, from thermoregulators to thermoconformers.
Fractals, Coherence and Brain Dynamics
Vitiello, Giuseppe
2010-11-01
I show that the self-similarity property of deterministic fractals provides a direct connection with the space of the entire analytical functions. Fractals are thus described in terms of coherent states in the Fock-Bargmann representation. Conversely, my discussion also provides insights on the geometrical properties of coherent states: it allows to recognize, in some specific sense, fractal properties of coherent states. In particular, the relation is exhibited between fractals and q-deformed coherent states. The connection with the squeezed coherent states is also displayed. In this connection, the non-commutative geometry arising from the fractal relation with squeezed coherent states is discussed and the fractal spectral properties are identified. I also briefly discuss the description of neuro-phenomenological data in terms of squeezed coherent states provided by the dissipative model of brain and consider the fact that laboratory observations have shown evidence that self-similarity characterizes the brain background activity. This suggests that a connection can be established between brain dynamics and the fractal self-similarity properties on the basis of the relation discussed in this report between fractals and squeezed coherent states. Finally, I do not consider in this paper the so-called random fractals, namely those fractals obtained by randomization processes introduced in their iterative generation. Since self-similarity is still a characterizing property in many of such random fractals, my conjecture is that also in such cases there must exist a connection with the coherent state algebraic structure. In condensed matter physics, in many cases the generation by the microscopic dynamics of some kind of coherent states is involved in the process of the emergence of mesoscopic/macroscopic patterns. The discussion presented in this paper suggests that also fractal generation may provide an example of emergence of global features, namely long range
Langbein, John O.
2012-01-01
Recent studies have documented that global positioning system (GPS) time series of position estimates have temporal correlations which have been modeled as a combination of power-law and white noise processes. When estimating quantities such as a constant rate from GPS time series data, the estimated uncertainties on these quantities are more realistic when using a noise model that includes temporal correlations than simply assuming temporally uncorrelated noise. However, the choice of the specific representation of correlated noise can affect the estimate of uncertainty. For many GPS time series, the background noise can be represented by either: (1) a sum of flicker and random-walk noise or, (2) as a power-law noise model that represents an average of the flicker and random-walk noise. For instance, if the underlying noise model is a combination of flicker and random-walk noise, then incorrectly choosing the power-law model could underestimate the rate uncertainty by a factor of two. Distinguishing between the two alternate noise models is difficult since the flicker component can dominate the assessment of the noise properties because it is spread over a significant portion of the measurable frequency band. But, although not necessarily detectable, the random-walk component can be a major constituent of the estimated rate uncertainty. None the less, it is possible to determine the upper bound on the random-walk noise.
Zhou, Haijun
2010-02-01
Random K-satisfiability (K-SAT) is a model system for studying typical-case complexity of combinatorial optimization. Recent theoretical and simulation work revealed that the solution space of a random K-SAT formula has very rich structures, including the emergence of solution communities within single solution clusters. In this paper we investigate the influence of the solution space landscape to a simple stochastic local search process SEQSAT, which satisfies a K-SAT formula in a sequential manner. Before satisfying each newly added clause, SEQSAT walk randomly by single-spin flips in a solution cluster of the old subformula. This search process is efficient when the constraint density α of the satisfied subformula is less than certain value αcm; however it slows down considerably as α> αcm and finally reaches a jammed state at α≈αj. The glassy dynamical behavior of SEQSAT for α≥αcm probably is due to the entropic trapping of various communities in the solution cluster of the satisfied subformula. For random 3-SAT, the jamming transition point αj is larger than the solution space clustering transition point αd, and its value can be predicted by a long-range frustration mean-field theory. For random K-SAT with K ≥ 4, however, our simulation results indicate that αj = αd. The relevance of this work for understanding the dynamic properties of glassy systems is also discussed.
Fractal gait patterns are retained after entrainment to a fractal stimulus.
Directory of Open Access Journals (Sweden)
Christopher K Rhea
Full Text Available Previous work has shown that fractal patterns in gait can be altered by entraining to a fractal stimulus. However, little is understood about how long those patterns are retained or which factors may influence stronger entrainment or retention. In experiment one, participants walked on a treadmill for 45 continuous minutes, which was separated into three phases. The first 15 minutes (pre-synchronization phase consisted of walking without a fractal stimulus, the second 15 minutes consisted of walking while entraining to a fractal visual stimulus (synchronization phase, and the last 15 minutes (post-synchronization phase consisted of walking without the stimulus to determine if the patterns adopted from the stimulus were retained. Fractal gait patterns were strengthened during the synchronization phase and were retained in the post-synchronization phase. In experiment two, similar methods were used to compare a continuous fractal stimulus to a discrete fractal stimulus to determine which stimulus type led to more persistent fractal gait patterns in the synchronization and post-synchronization (i.e., retention phases. Both stimulus types led to equally persistent patterns in the synchronization phase, but only the discrete fractal stimulus led to retention of the patterns. The results add to the growing body of literature showing that fractal gait patterns can be manipulated in a predictable manner. Further, our results add to the literature by showing that the newly adopted gait patterns are retained for up to 15 minutes after entrainment and showed that a discrete visual stimulus is a better method to influence retention.
Random Multi-Hopper Model. Super-Fast Random Walks on Graphs
Estrada, Ernesto; Delvenne, Jean-Charles; Hatano, Naomichi; Mateos, José L.; Metzler, Ralf; Riascos ( Universidad Mariana, Pasto, Colombia), Alejandro P; Schaub, Michael T.
2016-01-01
We develop a model for a random walker with long-range hops on general graphs. This random multi-hopper jumps from a node to any other node in the graph with a probability that decays as a function of the shortest-path distance between the two nodes. We consider here two decaying functions in the form of the Laplace and Mellin transforms of the shortest-path distances. Remarkably, when the parameters of these transforms approach zero asymptotically, the multi-hopper's hitting times between an...
Ruffolo, D. J.; Snodin, A. P.; Oughton, S.; Servidio, S.; Matthaeus, W. H.
2013-12-01
The random walk of magnetic field lines is examined analytically and numerically in the context of reduced magnetohydrodynamic (RMHD) turbulence, which provides a useful description of plasmas dominated by a strong mean field, such as in the solar corona. A nonperturbative theory of magnetic field line diffusion [1] is compared with the diffusion coefficients obtained by accurate numerical tracing of magnetic field lines for both synthetic models and direct numerical simulations of RMHD. Statistical analysis of an ensemble of trajectories confirms the applicability of the theory, which very closely matches the numerical field line diffusion coefficient as a function of distance z along the mean magnetic field for a wide range of the Kubo number R. The theory employs Corrsin's independence hypothesis, sometimes thought to be valid only at low R. However, the results demonstrate that it works well up to R=10, both for a synthetic RMHD model and an RMHD simulation. The numerical results from RMHD simulation are compared with and without phase randomization, demonstrating an effect of coherent structures on the field line random walk for low Kubo number. Partially supported by a postdoctoral fellowship from Mahidol University, the Thailand Research Fund, POR Calabria FSE-2007/2013, the US NSF (AGS-1063439 and SHINE AGS-1156094), NASA (Heliophysics Theory NNX08AI47G & NNX11AJ44G), by the Solar Probe Plus Project through the ISIS Theory team, by the MMS Theory and Modeling team, and by EU Marie Curie Project FP7 PIRSES-2010-269297 'Turboplasmas' at Università della Calabria. [1] D. Ruffolo and W. H. Matthaeus, Phys. Plasmas, 20, 012308 (2013).
Effects of exercise on brain activity during walking in older adults: a randomized controlled trial.
Shimada, Hiroyuki; Ishii, Kenji; Makizako, Hyuma; Ishiwata, Kiichi; Oda, Keiichi; Suzukawa, Megumi
2017-05-30
Physical activity may preserve neuronal plasticity, increase synapse formation, and cause the release of hormonal factors that promote neurogenesis and neuronal function. Previous studies have reported enhanced neurocognitive function following exercise training. However, the specific cortical regions activated during exercise training remain largely undefined. In this study, we quantitatively and objectively evaluated the effects of exercise on brain activity during walking in healthy older adults. A total of 24 elderly women (75-83 years old) were randomly allocated to either an intervention group or a control group. Those in the intervention group attended 3 months of biweekly 90-min sessions focused on aerobic exercise, strength training, and physical therapy. We monitored changes in regional cerebral glucose metabolism during walking in both groups using positron emission tomography (PET) and [ 18 F]fluorodeoxyglucose (FDG). All subjects completed the 3-month experiment and the adherence to the exercise program was 100%. Compared with the control group, the intervention group showed a significantly greater step length in the right foot after 3 months of physical activity. The FDG-PET assessment revealed a significant post-intervention increase in regional glucose metabolism in the left posterior entorhinal cortex, left superior temporal gyrus, and right superior temporopolar area in the intervention group. Interestingly, the control group showed a relative increase in regional glucose metabolism in the left premotor and supplemental motor areas, left and right somatosensory association cortex, and right primary visual cortex after the 3-month period. We found no significant differences in FDG uptake between the intervention and control groups before vs. after the intervention. Exercise training increased activity in specific brain regions, such as the precuneus and entorhinal cortices, which play an important role in episodic and spatial memory. Further
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...
The distribution of first hitting times of non-backtracking random walks on Erdős-Rényi networks
Tishby, Ido; Biham, Ofer; Katzav, Eytan
2017-05-01
We present analytical results for the distribution of first hitting times of non-backtracking random walks on finite Erdős-Rényi networks of N nodes. The walkers hop randomly between adjacent nodes on the network, without stepping back to the previous node, until they hit a node which they have already visited before or get trapped in a dead-end node. At this point, the path is terminated. The length, d, of the resulting path, is called the first hitting time. Using recursion equations, we obtain analytical results for the tail distribution of first hitting times, P(d > \\ell) , \\ell=0, 1, 2, \\dots , of non-backtracking random walks starting from a random initial node. It turns out that the distribution P(d > \\ell) is given by a product of a discrete Rayleigh distribution and an exponential distribution. We obtain analytical expressions for central measures (mean and median) and a dispersion measure (standard deviation) of this distribution. It is found that the paths of non-backtracking random walks, up to their termination at the first hitting time, are longer, on average, than those of the corresponding simple random walks. However, they are shorter than those of self avoiding walks on the same network, which terminate at the last hitting time. We obtain analytical results for the probabilities, p ret and p trap, that a path will terminate by retracing, namely stepping into an already visited node, or by trapping, namely entering a node of degree k = 1, which has no exit link, respectively. It is shown that in dilute networks the dominant termination scenario is trapping while in dense networks most paths terminate by retracing. We obtain expressions for the conditional tail distributions of path lengths, P(d> \\ell \\vert ret) and P(d> \\ell \\vert {trap}) , for those paths which terminate by retracing or by trapping, respectively. We also study a class of generalized non-backtracking random walk models which not only avoid the backtracking step
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.
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. PMID:26172045
Generalized Pareto for Pattern-Oriented Random Walk Modelling of Organisms' Movements.
Directory of Open Access Journals (Sweden)
Sophie Bertrand
Full Text Available How organisms move and disperse is crucial to understand how population dynamics relates to the spatial heterogeneity of the environment. Random walk (RW models are typical tools to describe movement patterns. Whether Lévy or alternative RW better describes forager movements is keenly debated. We get around this issue using the Generalized Pareto Distribution (GPD. GPD includes as specific cases Normal, exponential and power law distributions, which underlie Brownian, Poisson-like and Lévy walks respectively. Whereas previous studies typically confronted a limited set of candidate models, GPD lets the most likely RW model emerge from the data. We illustrate the wide applicability of the method using GPS-tracked seabird foraging movements and fishing vessel movements tracked by Vessel Monitoring System (VMS, both collected in the Peruvian pelagic ecosystem. The two parameters from the fitted GPD, a scale and a shape parameter, provide a synoptic characterization of the observed movement in terms of characteristic scale and diffusive property. They reveal and quantify the variability, among species and individuals, of the spatial strategies selected by predators foraging on a common prey field. The GPD parameters constitute relevant metrics for (1 providing a synthetic and pattern-oriented description of movement, (2 using top predators as ecosystem indicators and (3 studying the variability of spatial behaviour among species or among individuals with different personalities.
Bantoft, Christina; Summers, Mathew J; Tranent, Peter J; Palmer, Matthew A; Cooley, P Dean; Pedersen, Scott J
2016-02-01
In the present study, we examined the effect of working while seated, while standing, or while walking on measures of short-term memory, working memory, selective and sustained attention, and information-processing speed. The advent of computer-based technology has revolutionized the adult workplace, such that average adult full-time employees spend the majority of their working day seated. Prolonged sitting is associated with increasing obesity and chronic health conditions in children and adults. One possible intervention to reduce the negative health impacts of the modern office environment involves modifying the workplace to increase incidental activity and exercise during the workday. Although modifications, such as sit-stand desks, have been shown to improve physiological function, there is mixed information regarding the impact of such office modification on individual cognitive performance and thereby the efficiency of the work environment. In a fully counterbalanced randomized control trial, we assessed the cognitive performance of 45 undergraduate students for up to a 1-hr period in each condition. The results indicate that there is no significant change in the measures used to assess cognitive performance associated with working while seated, while standing, or while walking at low intensity. These results indicate that cognitive performance is not degraded with short-term use of alternate workstations. © 2015, Human Factors and Ergonomics Society.
Mazari, Fayyaz Ali Khan; Mockford, Katherine; Barnett, Cleveland; Khan, Junaid A; Brown, Barbara; Smith, Lynne; Polman, Remco C; Hancock, Amanda; Vanicek, Natalie K; Chetter, Ian C
2010-12-01
To compare articulated and nonarticulated early walking aids (EWAs) for clinical and quality-of-life outcomes in transtibial amputees. Patients undergoing lower limb amputation in a tertiary-care vascular surgical unit were screened over a 4-year period. Recruited patients were randomized to receive articulated amputee mobility aid (AMA) or nonarticulated pneumatic postamputation mobility aid (PPAMA) during early rehabilitation. Primary (10-meter walking velocity) and secondary clinical (number and duration of physiotherapy treatments during EWA/prosthesis use) and quality-of-life (SF-36) outcome measures were recorded at five standardized assessment visits. Inter-group and intra-group analyses were performed. Two hundred seventy-two patients were screened and 29 transtibial amputees (median age, 56 years) were recruited (14/treatment arm). No significant difference was seen in demographics and comorbidities at baseline. Inter-group analysis: Median 10-meter walking velocity was significantly (Mann-Whitney, P = .020) faster in the PPAMA group (0.245 m/s, interquartile range [IQR] 0.218-0.402 m/s) compared with the AMA group (0.165 m/s; IQR, 0.118-0.265 m/s) at visit 1. However, there was no difference between the groups at any other visit. Similarly, the number of treatments using EWA was significantly (P = .045) lower in the PPAMA group (5.0; IQR, 3.5-8.0) compared with the AMA group (6.0; IQR, 6.0-10.5). No difference was observed between the groups in duration of physiotherapy or SF-36 domain and summary scores. Intra-group analysis: Both treatment groups showed significant improvement in 10-meter walking velocity (Friedman test; AMA P = .001; PPAMA P = .007); however, other clinical outcomes did not show any statistically significant improvement. Only physical function domain of SF-36 demonstrated significant improvement (Friedman test; AMA P = .037; PPAMA P = .029). There is no difference in clinical and QOL outcomes between articulated and nonarticulated EWAs
A randomized trial of two home-based exercise programmes to improve functional walking post-stroke.
Mayo, Nancy E; MacKay-Lyons, Marilyn J; Scott, Susan C; Moriello, Carolina; Brophy, James
2013-07-01
To estimate the relative effectiveness in improving walking ability and other mobility and health outcomes post-stroke of two home-based exercise programmes - stationary cycling and an exercise and walking programme. An observer-blinded, randomized, pragmatic, trial with repeated measures. Hospital centers in two Canadian cities. People within 12 months of acute stroke who were able to walk >10 meters independently and healthy enough to engage in exercise. Two dose-equivalent interventions, one involving stationary cycling and the other disability-targeted interventions were tested. Both protocols required daily moderate intensity exercise at home building up to 30 minutes per day. One group exercised on a stationary bicycle, the second group carried out mobility exercises and brisk walking. The primary outcome was walking capacity as measured by the six-minute walk test (6MWT). Secondary outcomes were physical function, role participation, health-related quality of life exercise adherence, and adverse events. The study failed to meet recruitment targets: 87 participants (cycle group, n = 43; exercise group, n = 44) participated. No significant effects of group or time were revealed for the 6MWT, which was approximately 320 m at randomization. A significant effect for role participation was found in favor of the exercise group (global odds ratio (OR) for cycling vs. exercise was 0.51; 95% confidence interval (CI), 0.27-0.95). Change in the 6MWT between highest and lowest adherence categories was statistically significant (p = 0.022). Both programmes were equally effective in maintaining walking capacity after discharge from stroke rehabilitation; or were equally ineffective in improving walking capacity. Clinical Trials Gov number: NCT00786045.
Energy Technology Data Exchange (ETDEWEB)
Kwok Sau Fa [Departamento de Fisica, Universidade Estadual de Maringa, Av. Colombo 5790, 87020-900 Maringa-PR (Brazil); Joni Fat, E-mail: kwok@dfi.uem.br [Jurusan Teknik Elektro-Fakultas Teknik, Universitas Tarumanagara, Jl. Let. Jend. S. Parman 1, Blok L, Lantai 3 Grogol, Jakarta 11440 (Indonesia)
2011-10-15
We consider the decoupled continuous-time random walk model with a finite characteristic waiting time and approximate jump length variance. We take the waiting time probability density function (PDF) given by a combination of the exponential and the Mittag-Leffler function. Using this waiting time PDF, we investigate the diffusion behavior for all times. We obtain exact solutions for the first two moments and the PDF for the force-free and linear force cases. Due to the finite characteristic waiting time and jump length variance, the model presents, for the force-free case, normal diffusive behavior in the long-time limit. Further, the model can describe anomalous behavior at intermediate times.
Random walk in nonhomogeneous environments: A possible approach to human and animal mobility
Srokowski, Tomasz
2017-03-01
The random walk process in a nonhomogeneous medium, characterized by a Lévy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is affected by the variable width and the variance may be finite; then all kinds of the anomalous diffusion are predicted. In the former case, only the time characteristics are sensitive to the variable width. The corresponding Langevin equation with different interpretations of the multiplicative noise is discussed. The dependence of the distribution width on position after jump is interpreted in terms of cognitive abilities and related to such problems as migration in a human population and foraging habits of animals.
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.
Critical behaviour of annihilating random walk of two species with exclusion in one dimension
Ódor, G; Odor, Geza; Menyhard, Nora
2000-01-01
The $A+A\\to 0$, $B+B\\to 0 $ process with exclusion between the differentkinds is investigated here numerically. Before treating this model explicitly,we study the generalized Domany-Kinzel cellular automaton model of Hinrichsenon the line of the parameter space where only compact clusters can grow. Thesimplest version is treated with two absorbing phases in addition to the activeone. The two kinds of kinks which arise in this case do not react leading tokinetics differing from standard annihilating random walk of two species. Timedependent simulations are presented here to illustrate the differences causedby exclusion in the scaling properties of usually discussed characteristicquantities. The dependence on the density and composition of the initial stateis most apparent. Making use of the parallelism between this process anddirected percolation limited by a reflecting parabolic surface we argue thatthe two kinds of kinks exert marginal perturbation on each other leading todeviations from standard annihilatin...
Biased Random-Walk Learning A Neurobiological Correlate to Trial-and-Error
Anderson, R W
1993-01-01
Neural network models offer a theoretical testbed for the study of learning at the cellular level. The only experimentally verified learning rule, Hebb's rule, is extremely limited in its ability to train networks to perform complex tasks. An identified cellular mechanism responsible for Hebbian-type long-term potentiation, the NMDA receptor, is highly versatile. Its function and efficacy are modulated by a wide variety of compounds and conditions and are likely to be directed by non-local phenomena. Furthermore, it has been demonstrated that NMDA receptors are not essential for some types of learning. We have shown that another neural network learning rule, the chemotaxis algorithm, is theoretically much more powerful than Hebb's rule and is consistent with experimental data. A biased random-walk in synaptic weight space is a learning rule immanent in nervous activity and may account for some types of learning -- notably the acquisition of skilled movement.
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...
Mean perimeter and mean area of the convex hull over planar random walks
Grebenkov, Denis S.; Lanoiselée, Yann; Majumdar, Satya N.
2017-10-01
We investigate the geometric properties of the convex hull over n successive positions of a planar random walk, with a symmetric continuous jump distribution. We derive the large n asymptotic behavior of the mean perimeter. In addition, we compute the mean area for the particular case of isotropic Gaussian jumps. While the leading terms of these asymptotics are universal, the subleading (correction) terms depend on the finer details of the jump distribution and describe a ‘finite size effect’ of discrete-time jump processes, allowing one to accurately compute the mean perimeter and the mean area even for small n, as verified by Monte Carlo simulations. This is particularly valuable for applications dealing with discrete-time jumps processes and ranging from the statistical analysis of single-particle tracking experiments in microbiology to home range estimations in ecology.
Modeling observation error and its effects in a random walk/extinction model.
Buonaccorsi, John P; Staudenmayer, John; Carreras, Maximo
2006-11-01
This paper examines the consequences of observation errors for the "random walk with drift", a model that incorporates density independence and is frequently used in population viability analysis. Exact expressions are given for biases in estimates of the mean, variance and growth parameters under very general models for the observation errors. For other quantities, such as the finite rate of increase, and probabilities about population size in the future we provide and evaluate approximate expressions. These expressions explain the biases induced by observation error without relying exclusively on simulations, and also suggest ways to correct for observation error. A secondary contribution is a careful discussion of observation error models, presented in terms of either log-abundance or abundance. This discussion recognizes that the bias and variance in observation errors may change over time, the result of changing sampling effort or dependence on the underlying population being sampled.
Continuous time random walk with generic waiting time and external force.
