Karpatkin, Herb; Cohen, Evan T; Rzetelny, Adam; Parrott, J Scott; Breismeister, Breanne; Hartman, Ryan; Luu, Ronald; Napolione, Danielle
2015-07-01
Fatigue is a common, disabling symptom experienced by persons with multiple sclerosis (MS). Evidence shows that intermittent exercise is associated in improved performance and negligible fatigue. The purpose of this study was to examine whether subjects with MS walk greater distances with less fatigue under intermittent (INT) or continuous (CONT) walking condition. Twenty-seven subjects with MS (median Extended Disability Severity Scale 3.5, interquartile range 1.6) walked in the CONT (ie, 6 uninterrupted minutes) and INT (ie, three 2-minute walking bouts) conditions in a randomized crossover. Distance was measured for the entire 6-minute walking period and each 2-minute increment. Fatigue was measured as the difference in a visual analog scale of fatigue (ΔVAS-F) immediately preceding and following each trial. Participants walked greater distances in the INT condition compared to the CONT condition (P = 0.005). There was a significant interaction of walking condition and time (P walked in the INT condition changed across time. ΔVAS-F was significantly lower in the INT condition than in the CONT condition (P = 0.036). Subjects with MS walked farther, and with less fatigue, when walking intermittently rather than continuously. Persons with MS may be able to tolerate a greater dose of walking training if the walking bouts are intermittent. Further study to determine the benefits of a walking exercise program using intermittent walking is recommended.Video Abstract available for additional insights from the authors (Supplemental Digital Content 1, http://links.lww.com/JNPT/A103).
Random walk polynomials and random walk measures
van Doorn, Erik A.; Schrijner, Pauline
1993-01-01
Random walk polynomials and random walk measures play a prominent role in the analysis of a class of Markov chains called random walks. Without any reference to random walks, however, a random walk polynomial sequence can be defined (and will be defined in this paper) as a polynomial sequence{Pn(x)}
Parmenter, Belinda J; Raymond, Jacqueline; Dinnen, Paul; Singh, Maria A Fiatarone
2011-09-01
There is a subset of older adults with peripheral arterial disease (PAD) who are unable to complete current walking exercise therapy guidelines due to the severity of claudication, presence of foot pathology, arthritis and/or other co-morbidities. Our aim was to therefore systematically review the evidence for the effectiveness of all forms of exercise on claudication in PAD, and subsequently compare walking to alternative modes. An electronic search of the literature was performed from earliest record until March 2011 using a variety of electronic databases. To be included trials must have been a randomized controlled trial of an exercise intervention for adults with intermittent claudication and have reported at least one claudication parameter such as initial (ICT/D) and/or absolute claudication time or distance (ACT/D) measured via a treadmill protocol. Assessment of study quality was performed using a modified version of the Physiotherapy Evidence Database Scale (PEDro). Mean difference and relative effect sizes (ESs) were calculated and adjusted via Hedges' bias-corrected for small sample sizes. Thirty-six trials reported on walking distance in PAD: 32 aerobic (including 20 walking); 4 progressive resistance training (PRT) or graduated weight lifting exercise. In total 1644 subjects (73% male) were studied (1183 underwent exercise training); with few over 75. Most modes and intensities of exercise, irrespective of pain level, significantly improved walking capability (ACD/T Relative ES range 0.5-3.53). However, overall quality of the trials was only modest with on average 6 of the 11 PEDro quality criteria being present (mean 5.8 ± 1.3), and on average sample sizes were small (mean 44 ± 51). Modes of aerobic exercise other than walking appear equally beneficial for claudication and the benefits of PRT and upper body exercise appear promising, but little data are published on these modalities. Additional studies of high quality are required to validate these
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.
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.
Walking training for intermittent claudication in diabetes
Ubels, FL; Links, TP; Sluiter, WJ; Smit, AJ
OBJECTIVE - Walking training (WT) is an established treatment for patients with intermittent claudication (IC). Abnormalities specific to diabetes, such as a relative preponderance of distal lesions and the contribution of microcirculatory disease, might well influence the results of WT. We compared
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.
Daily intermittent hypoxia enhances walking after chronic spinal cord injury
Hayes, Heather B.; Jayaraman, Arun; Herrmann, Megan; Mitchell, Gordon S.; Rymer, William Z.