Fa, Kwok Sau; Wang, K G
2010-05-01
We derive an integrodifferential diffusion equation for decoupled continuous time random walk that is valid for a generic waiting time probability density function and external force. Using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential, a combination of power law and generalized Mittag-Leffler function and a sum of exponentials under the influence of a harmonic trap. We show that first two waiting time probability density functions can reproduce the results of the ordinary and fractional diffusion equations for all the time regions from small to large times. But the third one shows a much more complicated pattern. Furthermore, from the integrodifferential diffusion equation we show that the second Einstein relation can hold for any waiting time probability density function.
Penentuan Distribusi Suhu pada Permukaan Geometri Tak Tentu Menggunakan Metode Random Walk
Directory of Open Access Journals (Sweden)
Balduyanus Yosep Godja
2016-05-01
Full Text Available Telah dilakukan penentuan distribusi suhu dalam keadaan tunak pada sebuah plat bergeometri tak tentu menggunakan metode Random Walk yang dilengkapi fungsi green. Setiap sisi plat dikondisikan bervariasi terhadap suhu dalam rentang 10°C sampai 100°C dengan 4 (empat konfigurasi berkeadaan steady. Persamaan Laplace yang mendeskripsikan permasalahan ini dihampiri dengan mensimulasikan sejumlah walker pada setiap titik domain permasalahan untuk kemudian secara acak disebar menuju ke setiap sisi plat. Hasil yang diperoleh untuk setiap kondisi plat menunjukkan kesalahan relatif terhadap solusi numerik metode iterasi jacobi yang telah menghampiri solusi analitik, secara rata-rata adalah 0,85%. Nilai kesalahan tersebut diperoleh dengan menggunakan 5000 walker. Penelitian ini juga mendapatkan bahwa akurasi hampiran ditentukan oleh banyaknya walker yang digunakan. Secara umum, semakin banyak jumlah walker yang digunakan maka akurasi hampiran akan semakin baik.
Analytical description of field-line random walk in Goldreich-Sridhar turbulence
Shalchi, A.; Kolly, A.
2013-05-01
We describe analytically the random walk of magnetic field lines for two correlation tensors based on the Goldreich-Sridhar model. We show that for this type of tensor, field-line wandering is normal diffusive in contrast to subdiffusive and superdiffusive transport obtained for other turbulence models. Furthermore, we demonstrate that there are two transport regimes. The first one corresponds to quasi-linear theory, whereas the second one is non-linear. We show that for one of the tensors the quasi-linear regime is obtained in the limit of strong turbulence, whereas the non-linear regime is found for weak turbulence. For the other tensor, we obtain a field-line diffusion coefficient which behaves more like diffusion parameters derived previously.
A random walk evolution model of wireless sensor networks and virus spreading
Wang, Ya-Qi; Yang, Xiao-Yuan
2013-01-01
In this paper, considering both cluster heads and sensor nodes, we propose a novel evolving a network model based on a random walk to study the fault tolerance decrease of wireless sensor networks (WSNs) due to node failure, and discuss the spreading dynamic behavior of viruses in the evolution model. A theoretical analysis shows that the WSN generated by such an evolution model not only has a strong fault tolerance, but also can dynamically balance the energy loss of the entire network. It is also found that although the increase of the density of cluster heads in the network reduces the network efficiency, it can effectively inhibit the spread of viruses. In addition, the heterogeneity of the network improves the network efficiency and enhances the virus prevalence. We confirm all the theoretical results with sufficient numerical simulations.
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.)
Random walk-based similarity measure method for patterns in complex object
Directory of Open Access Journals (Sweden)
Liu Shihu
2017-04-01
Full Text Available This paper discusses the similarity of the patterns in complex objects. The complex object is composed both of the attribute information of patterns and the relational information between patterns. Bearing in mind the specificity of complex object, a random walk-based similarity measurement method for patterns is constructed. In this method, the reachability of any two patterns with respect to the relational information is fully studied, and in the case of similarity of patterns with respect to the relational information can be calculated. On this bases, an integrated similarity measurement method is proposed, and algorithms 1 and 2 show the performed calculation procedure. One can find that this method makes full use of the attribute information and relational information. Finally, a synthetic example shows that our proposed similarity measurement method is validated.
Flexible sampling large-scale social networks by self-adjustable random walk
Xu, Xiao-Ke; Zhu, Jonathan J. H.
2016-12-01
Online social networks (OSNs) have become an increasingly attractive gold mine for academic and commercial researchers. However, research on OSNs faces a number of difficult challenges. One bottleneck lies in the massive quantity and often unavailability of OSN population data. Sampling perhaps becomes the only feasible solution to the problems. How to draw samples that can represent the underlying OSNs has remained a formidable task because of a number of conceptual and methodological reasons. Especially, most of the empirically-driven studies on network sampling are confined to simulated data or sub-graph data, which are fundamentally different from real and complete-graph OSNs. In the current study, we propose a flexible sampling method, called Self-Adjustable Random Walk (SARW), and test it against with the population data of a real large-scale OSN. We evaluate the strengths of the sampling method in comparison with four prevailing methods, including uniform, breadth-first search (BFS), random walk (RW), and revised RW (i.e., MHRW) sampling. We try to mix both induced-edge and external-edge information of sampled nodes together in the same sampling process. Our results show that the SARW sampling method has been able to generate unbiased samples of OSNs with maximal precision and minimal cost. The study is helpful for the practice of OSN research by providing a highly needed sampling tools, for the methodological development of large-scale network sampling by comparative evaluations of existing sampling methods, and for the theoretical understanding of human networks by highlighting discrepancies and contradictions between existing knowledge/assumptions of large-scale real OSN data.
Learning of Multimodal Representations With Random Walks on the Click Graph.
Wu, Fei; Lu, Xinyan; Song, Jun; Yan, Shuicheng; Zhang, Zhongfei Mark; Rui, Yong; Zhuang, Yueting
2016-02-01
In multimedia information retrieval, most classic approaches tend to represent different modalities of media in the same feature space. With the click data collected from the users' searching behavior, existing approaches take either one-to-one paired data (text-image pairs) or ranking examples (text-query-image and/or image-query-text ranking lists) as training examples, which do not make full use of the click data, particularly the implicit connections among the data objects. In this paper, we treat the click data as a large click graph, in which vertices are images/text queries and edges indicate the clicks between an image and a query. We consider learning a multimodal representation from the perspective of encoding the explicit/implicit relevance relationship between the vertices in the click graph. By minimizing both the truncated random walk loss as well as the distance between the learned representation of vertices and their corresponding deep neural network output, the proposed model which is named multimodal random walk neural network (MRW-NN) can be applied to not only learn robust representation of the existing multimodal data in the click graph, but also deal with the unseen queries and images to support cross-modal retrieval. We evaluate the latent representation learned by MRW-NN on a public large-scale click log data set Clickture and further show that MRW-NN achieves much better cross-modal retrieval performance on the unseen queries/images than the other state-of-the-art methods.
An improved random walk algorithm for the implicit Monte Carlo method
Energy Technology Data Exchange (ETDEWEB)
Keady, Kendra P., E-mail: keadyk@lanl.gov; Cleveland, Mathew A.
2017-01-01
In this work, we introduce a modified Implicit Monte Carlo (IMC) Random Walk (RW) algorithm, which increases simulation efficiency for multigroup radiative transfer problems with strongly frequency-dependent opacities. To date, the RW method has only been implemented in “fully-gray” form; that is, the multigroup IMC opacities are group-collapsed over the full frequency domain of the problem to obtain a gray diffusion problem for RW. This formulation works well for problems with large spatial cells and/or opacities that are weakly dependent on frequency; however, the efficiency of the RW method degrades when the spatial cells are thin or the opacities are a strong function of frequency. To address this inefficiency, we introduce a RW frequency group cutoff in each spatial cell, which divides the frequency domain into optically thick and optically thin components. In the modified algorithm, opacities for the RW diffusion problem are obtained by group-collapsing IMC opacities below the frequency group cutoff. Particles with frequencies above the cutoff are transported via standard IMC, while particles below the cutoff are eligible for RW. This greatly increases the total number of RW steps taken per IMC time-step, which in turn improves the efficiency of the simulation. We refer to this new method as Partially-Gray Random Walk (PGRW). We present numerical results for several multigroup radiative transfer problems, which show that the PGRW method is significantly more efficient than standard RW for several problems of interest. In general, PGRW decreases runtimes by a factor of ∼2–4 compared to standard RW, and a factor of ∼3–6 compared to standard IMC. While PGRW is slower than frequency-dependent Discrete Diffusion Monte Carlo (DDMC), it is also easier to adapt to unstructured meshes and can be used in spatial cells where DDMC is not applicable. This suggests that it may be optimal to employ both DDMC and PGRW in a single simulation.
Fayolle, Guy; Malyshev, Vadim
2017-01-01
This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts. Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows spec...
Mishra, Jibitesh
2007-01-01
The book covers all the fundamental aspects of generating fractals through L-system. Also it provides insight to various researches in this area for generating fractals through L-system approach & estimating dimensions. Also it discusses various applications of L-system fractals. Key Features: - Fractals generated from L-System including hybrid fractals - Dimension calculation for L-system fractals - Images & codes for L-system fractals - Research directions in the area of L-system fractals - Usage of various freely downloadable tools in this area - Fractals generated from L-System including hybrid fractals- Dimension calculation for L-system fractals- Images & codes for L-system fractals- Research directions in the area of L-system fractals- Usage of various freely downloadable tools in this area
B. Chen (Bohan); J. Blanchet; C.H. Rhee (Chang-Han); A.P. Zwart (Bert)
2017-01-01
textabstractWe propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based on an importance sampling strategy that hinges
Monte Carlo Random-Walk Experiments as a Test of Chaotic Orbits of Maps of the Interval
Arneodo, A.; Sornette, D.
1984-05-01
We have performed Monte Carlo random-walk experiments on a one-dimensional periodic lattice with a trapping site using the logistic map as a generator of pseudorandom numbers. Comparison with analytical results indicates that, when it has sensitive dependence to the initial conditions, this map provides a true pseudorandom generator.
Reike, Dennis; Schwarz, Wolf
2016-01-01
The time required to determine the larger of 2 digits decreases with their numerical distance, and, for a given distance, increases with their magnitude (Moyer & Landauer, 1967). One detailed quantitative framework to account for these effects is provided by random walk models. These chronometric models describe how number-related noisy…
Scholtes, Vanessa A.; Becher, Jules G.; Janssen-Potten, Yvonne J.; Dekkers, Hurnet; Smallenbroek, Linda; Dallmeijer, Annet J.
2012-01-01
The objective of the study was to evaluate the effectiveness of functional progressive resistance exercise (PRE) training on walking ability in children with cerebral palsy (CP). Fifty-one ambulant children with spastic CP (mean age 10 years 5 months, 29 boys) were randomized to an intervention (n=26) or control group (n=25, receiving usual care).…
Scholtes, V.A.; Becher, J.G.; Janssen-Potten, Y.J.; Dekkers, H.; Smallenbroek, L.; Dallmeijer, A.J.
2012-01-01
The objective of the study was to evaluate the effectiveness of functional progressive resistance exercise (PRE) training on walking ability in children with cerebral palsy (CP).Fifty-one ambulant children with spastic CP (mean age 10 years 5 months, 29 boys) were randomized to an intervention (n=
Fractional Brownian Motion:. Theory and Application to DNA Walk
Lim, S. C.; Muniandy, S. V.
2001-09-01
This paper briefly reviews the theory of fractional Brownian motion (FBM) and its generalization to multifractional Brownian motion (MBM). FBM and MBM are applied to a biological system namely the DNA sequence. By considering a DNA sequence as a fractal random walk, it is possible to model the noncoding sequence of human retinoblastoma DNA as a discrete version of FBM. The average scaling exponent or Hurst exponent of the DNA walk is estimated to be H = 0.60 ± 0.05 using the monofractal R/S analysis. This implies that the mean square fluctuation of DNA walk belongs to anomalous superdiffusion type. We also show that the DNA landscape is not monofractal, instead one has multifractal DNA landscape. The empirical estimates of the Hurst exponent falls approximately within the range H ~ 0.62 - 0.72. We propose two multifractal models, namely the MBM and multiscale FBM to describe the existence of different Hurst exponents in DNA walk.
Zhu, Zhizhong; Cui, Liling; Yin, Miaomiao; Yu, Yang; Zhou, Xiaona; Wang, Hongtu; Yan, Hua
2016-06-01
To investigate the effects of hydrotherapy on walking ability and balance in patients with chronic stroke. Single-blind, randomized controlled pilot trial. Outpatient rehabilitation clinic at a tertiary neurological hospital in China. A total of 28 participants with impairments in walking and controlling balance more than six months post-stroke. After baseline evaluations, participants were randomly assigned to a land-based therapy (control group, n = 14) or hydrotherapy (study group, n = 14). Participants underwent individual sessions for four weeks, five days a week, for 45 minutes per session. After four weeks of rehabilitation, all participants were evaluated by a blinded assessor. Functional assessments included the Functional Reach Test, Berg Balance Scale, 2-minute walk test, and Timed Up and Go Test. After four weeks of treatment, the Berg Balance Scale, functional reach test, 2-minute walk test, and the Timed Up and Go Test scores had improved significantly in each group (P hydrotherapy exercise resulted in a large improvement in a small group (n = 14) of individuals with relatively high balance and walking function following a stroke. © The Author(s) 2015.
Kalron, Alon; Rosenblum, Uri; Frid, Lior; Achiron, Anat
2017-03-01
Evaluate the effects of a Pilates exercise programme on walking and balance in people with multiple sclerosis and compare this exercise approach to conventional physical therapy sessions. Randomized controlled trial. Multiple Sclerosis Center, Sheba Medical Center, Tel-Hashomer, Israel. Forty-five people with multiple sclerosis, 29 females, mean age (SD) was 43.2 (11.6) years; mean Expanded Disability Status Scale (S.D) was 4.3 (1.3). Participants received 12 weekly training sessions of either Pilates ( n=22) or standardized physical therapy ( n=23) in an outpatient basis. Spatio-temporal parameters of walking and posturography parameters during static stance. Functional tests included the Time Up and Go Test, 2 and 6-minute walk test, Functional Reach Test, Berg Balance Scale and the Four Square Step Test. In addition, the following self-report forms included the Multiple Sclerosis Walking Scale and Modified Fatigue Impact Scale. At the termination, both groups had significantly increased their walking speed ( P=0.021) and mean step length ( P=0.023). According to the 2-minute and 6-minute walking tests, both groups at the end of the intervention program had increased their walking speed. Mean (SD) increase in the Pilates and physical therapy groups were 39.1 (78.3) and 25.3 (67.2) meters, respectively. There was no effect of group X time in all instrumented and clinical balance and gait measures. Pilates is a possible treatment option for people with multiple sclerosis in order to improve their walking and balance capabilities. However, this approach does not have any significant advantage over standardized physical therapy.
Comolli, Alessandro; Hakoun, Vivien; Dentz, Marco
2017-04-01
Achieving the understanding of the process of solute transport in heterogeneous porous media is of crucial importance for several environmental and social purposes, ranging from aquifers contamination and remediation, to risk assessment in nuclear waste repositories. The complexity of this aim is mainly ascribable to the heterogeneity of natural media, which can be observed at all the scales of interest, from pore scale to catchment scale. In fact, the intrinsic heterogeneity of porous media is responsible for the arising of the well-known non-Fickian footprints of transport, including heavy-tailed breakthrough curves, non-Gaussian spatial density profiles and the non-linear growth of the mean squared displacement. Several studies investigated the processes through which heterogeneity impacts the transport properties, which include local modifications to the advective-dispersive motion of solutes, mass exchanges between some mobile and immobile phases (e.g. sorption/desorption reactions or diffusion into solid matrix) and spatial correlation of the flow field. In the last decades, the continuous time random walk (CTRW) model has often been used to describe solute transport in heterogenous conditions and to quantify the impact of point heterogeneity, spatial correlation and mass transfer on the average transport properties [1]. Open issues regarding this approach are the possibility to relate measurable properties of the medium to the parameters of the model, as well as its capability to provide predictive information. In a recent work [2] the authors have shed new light on understanding the relationship between Lagrangian and Eulerian dynamics as well as on their evolution from arbitrary initial conditions. On the basis of these results, we derive a CTRW model for the description of Darcy-scale transport in d-dimensional media characterized by spatially random permeability fields. The CTRW approach models particle velocities as a spatial Markov process, which is
A random walk model to simulate the atmospheric dispersion of radionuclide
Zhuo, Jun; Huang, Liuxing; Niu, Shengli; Xie, Honggang; Kuang, Feihong
2018-01-01
To investigate the atmospheric dispersion of radionuclide in large-medium scale, a numerical simulation method based on random walk model for radionuclide atmospheric dispersion was established in the paper. The route of radionuclide migration and concentration distribution of radionuclide can be calculated out by using the method with the real-time or historical meteorological fields. In the simulation, a plume of radionuclide is treated as a lot of particles independent of each other. The particles move randomly by the fluctuations of turbulence, and disperse, so as to enlarge the volume of the plume and dilute the concentration of radionuclide. The dispersion of the plume over time is described by the variance of the particles. Through statistical analysis, the relationships between variance of the particles and radionuclide dispersion characteristics can be derived. The main mechanisms considered in the physical model are: (1) advection of radionuclide by mean air motion, (2) mixing of radionuclide by atmospheric turbulence, (3) dry and wet deposition, (4) disintegration. A code named RADES was developed according the method. And then, the European Tracer Experiment (ETEX) in 1994 is simulated by the RADES and FLEXPART codes, the simulation results of the concentration distribution of tracer are in good agreement with the experimental data.
Applications of fractal analysis to physiology
Glenny, Robb W.; Robertson, H. Thomas; Yamashiro, Stanley; Bassingthwaighte, James B.
2010-01-01
This review describes approaches to the analysis of fractal properties of physiological observations. Fractals are useful to describe the natural irregularity of physiological systems because their irregularity is not truly random and can be demonstrated to have spatial or temporal correlation. The concepts of fractal analysis are introduced from intuitive, visual, and mathematical perspectives. The regional heterogeneities of pulmonary and myocardial flows are discussed as applications of spatial fractal analysis, and methods for estimating a fractal dimension from physiological data are presented. Although the methods used for fractal analyses of physiological data are still under development and will require additional validation, they appear to have great potential for the study of physiology at scales of resolution ranging from the microcirculation to the intact organism. PMID:1885430
Directory of Open Access Journals (Sweden)
Amato P
2008-01-01
Full Text Available Abstract Self-similar patterns are frequently observed in Nature. Their reproduction is possible on a length scale 102–105 nm with lithographic methods, but seems impossible on the nanometer length scale. It is shown that this goal may be achieved via a multiplicative variant of the multi-spacer patterning technology, in this way permitting the controlled preparation of fractal surfaces.
複雑ネットワーク上におけるRandom Walk とPreferential Walk のダイナミクス
野村, 宗広; 西成, 活裕
2009-01-01
複雑ネットワークとは単純化したネットワークモデルではなく実在するネットワークにみられるような複雑な構造を持つモデルという意味で複雑という。複雑ネットワーク上のRandom Walk とPreferential Walk のCA モデルによるシミュレーションを行い、幾何学的性質と動的性質の関係を明らかにした。またその理論解析を行いシミュレーション結果によい一致をえることができた。具体的には幾何学的性質としてクラスター係数と次数分布に焦点を当て、動的性質として流量と自由行程に注目した。これにより高いクラスター性が流量の増加に寄与することを明らかにし、スケールフリーネットワーク上のRandom Walk、Preferential Walk における粒子の自由行程分布にスケールフリー性が現れることを示した。...
Mansfield, Avril; Wong, Jennifer S; Bayley, Mark; Biasin, Lou; Brooks, Dina; Brunton, Karen; Howe, Jo-Anne; Inness, Elizabeth L; Jones, Simon; Lymburner, Jackie; Mileris, Ramona; McIlroy, William E
2013-07-18
Regaining independent ambulation is the top priority for individuals recovering from stroke. Thus, physical rehabilitation post-stroke should focus on improving walking function and endurance. However, the amount of walking completed by individuals with stroke attending rehabilitation is far below that required for independent community ambulation. There has been increased interest in accelerometer-based monitoring of walking post-stroke. Walking monitoring could be integrated within the goal-setting process for those with ambulation goals in rehabilitation. The feedback from these devices can be downloaded to a computer to produce reports. The purpose of this study is to determine the effect of accelerometer-based feedback of daily walking activity during rehabilitation on the frequency and duration of walking post-stroke. Participants will be randomly assigned to one of two groups: feedback or no feedback. Participants will wear accelerometers daily during in- and out-patient rehabilitation and, for participants in the feedback group, the participants' treating physiotherapist will receive regular reports of walking activity. The primary outcome measures are the amount of daily walking completed, as measured using the accelerometers, and spatio-temporal characteristics of walking (e.g. walking speed). We will also examine goal attainment, satisfaction with progress towards goals, stroke self-efficacy, and community-integration. Increased walking activity during rehabilitation is expected to improve walking function and community re-integration following discharge. In addition, a focus on altering walking behaviour within the rehabilitation setting may lead to altered behaviour and increased activity patterns after discharge. ClinicalTrials.gov NCT01521234.
Gusi, Narcís; Raimundo, Armando; Leal, Alejo
2006-11-30
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. 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 degrees 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. 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. 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.
Bernard, P; Ninot, G; Bernard, P L; Picot, M C; Jaussent, A; Tallon, G; Blain, H
2015-01-01
Physical inactivity and advanced age are associated with risk of depressive disorders. Physical activity can reduce depressive symptoms in older subjects with depressive disorders. We investigated whether a walking intervention program may decrease the occurrence of depressive symptoms in inactive post-menopausal women without depression. A total of 121 participants aged 57-75 years were randomly assigned to a six-month moderate intensity walking intervention (three times a week, 40 minutes per session, supervised and home-based) or to a control group (waiting list). Inactivity was assessed using the Physical Activity Questionnaire for the Elderly. Depression levels were measured pre- and post-intervention with the Beck depression inventory (BDI). Several baseline measures were considered as possible predictors of post-intervention BDI score. Participants in the walking intervention showed a significant decrease in depression as compared with controls. Baseline cognitive-BDI subscore, subjective health status, body mass index and adherence were post-intervention BDI score predictors. A six-month, three-session per week, moderate intensity walking intervention with a minimal 50% adherence rate reduces depression in post-menopausal women at risk for depression due to physical inactivity. This type of walking intervention could be considered as a widely accessible prevention strategy to prevent depressive symptoms in post-menopausal women at risk of depression.
Identifying and Analyzing Novel Epilepsy-Related Genes Using Random Walk with Restart Algorithm
Directory of Open Access Journals (Sweden)
Wei Guo
2017-01-01
Full Text Available As a pathological condition, epilepsy is caused by abnormal neuronal discharge in brain which will temporarily disrupt the cerebral functions. Epilepsy is a chronic disease which occurs in all ages and would seriously affect patients’ personal lives. Thus, it is highly required to develop effective medicines or instruments to treat the disease. Identifying epilepsy-related genes is essential in order to understand and treat the disease because the corresponding proteins encoded by the epilepsy-related genes are candidates of the potential drug targets. In this study, a pioneering computational workflow was proposed to predict novel epilepsy-related genes using the random walk with restart (RWR algorithm. As reported in the literature RWR algorithm often produces a number of false positive genes, and in this study a permutation test and functional association tests were implemented to filter the genes identified by RWR algorithm, which greatly reduce the number of suspected genes and result in only thirty-three novel epilepsy genes. Finally, these novel genes were analyzed based upon some recently published literatures. Our findings implicate that all novel genes were closely related to epilepsy. It is believed that the proposed workflow can also be applied to identify genes related to other diseases and deepen our understanding of the mechanisms of these diseases.
Unsupervised Change Detection for Multispectral Remote Sensing Images Using Random Walks
Directory of Open Access Journals (Sweden)
Qingjie Liu
2017-05-01
Full Text Available In this paper, the change detection of Multi-Spectral (MS remote sensing images is treated as an image segmentation issue. An unsupervised method integrating histogram-based thresholding and image segmentation techniques is proposed. In order to overcome the poor performance of thresholding techniques for strongly overlapped change/non-change signals, a Gaussian Mixture Model (GMM with three components, including non-change, non-labeling and change, is adopted to model the statistical characteristics of the different images between two multi-temporal MS images. The non-labeling represents the pixels that are difficult to be classified. A random walk based segmentation method is applied to solve this problem, in which the different images are modeled as graphs and the classification results of GMM are imported as the labeling seeds. The experimental results of three remote sensing image pairs acquired by different sensors suggest a superiority of the proposed approach comparing with the existing unsupervised change detection methods.
Random walk with nonuniform angular distribution biased by an external periodic pulse
Acharyya, Aranyak
2016-11-01
We studied the motion of a random walker in two dimensions with nonuniform angular distribution biased by an external periodic pulse. Here, we analytically calculated the mean square displacement (end-to-end distance of a walk after n time steps), without bias and with bias. We determined the average x-component of the final displacement of the walker. Interestingly, we noted that for a particular periodicity of the bias, this average x-component of the final displacement becomes approximately zero. The average y-component of the final displacement is found to be zero for any perodicity of the bias, and its reason can be attributed to the nature of the probability density function of the angle (subtended by the displacement vector with the x-axis). These analytical results are also supported by computer simulations. The present study may be thought of as a model for arresting the bacterial motion (along a preferred direction) by an external periodic bias. This article will be useful for undergraduate students of physics, statistics and biology as an example of an interdisciplinary approach to understand a way to control bacterial motion.
Network Location-Aware Service Recommendation with Random Walk in Cyber-Physical Systems.
Yin, Yuyu; Yu, Fangzheng; Xu, Yueshen; Yu, Lifeng; Mu, Jinglong
2017-09-08
Cyber-physical systems (CPS) have received much attention from both academia and industry. An increasing number of functions in CPS are provided in the way of services, which gives rise to an urgent task, that is, how to recommend the suitable services in a huge number of available services in CPS. In traditional service recommendation, collaborative filtering (CF) has been studied in academia, and used in industry. However, there exist several defects that limit the application of CF-based methods in CPS. One is that under the case of high data sparsity, CF-based methods are likely to generate inaccurate prediction results. In this paper, we discover that mining the potential similarity relations among users or services in CPS is really helpful to improve the prediction accuracy. Besides, most of traditional CF-based methods are only capable of using the service invocation records, but ignore the context information, such as network location, which is a typical context in CPS. In this paper, we propose a novel service recommendation method for CPS, which utilizes network location as context information and contains three prediction models using random walking. We conduct sufficient experiments on two real-world datasets, and the results demonstrate the effectiveness of our proposed methods and verify that the network location is indeed useful in QoS prediction.
Identifying and Analyzing Novel Epilepsy-Related Genes Using Random Walk with Restart Algorithm.
Guo, Wei; Shang, Dong-Mei; Cao, Jing-Hui; Feng, Kaiyan; He, Yi-Chun; Jiang, Yang; Wang, ShaoPeng; Gao, Yu-Fei
2017-01-01
As a pathological condition, epilepsy is caused by abnormal neuronal discharge in brain which will temporarily disrupt the cerebral functions. Epilepsy is a chronic disease which occurs in all ages and would seriously affect patients' personal lives. Thus, it is highly required to develop effective medicines or instruments to treat the disease. Identifying epilepsy-related genes is essential in order to understand and treat the disease because the corresponding proteins encoded by the epilepsy-related genes are candidates of the potential drug targets. In this study, a pioneering computational workflow was proposed to predict novel epilepsy-related genes using the random walk with restart (RWR) algorithm. As reported in the literature RWR algorithm often produces a number of false positive genes, and in this study a permutation test and functional association tests were implemented to filter the genes identified by RWR algorithm, which greatly reduce the number of suspected genes and result in only thirty-three novel epilepsy genes. Finally, these novel genes were analyzed based upon some recently published literatures. Our findings implicate that all novel genes were closely related to epilepsy. It is believed that the proposed workflow can also be applied to identify genes related to other diseases and deepen our understanding of the mechanisms of these diseases.
Uncoupled continuous-time random walk model: analytical and numerical solutions.
Fa, Kwok Sau
2014-05-01
Solutions for the continuous-time random walk (CTRW) model are known in few cases. In this work, the uncoupled CTRW model is investigated analytically and numerically. In particular, the probability density function (PDF) and n-moment are obtained and analyzed. Exponential and Gaussian functions are used for the jump length PDF, whereas the Mittag-Leffler function and a combination of exponential and power-laws function is used for the waiting time PDF. The exponential and Gaussian jump length PDFs have finite jump length variances and they give the same second moment; however, their distribution functions present different behaviors near the origin. The combination of exponential and power-law function for the waiting time PDF can generate a crossover from anomalous regime to normal regime. Moreover, the parameter of the exponential jump length PDF does not change the behavior of the n-moment for all time intervals, and for the Gaussian jump length PDF the n-moment also indicates a similar behavior.
Ingo, Carson; Magin, Richard L; Colon-Perez, Luis; Triplett, William; Mareci, Thomas H
2014-02-01
In diffusion-weighted MRI studies of neural tissue, the classical model assumes the statistical mechanics of Brownian motion and predicts a monoexponential signal decay. However, there have been numerous reports of signal decays that are not monoexponential, particularly in the white matter. We modeled diffusion in neural tissue from the perspective of the continuous time random walk. The characteristic diffusion decay is represented by the Mittag-Leffler function, which relaxes a priori assumptions about the governing statistics. We then used entropy as a measure of the anomalous features for the characteristic function. Diffusion-weighted MRI experiments were performed on a fixed rat brain using an imaging spectrometer at 17.6 T with b-values arrayed up to 25,000 s/mm(2). Additionally, we examined the impact of varying either the gradient strength, q, or mixing time, Δ, on the observed diffusion dynamics. In white and gray matter regions, the Mittag-Leffler and entropy parameters demonstrated new information regarding subdiffusion and produced different image contrast from that of the classical diffusion coefficient. The choice of weighting on q and Δ produced different image contrast within the regions of interest. We propose these parameters have the potential as biomarkers for morphology in neural tissue. Copyright © 2013 Wiley Periodicals, Inc.
Uncoupled continuous-time random walk model: Analytical and numerical solutions
Fa, Kwok Sau
2014-05-01
Solutions for the continuous-time random walk (CTRW) model are known in few cases. In this work, the uncoupled CTRW model is investigated analytically and numerically. In particular, the probability density function (PDF) and n-moment are obtained and analyzed. Exponential and Gaussian functions are used for the jump length PDF, whereas the Mittag-Leffler function and a combination of exponential and power-laws function is used for the waiting time PDF. The exponential and Gaussian jump length PDFs have finite jump length variances and they give the same second moment; however, their distribution functions present different behaviors near the origin. The combination of exponential and power-law function for the waiting time PDF can generate a crossover from anomalous regime to normal regime. Moreover, the parameter of the exponential jump length PDF does not change the behavior of the n-moment for all time intervals, and for the Gaussian jump length PDF the n-moment also indicates a similar behavior.
A continuous time random walk (CTRW) integro-differential equation with chemical interaction
Ben-Zvi, Rami; Nissan, Alon; Scher, Harvey; Berkowitz, Brian
2018-01-01
A nonlocal-in-time integro-differential equation is introduced that accounts for close coupling between transport and chemical reaction terms. The structure of the equation contains these terms in a single convolution with a memory function M ( t), which includes the source of non-Fickian (anomalous) behavior, within the framework of a continuous time random walk (CTRW). The interaction is non-linear and second-order, relevant for a bimolecular reaction A + B → C. The interaction term ΓP A ( s, t) P B ( s, t) is symmetric in the concentrations of A and B (i.e. P A and P B ); thus the source terms in the equations for A, B and C are similar, but with a change in sign for that of C. Here, the chemical rate coefficient, Γ, is constant. The fully coupled equations are solved numerically using a finite element method (FEM) with a judicious representation of M ( t) that eschews the need for the entire time history, instead using only values at the former time step. To begin to validate the equations, the FEM solution is compared, in lieu of experimental data, to a particle tracking method (CTRW-PT); the results from the two approaches, particularly for the C profiles, are in agreement. The FEM solution, for a range of initial and boundary conditions, can provide a good model for reactive transport in disordered media.
How Far Is Quasar UV/Optical Variability from a Damped Random Walk at Low Frequency?
Guo, Hengxiao; Wang, Junxian; Cai, Zhenyi; Sun, Mouyuan
2017-10-01
Studies have shown that UV/optical light curves of quasars can be described using the prevalent damped random walk (DRW) model, also known as the Ornstein-Uhlenbeck process. A white noise power spectral density (PSD) is expected at low frequency in this model; however, a direct observational constraint to the low-frequency PSD slope is difficult due to the limited lengths of the light curves available. Meanwhile, quasars show scatter in their DRW parameters that is too large to be attributed to uncertainties in the measurements and dependence on the variation of known physical factors. In this work we present simulations showing that, if the low-frequency PSD deviates from the DRW, the red noise leakage can naturally produce large scatter in the variation parameters measured from simulated light curves. The steeper the low-frequency PSD slope, the larger scatter we expect. Based on observations of SDSS Stripe 82 quasars, we find that the low-frequency PSD slope should be no steeper than -1.3. The actual slope could be flatter, which consequently requires that the quasar variabilities should be influenced by other unknown factors. We speculate that the magnetic field and/or metallicity could be such additional factors.
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...
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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.
Haron, Zaiton; Bakar, Suhaimi Abu; Dimon, Mohamad Ngasri
2015-01-01
Strategic noise mapping provides important information for noise impact assessment and noise abatement. However, producing reliable strategic noise mapping in a dynamic, complex working environment is difficult. This study proposes the implementation of the random walk approach as a new stochastic technique to simulate noise mapping and to predict the noise exposure level in a workplace. A stochastic simulation framework and software, namely RW-eNMS, were developed to facilitate the random walk approach in noise mapping prediction. This framework considers the randomness and complexity of machinery operation and noise emission levels. Also, it assesses the impact of noise on the workers and the surrounding environment. For data validation, three case studies were conducted to check the accuracy of the prediction data and to determine the efficiency and effectiveness of this approach. The results showed high accuracy of prediction results together with a majority of absolute differences of less than 2 dBA; also, the predicted noise doses were mostly in the range of measurement. Therefore, the random walk approach was effective in dealing with environmental noises. It could predict strategic noise mapping to facilitate noise monitoring and noise control in the workplaces. PMID:25875019
A non-Lévy 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.
Harper, David William (Inventor)
2017-01-01
A structural support having fractal-stiffening and method of fabricating the support is presented where an optimized location of at least three nodes is predetermined prior to fabricating the structural support where a first set of webs is formed on one side of the support and joined to the nodes to form a first pocket region. A second set of webs is formed within the first pocket region forming a second pocket region where the height of the first set of webs extending orthogonally from the side of the support is greater than the second set of webs extending orthogonally from the support.
Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.
2017-12-01
We analyze a Markovian random walk strategy on undirected regular networks involving power matrix functions of the type L\\frac{α{2}} where L indicates a ‘simple’ Laplacian matrix. We refer to such walks as ‘fractional random walks’ with admissible interval 0 α (recurrent for d≤slantα ) of the lattice. As a consequence, for 0global mean first passage times (Kemeny constant) for the fractional random walk. For an infinite 1D lattice (infinite ring) we obtain for the transient regime 0world properties with the emergence of Lévy flights on large (infinite) lattices.
Esophagus segmentation in CT via 3D fully convolutional neural network and random walk.
Fechter, Tobias; Adebahr, Sonja; Baltas, Dimos; Ben Ayed, Ismail; Desrosiers, Christian; Dolz, Jose
2017-12-01
the results of this model can be refined by a random walk step taking pixel intensities and neighborhood relationships into account. One of the main advantages of our network over previous methods is that it performs 3D convolutions, thus fully exploiting the 3D spatial context and performing an efficient volume-wise prediction. The whole segmentation process is fully automatic and yields esophagus delineations in very good agreement with the gold standard, showing that it can compete with previously published methods. © 2017 American Association of Physicists in Medicine.
Godrèche, Claude
2017-05-01
The probability distribution of the longest interval between two zeros of a simple random walk starting and ending at the origin, and of its continuum limit, the Brownian bridge, was analysed in the past by Rosén and Wendel, then extended by the latter to stable processes. We recover and extend these results using simple concepts of renewal theory, which allows to revisit past and recent works of the physics literature.
Sun, Min; Chen, Xinjian; Zhang, Zhiqiang; Ma, Chiyuan
2017-02-01
Accurate volume measurements of pituitary adenoma are important to the diagnosis and treatment for this kind of sellar tumor. The pituitary adenomas have different pathological representations and various shapes. Particularly, in the case of infiltrating to surrounding soft tissues, they present similar intensities and indistinct boundary in T1-weighted (T1W) magnetic resonance (MR) images. Then the extraction of pituitary adenoma from MR images is still a challenging task. In this paper, we propose an interactive method to segment the pituitary adenoma from brain MR data, by combining graph cuts based active contour model (GCACM) and random walk algorithm. By using the GCACM method, the segmentation task is formulated as an energy minimization problem by a hybrid active contour model (ACM), and then the problem is solved by the graph cuts method. The region-based term in the hybrid ACM considers the local image intensities as described by Gaussian distributions with different means and variances, expressed as maximum a posteriori probability (MAP). Random walk is utilized as an initialization tool to provide initialized surface for GCACM. The proposed method is evaluated on the three-dimensional (3-D) T1W MR data of 23 patients and compared with the standard graph cuts method, the random walk method, the hybrid ACM method, a GCACM method which considers global mean intensity in region forces, and a competitive region-growing based GrowCut method planted in 3D Slicer. Based on the experimental results, the proposed method is superior to those methods.
Lee, Chul-Ho; Eun, Do Young
2012-01-01
Graph sampling via crawling has been actively considered as a generic and important tool for collecting uniform node samples so as to consistently estimate and uncover various characteristics of complex networks. The so-called simple random walk with re-weighting (SRW-rw) and Metropolis-Hastings (MH) algorithm have been popular in the literature for such unbiased graph sampling. However, an unavoidable downside of their core random walks -- slow diffusion over the space, can cause poor estimation accuracy. In this paper, we propose non-backtracking random walk with re-weighting (NBRW-rw) and MH algorithm with delayed acceptance (MHDA) which are theoretically guaranteed to achieve, at almost no additional cost, not only unbiased graph sampling but also higher efficiency (smaller asymptotic variance of the resulting unbiased estimators) than the SRW-rw and the MH algorithm, respectively. In particular, a remarkable feature of the MHDA is its applicability for any non-uniform node sampling like the MH algorithm,...
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.
Random Walk Graph Laplacian-Based Smoothness Prior for Soft Decoding of JPEG Images.
Liu, Xianming; Cheung, Gene; Wu, Xiaolin; Zhao, Debin
2017-02-01
Given the prevalence of joint photographic experts group (JPEG) compressed images, optimizing image reconstruction from the compressed format remains an important problem. Instead of simply reconstructing a pixel block from the centers of indexed discrete cosine transform (DCT) coefficient quantization bins (hard decoding), soft decoding reconstructs a block by selecting appropriate coefficient values within the indexed bins with the help of signal priors. The challenge thus lies in how to define suitable priors and apply them effectively. In this paper, we combine three image priors-Laplacian prior for DCT coefficients, sparsity prior, and graph-signal smoothness prior for image patches-to construct an efficient JPEG soft decoding algorithm. Specifically, we first use the Laplacian prior to compute a minimum mean square error initial solution for each code block. Next, we show that while the sparsity prior can reduce block artifacts, limiting the size of the overcomplete dictionary (to lower computation) would lead to poor recovery of high DCT frequencies. To alleviate this problem, we design a new graph-signal smoothness prior (desired signal has mainly low graph frequencies) based on the left eigenvectors of the random walk graph Laplacian matrix (LERaG). Compared with the previous graph-signal smoothness priors, LERaG has desirable image filtering properties with low computation overhead. We demonstrate how LERaG can facilitate recovery of high DCT frequencies of a piecewise smooth signal via an interpretation of low graph frequency components as relaxed solutions to normalized cut in spectral clustering. Finally, we construct a soft decoding algorithm using the three signal priors with appropriate prior weights. Experimental results show that our proposal outperforms the state-of-the-art soft decoding algorithms in both objective and subjective evaluations noticeably.
Identifying co-targets to fight drug resistance based on a random walk model
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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.
Fast Inbound Top-K Query for Random Walk with Restart.
Zhang, Chao; Jiang, Shan; Chen, Yucheng; Sun, Yidan; Han, Jiawei
2015-09-01
Random walk with restart (RWR) is widely recognized as one of the most important node proximity measures for graphs, as it captures the holistic graph structure and is robust to noise in the graph. In this paper, we study a novel query based on the RWR measure, called the inbound top-k (Ink) query. Given a query node q and a number k , the Ink query aims at retrieving k nodes in the graph that have the largest weighted RWR scores to q . Ink queries can be highly useful for various applications such as traffic scheduling, disease treatment, and targeted advertising. Nevertheless, none of the existing RWR computation techniques can accurately and efficiently process the Ink query in large graphs. We propose two algorithms, namely Squeeze and Ripple, both of which can accurately answer the Ink query in a fast and incremental manner. To identify the top- k nodes, Squeeze iteratively performs matrix-vector multiplication and estimates the lower and upper bounds for all the nodes in the graph. Ripple employs a more aggressive strategy by only estimating the RWR scores for the nodes falling in the vicinity of q , the nodes outside the vicinity do not need to be evaluated because their RWR scores are propagated from the boundary of the vicinity and thus upper bounded. Ripple incrementally expands the vicinity until the top- k result set can be obtained. Our extensive experiments on real-life graph data sets show that Ink queries can retrieve interesting results, and the proposed algorithms are orders of magnitude faster than state-of-the-art method.
MicroRNA prediction with a novel ranking algorithm based on random walks.
Xu, Yunpen; Zhou, Xuefeng; Zhang, Weixiong
2008-07-01
MicroRNA (miRNAs) play essential roles in post-transcriptional gene regulation in animals and plants. Several existing computational approaches have been developed to complement experimental methods in discovery of miRNAs that express restrictively in specific environmental conditions or cell types. These computational methods require a sufficient number of characterized miRNAs as training samples, and rely on genome annotation to reduce the number of predicted putative miRNAs. However, most sequenced genomes have not been well annotated and many of them have a very few experimentally characterized miRNAs. As a result, the existing methods are not effective or even feasible for identifying miRNAs in these genomes. Aiming at identifying miRNAs from genomes with a few known miRNA and/or little annotation, we propose and develop a novel miRNA prediction method, miRank, based on our new random walks- based ranking algorithm. We first tested our method on Homo sapiens genome; using a very few known human miRNAs as samples, our method achieved a prediction accuracy greater than 95%. We then applied our method to predict 200 miRNAs in Anopheles gambiae, which is the most important vector of malaria in Africa. Our further study showed that 78 out of the 200 putative miRNA precursors encode mature miRNAs that are conserved in at least one other animal species. These conserved putative miRNAs are good candidates for further experimental study to understand malaria infection. MiRank is programmed in Matlab on Windows platform. The source code is available upon request.
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.
Aittasalo, Minna; Rinne, Marjo; Pasanen, Matti; Kukkonen-Harjula, Katriina; Vasankari, Tommi
2012-06-06
The purpose of the study was to evaluate a 6-month intervention to promote office-employees' walking with pedometers and e-mail messages. Participants were recruited by 10 occupational health care units (OHC) from 20 worksites with 2,230 employees. Voluntary and insufficiently physically active employees (N = 241) were randomized to a pedometer (STEP, N = 123) and a comparison group (COMP, N = 118). STEP included one group meeting, log-monitored pedometer-use and six e-mail messages from OHC. COMP participated in data collection. Reach, effectiveness, adoption, implementation, maintenance (RE-AIM) and costs were assessed with questionnaires (0, 2, 6, 12 months), process evaluation and interviews (12 months). The intervention reached 29% (N = 646) of employees in terms of participation willingness. Logistic regression showed that the proportion of walkers tended to increase more in STEP than in COMP at 2 months in "walking for transportation" (Odds ratio 2.12, 95%CI 0.94 to 4.81) and at 6 months in "walking for leisure" (1.86, 95%CI 0.94 to 3.69). Linear model revealed a modest increase in the mean duration of "walking stairs" at 2 and 6 months (Geometric mean ratio 1.26, 95%CI 0.98 to 1.61; 1.27, 0.98 to 1.64). Adoption and implementation succeeded as intended. At 12 months, some traces of the intervention were sustained in 15 worksites, and a slightly higher number of walkers in STEP in comparison with COMP was observed in "walking stairs" (OR 2.24, 95%CI 0.94 to 5.31) and in "walking for leisure" (2.07, 95%CI 0.99 to 4.34). The direct costs of the intervention were 43 Euros per participant. The findings indicate only modest impact on some indicators of walking. Future studies should invest in reaching the employees, minimizing attrition rate and using objective walking assessment. TRIAL REGISTERATION: ISRCTN79432107.