2014-01-01
Objectives: To test the hypothesis that daily acute intermittent hypoxia (dAIH) and dAIH combined with overground walking improve walking speed and endurance in persons with chronic incomplete spinal cord injury (iSCI). Methods: Nineteen subjects completed the randomized, double-blind, placebo-controlled, crossover study. Participants received 15, 90-second hypoxic exposures (dAIH, fraction of inspired oxygen [Fio2] = 0.09) or daily normoxia (dSHAM, Fio2 = 0.21) at 60-second normoxic intervals on 5 consecutive days; dAIH was given alone or combined with 30 minutes of overground walking 1 hour later. Walking speed and endurance were quantified using 10-Meter and 6-Minute Walk Tests. The trial is registered at ClinicalTrials.gov (NCT01272349). Results: dAIH improved walking speed and endurance. Ten-Meter Walk time improved with dAIH vs dSHAM after 1 day (mean difference [MD] 3.8 seconds, 95% confidence interval [CI] 1.1–6.5 seconds, p = 0.006) and 2 weeks (MD 3.8 seconds, 95% CI 0.9–6.7 seconds, p = 0.010). Six-Minute Walk distance increased with combined dAIH + walking vs dSHAM + walking after 5 days (MD 94.4 m, 95% CI 17.5–171.3 m, p = 0.017) and 1-week follow-up (MD 97.0 m, 95% CI 20.1–173.9 m, p = 0.014). dAIH + walking increased walking distance more than dAIH after 1 day (MD 67.7 m, 95% CI 1.3–134.1 m, p = 0.046), 5 days (MD 107.0 m, 95% CI 40.6–173.4 m, p = 0.002), and 1-week follow-up (MD 136.0 m, 95% CI 65.3–206.6 m, p walking improved walking speed and distance in persons with chronic iSCI. The impact of dAIH is enhanced by combination with walking, demonstrating that combinatorial therapies may promote greater functional benefits in persons with iSCI. Classification of evidence: This study provides Class I evidence that transient hypoxia (through measured breathing treatments), along with overground walking training, improves walking speed and endurance after iSCI. PMID:24285617
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.
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 ...
Mak, Chi H.; Pham, Phuong; Afif, Samir A.; Goodman, Myron F.
2015-01-01
Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C → U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics. PMID:26465508
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.
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 0expressions 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.
Drug therapy for improving walking distance in intermittent claudication
DEFF Research Database (Denmark)
Momsen, Anne-Mette; Jensen, M B; Norager, C B
2009-01-01
To evaluate the efficacy of pharmacological interventions in improving walking capacity and health-related quality of life for people with intermittent claudication. DATASOURCES: We searched Medline, EMBASE, Cochrane library and relevant websites for studies published from the start of the databa...... of the databases to February 2009. In addition, reference lists were manually searched....
When Human Walking is a Random Walk
Hausdorff, J. M.
1998-03-01
The complex, hierarchical locomotor system normally does a remarkable job of controlling an inherently unstable, multi-joint system. Nevertheless, the stride interval --- the duration of a gait cycle --- fluctuates from one stride to the next, even under stationary conditions. We used random walk analysis to study the dynamical properties of these fluctuations under normal conditions and how they change with disease and aging. Random walk analysis of the stride-to-stride fluctuations of healthy, young adult men surprisingly reveals a self-similar pattern: fluctuations at one time scale are statistically similar to those at multiple other time scales (Hausdorff et al, J Appl Phsyiol, 1995). To study the stability of this fractal property, we analyzed data obtained from healthy subjects who walked for 1 hour at their usual pace, as well as at slower and faster speeds. The stride interval fluctuations exhibited long-range correlations with power-law decay for up to a thousand strides at all three walking rates. In contrast, during metronomically-paced walking, these long-range correlations disappeared; variations in the stride interval were uncorrelated and non-fractal (Hausdorff et al, J Appl Phsyiol, 1996). To gain insight into the mechanism(s) responsible for this fractal property, we examined the effects of aging and neurological impairment. Using detrended fluctuation analysis (DFA), we computed α, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. α was significantly lower in healthy elderly subjects compared to young adults (p < .003) and in subjects with Huntington's disease, a neuro-degenerative disorder of the central nervous system, compared to disease-free controls (p < 0.005) (Hausdorff et al, J Appl Phsyiol, 1997). α was also significantly related to degree of functional impairment in subjects with Huntington's disease (r=0.78). Recently, we have observed that just as
Topics in random walks in random environment
International Nuclear Information System (INIS)
Sznitman, A.-S.
2004-01-01
Over the last twenty-five years random motions in random media have been intensively investigated and some new general methods and paradigms have by now emerged. Random walks in random environment constitute one of the canonical models of the field. However in dimension bigger than one they are still poorly understood and many of the basic issues remain to this day unresolved. The present series of lectures attempt to give an account of the progresses which have been made over the last few years, especially in the study of multi-dimensional random walks in random environment with ballistic behavior. (author)
On Convergent Probability of a Random Walk
Lee, Y.-F.; Ching, W.-K.
2006-01-01
This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.
Random walk over a hypersphere
Directory of Open Access Journals (Sweden)
J. M. C. Joshi
1985-01-01
A generalization of Hammersley's result has also been developed. The main purpose of the paper is to show that although the use of characteristic functions, using the method of Bochner, is available in problems of random walk yet distributional S. M. Joshi transform can be used as a natural tool has been proved for the first time in the paper.
A botanical compound, Padma 28, increases walking distance in stable intermittent claudication
DEFF Research Database (Denmark)
Drabaek, H; Mehlsen, J; Himmelstrup, H
1993-01-01
and by measurements of the pain-free and the maximal walking distance on a treadmill. The ankle pressure index (ankle systolic pressure/arm systolic pressure) was calculated. The group randomized to active treatment received two tablets bid containing 340 mg of a dried herbal mixture composed according to an ancient...... lamaistic preparation (Padma 28). After active treatments, administered over a period of four months in a double-blinded, randomized design, the patients allocated to this group attained a significant increase in the pain-free walking distance from 52 m (20-106) to 86 m (24-164; P ...Thirty-six patients with a median age of sixty-seven years and a median duration of intermittent claudication of five years were randomized to either active treatment with Padma 28 or placebo. The effect of treatment was quantified by measurements of systemic and peripheral systolic blood pressures...
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.
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...
Chemical Continuous Time Random Walks
Aquino, Tomás; Dentz, Marco
2017-12-01
Kinetic Monte Carlo methods such as the Gillespie algorithm model chemical reactions as random walks in particle number space. The interreaction times are exponentially distributed under the assumption that the system is well mixed. We introduce an arbitrary interreaction time distribution, which may account for the impact of incomplete mixing on chemical reactions, and in general stochastic reaction delay, which may represent the impact of extrinsic noise. This process defines an inhomogeneous continuous time random walk in particle number space, from which we derive a generalized chemical master equation. This leads naturally to a generalization of the Gillespie algorithm. Based on this formalism, we determine the modified chemical rate laws for different interreaction time distributions. This framework traces Michaelis-Menten-type kinetics back to finite-mean delay times, and predicts time-nonlocal macroscopic reaction kinetics as a consequence of broadly distributed delays. Non-Markovian kinetics exhibit weak ergodicity breaking and show key features of reactions under local nonequilibrium.
Random walks, random fields, and disordered systems
Černý, Jiří; Kotecký, Roman
2015-01-01
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a mod...
Random walks on reductive groups
Benoist, Yves
2016-01-01
The classical theory of Random Walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
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.
Random walks and diffusion on networks
Masuda, Naoki; Porter, Mason A.; Lambiotte, Renaud
2017-11-01
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.
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.
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.
Calf raise exercise increases walking performance in patients with intermittent claudication.
Van Schaardenburgh, Michel; Wohlwend, Martin; Rognmo, Øivind; Mattsson, Erney
2017-05-01
Symptoms of intermittent claudication (IC) are improved by exercise. The improvement might be secondary to increased blood perfusion or increased muscle mitochondrial capacity. Ischemia followed by reperfusion, also named preconditioning, is known to stimulate the mitochondria. We focused on a calf raise exercise inducing preconditioning in the calf muscle of patients with IC. We hypothesized that 8 weeks of this exercise would increase walking performance and mitochondrial capacity without a change in blood flow. Patients with IC were randomized to either a calf raise exercise group (n = 14) or a traditional walking exercise group (n = 15). The calf raise group was instructed to perform a specific type of calf raise exercise three times a day. The walking group was instructed to walk near the pain threshold at least 30 minutes three times a week. Both interventions lasted 8 weeks and were not supervised. Measurements of walking performance, mitochondrial capacity, peak oxygen uptake, peripheral hemodynamics, and health-related quality of life were obtained on each patient before and after the intervention period. Adherence was measured by a training diary, and an activity monitor was used. The calf raise group improved pain-free walking distance by 44 meters (P = .04) and maximal walking distance by 99 meters (P = .047). Furthermore, claudication onset time increased by 123 seconds (P = .02), and peak walking time increased by 104 seconds (P = .01). The calf raise group increased the enzyme citrate synthase activity, which is a biomarker of mitochondrial volume-density in the muscle tissue (P = .02). The walking group did not increase any of these variables. Maximal blood flow, peak oxygen uptake, and mitochondrial respiration did not change in any group. The calf raise group experienced less disease anxiety (P calf raise group and 80% in the walking group. The calf raise group maintained physical activity. A reduction in activity (P Calf raise
Cavalcante, Bruno Remígio; Ritti-Dias, Raphael Mendes; Germano Soares, Antônio Henrique; Domingues, Wagner Jorge Ribeiro; Saes, Glauco Fernandes; Duarte, Flávio Henrique; da Cruz, Aline de Paula; Wolosker, Nelson; Puech-Leão, Pedro; Cucato, Gabriel Grizzo; Zerati, Antonio Eduardo
2017-04-01
We analyze the effects of graduated compression stoking (GCS) on walking capacity and oxygen saturation in intermittent claudication (IC) patients. Eighteen patients with IC performed the 6-minute walking test in 2 conditions in random order: GCS or placebo sock. Onset claudication distance and total walking distance were obtained. The calf muscle oxygen saturation was continuously monitored before, during, and after 6-minute walk test. Comparisons of the walking capacity and StO 2 parameters between GCS and placebo conditions were analyzed by Wilcoxon rank-sum test. The onset claudication distance (GCS: 120 ± 99 meters vs. placebo: 150 ± 126 meters; P = 0.798) and total walking distance (GCS: 330 ± 108 meters vs. placebo: 324 ± 60 meters; P = 0.130) were similar between conditions. There were no differences in StO 2 parameters between conditions (P > 0.05). GCS does not decrease walking performance and calf muscle oxygenation saturation during 6-minute walk test in patients with IC. Copyright © 2016 Elsevier Inc. All rights reserved.