Directory of Open Access Journals (Sweden)
Aittasalo Minna
2012-06-01
Full Text Available Abstract Background The purpose of the study was to evaluate a 6-month intervention to promote office-employees’ walking with pedometers and e-mail messages. Methods Participants were recruited by 10 occupational health care units (OHC from 20 worksites with 2,230 employees. Voluntary and insufficiently physically active employees (N = 241 were randomized to a pedometer (STEP, N = 123 and a comparison group (COMP, N = 118. STEP included one group meeting, log-monitored pedometer-use and six e-mail messages from OHC. COMP participated in data collection. Reach, effectiveness, adoption, implementation, maintenance (RE-AIM and costs were assessed with questionnaires (0, 2, 6, 12 months, process evaluation and interviews (12 months. Results The intervention reached 29% (N = 646 of employees in terms of participation willingness. Logistic regression showed that the proportion of walkers tended to increase more in STEP than in COMP at 2 months in “walking for transportation” (Odds ratio 2.12, 95%CI 0.94 to 4.81 and at 6 months in “walking for leisure” (1.86, 95%CI 0.94 to 3.69. Linear model revealed a modest increase in the mean duration of “walking stairs” at 2 and 6 months (Geometric mean ratio 1.26, 95%CI 0.98 to 1.61; 1.27, 0.98 to 1.64. Adoption and implementation succeeded as intended. At 12 months, some traces of the intervention were sustained in 15 worksites, and a slightly higher number of walkers in STEP in comparison with COMP was observed in “walking stairs” (OR 2.24, 95%CI 0.94 to 5.31 and in “walking for leisure” (2.07, 95%CI 0.99 to 4.34. The direct costs of the intervention were 43 Euros per participant. Conclusions The findings indicate only modest impact on some indicators of walking. Future studies should invest in reaching the employees, minimizing attrition rate and using objective walking assessment. Trial registeration ISRCTN79432107
Nechaev, S
2003-01-01
We investigate the statistical properties of random walks on the simplest nontrivial braid group B sub 3 , and on related hyperbolic groups. We provide a method using Cayley graphs of groups allowing us to compute explicitly the probability distribution of the basic statistical characteristics of random trajectories - the drift and the return probability. The action of the groups under consideration in the hyperbolic plane is investigated, and the distribution of a geometric invariant - the hyperbolic distance - is analysed. It is shown that a random walk on B sub 3 can be viewed as a 'magnetic random walk' on the group PSL(2, Z).
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Nechaev, Sergei [Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris Sud, 91405 Orsay Cedex (France); Voituriez, Raphael [Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris Sud, 91405 Orsay Cedex (France)
2003-01-10
We investigate the statistical properties of random walks on the simplest nontrivial braid group B{sub 3}, and on related hyperbolic groups. We provide a method using Cayley graphs of groups allowing us to compute explicitly the probability distribution of the basic statistical characteristics of random trajectories - the drift and the return probability. The action of the groups under consideration in the hyperbolic plane is investigated, and the distribution of a geometric invariant - the hyperbolic distance - is analysed. It is shown that a random walk on B{sub 3} can be viewed as a 'magnetic random walk' on the group PSL(2, Z)
Matzer, Franziska; Nagele, Eva; Lerch, Nikolaus; Vajda, Christian; Fazekas, Christian
2017-08-25
Both physical activity and relaxation have stress-relieving potential. This study investigates their combined impact on the relaxation response while considering participants' initial stress level. In a randomized cross-over trial, 81 healthy adults completed 4 types of short-term interventions for stress reduction, each lasting for 1 hr: (1) physical activity (walking) combined with resting, (2) walking combined with balneotherapy, (3) combined resting and balneotherapy, and (4) resting only. Saliva cortisol, blood pressure, state of mood, and relaxation were measured preintervention and postintervention. Stress levels were determined by validated questionnaires. All interventions were associated with relaxation responses in the variables saliva cortisol, blood pressure, state of mood, and subjective relaxation. No significant differences were found regarding the reduction of salivary cortisol (F = 1.30; p = .281). The systolic blood pressure was reduced best when walking was combined with balneotherapy or resting (F = 7.34; p < .001). Participants with high stress levels (n = 25) felt more alert after interventions including balneotherapy, whereas they reported an increase of tiredness when walking was combined with resting (F = 3.20; p = .044). Results suggest that combining physical activity and relaxation (resting or balneotherapy) is an advantageous short-term strategy for stress reduction as systolic blood pressure is reduced best while similar levels of relaxation can be obtained. Copyright © 2017 John Wiley & Sons, Ltd.
Continuous-time random-walk model for anomalous diffusion in expanding media
Le Vot, F.; Abad, E.; Yuste, S. B.
2017-09-01
Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium
The coastline and lake shores on a fractal island
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Blaudeck, Peter [Institut fuer Physik, Technische Universitaet, 09107 Chemnitz (Germany); Seeger, Steffen [Institut fuer Physik, Technische Universitaet, 09107 Chemnitz (Germany); Schulzky, Christian [Institut fuer Physik, Technische Universitaet, 09107 Chemnitz (Germany); Hoffmann, Karl Heinz [Institut fuer Physik, Technische Universitaet, 09107 Chemnitz (Germany); Dutta, Tapati [Physics Department, St Xavier' s College, Kolkata 700 016 (India); Tarafdar, Sujata [Condensed Matter Physics Research Centre, Jadavpur University, Kolkata 700 032 (India)
2006-02-17
We compute the fractal dimensions of the 'hulls' or external boundary and the boundaries of the internal cavities in several deterministic as well as random fractal structures. Our conclusion is that the two fractal dimensions are in fact identical. The deterministic fractals we study are Sierpinski carpets (SC) in a two-dimensional space and the random fractals are percolation clusters at criticality. As an intermediate case, we present results on some randomized SC. In the random structures, statistics of the area and perimeters of all internal cavities or holes are taken and the fractal dimension of the hull borderline is computed. Two different definitions of the borderline are used, considering nearest neighbours as well as nearest and second nearest neighbours as connected. The conclusion is valid for both cases.
Thøgersen-Ntoumani, C; Loughren, E A; Kinnafick, F-E; Taylor, I M; Duda, J L; Fox, K R
2015-12-01
Physical activity may regulate affective experiences at work, but controlled studies are needed and there has been a reliance on retrospective accounts of experience. The purpose of the present study was to examine the effect of lunchtime walks on momentary work affect at the individual and group levels. Physically inactive employees (N = 56; M age = 47.68; 92.86% female) from a large university in the UK were randomized to immediate treatment or delayed treatment (DT). The DT participants completed both a control and intervention period. During the intervention period, participants partook in three weekly 30-min lunchtime group-led walks for 10 weeks. They completed twice daily affective reports at work (morning and afternoon) using mobile phones on two randomly chosen days per week. Multilevel modeling was used to analyze the data. Lunchtime walks improved enthusiasm, relaxation, and nervousness at work, although the pattern of results differed depending on whether between-group or within-person analyses were conducted. The intervention was effective in changing some affective states and may have broader implications for public health and workplace performance. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Jacq, Thomas S.; Lardizabal, Carlos F.
2017-09-01
In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability expressions for classes of walks via a matrix version of the Karlin-McGregor formula. We focus on absorbing boundary conditions and, for simpler classes of examples, we consider path counting and the corresponding combinatorial tools. A non-commutative version of the gambler's ruin is studied by obtaining the probability of reaching a certain fortune and the mean time to reach a fortune or ruin in terms of generating functions. In the case of the Hadamard coin, a counting technique for boundary restricted paths in a lattice is also presented. We discuss an open quantum version of Foster's Theorem for the expected return time together with applications.
Jacq, Thomas S.; Lardizabal, Carlos F.
2017-11-01
In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability expressions for classes of walks via a matrix version of the Karlin-McGregor formula. We focus on absorbing boundary conditions and, for simpler classes of examples, we consider path counting and the corresponding combinatorial tools. A non-commutative version of the gambler's ruin is studied by obtaining the probability of reaching a certain fortune and the mean time to reach a fortune or ruin in terms of generating functions. In the case of the Hadamard coin, a counting technique for boundary restricted paths in a lattice is also presented. We discuss an open quantum version of Foster's Theorem for the expected return time together with applications.
The worst visibility walk in a random Delaunay triangulation is $O(\\sqrt{n}$
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Olivier Devillers
2016-07-01
Full Text Available We show that the memoryless routing algorithms Greedy Walk, Compass Walk, and all variants of visibility walk based on orientation predicates are asymptotically optimal in the average case on the Delaunay triangulation. More specifically, we consider the Delaunay triangulation of an unbounded Poisson point process of unit rate and demonstrate that, for any pair of vertices $(s,t$ inside $[0,n]^2$, the ratio between the longest and shortest visibility walks between $s$ and $t$ is bounded by a constant with probability converging to one (as long as the vertices are sufficiently far apart. As a corollary, it follows that the worst-case path has $O(\\sqrt{n}\\,$ steps in the limiting case, under the same conditions. Our results have applications in routing in mobile networks and also settle a long-standing conjecture in point location using walking algorithms. Our proofs use techniques from percolation theory and stochastic geometry.
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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.
Pastor, María-Ángeles; López-Roig, Sofía; Lledó, Ana; Peñacoba, Cecilia; Velasco, Lilian; Schweiger-Gallo, Inge; Cigarán, Margarita; Ecija, Carmen; Limón, Ramón; Sanz, Yolanda
2014-04-11
Fibromyalgia patients are often advised to engage in regular low- to moderate-intensity physical exercise. The need of fibromyalgia patients to walk has been stressed in previous research. Behavioral self-regulation theories suggest that a combination of motivational aspects (to develop or strengthen a behavioral intention: Theory of Planned Behavior) and volitional aspects (engagement of intention in behavior: implementation intentions) is more effective than a single intervention. In this paper, we describe a protocol for identifying the motivational processes (using the Theory of Planned Behavior) involved in the practice of walking (phase I) and for studying the efficacy of an intervention that combines motivational and volitional contents to enhance the acquisition and continuation of this exercise behavior (phase II). The paper also shows the characteristics of eligible individuals (women who do not walk) and ineligible populations (women who walk or do not walk because of comorbidity without medical recommendation to walk). Both groups consist of members of any of four patients' associations in Spain who are between 18 and 70 years of age and meet the London Fibromyalgia Epidemiology Study Screening Questionnaire criteria for fibromyalgia. Furthermore, using this study protocol, we will explore the characteristics of participants (eligible women who agreed to participate in the study) and nonparticipants (eligible women who refused to participate). Two studies will be conducted: Phase I will be a cross-sectional study, and phase II will be a triple-blind, randomized longitudinal study with two treatment groups and one active control group. The questionnaires were sent to a total of 2,227 members of four patients' associations in Spain. A total of 920 participants with fibromyalgia returned the questionnaires, and 582 were ultimately selected to participate. The first data gathered have allowed us to identify the characteristics of the study population and
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Cameron-Tucker HL
2016-08-01
Full Text Available Helen Laura Cameron-Tucker,1 Richard Wood-Baker,1 Lyn Joseph,1 Julia A Walters,1 Natalie Schüz,2 E Haydn Walters1 1Centre of Research Excellence for Chronic Respiratory Disease and Lung Aging, School of Medicine, 2School of Health Sciences, Faculty of Health, University of Tasmania, Hobart, Tasmania, Australia Purpose: With the limited reach of pulmonary rehabilitation (PR and low levels of daily physical activity in chronic obstructive pulmonary disease (COPD, a need exists to increase daily exercise. This study evaluated telephone health-mentoring targeting home-based walking (tele-rehab compared to usual waiting time (usual care followed by group PR. Patients and methods: People with COPD were randomized to tele-rehab (intervention or usual care (controls. Tele-rehab delivered by trained nurse health-mentors supported participants’ home-based walking over 8–12 weeks. PR, delivered to both groups simultaneously, included 8 weeks of once-weekly education and self-management skills, with separate supervised exercise. Data were collected at three time-points: baseline (TP1, before (TP2, and after (TP3 PR. The primary outcome was change in physical capacity measured by 6-minute walk distance (6MWD with two tests performed at each time-point. Secondary outcomes included changes in self-reported home-based walking, health-related quality of life, and health behaviors. Results: Of 65 recruits, 25 withdrew before completing PR. Forty attended a median of 6 (4 education sessions. Seventeen attended supervised exercise (5±2 sessions. Between TP1 and TP2, there was a statistically significant increase in the median 6MWD of 12 (39.1 m in controls, but no change in the tele-rehab group. There were no significant changes in 6MWD between other time-points or groups, or significant change in any secondary outcomes. Participants attending supervised exercise showed a nonsignificant improvement in 6MWD, 12.3 (71 m, while others showed no change, 0 (33 m
On random walk de Lévy aplicado aos mapas de variâncias
Klafke, J. C.
2003-08-01
Uma pergunta que surge ao nos confrontarmos com os mapas de variâncias, ou s-Maps [Klafke, J. C. "Estudo da Difusão Caótica em Ressonâncias Asteroidais", Tese de Doutorado, IAG/USP, 2002] diz respeito ao conteúdo físico de tais representações do espaço de fase. Ou seja, o que representa as variâncias das ações obtidas para uma determinada condição inicial e como relacioná-las com o tempo de difusão das órbitas, supondo-se que estas de fato estejam envolvidas em um processo difusivo? Para discutirmos essa questão, lançamos mão da modelagem dos processos estocásticos subjacentes às variâncias determinadas e implementamos uma série de simulações do tipo Monte Carlo a partir das informações registradas nos s-Maps calculados para algumas ressonâncias asteroidais bem estudadas (p.ex. 3: 1, 2: 1 e 3: 2). Para tanto, temos usado uma função de densidade de probabilidade gaussiana ao definir os n passos que permitirão estabelecer uma relação direta entre o Mapa de Difusão e o Mapa de Variâncias. Contudo, os resultados obtidos até agora tem subestimado o tempo de difusão esperado para os fenômenos conhecidos. Tal se deve ao fato de que, no processo difusivo real, é possível existirem passos de comprimento consideravelmente maiores que a média estabelecida pelas distribuições gaussiana ou normal, sobretudo quando se cruza uma região caótica. Neste trabalho, apresentamos os resultados comparativos de simulações de Monte Carlo com base no random walk de Lévy [Klafter, J. et al. 2002. "Beyond Brownian motion", Phys. Today, Feb, 33-39.], o qual possibilita passos esporádicos de comprimento acima do valor médio (saltos) permitindo estabelecer uma escala de tempo mais próxima da esperada para a difusão.
Fractality Evidence and Long-Range Dependence on Capital Markets: a Hurst Exponent Evaluation
Oprean, Camelia; Tănăsescu, Cristina
2014-07-01
Since the existence of market memory could implicate the rejection of the efficient market hypothesis, the aim of this paper is to find any evidence that selected emergent capital markets (eight European and BRIC markets, namely Hungary, Romania, Estonia, Czech Republic, Brazil, Russia, India and China) evince long-range dependence or the random walk hypothesis. In this paper, the Hurst exponent as calculated by R/S fractal analysis and Detrended Fluctuation Analysis is our measure of long-range dependence in the series. The results reinforce our previous findings and suggest that if stock returns present long-range dependence, the random walk hypothesis is not valid anymore and neither is the market efficiency hypothesis.
3D exemplar-based random walks for tooth segmentation from cone-beam computed tomography images.
Pei, Yuru; Ai, Xingsheng; Zha, Hongbin; Xu, Tianmin; Ma, Gengyu
2016-09-01
Tooth segmentation is an essential step in acquiring patient-specific dental geometries from cone-beam computed tomography (CBCT) images. Tooth segmentation from CBCT images is still a challenging task considering the comparatively low image quality caused by the limited radiation dose, as well as structural ambiguities from intercuspation and nearby alveolar bones. The goal of this paper is to present and discuss the latest accomplishments in semisupervised tooth segmentation with adaptive 3D shape constraints. The authors propose a 3D exemplar-based random walk method of tooth segmentation from CBCT images. The proposed method integrates semisupervised label propagation and regularization by 3D exemplar registration. To begin with, the pure random walk method is to get an initial segmentation of the teeth, which tends to be erroneous because of the structural ambiguity of CBCT images. And then, as an iterative refinement, the authors conduct a regularization by using 3D exemplar registration, as well as label propagation by random walks with soft constraints, to improve the tooth segmentation. In the first stage of the iteration, 3D exemplars with well-defined topologies are adapted to fit the tooth contours, which are obtained from the random walks based segmentation. The soft constraints on voxel labeling are defined by shape-based foreground dentine probability acquired by the exemplar registration, as well as the appearance-based probability from a support vector machine (SVM) classifier. In the second stage, the labels of the volume-of-interest (VOI) are updated by the random walks with soft constraints. The two stages are optimized iteratively. Instead of the one-shot label propagation in the VOI, an iterative refinement process can achieve a reliable tooth segmentation by virtue of exemplar-based random walks with adaptive soft constraints. The proposed method was applied for tooth segmentation of twenty clinically captured CBCT images. Three metrics
Merom, D; Gebel, K; Fahey, P; Astell-Burt, T; Voukelatos, A; Rissel, C; Sherrington, C
2015-01-01
In older adults the relationships between health, fall-related risk factors, perceived neighborhood walkability, walking behavior and intervention impacts are poorly understood. To determine whether: i) health and fall-related risk factors were associated with perceptions of neighborhood walkability; ii) perceived environmental attributes, and fall-related risk factors predicted change in walking behavior at 12 months; and iii) perceived environmental attributes and fall-related risk factors moderated the effect of a self-paced walking program on walking behavior. Randomized trial on walking and falls conducted between 2009 and 2012 involving 315 community-dwelling inactive adults ≥ 65 years living in Sydney, Australia. Measures were: mobility status, fall history, injurious fall and fear of falling (i.e., fall-related risk factors), health status, walking self-efficacy and 11 items from the neighborhood walkability scale and planned walking ≥ 150 min/week at 12 months. Participants with poorer mobility, fear of falling, and poor health perceived their surroundings as less walkable. Walking at 12 months was significantly greater in "less greenery" (AOR = 3.3, 95% CI: 1.11-9.98) and "high traffic" (AOR = 1.98, 95% CI: 1.00-3.91) neighborhoods. The intervention had greater effects in neighborhoods perceived to have poorer pedestrian infrastructure (p for interaction = 0.036). Low perceived walkability was shaped by health status and did not appear to be a barrier to walking behavior. There appears to be a greater impact of, and thus, need for, interventions to encourage walking in environments perceived not to have supportive walking infrastructure. Future studies on built environments and walking should gather information on fall-related risk factors to better understand how these characteristics interact.
Avelino, Patrick Roberto; Nascimento, Lucas R; Menezes, Kênia K P; Scianni, Aline A; Ada, Louise; Teixeira-Salmela, Luci F
2017-12-02
Canes are usually prescribed for individuals with stroke with the purpose of improving walking and increasing safety. However, there is no consensus regarding the clinical effects of these aids on walking and participation. This study will examine the efficacy of the provision of a cane to improve walking and increase participation after stroke. This is a two-arm, prospectively registered, randomized trial with concealed allocation, blinded measurers, and intention-to-treat analysis. Fifty individuals with chronic stroke, categorized as slow or intermediate walkers (walking speeds ≤0.8m/s), will participate. The experimental group will receive a single-point cane and instructions to use the cane anytime they need to walk. The control group will receive a placebo intervention, consisting of self-stretching exercises of the lower limb muscles and instructions to not use assistive devices. The primary outcome will be comfortable walking speed. Secondary outcomes will include walking step length, walking cadence, walking capacity, walking confidence, and participation. Outcomes will be collected by a researcher blinded to group allocation at baseline (Week 0), after intervention (Week 4), and one month beyond intervention (Week 8). The provision of a single-point cane may help improving walking of slow and intermediate walkers after stroke. If walking is enhanced, the benefits may be carried over to participation, and individuals may experience greater free-living physical activity at home and in the community. Copyright © 2017 Associação Brasileira de Pesquisa e Pós-Graduação em Fisioterapia. Publicado por Elsevier Editora Ltda. All rights reserved.
Effects of nordic walking and exercise in type 2 diabetes mellitus: a randomized controlled trial
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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...
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Mawanga Freddie Festo
2017-04-01
Full Text Available Since the 1990s exports of fresh agricultural products by air from Uganda have been increasing and making a significant contribution to her International trade. Products include mostly fish, flowers, papain, and vanilla constituting over 95% of all air exports. Farming of the items is mainly by small scale farmers who depend on the natural climate of the country. Consequently, monthly yields are also climate dependent making individual export volumes unpredictable. In spite of these uncertainties, this study was intended to investigate possible existence of a model in the trends. Monthly data were collected from Uganda Civil Aviation Authority from 2009 to 2012. Analysis was by using ARIMA Approach with the help of Eviews 8. Visually the data exhibited irregular patterns and without a trend or seasonality. First order differencing stationarised the data and the residuals had a random non-significant noise suggesting a Random Walk Model expressed as ARIMA (0, 1, 0 and a negative drift. The model shows a link between current and one lag export volumes and the negative drift is a convergence of successive differences in export volumes. These findings have policy implications in expansion and forecasting of the exports potential of applicability of Random Walk Theory in practice.
Thamrin, Cindy; Stern, Georgette; Frey, Urs
2010-06-01
There is increasing interest in the study of fractals in medicine. In this review, we provide an overview of fractals, of techniques available to describe fractals in physiological data, and we propose some reasons why a physician might benefit from an understanding of fractals and fractal analysis, with an emphasis on paediatric respiratory medicine where possible. Among these reasons are the ubiquity of fractal organisation in nature and in the body, and how changes in this organisation over the lifespan provide insight into development and senescence. Fractal properties have also been shown to be altered in disease and even to predict the risk of worsening of disease. Finally, implications of a fractal organisation include robustness to errors during development, ability to adapt to surroundings, and the restoration of such organisation as targets for intervention and treatment. Copyright 2010 Elsevier Ltd. All rights reserved.
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325
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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
Griffith, Garett; Klaren, Rachel E; Motl, Robert W; Baynard, Tracy; Fernhall, Bo
2015-03-01
This randomized controlled trial (RCT) will investigate the effects of a home-based aerobic exercise training regimen (i.e., cycle ergometry) on subclinical atherosclerosis and walking mobility in persons with multiple sclerosis (MS) and minimal disability. This RCT will recruit 54 men and women who have an Expanded Disability Status Scale characteristic of the 1st stage of MS (i.e., 0-4.0) to participate in a 3 month exercise or stretching intervention, with assessments of subclinical atherosclerosis and walking mobility conducted at baseline, week 6 (midpoint), and week 12 (conclusion) of the program. The exercise intervention will consist of 3 days/week of cycling, with a gradual increase of duration followed by an increase in intensity across the 3 month period. The attention-control condition will incorporate stretching activities and will require the same contact time commitment as the exercise condition. Both study groups will participate in weekly video chat sessions with study personnel in order to monitor and track program adherence. Primary outcomes will consist of assessments of vascular structure and function, as well as several walking tasks. Additional outcomes will include questionnaires, cardiorespiratory fitness assessment, and a 1-week free-living physical activity assessment. This investigation will increase understanding of the role of aerobic exercise as part of a treatment plan for managing subclinical atherosclerosis and improving walking mobility persons in the 1st stage of MS. Overall, this study design has the potential to lead to effective aerobic exercise intervention strategies for this population and improve program adherence. Copyright © 2015 Elsevier Inc. All rights reserved.
Fraboni, Michael; Moller, Trisha
2008-01-01
Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…
Giangregorio, Lora; Craven, Catharine; Richards, Kieva; Kapadia, Naaz; Hitzig, Sander L; Masani, Kei; Popovic, Milos R
2012-09-01
To evaluate the effects of functional electrical stimulation (FES)-assisted walking on body composition, compared to a non-FES exercise program in individuals with a spinal cord injury (SCI). Parallel-group randomized controlled trial. Individuals with chronic (≥ 18 months) incomplete SCI (level C2 to T12, AIS C or D) were recruited and randomized to FES-assisted walking (intervention), or aerobic and resistance training (control) sessions thrice-weekly for 16 weeks. Whole body and leg lean mass and whole body fat mass, measured with dual-energy X-ray absorptiometry, and lower-limb muscle cross-sectional area (CSA) and fat CSA, measured with peripheral computed tomography were assessed at baseline, 4 months, and 12 months. Intention-to-treat analyses using repeated measures general linear models were used to assess between-group differences. Thirty-four individuals were randomized (17 per group); 27 remained at 12 months. There were no significant main effects of FES-assisted walking on body composition variables in intention-to-treat analyses with group means. There was a significant group-by-time interaction for muscle area from baseline to 12 months (P = 0.04). Intention-to-treat analysis of muscle area change scores between baseline and 12 months revealed a significant difference between groups (mean (SD) muscle area change score 212 (517) mm(s) for FES, -136 (268) mm(s) for control, P = 0.026). There were 13 side effects or adverse events deemed related to study participation (7 intervention, 5 control); most were resolved with modifications to the protocol. One fainting episode resulted in a hospital visit and study withdrawal. Thrice-weekly FES-assisted walking exercise over 4 months did not result in a change in body composition in individuals with chronic, motor incomplete C2 to T12 SCI (AIS classification C and D). However, longer-term follow-up revealed that it might maintain muscle area.
Exact two-point resistance, and the simple random walk on the complete graph minus N edges
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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.
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FELICIA RAMONA BIRAU
2012-05-01
Full Text Available In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and of course, the manner in which they interpret that information may be different. Also, Fractal Market Hypothesis refers to the way that liquidity and investment horizons influence the behaviour of financial investors.
Du, Huiyun; Newton, Phillip J; Budhathoki, Chakra; Everett, Bronwyn; Salamonson, Yenna; Macdonald, Peter S; Davidson, Patricia M
2017-08-01
Adherence to self-care recommendations is associated with improved patient outcomes and improved quality of life for people living with heart failure. The Home-Heart-Walk (HHW) is an intervention to promote physical activity adapting the elements of a six minute walk test, a reliable and valid measure. This adaptation was designed to support self-monitoring of physical functioning and promote the self-care of people with heart failure. The primary outcome of the Home-Heart-Walk was perceived physical functioning and the secondary outcomes were six-minute walk test distance, health related quality of life, self-care behaviour, self-efficacy and physical activity level. A multicentre randomized controlled trial. Participants ( N=132) were recruited from three academic hospitals in Sydney, Australia. Participants were randomized to either the Home-Heart-Walk group or the control group. Perceived physical functioning, health related quality of life, self-care behaviour, exercise self-efficacy and physical activity level were measured at baseline and at three- and six-month follow-up. After adjusting for baseline scores, there were no statistically significant between-group differences in perceived physical functioning, six-minute walk test distance, health related quality of life and exercise self-efficacy at follow-up. The intervention group had improvement in self-care behaviour ( F(1,129) = 4.75, p = 0.031) and physical activity level ( U = 1713, z = -2.12, p = 0.034) at the six-month follow-up compared with the control group. The Home-Heart-Walk did not improve the perceived physical functioning of the intervention group. Although the feasibility and acceptability of this strategy to support self-monitoring and improve self-care behaviour was demonstrated, self-reported adherence was unreliable; newer technologies may offer better assessment of adherence.
Percolation on infinitely ramified fractal networks
Balankin, Alexander S.; Martínez-Cruz, M. A.; Susarrey-Huerta, O.; Damian Adame, L.
2018-01-01
We study how fractal features of an infinitely ramified network affect its percolation properties. The fractal attributes are characterized by the Hausdorff (DH), topological Hausdorff (DtH), and spectral (ds) dimensions. Monte Carlo simulations of site percolation were performed on pre-fractal standard Sierpiński carpets with different fractal attributes. Our findings suggest that within the universality class of random percolation the values of critical percolation exponents are determined by the set of dimension numbers (DH, DtH, ds), rather than solely by the spatial dimension (d). We also argue that the relevant dimension number for the percolation threshold is the topological Hausdorff dimension DtH, whereas the hyperscaling relations between critical exponents are governed by the Hausdorff dimension DH. The effect of the network connectivity on the site percolation threshold is revealed.
Imam, Bita; Miller, William C; Finlayson, Heather C; Eng, Janice J; Payne, Michael Wc; Jarus, Tal; Goldsmith, Charles H; Mitchell, Ian M
2014-12-22
The number of older adults living with lower limb amputation (LLA) who require rehabilitation for improving their walking capacity and mobility is growing. Existing rehabilitation practices frequently fail to meet this demand. Nintendo Wii Fit may be a valuable tool to enable rehabilitation interventions. Based on pilot studies, we have developed "Wii.n.Walk", an in-home telehealth Wii Fit intervention targeted to improve walking capacity in older adults with LLA. The objective of this study is to determine whether the Wii.n.Walk intervention enhances walking capacity compared to an attention control group. This project is a multi-site (Vancouver BC, London ON), parallel, evaluator-blind randomized controlled trial. Participants include community-dwelling older adults over the age of 50 years with unilateral transtibial or transfemoral amputation. Participants will be stratified by site and block randomized in triplets to either the Wii.n.Walk intervention or an attention control group employing the Wii Big Brain cognitive software. This trial will include both supervised and unsupervised phases. During the supervised phase, both groups will receive 40-minute sessions of supervised group training three times per week for a duration of 4 weeks. Participants will complete the first week of the intervention in groups of three at their local rehabilitation center with a trainer. The remaining 3 weeks will take place at participants' homes using remote supervision by the trainer using Apple iPad technology. At the end of 4 weeks, the supervised period will end and the unsupervised period will begin. Participants will retain the Wii console and be encouraged to continue using the program for an additional 4 weeks' duration. The primary outcome measure will be the "Two-Minute Walk Test" to measure walking capacity. Outcome measures will be evaluated for all participants at baseline, after the end of both the supervised and unsupervised phases, and after 1-year follow up
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.
Fractal dimension for fractal structures: A Hausdorff approach
Fernández-Martínez, M.; Sánchez-Granero, M. A.
2012-01-01
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a suitable discretization of the Hausdorff theory of fractal dimension. We also find some connections between our definition and the classical ones and also with fractal dimensions I & II (see http://arxiv.org/submit/0080421/pdf). Therefore, we generalize them and ...
Shape characteristics of equilibrium and non-equilibrium fractal clusters.
Mansfield, Marc L; Douglas, Jack F
2013-07-28
It is often difficult in practice to discriminate between equilibrium and non-equilibrium nanoparticle or colloidal-particle clusters that form through aggregation in gas or solution phases. Scattering studies often permit the determination of an apparent fractal dimension, but both equilibrium and non-equilibrium clusters in three dimensions frequently have fractal dimensions near 2, so that it is often not possible to discriminate on the basis of this geometrical property. A survey of the anisotropy of a wide variety of polymeric structures (linear and ring random and self-avoiding random walks, percolation clusters, lattice animals, diffusion-limited aggregates, and Eden clusters) based on the principal components of both the radius of gyration and electric polarizability tensor indicates, perhaps counter-intuitively, that self-similar equilibrium clusters tend to be intrinsically anisotropic at all sizes, while non-equilibrium processes such as diffusion-limited aggregation or Eden growth tend to be isotropic in the large-mass limit, providing a potential means of discriminating these clusters experimentally if anisotropy could be determined along with the fractal dimension. Equilibrium polymer structures, such as flexible polymer chains, are normally self-similar due to the existence of only a single relevant length scale, and are thus anisotropic at all length scales, while non-equilibrium polymer structures that grow irreversibly in time eventually become isotropic if there is no difference in the average growth rates in different directions. There is apparently no proof of these general trends and little theoretical insight into what controls the universal anisotropy in equilibrium polymer structures of various kinds. This is an obvious topic of theoretical investigation, as well as a matter of practical interest. To address this general problem, we consider two experimentally accessible ratios, one between the hydrodynamic and gyration radii, the other
DEFF Research Database (Denmark)
In this presentation we consider a new method first introduced by Kristensen et al. [1] to improve the model for bacterial growth. Traditionally the substrate dependent growth rate μ(S) is modeled using the Monod expression, however it fails to describe the growth of bacteria in rich media. For P...... contains two state variables, the bacterial and substrate densities. To improve the growth model we initially allow the growth rate μ(S) to vary as a random walk, i.e. we reformulate the SDE model to include μ(S) as an extra state variable which change is described by the Wiener process. We use data from....... aeruginosa we observe a growth pattern far from Monod growth. Therefore a reformulation of the growth expression is necessary. Without any pre-knowledge about the functional dependence between the growth rate and the substrate content and with only limited experimental resources necessary, the proposed...
Random walk approach to spin dynamics in a two-dimensional electron gas with spin-orbit coupling
Energy Technology Data Exchange (ETDEWEB)
Yang, Luyi; Orenstein, J.; Lee, Dung-Hai
2010-09-27
We introduce and solve a semiclassical random walk (RW) model that describes the dynamics of spin polarization waves in zinc-blende semiconductor quantum wells. We derive the dispersion relations for these waves, including the Rashba, linear and cubic Dresselhaus spin-orbit interactions, as well as the effects of an electric field applied parallel to the spin polarization wave vector. In agreement with calculations based on quantum kinetic theory [P. Kleinert and V. V. Bryksin, Phys. Rev. B 76, 205326 (2007)], the RW approach predicts that spin waves acquire a phase velocity in the presence of the field that crosses zero at a nonzero wave vector, q{sub 0}. In addition, we show that the spin-wave decay rate is independent of field at q{sub 0} but increases as (q-q{sub 0}){sup 2} for q {ne} q{sub 0}. These predictions can be tested experimentally by suitable transient spin grating experiments.
Baryshev, Yuri
2002-01-01
This is the first book to present the fascinating new results on the largest fractal structures in the universe. It guides the reader, in a simple way, to the frontiers of astronomy, explaining how fractals appear in cosmic physics, from our solar system to the megafractals in deep space. It also offers a personal view of the history of the idea of self-similarity and of cosmological principles, from Plato's ideal architecture of the heavens to Mandelbrot's fractals in the modern physical cosmos. In addition, this invaluable book presents the great fractal debate in astronomy (after Luciano Pi
Colloidal Dancers: Designing networks of DNA-functionalized colloids for non-random walks
Gehrels, Emily W.; Rogers, W. Benjamin; Zeravcic, Zorana; Manoharan, Vinothan N.
2014-03-01
We present experimental developments of a system of DNA-functionalized colloidal particles with the goal of creating directed motion (`dancing') along patterned substrates in response to temperature cycling. We take advantage of toehold exchange in the design of the DNA sequences that mediate the colloidal interactions to produce broadened, flat, or even re-entrant binding and unbinding transitions between the particles and substrate. Using this new freedom of design, we devise systems where, by thermal ratcheting, we can externally control the direction of motion and sequence of steps of the colloidal dancer. In comparison to DNA-based walkers, which move autonomously and whose motion is controlled by the substrate, our colloidal dancers respond to external driving, and their motion can be controlled in situ. Our use of DNA-functionalized colloidal particles instead of pure DNA systems also enables walking on the mesoscale in contrast to the molecular length scales previously demonstrated, allowing for the future prospect of directed transport over larger distances.
Kim, Ha Yeon; Kim, Eun Joo; You, Joshua Sung H
2017-07-20
An improved understanding of the mechanisms underlying locomotor networks has the potential to benefit the neurorehabilitation of patients with neurological locomotor deficits. However, the specific locomotor networks that mediate adaptive locomotor performance and changes in gait speed remain unknown. The aim of the present study was to examine patterns of cortical activation associated with the walking speeds of 1.5, 2.0, 2.5, and 3.0 km/h on a treadmill. Functional near-infrared spectroscopy (fNIRS) was performed on a 30-year-old right-handed healthy female subject, and cerebral hemodynamic changes were observed in cortical locomotor network areas including the primary sensorimotor cortex (SMC), premotor cortex (PMC), supplementary motor area (SMA), prefrontal cortex (PFC), and sensory association cortex (SAC). The software package NIRS-statistical parametric mapping (NIRS-SPM) was utilized to analyze fNIRS data in the MATLAB environment. SPM t-statistic maps were computed at an uncorrected threshold of pglobalized locomotor network activation of the SMC, PMC, SMA, and PMC; additionally, the site with the highest cortical activation ratio shifted from the SMC to the SMA. Global locomotor network recruitment, in particular PFC activation indicated by OxyHb in our study, may indicate a response to increased cognitive-locomotor demand due to simultaneous postural maintenance and leg movement coordination.
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…
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.
Williams, Stefanie L; Michie, Susan; Dale, Jeremy; Stallard, Nigel; French, David P
2015-05-01
Perceived behavioral control (PBC) is a consistent predictor of intentions to walk more. A previously successful intervention to promote walking by altering PBC has been adapted for delivery in general practice. This study aimed to evaluate the effect of this intervention on Theory of Planned Behavior (TPB) constructs in this context. Cluster randomized controlled trial, with n = 315 general practice patients. Practice nurses and Healthcare Assistants delivered a self-regulation intervention or information provision (control). Questionnaires assessed TPB variables at baseline, post-intervention, 6 weeks and 6 months. Walking was measured by pedometer. The control group reported significantly higher subjective norm at all follow-up time points. There were no significant differences between the two groups in PBC, intention, attitude or walking behavior. TPB variables significantly predicted intentions to walk more, but not objective walking behavior, after accounting for clustering. The lack of effect of the intervention was probably due to a failure to maintain intervention fidelity, and the unsuitability of the behavior change techniques included in the intervention for the population investigated. This previously successful intervention was not successful when delivered in this context, calling into question whether practice nurses are best placed to deliver such interventions. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.
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Cocco, S [Laboratoire de Physique Statistique de l' ENS, CNRS, UMPC, 24 rue Lhomond, 75005 Paris (France); Monasson, R, E-mail: cocco@lps.ens.f, E-mail: monasson@lpt.ens.f [Laboratoire de Physique Theorique de l' ENS, CNRS, UPMC, 24 rue Lhomond, 75005 Paris (France)
2009-12-01
We consider the Sinai model, in which a random walker moves in a random quenched potential V, and ask the following questions: 1. how can the quenched potential V be inferred from the observations of one or more realizations of the random motion? 2. how many observations (walks) are required to make a reliable inference, that is, to be able to distinguish between two similar but distinct potentials, V{sub 1} and V{sub 2}? We show how question 1 can be easily solved within the Bayesian framework. In addition, we show that the answer to question 2 is, in general, intimately connected to the calculation of the survival probability of a fictitious walker in a potential W defined from V{sub 1} and V{sub 2}, with partial absorption at sites where V{sub 1} and V{sub 2} do not coincide. For the one-dimensional Sinai model, this survival probability can be analytically calculated, in excellent agreement with numerical simulations.
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…
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Kim, Diane N. H.; Teitell, Michael A.; Reed, Jason; Zangle, Thomas A.
2015-11-01
Standard algorithms for phase unwrapping often fail for interferometric quantitative phase imaging (QPI) of biological samples due to the variable morphology of these samples and the requirement to image at low light intensities to avoid phototoxicity. We describe a new algorithm combining random walk-based image segmentation with linear discriminant analysis (LDA)-based feature detection, using assumptions about the morphology of biological samples to account for phase ambiguities when standard methods have failed. We present three versions of our method: first, a method for LDA image segmentation based on a manually compiled training dataset; second, a method using a random walker (RW) algorithm informed by the assumed properties of a biological phase image; and third, an algorithm which combines LDA-based edge detection with an efficient RW algorithm. We show that the combination of LDA plus the RW algorithm gives the best overall performance with little speed penalty compared to LDA alone, and that this algorithm can be further optimized using a genetic algorithm to yield superior performance for phase unwrapping of QPI data from biological samples.
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 0PDF \\Psi(τ ) has a power law tail, \\Psi(τ )\\propto {τ-1-γ} , with 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).
Most, S.; Jia, N.; Bijeljic, B.; Nowak, W.
2016-12-01
Pre-asymptotic characteristics are almost ubiquitous when analyzing solute transport processes in porous media. These pre-asymptotic aspects are caused by spatial coherence in the velocity field and by its heterogeneity. For the Lagrangian perspective of particle displacements, the causes of pre-asymptotic, non-Fickian transport are skewed velocity distribution, statistical dependencies between subsequent increments of particle positions (memory) and dependence between the x, y and z-components of particle increments. Valid simulation frameworks should account for these factors. We propose a particle tracking random walk (PTRW) simulation technique that can use empirical pore-space velocity distributions as input, enforces memory between subsequent random walk steps, and considers cross dependence. Thus, it is able to simulate pre-asymptotic non-Fickian transport phenomena. Our PTRW framework contains an advection/dispersion term plus a diffusion term. The advection/dispersion term produces time-series of particle increments from the velocity CDFs. These time series are equipped with memory by enforcing that the CDF values of subsequent velocities change only slightly. The latter is achieved through a random walk on the axis of CDF values between 0 and 1. The virtual diffusion coefficient for that random walk is our only fitting parameter. Cross-dependence can be enforced by constraining the random walk to certain combinations of CDF values between the three velocity components in x, y and z. We will show that this modelling framework is capable of simulating non-Fickian transport by comparison with a pore-scale transport simulation and we analyze the approach to asymptotic behavior.
Zaburdaev, V.; Denisov, S.; Klafter, J.
2015-04-01
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The Lévy-walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, biophysics, and behavioral science demonstrate that this particular type of random walk provides significant insight into complex transport phenomena. This review gives a self-consistent introduction to Lévy walks, surveys their existing applications, including latest advances, and outlines further perspectives.
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
The role of the circadian system in fractal neurophysiological control.
Pittman-Polletta, Benjamin R; Scheer, Frank A J L; Butler, Matthew P; Shea, Steven A; Hu, Kun
2013-11-01
Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system's role in fractal regulation. © 2013 The Authors. Biological Reviews © 2013 Cambridge Philosophical Society.
Automatic skeletal muscle segmentation through random walks and graph-based seed placement
Baudin, Pierre-Yves; Azzabou, Noura; Carlier, Pierre; Paragios, Nikos
2012-01-01
International audience; In this paper we propose a novel skeletal muscle segmentation method driven from discrete optimization. We introduce a graphical model that is able to automatically determine appropriate seed positions with respect to the different muscle classes. This is achieved by taking into account the expected local visual and geometric properties of the seeds through a pair-wise Markov Random Field. The outcome of this optimization process is fed to a powerful graphbased diffusi...
Price Formation Modelling by Continuous-Time Random Walk: An Empirical Study
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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.
Fractal images induce fractal pupil dilations and constrictions.
Moon, P; Muday, J; Raynor, S; Schirillo, J; Boydston, C; Fairbanks, M S; Taylor, R P
2014-09-01
Fractals are self-similar structures or patterns that repeat at increasingly fine magnifications. Research has revealed fractal patterns in many natural and physiological processes. This article investigates pupillary size over time to determine if their oscillations demonstrate a fractal pattern. We predict that pupil size over time will fluctuate in a fractal manner and this may be due to either the fractal neuronal structure or fractal properties of the image viewed. We present evidence that low complexity fractal patterns underlie pupillary oscillations as subjects view spatial fractal patterns. We also present evidence implicating the autonomic nervous system's importance in these patterns. Using the variational method of the box-counting procedure we demonstrate that low complexity fractal patterns are found in changes within pupil size over time in millimeters (mm) and our data suggest that these pupillary oscillation patterns do not depend on the fractal properties of the image viewed. Copyright © 2014 Elsevier B.V. All rights reserved.