A weighted random walk approximation to fractional Brownian motion
Lindstrøm, Tom
2007-01-01
We present a random walk approximation to fractional Brownian motion where the increments of the fractional random walk are defined as a weighted sum of the past increments of a Bernoulli random walk.
A random walk approximation to fractional Brownian motion
Lindstrøm, Tom
2007-01-01
We present a random walk approximation to fractional Brownian motion where the increments of the fractional random walk are defined as a weighted sum of the past increments of a Bernoulli random walk.
The random walk model of intrafraction movement
International Nuclear Information System (INIS)
Ballhausen, H; Reiner, M; Kantz, S; Belka, C; Söhn, M
2013-01-01
The purpose of this paper is to understand intrafraction movement as a stochastic process driven by random external forces. The hypothetically proposed three-dimensional random walk model has significant impact on optimal PTV margins and offers a quantitatively correct explanation of experimental findings. Properties of the random walk are calculated from first principles, in particular fraction-average population density distributions for displacements along the principal axes. When substituted into the established optimal margin recipes these fraction-average distributions yield safety margins about 30% smaller as compared to the suggested values from end-of-fraction Gaussian fits. Stylized facts of a random walk are identified in clinical data, such as the increase of the standard deviation of displacements with the square root of time. Least squares errors in the comparison to experimental results are reduced by about 50% when accounting for non-Gaussian corrections from the random walk model. (paper)
The random walk model of intrafraction movement.
Ballhausen, H; Reiner, M; Kantz, S; Belka, C; Söhn, M
2013-04-07
The purpose of this paper is to understand intrafraction movement as a stochastic process driven by random external forces. The hypothetically proposed three-dimensional random walk model has significant impact on optimal PTV margins and offers a quantitatively correct explanation of experimental findings. Properties of the random walk are calculated from first principles, in particular fraction-average population density distributions for displacements along the principal axes. When substituted into the established optimal margin recipes these fraction-average distributions yield safety margins about 30% smaller as compared to the suggested values from end-of-fraction gaussian fits. Stylized facts of a random walk are identified in clinical data, such as the increase of the standard deviation of displacements with the square root of time. Least squares errors in the comparison to experimental results are reduced by about 50% when accounting for non-gaussian corrections from the random walk model.
Many random walks are faster than one
Czech Academy of Sciences Publication Activity Database
Alon, N.; Avin, Ch.; Koucký, Michal; Kozma, G.; Lotker, Z.; Tuttle, M.R.
2011-01-01
Roč. 20, č. 4 (2011), s. 481-502 ISSN 0963-5483 R&D Projects: GA ČR GP201/07/P276; GA ČR GA201/05/0124 Institutional research plan: CEZ:AV0Z10190503 Keywords : multiple random walks * parallel random walks Subject RIV: BA - General Mathematics Impact factor: 0.778, year: 2011 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8280727
Lundgren, F; Dahllöf, A G; Lundholm, K; Scherstén, T; Volkmann, R
1989-01-01
This study reports the initial evaluation of treatment efficiency in 75 patients with intermittent claudication who were randomized to three treatment groups: 1) reconstructive surgery, 2) reconstructive surgery with subsequent physical training, and 3) physical training alone. Before treatment, there were no statistically significant differences between the groups in age, sex, smoking habits, symptom duration of claudication, ankle-arm blood pressure quotient (ankle-index), maximal plethysmographic calf blood flow, symptom-free and maximal walking distance, the history of other atherosclerotic manifestations or in the medical treatment. The walking performance was improved in all three groups at follow-up 13 +/- 0.5 months after randomization. Surgery was most effective, but the addition of training to surgery improved the symptom-free walking distance even further. In pooled observations of the three groups, age, symptom duration, and a history of myocardial ischemic disease correlated negatively with walking performance after treatment. In the operated group, the duration of claudication and a history of myocardial ischemic disease correlated negatively with the walking performance. This was not the case when patients were censored if limited by other symptoms than intermittent claudication after treatment. In the trained group, the duration of claudication correlated negatively to symptom-free and maximal walking distance. Ankle-index and maximal plethysmographic calf blood flow after treatment and the change of these variables with treatment correlated positively with both symptom-free and maximal walking distance when results were pooled for all patients. Although this mainly was a consequence of the improved blood flow after surgery, the change of maximal plethysmographic calf blood flow also correlated with symptom-free but not with maximal walking distance in the trained group. The results demonstrate that, compared with physical training alone, operation
Random walk statistics on fractal structures
Rammal, R.
1984-09-01
We consider some statistical properties of simple random walks on fractal structures viewed as networks of sites and bonds: range, renewal theory, mean first passage time, etc. Asymptotic behaviors are shown to be controlled by the fractal ( ¯d) and spectral ( ¯d) dimensionalities of the considered structure. A simple decimation procedure giving the value of ( ¯d) is outlined and illustrated in the case of the Sierpinski gaskets. Recent results for the trapping problem, the self-avoiding walk, and the true-self-avoiding walk are briefly reviewed. New numerical results for diffusion on percolation clusters are also presented.