Simple unified view of branching process statistics: Random walks in balanced logarithmic potentials
di Santo, Serena; Villegas, Pablo; Burioni, Raffaella; Muñoz, Miguel A.
2017-03-01
We revisit the problem of deriving the mean-field values of avalanche exponents in systems with absorbing states. These are well known to coincide with those of unbiased branching processes. Here we show that for at least four different universality classes (directed percolation, dynamical percolation, the voter model or compact directed percolation class, and the Manna class of stochastic sandpiles) this common result can be obtained by mapping the corresponding Langevin equations describing each of them into a random walker confined to the origin by a logarithmic potential. We report on the emergence of nonuniversal continuously varying exponent values stemming from the presence of small external driving - that might induce avalanche merging - that, to the best of our knowledge, has not been noticed in the past. Many of the other results derived here appear in the literature as independently derived for individual universality classes or for the branching process itself. Still, we believe that a simple and unified perspective as the one presented here can help (1) clarify the overall picture, (2) underline the superuniversality of the behavior as well as the dependence on external driving, and (3) avoid the common existing confusion between unbiased branching processes (equivalent to a random walker in a balanced logarithmic potential) and standard (unconfined) random walkers.
Limiting distribution for the maximal standardized increment of a random walk
Kabluchko, Zakhar; Wang, Yizao
2012-01-01
Let $X_1,X_2,...$ be independent identically distributed random variables with $\\mathbb E X_k=0$, $\\mathrm{Var} X_k=1$. Suppose that $\\varphi(t):=\\log \\mathbb E e^{t X_k}-\\sigma_0$ and some $\\sigma_0>0$. Let $S_k=X_1+...+X_k$ and $S_0=0$. We are interested in the limiting distribution of the multiscale scan statistic $$ M_n=\\max_{0\\leq i 0$. We argue that our results cover most interesting distributions with light tails.
Electromagnetic fields in fractal continua
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Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Mena, Baltasar [Instituto de Ingeniería, Universidad Nacional Autónoma de México, México D.F. (Mexico); Patiño, Julián [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Morales, Daniel [Instituto Mexicano del Petróleo, México D.F., 07730 Mexico (Mexico)
2013-04-01
Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum Φ{sub D}{sup 3}⊂E{sup 3} with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space F{sup α} accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.
Kwon, Ivy; Choi, Sarah; Mittman, Brian; Bharmal, Nazleen; Liu, Honghu; Vickrey, Barbara; Song, Sarah; Araiza, Daniel; McCreath, Heather; Seeman, Teresa; Oh, Sang-Mi; Trejo, Laura; Sarkisian, Catherine
2015-06-15
Stroke disproportionately kills and disables ethnic minority seniors. Up to 30 % of ischemic strokes in the U.S. can be attributed to physical inactivity, yet most Americans, especially older racial/ethnic minorities, fail to participate in regular physical activity. We are conducting a randomized controlled trial (RCT) to test a culturally-tailored community-based walking intervention designed to reduce stroke risk by increasing physical activity among African American, Latino, Chinese, and Korean seniors with hypertension. We hypothesize that the intervention will yield meaningful changes in seniors' walking levels and stroke risk with feasibility to sustain and scale up across the aging services network. In this randomized single-blind wait-list control study, high-risk ethnic minority seniors are enrolled at senior centers, complete baseline data collection, and are randomly assigned to receive the intervention "Worth the Walk" immediately (N = 120, intervention group) or in 90 days upon completion of follow-up data collection (N = 120, control group). Trained case managers employed by the senior centers implement hour-long intervention sessions twice weekly for four consecutive weeks to the intervention group. Research staff blinded to participants' group assignment collect outcome data from both intervention and wait-list control participants 1 and 3-months after baseline data collection. Primary outcome measures are mean steps/day over 7 days, stroke knowledge, and self-efficacy for reducing stroke risk. Secondary and exploratory outcome measures include selected biological markers of health, healthcare seeking, and health-related quality of life. Outcomes will be compared between the two groups using standard analytic methods for randomized trials. We will conduct a formal process evaluation to assess barriers and facilitators to successful integration of Worth the Walk into the aging services network and to calculate estimated costs to sustain
Directory of Open Access Journals (Sweden)
Martin Rosvall
Full Text Available To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between compression and pattern detection; by compressing a description of a random walker as a proxy for real flow on a network, we find regularities in the network that induce this system-wide flow. Finding the shortest multilevel description of the random walker therefore gives us the best hierarchical clustering of the network--the optimal number of levels and modular partition at each level--with respect to the dynamics on the network. With a novel search algorithm, we extract and illustrate the rich multilevel organization of several large social and biological networks. For example, from the global air traffic network we uncover countries and continents, and from the pattern of scientific communication we reveal more than 100 scientific fields organized in four major disciplines: life sciences, physical sciences, ecology and earth sciences, and social sciences. In general, we find shallow hierarchical structures in globally interconnected systems, such as neural networks, and rich multilevel organizations in systems with highly separated regions, such as road networks.
Radiation breakage of DNA: a model based on random-walk chromatin structure
Ponomarev, A. L.; Sachs, R. K.
2001-01-01
Monte Carlo computer software, called DNAbreak, has recently been developed to analyze observed non-random clustering of DNA double strand breaks in chromatin after exposure to densely ionizing radiation. The software models coarse-grained configurations of chromatin and radiation tracks, small-scale details being suppressed in order to obtain statistical results for larger scales, up to the size of a whole chromosome. We here give an analytic counterpart of the numerical model, useful for benchmarks, for elucidating the numerical results, for analyzing the assumptions of a more general but less mechanistic "randomly-located-clusters" formalism, and, potentially, for speeding up the calculations. The equations characterize multi-track DNA fragment-size distributions in terms of one-track action; an important step in extrapolating high-dose laboratory results to the much lower doses of main interest in environmental or occupational risk estimation. The approach can utilize the experimental information on DNA fragment-size distributions to draw inferences about large-scale chromatin geometry during cell-cycle interphase.
The distribution of first hitting times of random walks on directed Erdős-Rényi networks
Tishby, Ido; Biham, Ofer; Katzav, Eytan
2017-04-01
We present analytical results for the distribution of first hitting times of random walkers (RWs) on directed Erdős-Rényi (ER) networks. Starting from a random initial node, a random walker hops randomly along directed edges between adjacent nodes in the network. The path terminates either by the retracing scenario, when the walker enters a node which it has already visited before, or by the trapping scenario, when it becomes trapped in a dead-end node from which it cannot exit. The path length, namely the number of steps, d, pursued by the random walker from the initial node up to its termination, is called the first hitting time. Using recursion equations, we obtain analytical results for the tail distribution of first hitting times, P≤ft(d>\\ell \\right) . The results are found to be in excellent agreement with numerical simulations. It turns out that the distribution P≤ft(d>\\ell \\right) can be expressed as a product of an exponential distribution and a Rayleigh distribution. We obtain expressions for the mean, median and standard deviation of this distribution in terms of the network size and its mean degree. We also calculate the distribution of last hitting times, namely the path lengths of self-avoiding walks on directed ER networks, which do not retrace their paths. The last hitting times are found to be much longer than the first hitting times. The results are compared to those obtained for undirected ER networks. It is found that the first hitting times of RWs in a directed ER network are much longer than in the corresponding undirected network. This is due to the fact that RWs on directed networks do not exhibit the backtracking scenario, which is a dominant termination mechanism of RWs on undirected networks. It is shown that our approach also applies to a broader class of networks, referred to as semi-ER networks, in which the distribution of in-degrees is Poisson, while the out-degrees may follow any desired distribution with the same mean as
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
Wu, Ming; Kim, Janis; Arora, Pooja; Gaebler-Spira, Deborah J; Zhang, Yunhui
2017-11-01
The aim of the study was to determine whether applying an assistance force to the pelvis and legs during treadmill training can improve walking function in children with cerebral palsy. Twenty-three children with cerebral palsy were randomly assigned to the robotic or treadmill only group. For participants who were assigned to the robotic group, a controlled force was applied to the pelvis and legs during treadmill walking. For participants who were assigned to the treadmill only group, manual assistance was provided as needed. Each participant trained 3 times/wk for 6 wks. Outcome measures included walking speed, 6-min walking distance, and clinical assessment of motor function, which were evaluated before, after training, and 8 wks after the end of training, and were compared between two groups. Significant increases in walking speed and 6-min walking distance were observed after robotic training (P = 0.03), but no significant change was observed after treadmill training only. A greater increase in 6-min walking distance was observed after robotic training than that after treadmill only training (P = 0.01). Applying a controlled force to the pelvis and legs, for facilitating weight-shift and leg swing, respectively, during treadmill training may improve walking speed and endurance in children with cerebral palsy. Complete the self-assessment activity and evaluation online at http://www.physiatry.org/JournalCME CME OBJECTIVES: Upon completion of this article, the reader should be able to: (1) discuss the importance of physical activity at the participation level (sports programs) for children with cerebral palsy; (2) contrast the changes in walking ability and endurance for children in GMFCS level I, II and III following sports programs; and (3) identify the impact of higher frequency of sports program attendance over time on walking ability. Advanced ACCREDITATION: The Association of Academic Physiatrists is accredited by the Accreditation Council for Continuing
Chehuen, Marcel; Cucato, Gabriel G; Carvalho, Celso Ricardo F; Ritti-Dias, Raphael M; Wolosker, Nelson; Leicht, Anthony S; Forjaz, Cláudia Lúcia M
2017-10-01
This study investigated the effects of walking training (WT) on cardiovascular function and autonomic regulation in patents with intermittent claudication (IC). Randomized controlled trial. Forty-two male patients with IC (≥50years) were randomly allocated into two groups: control (CG, n=20, 30min of stretching exercises) and WT (WTG, n=22, 15 bouts of 2min of walking interpolated by 2min of upright rest-walking intensity was set at the heart rate of pain threshold). Both interventions were performed twice/week for 12 weeks. Walking capacity (maximal treadmill test), blood pressure (auscultatory), cardiac output (CO 2 rebreathing), heart rate (ECG), stroke volume, systemic vascular resistance, forearm and calf vascular resistance (plethysmography), and low (LF) and high frequency (HF) components of heart rate variability and spontaneous baroreflex sensitivity were measured at baseline and after 12 weeks of the study. WT increased total walking distance (+302±85m, p=0.001) and spontaneous baroreflex sensitivity (+2.13±1.07ms/mmHg, p=0.02). Additionally, at rest, WT decreased systolic and mean blood pressures (-10±3 and -5±2mmHg, p=0.001 and p=0.01, respectively), cardiac output (-0.37±0.24l/min, p=0.03), heart rate (-4±2bpm, p=0.001), forearm vascular resistance (-8.5±2.8U, p=0.02) and LF/HF (-1.24±0.99, p=0.001). No change was observed in the CG. In addition to increasing walking capacity, WT improved cardiovascular function and autonomic regulation in patients with IC. Copyright © 2017 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.
Wootton, Sally L; McKeough, Zoe; Ng, Cindy L W; Jenkins, Sue; Hill, Kylie; Eastwood, Peter R; Hillman, David; Jenkins, Christine; Cecins, Nola; Spencer, Lissa; Alison, Jennifer
2018-01-01
In patients with COPD, this study evaluated the effect on health-related quality of life (HRQoL) of adding ongoing feedback to a 12-month unsupervised maintenance walking programme. Participants were randomized to either an intervention group (IG) or control group (CG). Both groups completed the same 2-month supervised, walking training programme followed by a 12-month unsupervised maintenance walking programme. During the maintenance programme, the IG received ongoing feedback (telephone calls, biofeedback and progressive goal setting) and the CG received no feedback. A total of 75 participants completed the study (mean (SD): age 69 (8) years; forced expiratory volume in 1 s (FEV 1 ) 43 (15) % predicted). There was no between-group differences in the magnitude of change in HRQoL when data collected on completion of the 12-month maintenance programme were compared with that collected either before the 2-month supervised programme (mean between-group difference (MD) in total St George's Respiratory Questionnaire change scores: 1 point, 95% CI: -9 to 7) or on completion of the 2-month supervised programme (MD: 4 points, 95% CI -2 to 10). Following a 2-month supervised walking training programme, ongoing feedback was no more effective than no feedback in maintaining HRQoL during a 12-month unsupervised walking programme. © 2017 Asian Pacific Society of Respirology.
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Kyril Tintarev
2007-05-01
Full Text Available The paper studies energy functionals on quasimetric spaces, defined by quadratic measure-valued Lagrangeans. This general model of medium, known as metric fractals, includes nested fractals and sub-Riemannian manifolds. In particular, the quadratic form of the Lagrangean satisfies Sobolev inequalities with the critical exponent determined by the (quasimetric homogeneous dimension, which is also involved in the asymptotic distribution of the form's eigenvalues. This paper verifies that the axioms of the metric fractal are preserved by space products, leading thus to examples of non-differentiable media of arbitrary intrinsic dimension.
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.
Xing, Lizhi; Dong, Xianlei; Guan, Jun
2017-04-01
Input-output table is very comprehensive and detailed in describing the national economic system with lots of economic relationships, which contains supply and demand information among industrial sectors. The complex network, a theory and method for measuring the structure of complex system, can describe the structural characteristics of the internal structure of the research object by measuring the structural indicators of the social and economic system, revealing the complex relationship between the inner hierarchy and the external economic function. This paper builds up GIVCN-WIOT models based on World Input-Output Database in order to depict the topological structure of Global Value Chain (GVC), and assumes the competitive advantage of nations is equal to the overall performance of its domestic sectors' impact on the GVC. Under the perspective of econophysics, Global Industrial Impact Coefficient (GIIC) is proposed to measure the national competitiveness in gaining information superiority and intermediate interests. Analysis of GIVCN-WIOT models yields several insights including the following: (1) sectors with higher Random Walk Centrality contribute more to transmitting value streams within the global economic system; (2) Half-Value Ratio can be used to measure robustness of open-economy macroeconomics in the process of globalization; (3) the positive correlation between GIIC and GDP indicates that one country's global industrial impact could reveal its international competitive advantage.
Zhang, Yunhua; Dai, Li; Liu, Ying; Zhang, YuHang; Wang, ShaoPeng
2017-01-01
Fruit is essential for plant reproduction and is responsible for protection and dispersal of seeds. The development and maturation of fruit is tightly regulated by numerous genetic factors that respond to environmental and internal stimulation. In this study, we attempted to identify novel fruit-related genes in a model organism, Arabidopsis thaliana, using a computational method. Based on validated fruit-related genes, the random walk with restart (RWR) algorithm was applied on a protein-protein interaction (PPI) network using these genes as seeds. The identified genes with high probabilities were filtered by the permutation test and linkage tests. In the permutation test, the genes that were selected due to the structure of the PPI network were discarded. In the linkage tests, the importance of each candidate gene was measured from two aspects: (1) its functional associations with validated genes and (2) its similarity with validated genes on gene ontology (GO) terms and KEGG pathways. Finally, 255 inferred genes were obtained, subsequent extensive analysis of important genes revealed that they mainly contribute to ubiquitination (UBQ9, UBQ8, UBQ11, UBQ10), serine hydroxymethyl transfer (SHM7, SHM5, SHM6) or glycol-metabolism (HXKL2_ARATH, CSY5, GAPCP1), suggesting essential roles during the development and maturation of fruit in Arabidopsis thaliana.
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Frankel Allan
2005-04-01
Full Text Available Abstract Background Executive walk rounds (EWRs are a widely used but unstudied activity designed to improve safety culture in hospitals. Therefore, we measured the impact of EWRs on one important part of safety culture – provider attitudes about the safety climate in the institution. Methods Randomized study of EWRs for 23 clinical units in a tertiary care teaching hospital. All providers except physicians participated. EWRs were conducted at each unit by one of six hospital executives once every four weeks for three visits. Providers were asked about their concerns regarding patient safety and what could be done to improve patient safety. Suggestions were tabulated and when possible, changes were made. Provider attitudes about safety climate measured by the Safety Climate Survey before and after EWRs. We report mean scores, percent positive scores (percentage of providers who responded four or higher on a five point scale (agree slightly or agree strongly, and the odds of EWR participants agreeing with individual survey items when compared to non-participants. Results Before EWRs the mean safety climate scores for nurses were similar in the control units and EWR units (78.97 and 76.78, P = 0.458 as were percent positive scores (64.6% positive and 61.1% positive. After EWRs the mean safety climate scores were not significantly different for all providers nor for nurses in the control units and EWR units (77.93 and 78.33, P = 0.854 and (56.5% positive and 62.7% positive. However, when analyzed by exposure to EWRs, nurses in the control group who did not participate in EWRs (n = 198 had lower safety climate scores than nurses in the intervention group who did participate in an EWR session (n = 85 (74.88 versus 81.01, P = 0.02; 52.5% positive versus 72.9% positive. Compared to nurses who did not participate, nurses in the experimental group who reported participating in EWRs also responded more favorably to a majority of items on the survey
Fractal generalized Pascal matrices
Burlachenko, E.
2016-01-01
Set of generalized Pascal matrices whose elements are generalized binomial coefficients is considered as an integral object. The special system of generalized Pascal matrices, based on which we are building fractal generalized Pascal matrices, is introduced. Pascal matrix (Pascal triangle) is the Hadamard product of the fractal generalized Pascal matrices. The concept of zero generalized Pascal matrices, an example of which is the Pascal triangle modulo 2, arise in connection with the system ...
Revathi, S.; Balakrishnan, V.
1993-02-01
We study unbiased random walks in discrete time n on a square lattice, in the form of a strip of finite width N in the y direction, with a family of boundary conditions parametrized by a stay probability Γ per time step at the edge sites. The diffusion coefficient K=limn-->∞/n is computed analytically to exhibit its dependence on N and Γ. The result is generalized to the case of a strip with side branches attached to the boundary sites to simulate the effect of rough edges. A further generalization is made to obtain K for a random walk in d dimensions on a lattice bounded in one of the directions. Thus, K serves as a probe of both the transverse size of the region in which diffusion takes place and the nature of the bounding surfaces.
Chen, Haibin; Zhen, Xin; Gu, Xuejun; Yan, Hao; Cervino, Laura; Xiao, Yang; Zhou, Linghong
2015-03-08
In medical image processing, robust segmentation of inhomogeneous targets is a challenging problem. Because of the complexity and diversity in medical images, the commonly used semiautomatic segmentation algorithms usually fail in the segmentation of inhomogeneous objects. In this study, we propose a novel algorithm imbedded with a seed point autogeneration for random walks segmentation enhancement, namely SPARSE, for better segmentation of inhomogeneous objects. With a few user-labeled points, SPARSE is able to generate extended seed points by estimating the probability of each voxel with respect to the labels. The random walks algorithm is then applied upon the extended seed points to achieve improved segmentation result. SPARSE is implemented under the compute unified device architecture (CUDA) programming environment on graphic processing unit (GPU) hardware platform. Quantitative evaluations are performed using clinical homogeneous and inhomogeneous cases. It is found that the SPARSE can greatly decrease the sensitiveness to initial seed points in terms of location and quantity, as well as the freedom of selecting parameters in edge weighting function. The evaluation results of SPARSE also demonstrate substantial improvements in accuracy and robustness to inhomogeneous target segmentation over the original random walks algorithm.
Snow metamorphism: A fractal approach
Carbone, Anna; Chiaia, Bernardino M.; Frigo, Barbara; Türk, Christian
2010-09-01
Snow is a porous disordered medium consisting of air and three water phases: ice, vapor, and liquid. The ice phase consists of an assemblage of grains, ice matrix, initially arranged over a random load bearing skeleton. The quantitative relationship between density and morphological characteristics of different snow microstructures is still an open issue. In this work, a three-dimensional fractal description of density corresponding to different snow microstructure is put forward. First, snow density is simulated in terms of a generalized Menger sponge model. Then, a fully three-dimensional compact stochastic fractal model is adopted. The latter approach yields a quantitative map of the randomness of the snow texture, which is described as a three-dimensional fractional Brownian field with the Hurst exponent H varying as continuous parameters. The Hurst exponent is found to be strongly dependent on snow morphology and density. The approach might be applied to all those cases where the morphological evolution of snow cover or ice sheets should be conveniently described at a quantitative level.