Coupled continuous time-random walks in quenched random environment
Magdziarz, M.; Szczotka, W.
2018-02-01
We introduce a coupled continuous-time random walk with coupling which is characteristic for Lévy walks. Additionally we assume that the walker moves in a quenched random environment, i.e. the site disorder at each lattice point is fixed in time. We analyze the scaling limit of such a random walk. We show that for large times the behaviour of the analyzed process is exactly the same as in the case of uncoupled quenched trap model for Lévy flights.
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.
Path probabilities of continuous time random walks
International Nuclear Information System (INIS)
Eule, Stephan; Friedrich, Rudolf
2014-01-01
Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman–Kac formulae. (paper)
Path probabilities of continuous time random walks
Eule, Stephan; Friedrich, Rudolf
2014-12-01
Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman-Kac formulae.
Directory of Open Access Journals (Sweden)
Tetsuyou Watanabe
2014-01-01
Full Text Available Intermittent claudication is a walking symptom. Patients with intermittent claudication experience lower limb pain after walking for a short time. However, rest relieves the pain and allows the patient to walk again. Unfortunately, this symptom predominantly arises from not 1 but 2 different diseases: LSS (lumber spinal canal stenosis and PAD (peripheral arterial disease. Patients with LSS can be subdivided by the affected vertebra into 2 main groups: L4 and L5. It is clinically very important to determine whether patients with intermittent claudication suffer from PAD, L4, or L5. This paper presents a novel SVM- (support vector machine- based methodology for such discrimination/differentiation using minimally required data, simple walking motion data in the sagittal plane. We constructed a simple walking measurement system that is easy to set up and calibrate and suitable for use by nonspecialists in small spaces. We analyzed the obtained gait patterns and derived input parameters for SVM that are also visually detectable and medically meaningful/consistent differentiation features. We present a differentiation methodology utilizing an SVM classifier. Leave-one-out cross-validation of differentiation/classification by this method yielded a total accuracy of 83%.
Random walk centrality for temporal networks
International Nuclear Information System (INIS)
Rocha, Luis E C; Masuda, Naoki
2014-01-01
Nodes can be ranked according to their relative importance within a network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based on random walks, for example the PageRank, have focused on static structures. However, several realistic networks are indeed dynamic, meaning that their structure changes in time. In this paper, we propose a centrality measure for temporal networks based on random walks under periodic boundary conditions that we call TempoRank. It is known that, in static networks, the stationary density of the random walk is proportional to the degree or the strength of a node. In contrast, we find that, in temporal networks, the stationary density is proportional to the in-strength of the so-called effective network, a weighted and directed network explicitly constructed from the original sequence of transition matrices. The stationary density also depends on the sojourn probability q, which regulates the tendency of the walker to stay in the node, and on the temporal resolution of the data. We apply our method to human interaction networks and show that although it is important for a node to be connected to another node with many random walkers (one of the principles of the PageRank) at the right moment, this effect is negligible in practice when the time order of link activation is included. (paper)
Random walk centrality for temporal networks
Rocha, Luis E. C.; Masuda, Naoki
2014-06-01
Nodes can be ranked according to their relative importance within a network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based on random walks, for example the PageRank, have focused on static structures. However, several realistic networks are indeed dynamic, meaning that their structure changes in time. In this paper, we propose a centrality measure for temporal networks based on random walks under periodic boundary conditions that we call TempoRank. It is known that, in static networks, the stationary density of the random walk is proportional to the degree or the strength of a node. In contrast, we find that, in temporal networks, the stationary density is proportional to the in-strength of the so-called effective network, a weighted and directed network explicitly constructed from the original sequence of transition matrices. The stationary density also depends on the sojourn probability q, which regulates the tendency of the walker to stay in the node, and on the temporal resolution of the data. We apply our method to human interaction networks and show that although it is important for a node to be connected to another node with many random walkers (one of the principles of the PageRank) at the right moment, this effect is negligible in practice when the time order of link activation is included.
Momsen, A H; Jensen, M B; Norager, C B; Madsen, M R; Vestersgaard-Andersen, T; Lindholt, J S
2010-10-01
Intermittent claudication is a disabling symptom of peripheral arterial disease for which few medical treatments are available. This study investigated the effect of caffeine on physical capacity in patients with intermittent claudication. This randomized double-blind placebo-controlled crossover study included 88 patients recruited by surgeons from outpatient clinics. The participants abstained from caffeine for 48 h before each test and then received either a placebo or oral caffeine (6 mg/kg). After 75 min, pain-free and maximal walking distance on a treadmill, perceived pain, reaction times, postural stability, maximal isometric knee extension strength, submaximal knee extension endurance and cognitive function were measured. The analysis was by intention to treat. Caffeine increased the pain-free walking distance by 20.0 (95 per cent confidence interval 3.7 to 38.8) per cent (P = 0.014), maximal walking distance by 26.6 (12.1 to 43.0) per cent (P postural stability was reduced significantly, by 22.1 (11.7 to 33.4) per cent with eyes open (P < 0.001) and by 21.8 (7.6 to 37.8) per cent with eyes closed (P = 0.002). Neither reaction time nor cognition was affected. In patients with moderate intermittent claudication, caffeine increased walking distance, maximal strength and endurance, but affected balance adversely.
Random Walk Method for Potential Problems
Krishnamurthy, T.; Raju, I. S.
2002-01-01
A local Random Walk Method (RWM) for potential problems governed by Lapalace's and Paragon's equations is developed for two- and three-dimensional problems. The RWM is implemented and demonstrated in a multiprocessor parallel environment on a Beowulf cluster of computers. A speed gain of 16 is achieved as the number of processors is increased from 1 to 23.
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...
A Random Walk on a Circular Path
Ching, W.-K.; Lee, M. S.
2005-01-01
This short note introduces an interesting random walk on a circular path with cards of numbers. By using high school probability theory, it is proved that under some assumptions on the number of cards, the probability that a walker will return to a fixed position will tend to one as the length of the circular path tends to infinity.
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:
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 ...
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 ...
Iterated random walks with shape prior
DEFF Research Database (Denmark)
Pujadas, Esmeralda Ruiz; Kjer, Hans Martin; Piella, Gemma
2016-01-01
We propose a new framework for image segmentation using random walks where a distance shape prior is combined with a region term. The shape prior is weighted by a confidence map to reduce the influence of the prior in high gradient areas and the region term is computed with k-means to estimate th...
Random walks in Euclidean space
Varjú, Péter Pál
2012-01-01
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove a local limit theorem under a suitable moment condition and a necessary non-degeneracy condition. Under stronger hypothesis, we prove a limit theorem on a wide range of scales: between e^(-cl^(1/4)) and l^(1/2), where l is the number of steps.
Random walk of passive tracers among randomly moving obstacles.
Gori, Matteo; Donato, Irene; Floriani, Elena; Nardecchia, Ilaria; Pettini, Marco
2016-04-14
This study is mainly motivated by the need of understanding how the diffusion behavior of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target. By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle among randomly moving and interacting obstacles. The relevant physical quantity which is worked out is the diffusion coefficient of the passive tracer which is computed as a function of the average inter-obstacles distance. The results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its motion can be considerably slowed down.
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.
DEFF Research Database (Denmark)
Svendsen, T L; Jelnes, Rolf; Tønnesen, K H
1986-01-01
The effects of acebutolol (with intrinsic sympathomimetic activity (ISA] and metoprolol (without ISA) on arm blood pressure, ankle systolic blood pressure, claudication distances (CD) and maximal walking distances (MWD) were compared in patients with essential hypertension and intermittent...... claudication. Fourteen patients participated in a long-term, open, randomized cross-over study. After randomization the patients received either acebutolol, 200 mg b.i.d., or metoprolol, 100 mg b.i.d. After eight weeks the drugs were shifted and after another eight weeks they were withdrawn. Arm and ankle...... blood pressure, CD and MWD were determined before randomization and after 4, 8, 12 and 16 weeks, and again 4-6 weeks after withdrawal of the drugs. The arm blood pressure was reduced by 20/13 mmHg after acebutolol and by 22/21 mmHg after metoprolol. In spite of a significant decrease in arm blood...
Malicet, Dominique
2017-12-01
In this paper, we study random walks {g_n=f_{n-1}\\ldots f_0} on the group Homeo ( S 1) of the homeomorphisms of the circle, where the homeomorphisms f k are chosen randomly, independently, with respect to a same probability measure {ν}. We prove that under the only condition that there is no probability measure invariant by {ν}-almost every homeomorphism, the random walk almost surely contracts small intervals. It generalizes what has been known on this subject until now, since various conditions on {ν} were imposed in order to get the phenomenon of contractions. Moreover, we obtain the surprising fact that the rate of contraction is exponential, even in the lack of assumptions of smoothness on the f k 's. We deduce various dynamical consequences on the random walk ( g n ): finiteness of ergodic stationary measures, distribution of the trajectories, asymptotic law of the evaluations, etc. The proof of the main result is based on a modification of the Ávila-Viana's invariance principle, working for continuous cocycles on a space fibred in circles.
The intermittency of vector fields and random-number generators
Kalinin, A. O.; Sokoloff, D. D.; Tutubalin, V. N.
2017-09-01
We examine how well natural random-number generators can reproduce the intermittency phenomena that arise in the transfer of vector fields in random media. A generator based on the analysis of financial indices is suggested as the most promising random-number generator. Is it shown that even this generator, however, fails to reproduce the phenomenon long enough to confidently detect intermittency, while the C++ generator successfully solves this problem. We discuss the prospects of using shell models of turbulence as the desired generator.
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
Jul 4, 2015 ... What is a Branching Random Walk ? Rougly speaking, a branching random walk is a growing collection of particles (or organisms) which starts from a single particle, branch and spread independently of their positions and of the other particles. Parthanil Roy (I.S.I.). Branching random walk. July 04, 2015.
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 ...
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
Jul 4, 2015 ... Branching Random Walk: Description in Words. Parthanil Roy (I.S.I.). Branching random walk. July 04, 2015. 6 / 14 ... independent of each other. This gives rise to the Generation 1. The displacements are (positive and) independent of the branching mechanism. Parthanil Roy (I.S.I.). Branching random walk.