Burnell, Daniel K.; Hansen, Scott K.; Xu, Jie
2017-09-01
Contaminants in groundwater may experience a broad spectrum of velocities and multiple rates of mass transfer between mobile and immobile zones during transport. These conditions may lead to non-Fickian plume evolution which is not well described by the advection-dispersion equation (ADE). Simultaneously, many groundwater contaminants are degraded by processes that may be modeled as first-order decay. It is now known that non-Fickian transport and reaction are intimately coupled, with reaction affecting the transport operator. However, closed-form solutions for these important scenarios have not been published for use in applications. In this paper, we present four new Green's function analytic solutions in the uncoupled, uncorrelated continuous time random walk (CTRW) framework for reactive non-Fickian transport, corresponding to the quartet of conservative tracer solutions presented by Kreft and Zuber (1978) for Fickian transport. These consider pulse injection for both resident and flux concentration combined with detection in both resident and flux concentration. A pair of solutions for resident concentration temporal pulses with detection in both flux and resident concentration is also presented. We also derive the relationship between flux and resident concentration for non-Fickian transport with first-order reaction for this CTRW formulation. An explicit discussion of employment of the new solutions to model transport with arbitrary upgradient boundary conditions as well as mobile-immobile mass transfer is then presented. Using the new solutions, we show that first-order reaction has no effect on the anomalous spatial spreading rate of concentration profiles, but produces breakthrough curves at fixed locations that appear to have been generated by Fickian transport. Under the assumption of a Pareto CTRW transition distribution, we present a variety of numerical simulations including results showing coherence of our analytic solutions and CTRW particle
Navarrete-Opazo, Angela; Alcayaga, Julio; Sepúlveda, Oscar; Rojas, Enrique; Astudillo, Carolina
2017-05-01
Incomplete spinal cord injuries (iSCI) leave spared synaptic pathways below the level of injury. Intermittent hypoxia (IH) elicits plasticity in the spinal cord and strengthens spared synaptic pathways, expressed as respiratory and somatic functional recovery in experimental animals and humans with iSCI. This study is a randomized, triple-blind, two-arm parallel clinical trial performed in Santiago, Chile. We compared the effects of a 4-week protocol of IH combined with body weight-supported treadmill training (BWSTT), with continuous normoxia (Nx) and BWSTT on 10-meter walk test (10MWT), 6-minute walk test (6MWT), and timed up and go (TUG) test in American Spinal Injury Association C and D individuals with iSCI. Subjects received daily IH (cycling 9%/21% O 2 every 1.5 min, 15 cycles/day) or continuous Nx (21% O 2 ) combined with 45 min BWSTT for 5 consecutive days, followed by IH/Nx 3 × per week (3 × wIH/Nx) for 3 additional weeks. Subjects were assessed at day 5, weekly from weeks 2-4, and at a 2-week follow-up. Daily IH plus BWSTT enhanced walking speed, expressed as decreased 10MWT time at day 5 versus baseline (IH: -10.2 ± 3.0 vs. Nx: -1.7 ± 1.7 sec, p = 0.006), and walking endurance expressed as increased 6MWT distance at day 5 versus baseline (IH: 43.0 ± 10.7 vs. Nx: 6.1 ± 3.4 m, p = 0.012), but not TUG time. Further, 3 × wIH maintained the daily IH-induced walking speed, and enhanced the daily IH-induced walking endurance, which is maintained up to the 2-week follow-up. We conclude that daily IH enhances walking recovery in subjects with iSCI, confirming previous findings. Moreover, 3 × wIH prolonged or enhanced daily IH-induced walking speed and endurance improvements, respectively, up to 5 weeks post-daily IH. Repetitive IH may be a safe and effective therapeutic alternative for persons with iSCI.
Kang, Tae-Woo; Oh, Duck-Won; Lee, Ji-Hyun; Cynn, Heon-Seock
2017-11-14
This study aimed to identify the effects of rhythmic arm swing during robot-assisted walking training on balance, gait, motor function, and activities of daily living among patients with subacute stroke. Twenty patients with subacute stroke were recruited, and thereafter randomly allocated to either the experimental group that performed the robot-assisted walking training with rhythmic arm swing, or the control group that performed the training in arm fixation. In total, 30 training sessions were carried out. The outcome measures included the 10-m walk test, Berg balance scale, timed up-and-go test, fall index that was measured using the Tetrax system, motor function test of Fugl-Meyer assessment, and modified Barthel index. The patients of both groups showed significant improvement in all parameters after the intervention (P<0.05). The Berg balance scale, Fugl-Meyer assessment, and modified Barthel index scores at post-test appeared to be significantly higher for the experimental group than for the control group (P<0.05). These findings indicate that more favorable effects from robot-assisted walking training in patients with subacute stroke may be obtained by the use of rhythmic arm swing.
Bang, Kyung Sook; Lee, In Sook; Kim, Sung Jae; Song, Min Kyung; Park, Se Eun
2016-02-01
This study was performed to determine the physical and psychological effects of an urban forest-walking program for office workers. For many workers, sedentary lifestyles can lead to low levels of physical activity causing various health problems despite an increased interest in health promotion. Fifty four office workers participated in this study. They were assigned to two groups (experimental group and control group) in random order and the experimental group performed 5 weeks of walking exercise based on Information-Motivation-Behavioral skills Model. The data were collected from October to November 2014. SPSS 21.0 was used for the statistical analysis. The results showed that the urban forest walking program had positive effects on the physical activity level (U=65.00, pforest-walking program may have positive effects on improving physical activity, health promotion behavior, and quality of life. The program can be used as an effective and efficient strategy for physical and psychological health promotion for office workers.
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
The fractal forest: fractal geometry and applications in forest science.
Nancy D. Lorimer; Robert G. Haight; Rolfe A. Leary
1994-01-01
Fractal geometry is a tool for describing and analyzing irregularity. Because most of what we measure in the forest is discontinuous, jagged, and fragmented, fractal geometry has potential for improving the precision of measurement and description. This study reviews the literature on fractal geometry and its applications to forest measurements.
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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
Fractal Analysis on Asphalt Mixture Using a Two-Dimensional Imaging Technique
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Yue Hou
2016-01-01
Full Text Available Fractal is a mathematical set that has a fractal dimension which usually exceeds its topological dimension and may be nonintegral. Since the asphalt pavement texture has limitations of randomness and self-similarity, fractal theory has been explored to quantify the asphalt pavement texture and employs good applicability in processing and analyzing the complex details of research object. In this paper, the 2D digital image of the pavement surface is measured in terms of area fractal dimension and contour fractal dimension, which are used to correlate with aggregate gradation and British Pendulum Number (BPN value, respectively. It turns out the area fractal dimension of aggregate provides a simple way to acquire the continuous gradation of asphalt concrete sample and the contour fractal dimension is an available parameter to characterize roughness and friction of pavement surface texture.
Fractal aspects and convergence of Newton`s method
Energy Technology Data Exchange (ETDEWEB)
Drexler, M. [Oxford Univ. Computing Lab. (United Kingdom)
1996-12-31
Newton`s Method is a widely established iterative algorithm for solving non-linear systems. Its appeal lies in its great simplicity, easy generalization to multiple dimensions and a quadratic local convergence rate. Despite these features, little is known about its global behavior. In this paper, we will explain a seemingly random global convergence pattern using fractal concepts and show that the behavior of the residual is entirely explicable. We will also establish quantitative results for the convergence rates. Knowing the mechanism of fractal generation, we present a stabilization to the orthodox Newton method that remedies the fractal behavior and improves convergence.
The Entrepreneur's Random Walk
National Research Council Canada - National Science Library
Robert Fiore
2012-01-01
... destruction" free-market mechanisms are discussed. The existence of fundamental attribution error may likewise lead to over-weight emphasis of a leader's input to organizational failure, however, the sample of entrepreneurs linked to successful...
Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga
2016-04-01
The effectiveness of fractal toolbox to capture the scaling or fractal probability distribution, and simply fractal statistics of main hydrocarbon reservoir attributes, was highlighted by Mandelbrot (1995) and confirmed by several researchers (Zhao et al., 2015). Notwithstanding, after more than twenty years, it's still common the opinion that fractals are not useful for the petroleum engineers and especially for Geoengineering (Corbett, 2012). In spite of this negative background, we have successfully applied the fractal and multifractal techniques to our project entitled "Petroleum Reservoir as a Fractal Reactor" (2013 up to now). The distinguishable feature of Fractal Reservoir is the irregular shapes and rough pore/solid distributions (Siler, 2007), observed across a broad range of scales (from SEM to seismic). At the beginning, we have accomplished the detailed analysis of Nelson and Kibler (2003) Catalog of Porosity and Permeability, created for the core plugs of siliciclastic rocks (around ten thousand data were compared). We enriched this Catalog by more than two thousand data extracted from the last ten years publications on PoroPerm (Corbett, 2012) in carbonates deposits, as well as by our own data from one of the PEMEX, Mexico, oil fields. The strong power law scaling behavior was documented for the major part of these data from the geological deposits of contrasting genesis. Based on these results and taking into account the basic principles and models of the Physics of Fractals, introduced by Per Back and Kan Chen (1989), we have developed new software (Muukíl Kaab), useful to process the multiscale geological and geophysical information and to integrate the static geological and petrophysical reservoir models to dynamic ones. The new type of fractal numerical model with dynamical power law relations among the shapes and sizes of mesh' cells was designed and calibrated in the studied area. The statistically sound power law relations were established
Marks-Tarlow, Terry
Linear concepts of time plus the modern capacity to track history emerged out of circular conceptions characteristic of ancient and traditional cultures. A fractal concept of time lies implicitly within the analog clock, where each moment is treated as unique. With fractal geometry the best descriptor of nature, qualities of self-similarity and scale invariance easily model her endless variety and recursive patterning, both in time and across space. To better manage temporal aspects of our lives, a fractal concept of time is non-reductive, based more on the fullness of being than on fragments of doing. By using a fractal concept of time, each activity or dimension of life is multiply and vertically nested. Each nested cycle remains simultaneously present, operating according to intrinsic dynamics and time scales. By adding the vertical axis of simultaneity to the horizontal axis of length, time is already full and never needs to be filled. To attend to time's vertical dimension is to tap into the imaginary potential for infinite depth. To switch from linear to fractal time allows us to relax into each moment while keeping in mind the whole.
Fractal Electrochemical Microsupercapacitors
Hota, Mrinal Kanti
2017-08-17
The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.
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V.L. dos Santos Alves
2015-05-01
Full Text Available Background: Monitored physical activities in patients with adolescent idiopathic scoliosis (AIS have been shown to improve physical performance, endurance and cardiopulmonary function and may be assessed by the 6-min walk test (6MWT. We aimed to evaluate the long-term results of the 6MWT after a rehabilitation protocol employed before surgical correction for AIS. Methods: This prospective randomized clinical trial studied the impact of a 4-month pre-operative physical rehabilitation protocol on post-operative cardiopulmonary function and physical endurance, by using the 6MWT, in patients with AIS submitted to surgical correction, comparing them to matched controls without physical rehabilitation. Studied variables were heart and respiratory rate, systolic and diastolic blood pressure, peripheral blood oxygen saturation, Borg score, and distance walked. Patients were assessed at baseline, after 4 months of rehabilitation, and 3, 6 and 12 months post-operatively. Results: A total of 50 patients with AIS were included in the study and allocated blindly, by simple randomization, into either one of the two groups, with 25 patients each: study group (pre-operative physical rehabilitation and control group. The physical rehabilitation protocol promoted significant progressive improvement in heart and respiratory rate, peripheral blood oxygen saturation, distance walked, and level of effort assessed by the Borg scale after surgery. Conclusions: Post-surgical recovery, evaluated by 6MWT, was significantly better in patients who underwent a 4-month pre-operative physical rehabilitation protocol. Keywords: Scoliosis, Exercise, Exercise movement techniques, Exercise therapy, Exercise test
Fractal geometry and stochastics IV
Bandt, Christoph
2010-01-01
Over the years fractal geometry has established itself as a substantial mathematical theory in its own right. This book collects survey articles covering many of the developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals.
Li, Jun; Ostoja-Starzewski, Martin
2012-01-01
Over the past few decades, various conjectures were advanced that Saturn's rings are Cantor-like sets, although no convincing fractal analysis of actual images has ever appeared. We focus on the images sent by the Cassini spacecraft mission: slide #42 "Mapping Clumps in Saturn's Rings" and slide #54 "Scattered Sunshine". Using the box-counting method, we determine the fractal dimension of rings seen here (and in several other images from the same source) to be consistently about 1.6~1.7. This...
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Deppman Airton
2017-01-01
Full Text Available The non extensive aspects of pT distributions obtained in high energy collisions are discussed in relation to possible fractal structure in hadrons, in the sense of the thermofractal structure recently introduced. The evidences of self-similarity in both theoretical and experimental works in High Energy and in Hadron Physics are discussed, to show that the idea of fractal structure of hadrons and fireballs have being under discussion for decades. The non extensive self-consistent thermodynamics and the thermofractal structure allow one to connect non extensivity to intermittence and possibly to parton distribution functions in a single theoretical framework.
Fractal elements and their applications
Gil’mutdinov, Anis Kharisovich; El-Khazali, Reyad
2017-01-01
This book describes a new type of passive electronic components, called fractal elements, from a theoretical and practical point of view. The authors discuss in detail the physical implementation and design of fractal devices for application in fractional-order signal processing and systems. The concepts of fractals and fractal signals are explained, as well as the fundamentals of fractional calculus. Several implementations of fractional impedances are discussed, along with comparison of their performance characteristics. Details of design, schematics, fundamental techniques and implementation of RC-based fractal elements are provided. .
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
The fractal based analysis of human face and DNA variations during aging.
Namazi, Hamidreza; Akrami, Amin; Hussaini, Jamal; Silva, Osmar N; Wong, Albert; Kulish, Vladimir V
2017-01-16
Human DNA is the main unit that shapes human characteristics and features such as behavior. Thus, it is expected that changes in DNA (DNA mutation) influence human characteristics and features. Face is one of the human features which is unique and also dependent on his gen. In this paper, for the first time we analyze the variations of human DNA and face simultaneously. We do this job by analyzing the fractal dimension of DNA walk and face during human aging. The results of this study show the human DNA and face get more complex by aging. These complexities are mapped on fractal exponents of DNA walk and human face. The method discussed in this paper can be further developed in order to investigate the direct influence of DNA mutation on the face variations during aging, and accordingly making a model between human face fractality and the complexity of DNA walk.
Earnshow, R; Jones, H
1991-01-01
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...
Fractal Representation of Exergy
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Yvain Canivet
2016-02-01
Full Text Available We developed a geometrical model to represent the thermodynamic concepts of exergy and anergy. The model leads to multi-scale energy lines (correlons that we characterised by fractal dimension and entropy analyses. A specific attention will be paid to overlapping points, rising interesting remarks about trans-scale dynamics of heat flows.
Bottorff, Mark; Ferland, Gary
2001-03-01
This paper examines whether a fractal cloud geometry can reproduce the emission-line spectra of active galactic nuclei (AGNs). The nature of the emitting clouds is unknown, but many current models invoke various types of magnetohydrodynamic confinement. Recent studies have argued that a fractal distribution of clouds, in which subsets of clouds occur in self-similar hierarchies, is a consequence of such confinement. Whatever the confinement mechanism, fractal cloud geometries are found in nature and may be present in AGNs too. We first outline how a fractal geometry can apply at the center of a luminous quasar. Scaling laws are derived that establish the number of hierarchies, typical sizes, column densities, and densities. Photoionization simulations are used to predict the integrated spectrum from the ensemble. Direct comparison with observations establishes all model parameters so that the final predictions are fully constrained. Theory suggests that denser clouds might form in regions of higher turbulence and that larger turbulence results in a wider dispersion of physical gas densities. An increase in turbulence is expected deeper within the gravitational potential of the black hole, resulting in a density gradient. We mimic this density gradient by employing two sets of clouds with identical fractal structuring but different densities. The low-density clouds have a lower column density and large covering factor similar to the warm absorber. The high-density clouds have high column density and smaller covering factor similar to the broad-line region (BLR). A fractal geometry can simultaneously reproduce the covering factor, density, column density, BLR emission-line strengths, and BLR line ratios as inferred from observation. Absorption properties of the model are consistent with the integrated line-of-sight column density as determined from observations of X-ray absorption, and when scaled to a Seyfert galaxy, the model is consistent with the number of
Ali Abd El Aziz Essa ., Mohamed
2012-01-01
Una nueva aproximación euleriana-lagarangiana, en su forma de acople en dos vías, para la simulación de flujo de burbujas, agua-aire es presentada en la tesis, en la que se incluyen los efectos de las colisiones entre burbujas, así como las posibles roturas o coalescencia de burbujas. Esta aproximación utiliza el modelo Continuous Random Walk, CRW, para tener en cuenta las fluctuaciones de la velocidad. Esta aproximación se enmarca dentro de un modelo de turbulencia k-epsilon para la fase ...
Brændvik, Siri Merete; Roeleveld, Karin; Andersen, Guro Lillemoen; Raftemo, Anne Elisabeth Ross; Ramstad, Kjersti; Majkic-Tajsic, Jasmina; Lamvik, Torarin; Lund, Bendik; Follestad, Turid; Vik, Torstein
2017-02-06
Intramuscular injections of botulinum toxin A (BoNT-A) have been a cornerstone in the treatment of spasticity for the last 20 years. In Norway, the treatment is now offered to two out of three children with spastic cerebral palsy (CP). However, despite its common use, the evidence for its functional effects is limited and inconclusive. The objective of this study is to determine whether BoNT-A makes walking easier in children with CP. We hypothesize that injections with BoNT-A in the calf muscles will reduce energy cost during walking, improve walking capacity, increase habitual physical activity, reduce pain and improve self-perceived performance and satisfaction. This randomized, double-blinded, placebo-controlled, multicenter trial is conducted in a clinical setting involving three health regions in Norway. Ninety-six children with spastic CP, referred for single-level injections with BoNT-A in the calf muscles, will be invited to participate. Those who are enrolled will be randomized to receive either injections with BoNT-A (Botox®) or 0.9% saline in the calf muscles. Stratification according to age and study center will be made. The allocation ratio will be 1:1. Main inclusion criteria are (1) age 4 - 17.5 years, (2) Gross Motor Function Classification System levels I and II, (3) no BoNT-A injections in the lower limbs during the past 6 months and (4) no orthopedic surgery to the lower limbs during the past 2 years. The outcome measures will be made at baseline and 4, 12 (primary endpoint) and 24 weeks after injections. Primary outcome is change in energy cost during walking. Secondary outcomes are change in walking capacity, change in activity, perceived change in performance and satisfaction in mobility tasks, and pain. The primary analysis will use a linear mixed model to test for difference in change in the outcome measures between the groups. The study is approved by the Regional Ethical Committee and The Norwegian Medicines Agency. Recruitment
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Plummer-D’Amato Prudence
2012-10-01
Full Text Available Abstract Background Community ambulation is a highly complex skill requiring the ability to adapt to increased environmental complexity and perform multiple tasks simultaneously. After stroke, individuals demonstrate a diminished ability to perform dual-tasks. Current evidence suggests that conventional rehabilitation does not adequately address gait-related dual-task impairments after stroke, which may be contributing to low levels of participation and physical inactivity in community-dwelling stroke survivors. The objective of this study is to investigate the efficacy of dual-task gait training in community-dwelling adults within 1 year of stroke. Specifically, we will compare the effects of dual-task gait training and single-task gait training on cognitive-motor interference during walking at preferred speed and at fastest comfortable speed (Aim 1, locomotor control during obstacle negotiation (Aim 2, and spontaneous physical activity (Aim 3. Methods/Design This single-blind randomized controlled trial will involve 44 individuals within 12 months of stroke. Following baseline evaluation, participants will be randomly allocated to single- or dual-task gait training. Both groups will receive 12, 30-minute sessions provided one-on-one over 4–6 weeks in an outpatient therapy setting. Single-task gait training involves practice of gait activities incorporating motor relearning principles. Dual-task gait training involves an identical gait training protocol; the critical difference being that the dual-task gait training group will practice the gait activities while simultaneously performing a cognitive task for 75% of the repetitions. Blinded assessors will measure outcomes at baseline, post-intervention, and 6 months after completion of the intervention. The primary outcome measure will be dual-task effects on gait speed and cognition during unobstructed walking. Secondary outcomes include spatiotemporal and kinetic gait parameters during
Kocur, Piotr; Pospieszna, Barbara; Choszczewski, Daniel; Michalowski, Lukasz; Wiernicka, Marzena; Lewandowski, Jacek
2017-01-01
Regular Nordic Walking training could improve fitness and reduce tenderness in selected muscle groups in office workers. An assessment of the effects of a 12-week Nordic Walking training program on the perceived pain threshold (PPT) and the flexibility of selected upper-body muscle groups in postmenopausal female office workers. 39 office workers were selected at random for the treatment group (NWg, n = 20) and the control group (Cg, n = 19). The persons from the NW group completed a 12-week Nordic Walking training program (3 times a week/1 hour). PPTs measurements in selected muscles and functional tests evaluating upper-body flexibility (Back Scratch - BS) were carried out twice in every participant of the study: before and after the training program. A significant increase in PPT (kg/cm2) was observed in the following muscles in the NW group only: upper trapezius (from 1,32 kg/cm2 to 1,99 kg/cm2), mid trapezius (from 2,92 kg/cm2 to 3,30 kg/cm2), latissimus dorsi (from 1,66 kg/cm2 to 2,21 kg/cm2) and infraspinatus (from 1,63 kg/cm2 to 2,93 kg/cm2). Moreover, a significant improvement in the BS test was noted in the NW group compared with the control group (from -1,16±5,7 cm to 2,18±5,1 cm in the NW group vs from -2,52±6,1 to -2,92±6,2 in the control group). A 12-week Nordic Walking training routine improves shoulder mobility and reduces tenderness in the following muscles: trapezius pars descendens and middle trapezius, infraspinatus and latissimus dorsi, in female office workers.
Zietek, P; Zietek, J; Szczypior, K; Safranow, K
2015-06-01
Earlier and more intensive physiotherapy exercise after total knee arthroplasty (TKA) enhance recovery, but the best combination of intensity and duration has not been determined. To determine whether adding a single, 15-minute walk on the day of surgery to a fast-track rehabilitation protocol would reduce knee pain and improve knee function after TKA. A randomized single-blind study. Inpatient. Patients with primary osteoarthrosis after TKA. Patients undergoing TKA were randomly assigned to a standard, fast-track rehabilitation protocol consisting of a single, 15-minute walk with a high-rolling walker 4 to 6 hours after recovery from spinal anesthesia or to an intensive protocol, in which patients took a second 15-minute walk at least 3 hours after the first, only on the day of surgery. Outcomes were pain measured on a visual analog scale, Knee Society's (KSS) clinical and functional scores, Oxford knee scores, and Spielberger State-Trait Anxiety Inventory scores. Patients were blinded to group assignment. Since most data were non-normally distributed non-parametric tests were used. Groups were compared with Mann-Whitney U test (for continuous variables). Association between continuous variables was evaluated with Spearman`s rank correlation coefficient. Chi-square or Fisher's exact test was used to assess differences in categorical variables. Of 86 patients assessed for eligibility, 66 were randomly assigned. The 31 evaluable patients on the intensive protocol (mean age, 68 years; 18 women) did not differ significantly from the 31 (mean age, 70 years; 20 women) on the standard protocol on any baseline characteristic or on any outcome measure on any day. On the second postoperative day, pain while walking dropped from a mean of 6.1 to a mean of 4.9 in the intensive group and from 6.4 to 5.4 in the standard group. Results for pain at rest were 3.3 to 2.2, respectively, for the intensive group and 4.0 to 3.0 for the standard group. At 2 weeks, pain at rest was 2
Dos Santos Alves, V L; Stirbulov, R; Avanzi, O
2015-01-01
Monitored physical activities in patients with adolescent idiopathic scoliosis (AIS) have been shown to improve physical performance, endurance and cardiopulmonary function and may be assessed by the 6-min walk test (6MWT). We aimed to evaluate the long-term results of the 6MWT after a rehabilitation protocol employed before surgical correction for AIS. This prospective randomized clinical trial studied the impact of a 4-month pre-operative physical rehabilitation protocol on post-operative cardiopulmonary function and physical endurance, by using the 6MWT, in patients with AIS submitted to surgical correction, comparing them to matched controls without physical rehabilitation. Studied variables were heart and respiratory rate, systolic and diastolic blood pressure, peripheral blood oxygen saturation, Borg score, and distance walked. Patients were assessed at baseline, after 4 months of rehabilitation, and 3, 6 and 12 months post-operatively. A total of 50 patients with AIS were included in the study and allocated blindly, by simple randomization, into either one of the two groups, with 25 patients each: study group (pre-operative physical rehabilitation) and control group. The physical rehabilitation protocol promoted significant progressive improvement in heart and respiratory rate, peripheral blood oxygen saturation, distance walked, and level of effort assessed by the Borg scale after surgery. Post-surgical recovery, evaluated by 6MWT, was significantly better in patients who underwent a 4-month pre-operative physical rehabilitation protocol. Copyright © 2013 Sociedade Portuguesa de Pneumologia. Published by Elsevier España, S.L.U. All rights reserved.