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
Random-walk model of precompound decay
International Nuclear Information System (INIS)
Akkermans, J.M.; Gruppelaar, H.
1981-01-01
It is demonstrated that the dynamics of precompound nuclear decay can be formulated, with regard to emission spectra as well as angular distributions, in terms of a simple random walk of the composite nuclear system. In distinction to other preequilibrium models a discrete time parameter is introduced, corresponding to the number of intranuclear interactions. This random-walk description can be employed to analytically calculate several characteristics of the equilibration process, such as the mean time to emission from an exciton state, the mean first passage time, and the attainment of isotropy. Also a simple and compact description of multi-particle emission is obtained. A necessary and sufficient condition is given for the equivalence of the random-walk and the usual exciton models. As an application some neutron emission spectra of neutron-induced reactions on 127 I at E = 15 to 50 MeV have been calculated. The results show that preequilibrium effects are very important in the first particle emission. In the emission of secondary particles preequilibrium effects need to be included at incoming energies above about 25 MeV. Preequilibrium effects in tertiary emission spectra are not significant below E = 50 MeV. (orig.)
Random walks on generalized Koch networks
International Nuclear Information System (INIS)
Sun, Weigang
2013-01-01
For deterministically growing networks, it is a theoretical challenge to determine the topological properties and dynamical processes. In this paper, we study random walks on generalized Koch networks with features that include an initial state that is a globally connected network to r nodes. In each step, every existing node produces m complete graphs. We then obtain the analytical expressions for first passage time (FPT), average return time (ART), i.e. the average of FPTs for random walks from node i to return to the starting point i for the first time, and average sending time (AST), defined as the average of FPTs from a hub node to all other nodes, excluding the hub itself with regard to network parameters m and r. For this family of Koch networks, the ART of the new emerging nodes is identical and increases with the parameters m or r. In addition, the AST of our networks grows with network size N as N ln N and also increases with parameter m. The results obtained in this paper are the generalizations of random walks for the original Koch network. (paper)
Randomness at the root of things 1: Random walks
Ogborn, Jon; Collins, Simon; Brown, Mick
2003-09-01
This is the first of a pair of articles about randomness in physics. In this article, we use some variations on the idea of a `random walk' to consider first the path of a particle in Brownian motion, and then the random variation to be expected in radioactive decay. The arguments are set in the context of the general importance of randomness both in physics and in everyday life. We think that the ideas could usefully form part of students' A-level work on random decay and quantum phenomena, as well as being good for their general education. In the second article we offer a novel and simple approach to Poisson sequences.
Hood, S C; Moher, D; Barber, G G
1996-10-15
To evaluate the efficacy of pentoxifylline therapy in improving the walking capacity of patients with moderate intermittent claudication. A search of MEDLINE for trials published between 1976 and 1994 inclusive, and a bibliographic review of all articles retrieved. Randomized, placebo-controlled, double-blind clinical trials were selected that evaluated the pain-free walking distance (the distanced walked on a treadmill before the onset of calf pain) and the absolute claudication distance (the maximum distance walked on a treadmill) among patients with moderate intermittent claudication. Twelve study groups in 11 trials were included in the analysis. In addition to information regarding the trial design, patient characteristics, dosages and treatment periods, the means and standard deviations were collected for both the pain-free walking and absolute claudication distances. Trial quality was also assessed. Overall, there was a statistically significant improvement in the pain-free walking distance after pentoxifylline therapy (weighted mean difference 29.4 m [95% confidence interval (CI) 13.0 to 45.9 m]); this finding was based on a total sample of 612 patients (308 in the treatment groups and 304 in the control groups). A significant improvement was also noted in the absolute claudication distance (weighted mean difference 48.4 m [95% CI 18.3 to 78.6 m]); this was based on a total sample of 511 patients (258 in the treatment group and 253 in the control group). In a sensitivity analysis of the pain-free walking distance, significant treatment effects and no statistically significant heterogeneity were found when only trials were included that were "medically eligible" (involved patients with stage II disease and a pain-free walking distance of 50 to 200 m). In a similar sensitivity analysis of the absolute claudication distance, the two conditions resulting in a significant treatment effect and no significant heterogeneity were the inclusion of "medically eligible
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.
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.