Multilayer adsorption on fractal surfaces.
Vajda, Péter; Felinger, Attila
2014-01-10
Multilayer adsorption is often observed in liquid chromatography. The most frequently employed model for multilayer adsorption is the BET isotherm equation. In this study we introduce an interpretation of multilayer adsorption measured on liquid chromatographic stationary phases based on the fractal theory. The fractal BET isotherm model was successfully used to determine the apparent fractal dimension of the adsorbent surface. The nonlinear fitting of the fractal BET equation gives us the estimation of the adsorption equilibrium constants and the monolayer saturation capacity of the adsorbent as well. In our experiments, aniline and proline were used as test molecules on reversed phase and normal phase columns, respectively. Our results suggest an apparent fractal dimension 2.88-2.99 in the case of reversed phase adsorbents, in the contrast with a bare silica column with a fractal dimension of 2.54. Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.
Martin, Demetri
2015-03-01
Demetri Maritn prepared this palindromic poem as his project for Michael Frame's fractal geometry class at Yale. Notice the first, fourth, and seventh words in the second and next-to-second lines are palindromes, the first two and last two lines are palindromes, the middle line, "Be still if I fill its ebb" minus its last letter is a palindrome, and the entire poem is a palindrome...
The Use of Fractals for the Study of the Psychology of Perception:
Mitina, Olga V.; Abraham, Frederick David
The present article deals with perception of time (subjective assessment of temporal intervals), complexity and aesthetic attractiveness of visual objects. The experimental research for construction of functional relations between objective parameters of fractals' complexity (fractal dimension and Lyapunov exponent) and subjective perception of their complexity was conducted. As stimulus material we used the program based on Sprott's algorithms for the generation of fractals and the calculation of their mathematical characteristics. For the research 20 fractals were selected which had different fractal dimensions that varied from 0.52 to 2.36, and the Lyapunov exponent from 0.01 to 0.22. We conducted two experiments: (1) A total of 20 fractals were shown to 93 participants. The fractals were displayed on the screen of a computer for randomly chosen time intervals ranging from 5 to 20 s. For each fractal displayed, the participant responded with a rating of the complexity and attractiveness of the fractal using ten-point scale with an estimate of the duration of the presentation of the stimulus. Each participant also answered the questions of some personality tests (Cattell and others). The main purpose of this experiment was the analysis of the correlation between personal characteristics and subjective perception of complexity, attractiveness, and duration of fractal's presentation. (2) The same 20 fractals were shown to 47 participants as they were forming on the screen of the computer for a fixed interval. Participants also estimated subjective complexity and attractiveness of fractals. The hypothesis on the applicability of the Weber-Fechner law for the perception of time, complexity and subjective attractiveness was confirmed for measures of dynamical properties of fractal images.
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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
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
. Indeed, as discussed in §4 with examples, and in [32], it is possible to solve certain fractal differential equations by mapping them to ordinary differential equations and fractalizing the solutions back. The organization of the paper is as follows: ...
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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.
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Brosseau Lucie
2012-10-01
Full Text Available Abstract Background The implementation of evidence based clinical practice guidelines on self-management interventions to patients with chronic diseases is a complex process. A multifaceted strategy may offer an effective knowledge translation (KT intervention to promote knowledge uptake and improve adherence in an effective walking program based on the Ottawa Panel Evidence Based Clinical Practice Guidelines among individuals with moderate osteoarthritis (OA. Methods A single-blind, randomized control trial was conducted. Patients with mild to moderate (OA of the knee (n=222 were randomized to one of three KT groups: 1 Walking and Behavioural intervention (WB (18 males, 57 females which included the supervised community-based aerobic walking program combined with a behavioural intervention and an educational pamphlet on the benefits of walking for OA; 2 Walking intervention (W (24 males, 57 females wherein participants only received the supervised community-based aerobic walking program intervention and the educational pamphlet; 3 Self-directed control (C (32 males, 52 females wherein participants only received the educational pamphlet. One-way analyses of variance were used to test for differences in quality of life, adherence, confidence, and clinical outcomes among the study groups at each 3 month assessment during the 12-month intervention period and 6-month follow-up period. Results Short-term program adherence was greater in WB compared to C (p 0.05 was observed for long-term adherence (6 to 12 months, and total adherence between the three groups. The three knowledge translation strategies demonstrated equivalent long-term results for the implementation of a walking program for older individuals with moderate OA. Lower dropout rates as well as higher retention rates were observed for WB at 12 and 18 months. Conclusion The additional knowledge translation behavioural component facilitated the implementation of clinical practice guidelines
Pohl, M; Werner, C; Holzgraefe, M; Kroczek, G; Mehrholz, J; Wingendorf, I; Hoölig, G; Koch, R; Hesse, S
2007-01-01
To evaluate the effect of repetitive locomotor training on an electromechanical gait trainer plus physiotherapy in subacute stroke patients. Randomized controlled trial. Four German neurological rehabilitation centres. One hundred and fifty-five non-ambulatory patients (first-time stroke or = 75. Secondary variables were walking velocity, endurance, mobility and leg power. The intention-to-treat analysis revealed that significantly greater number of patients in group A could walk independently: 41 of 77 versus 17 of 78 in group B (P B or = 75: 44 of 77 versus 21 of 78 (P B < 0.0001). At six-month follow-up, the superior gait ability in group A persisted (54 of 77 versus 28 of 78, P B < 0.0001), while the Barthel Index responder rate did not differ. For all secondary variables, group A patients had improved significantly more (P B < 0.0001) during the treatment period, but not during follow-up. Intensive locomotor training plus physiotherapy resulted in a significantly better gait ability and daily living competence in subacute stroke patients compared with physiotherapy alone.
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Galli Thiago Tafarel
2013-01-01
Full Text Available Abstract Background Pain is a negative factor in the recovery process of postoperative patients, causing pulmonary alterations and complications and affecting functional capacity. Thus, it is plausible to introduce transcutaneous electrical nerve stimulation (TENS for pain relief to subsequently reduce complications caused by this pain in the postoperative period. The objective of this paper is to assess the effects of TENS on pain, walking function, respiratory muscle strength and vital capacity in kidney donors. Methods/design Seventy-four patients will be randomly allocated into 2 groups: active TENS or placebo TENS. All patients will be assessed for pain intensity, walk function (Iowa Gait Test, respiratory muscle strength (maximal inspiratory pressure and maximal expiratory pressure and vital capacity before and after the TENS application. The data will be collected by an assessor who is blinded to the group allocation. Discussion This study is the first to examine the effects of TENS in this population. TENS during the postoperative period may result in pain relief and improvements in pulmonary tests and mobility, thus leading to an improved quality of life and further promoting organ donation. Trial registration Registro Brasileiro de Ensaios Clinicos (ReBEC, number RBR-8xtkjp.
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost dark energy model which was recently suggested to explain the present acceleration of the cosmic expansion. Next, we establish a connection between the quintessence scalar field and fractal ghost dark energy density.
Fractals and the Kepler equation
Kasten, Volker
1992-09-01
The application of fractal mathematics to Kepler's equation is addressed. Complex solutions to Kepler's equation are considered along with methods to determine them. The roles of regions of attraction and their boundaries, Julia quantities, Fatou quantities, and fractal quantities in these methods are discussed.
Simoson, Andrew J.
2009-01-01
This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)
Contour fractal analysis of grains
Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB
2017-06-01
Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.
Encounters with chaos and fractals
Gulick, Denny
2012-01-01
Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.
Contour fractal analysis of grains
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Guida Giulia
2017-01-01
Full Text Available Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]. Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.
Živić, I.; Elezović-Hadžić, S.; Milošević, S.
2018-01-01
We have studied the adsorption problem of self-attracting linear polymers, modeled by self-avoiding walks (SAWs), situated on three-dimensional fractal structures, exemplified by 3d Sierpinski gasket (SG) family of fractals as containers of a poor solvent. Members of SG family are enumerated by an integer b (b ≥ 2), and it is assumed that one side of each SG fractal is an impenetrable adsorbing surface. We calculate the critical exponents γ1 ,γ11, and γs, which are related to the numbers of all possible SAWs with one, both, and no ends anchored to the adsorbing boundary, respectively. By applying the exact renormalization group (RG) method (for the first three members of the SG fractal family, b = 2 , 3, and 4), we have obtained specific values of these exponents, for θ-chain and globular polymer phase. We discuss their mutual relations and relations with corresponding values pertinent to extended polymer chain phase.
Queralt, Tomás
1997-01-01
En el presente artículo se muestra el planteamiento, justificación y la puesta en practica de algunas actividades que forman parte de un taller de fractales. Estas se han tratado en clase en grupos de segundo ciclo de ESO, y se han utilizado para iniciar el curso con un resultado satisfactorio. Con este trabajo se pretende romper con algunos estereotipos y con algunas creencias que los estudiantes tienen acerca de las matemáticas, así como crear el contexto más adecuado para que el alumno hag...
Fractal actors and infrastructures
DEFF Research Database (Denmark)
Bøge, Ask Risom
2011-01-01
-network-theory (ANT) into surveillance studies (Ball 2002, Adey 2004, Gad & Lauritsen 2009). In this paper, I further explore the potential of this connection by experimenting with Marilyn Strathern’s concept of the fractal (1991), which has been discussed in newer ANT literature (Law 2002; Law 2004; Jensen 2007). I...... argue that the concept fits nicely into the ANT-oriented situated surveillance approach (Gad & Lauritsen 2009), not because it explains surveillance, but because it brings empirical sensitivity to our efforts to understanding what comprises a surveillance actor, its network and its relations to those...
Yang, Jing; Youssef, Mostafa; Yildiz, Bilge
2018-01-01
In this work, we quantify oxygen self-diffusion in monoclinic-phase zirconium oxide as a function of temperature and oxygen partial pressure. A migration barrier of each type of oxygen defect was obtained by first-principles calculations. Random walk theory was used to quantify the diffusivities of oxygen interstitials by using the calculated migration barriers. Kinetic Monte Carlo simulations were used to calculate diffusivities of oxygen vacancies by distinguishing the threefold- and fourfold-coordinated lattice oxygen. By combining the equilibrium defect concentrations obtained in our previous work together with the herein calculated diffusivity of each defect species, we present the resulting oxygen self-diffusion coefficients and the corresponding atomistically resolved transport mechanisms. The predicted effective migration barriers and diffusion prefactors are in reasonable agreement with the experimentally reported values. This work provides insights into oxygen diffusion engineering in Zr O2 -related devices and parametrization for continuum transport modeling.
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
Fulger, Daniel; Scalas, Enrico; Germano, Guido
2008-02-01
We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Lévy alpha -stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Lévy alpha -stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space- and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.
Directory of Open Access Journals (Sweden)
Alan D Dangour
2011-04-01
Full Text Available 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.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.Chile's nutritional supplementation program for older people is not effective in reducing the
Dangour, Alan D; Albala, Cecilia; Allen, Elizabeth; Grundy, Emily; Walker, Damian G; Aedo, Cristian; Sanchez, Hugo; Fletcher, Olivia; Elbourne, Diana; Uauy, Ricardo
2011-04-01
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. 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. Chile's nutritional supplementation program for older people is not effective in reducing the incidence of
Directory of Open Access Journals (Sweden)
Scherder Erik JA
2011-08-01
Full Text Available Abstract 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 physical functioning, the progressive cognitive decline, level of depression, anxiety, rest-activity rhythm, QoL, ADL and pain in older people with dementia. Methods/design This study is a longitudinal randomized controlled, single blind study. Ambulatory older people with dementia, who are regular visitors of daily care or living in a home for the elderly or nursing home in the Netherlands, will be randomly allocated to the experimental or control condition. Participants of the experimental group make supervised walks of 30 minutes a day, 5 days a week, as part of their daily nursing care. Participants of the control group will come together three times a week for tea or other sedentary activities to control for possible positive effects of social interaction. All dependent variables will be assessed at baseline and after 6 weeks, and 3, 6, 9, 12 and 18 months of intervention. The dependent variables include neuropsychological tests to assess cognition, physical tests to determine physical functioning, questionnaires to assess ADL, QoL, level of depression and anxiety, actigraphy to assess rest-activity rhythm and pain scales to determine pain levels. Potential moderating variables at baseline are: socio-demographic characteristics, body mass index, subtype of dementia, apolipoprotein E (ApoE genotype, medication use and comorbidities. Discussion This study evaluates the effect of regular walking as a treatment for older people with dementia. The strength of this study is that 1 it has a longitudinal design with multiple repeated measurements, 2 we assess many different health aspects, 3 the intervention is not performed by research staff, but by
Wicks, Keith R
1991-01-01
Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fracta...
Quantum search with multiple walk steps per oracle query
Wong, Thomas G.; Ambainis, Andris
2015-08-01
We identify a key difference between quantum search by discrete- and continuous-time quantum walks: a discrete-time walk typically performs one walk step per oracle query, whereas a continuous-time walk can effectively perform multiple walk steps per query while only counting query time. As a result, we show that continuous-time quantum walks can outperform their discrete-time counterparts, even though both achieve quadratic speedups over their corresponding classical random walks. To provide greater equity, we allow the discrete-time quantum walk to also take multiple walk steps per oracle query while only counting queries. Then it matches the continuous-time algorithm's runtime, but such that it is a cubic speedup over its corresponding classical random walk. This yields a greater-than-quadratic speedup for quantum search over its corresponding classical random walk.
Modeling the External Structure of a Fractals
Kravchenko, Galina
2017-10-01
The article describes the main provisions of the theory of fractal geometry, two- and three-dimensional fractals. The possibility of using the fractal theory in the design of buildings and structures, as well as individual elements of the building structures is proposed. The fractal structure has been developed by parametric methods using program «3D modeling of Fractals» with the help of finite element method.
Spatial Behaviour of Singularities in Fractal- and Gaussian Speckle Fields
DEFF Research Database (Denmark)
Angelsky, Oleg V.; Maksimyak, Alexander P.; Maksimyak, Peter P.
2009-01-01
Peculiarities of the spatial behaviour of the dislocation lines resulting from scattering of coherent radiation from random and fractal rough surfaces are studied. The technique of optical correlation is proposed for diagnostics of phase singularities in a complex speckle field by comparing...
'Human paced' walking: Followers adopt stride time dynamics of leaders
Marmelat, V.C.M.; Delignières, D.; Torre, K.; Beek, P.J.; Daffertshofer, A.
2014-01-01
Isochronous cueing is widely used in gait rehabilitation even though it alters the stride-time dynamics toward anti-persistent rather than the persistent, fractal fluctuations characteristic of human walking. In the present experiment we tested an alternative cueing method: pacing by a human. To
... your legs or feet Movement disorders such as Parkinson's disease Diseases such as arthritis or multiple sclerosis Vision or balance problems Treatment of walking problems depends on the cause. Physical therapy, surgery, or mobility aids may help.
The transience of virtual fractals.
Taylor, R P
2012-01-01
Artists have a long and fruitful tradition of exploiting electronic media to convert static images into dynamic images that evolve with time. Fractal patterns serve as an example: computers allow the observer to zoom in on virtual images and so experience the endless repetition of patterns in a matter that cannot be matched using static images. This year's featured cover artist, Susan Lowedermilk, instead plans to employ persistence of human vision to bring virtual fractals to life. This will be done by incorporating her prints of fractal patterns into zoetropes and phenakistoscopes.
Vlad, Marcel Ovidiu; Schönfisch, Birgitt; Mackey, Michael C.
1996-02-01
The possible occurrence of ergodic behavior for large times is investigated in the case of stationary random processes with memory. It is shown that for finite times the time average of a state function is generally a random variable and thus two types of cumulants can be introduced: for the time average and for the statistical ensemble, respectively. In the limit of infinite time a transition from the random to the deterministic behavior of the time average may occur, resulting in an ergodic behavior. The conditions of occurrence of this transition are investigated by analyzing the scaling behavior of the cumulants of the time average. A general approach for the computation of these cumulants is developed; explicit computations are presented both for short and long memory in the particular case of separable stationary processes for which the cumulants of a statistical ensemble can be factorized into products of functions depending on binary time differences. In both cases the ergodic behavior emerges for large times provided that the cumulants of a statistical ensemble decrease to zero as the time differences increase to infinity. The analysis leads to the surprising conclusion that the scaling behavior of the cumulants of the time average is relatively insensitive to the type of memory considered: both for short and long memory the cumulants of the time average obey inverse different from zero for large time differences, then the time averaage is random even as the length of the total time interval tends to infinity and the ergodic behavior no longer holds. The theory is applied to the study of long range correlations of nucleotide sequences in DNA; in this case the length t of a sequence of nucleotides plays the role of the time variable. A proportionality relationship is established between the cumulants of the pyrimidine excess in a sequence of length t and the cumulants of the time (length) average of the probability of occurrence of a pyrimidine. It is shown
Malagoni, Anna M; Cavazza, Stefano; Ferraresi, Giovanni; Grassi, Guido; Felisatti, Michele; Lamberti, Nicola; Basaglia, Nino; Manfredini, Fabio
2016-06-01
The loss of normal ambulatory function after stroke, besides causing disability, leads to progressive deconditioning and exposes patients to increased risk of cardiovascular diseases and recurrent stroke. Conventional rehabilitation is mainly limited to the subacute period after stroke. Effective, safe and sustainable interventions for patients and healthcare system, including the long-term, should be identified. To verify the feasibility, safety and preliminary efficacy of an original home-based rehabilitation model compared to a standard supervised program in chronic hemiplegic stroke survivors. Pilot, two-arm, parallel group, randomized, controlled clinical trial. Community-dwelling poststroke patient/Hospital. Twelve chronic hemiplegic stroke patients (age=66.5±11.9 years, males, N.=9). Participants were randomly assigned for a 10-week period to a structured home-based exercise program (N.=6) and a standard supervised group-setting program (N.=6). The feasibility outcomes included adherence to interventions, retention rate and safety. Satisfaction was also evaluated by the Client Satisfaction Questionnaire. Efficacy was assessed by the 6-minute walk test, Timed Up and Go and Stair Climb tests. The impact on Quality-of-life was estimated using the physical activity domain of the Short Form-36 questionnaire. Operators' time consuming was also calculated. Adherence was 91% in the home-based exercise group and 92% in the standard supervised group. The retention rate was 100%, with no adverse events reported and high satisfaction scores for both interventions. 6-minute walk test and physical activity domain significantly increased in both groups (P=0.03). Timed Up and Go improved in both groups, significantly for the home-based exercise group (P=0.03) while Stair Climb remained stable. Time required to operators to implement the home-based exercise program was 15 hours vs. 30 hours for the standard supervised one. In a sample of hemiplegic chronic stroke patients
Directory of Open Access Journals (Sweden)
Tsai Feng-Chou
2012-08-01
Full Text Available Abstract Background The invasion-metastasis cascade of cancer involves a process of parallel progression. A biological interface (module in which cells is linked with ECM (extracellular matrix by CAMs (cell adhesion molecules has been proposed as a tool for tracing cancer spatiotemporal dynamics. Methods A mathematical model was established to simulate cancer cell migration. Human uterine leiomyoma specimens, in vitro cell migration assay, quantitative real-time PCR, western blotting, dynamic viscosity, and an in vivo C57BL6 mouse model were used to verify the predictive findings of our model. Results The return to origin probability (RTOP and its related CAM expression ratio in tumors, so-called "tumor self-seeding", gradually decreased with increased tumor size, and approached the 3D Pólya random walk constant (0.340537 in a periodic structure. The biphasic pattern of cancer cell migration revealed that cancer cells initially grew together and subsequently began spreading. A higher viscosity of fillers applied to the cancer surface was associated with a significantly greater inhibitory effect on cancer migration, in accordance with the Stokes-Einstein equation. Conclusion The positional probability and cell-CAM-ECM interface (module in the fractal framework helped us decipher cancer spatiotemporal dynamics; in addition we modeled the methods of cancer control by manipulating the microenvironment plasticity or inhibiting the CAM expression to the Pólya random walk, Pólya constant.
Eternal fractal in the universe
Winitzki, Serge
2002-04-01
Models of eternal inflation predict a stochastic self-similar geometry of the universe at very large scales and allow the existence of points that never thermalize. I explore the fractal geometry of the resulting spacetime, using coordinate-independent quantities. The formalism of stochastic inflation can be used to obtain the fractal dimension of the set of eternally inflating points (the ``eternal fractal''). I also derive a nonlinear branching diffusion equation describing global properties of the eternal set and the probability of realizing eternal inflation. I show gauge invariance of the condition for the presence of eternal inflation. Finally, I consider the question of whether all thermalized regions merge into one connected domain. The fractal dimension of the eternal set provides a (weak) sufficient condition for merging.