Bäck, Maria; Jivegård, Lennart; Johansson, Anna; Nordanstig, Joakim; Svanberg, Therese; Adania, Ulla Wikberg; Sjögren, Petteri
2015-10-05
To evaluate the effects of home-based supervised exercise vs hospital-based supervised exercise, and the effects of home-based supervised exercise vs unsupervised "go home and walk advice" on daily life and corridor-walking capacity, health-related quality of life and patient-reported functional walking capacity in patients with intermittent claudication. Systematic literature searches were conducted in PubMed, EMBASE, ProQuest, the Cumulative Index to Nursing and Allied Health Literature (CINAHL), the Allied and Complementary Medicine Database (AMED), the Cochrane Library, and a number of Health Technology Assessment (HTA)-databases in October 2014. Randomized controlled trials and non-randomized controlled trials (> 100 patients) were considered for inclusion. Data extraction and risk of bias assessment was performed independently and discussed in meetings. Seven randomized controlled trials and 2 non-randomized controlled studies fulfilled the inclusion criteria. The included studies had some, or major, limitations. Based on a low quality of evidence, home-based supervised exercise may lead to less improvement in maximum and pain-free walking distance, and in more improvement in daily life walking capacity, compared with hospital-based supervised exercise. Home-based supervised exercise may improve maximum and pain-free walking distance compared with "go home and walk advice" and result in little or no difference in health-related quality of life and functional walking capacity compared with hospital-based supervised exercise or "go home and walk advice". Further research is needed to establish the optimal exercise modality for these patients.
Random Walk Quantum Clustering Algorithm Based on Space
Xiao, Shufen; Dong, Yumin; Ma, Hongyang
2018-01-01
In the random quantum walk, which is a quantum simulation of the classical walk, data points interacted when selecting the appropriate walk strategy by taking advantage of quantum-entanglement features; thus, the results obtained when the quantum walk is used are different from those when the classical walk is adopted. A new quantum walk clustering algorithm based on space is proposed by applying the quantum walk to clustering analysis. In this algorithm, data points are viewed as walking participants, and similar data points are clustered using the walk function in the pay-off matrix according to a certain rule. The walk process is simplified by implementing a space-combining rule. The proposed algorithm is validated by a simulation test and is proved superior to existing clustering algorithms, namely, Kmeans, PCA + Kmeans, and LDA-Km. The effects of some of the parameters in the proposed algorithm on its performance are also analyzed and discussed. Specific suggestions are provided.
Passive scalar intermittency in random flows
Lin, Zhi
2007-06-01
This thesis concentrates on reconstructing the complete probability density function (PDF) for a passive scalar governed by a random advection-diffusion equation using a variety of mathematical tools, primarily from partial differential equations, perturbation theory, numerical analysis and statistics. First we present a one-dimensional model which is essentially a random translation of pure heat equation. For some deterministic initial data, the ensuing scalar PDF and its statistical moments can be explicitly calculated. We use this model as a testbed for validating a numerical reconstruction procedure for the PDF via orthogonal polynomial expansion. In this model, the Peclet number is shown to be decisive in establishing the transition in the singularity structure of the PDF which affects the effectiveness of the series expansion, from only one algebraic singularity at unit scalar values (small Peclet), to two algebraic singularities at both unit and zero scalar values (large Peclet). Next, we study the more complicated, two-dimensional model in which the underlying flow is a random linear shear in one dimension. For planar, Gaussian random initial data, we identify the scalar PDF as an integral representing a conditional mixing of Gaussian probability measures averaged over all realizations of a single random variable, namely, the renormalized L2-norm of standard Wiener process. Rigorous asymptotic analyses and solid numerical simulation are performed to the integral formulation to study the evolution and the parametric dependence of the scalar PDF. During these analyses, we discover a transient, nonmonotonic "breathing" phenomena that is related to the multiple spatial scales in the initial random field. Lastly, some preliminary analytical and numerical results are presented to explore the potential of applying the reconstruction methodology to more general, physically relevant models, such as a rotating, viscous, wind-driven shallow water equation.
A botanical compound, Padma 28, increases walking distance in stable intermittent claudication
DEFF Research Database (Denmark)
Drabaek, H; Mehlsen, J; Himmelstrup, H
1993-01-01
Thirty-six patients with a median age of sixty-seven years and a median duration of intermittent claudication of five years were randomized to either active treatment with Padma 28 or placebo. The effect of treatment was quantified by measurements of systemic and peripheral systolic blood pressur...
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…
Nordanstig, Joakim; Broeren, Monica; Hensäter, Marlene; Perlander, Angelica; Osterberg, Klas; Jivegård, Lennart
2014-08-01
We used outdoor walking distance measured during 40 minutes as "real-life" outdoor walking capacity in 49 patients with intermittent claudication (IC). The outdoor walking distance was measured by a global positioning system application for a smartphone. The relationships of self-reported maximum walking distance (SR-MWD), the MWD on a graded treadmill test, and the 6-minute maximum walk distance (6MWD) vs outdoors walking capacity were investigated. Also studied were the associations of SR-MWD, MWD, and 6MWD with health-related quality of life assessed with the disease-specific instrument the Vascular Quality of Life Questionnaire (VascuQoL). In this prospective observational cohort study, 49 IC patients underwent an outdoor walking capacity test for 40 minutes, and MWD and 6MWD were measured. SR-MWD was recorded, and all subjects completed the VascuQoL questionnaire. Associations between the different walk estimates and outdoor walking capacity and health-related quality of life were investigated by correlation analysis (Spearman ρ). Outdoor walking distance during 40 minutes was a median 2495 m (range, 1110-3300 m). SR-MWD correlated moderately and MWD correlated strongly to outdoor walking capacity (r = 0.56 and r = 0.65; P walking capacity (r = 0.78; P walked during the 6-minute walk test is closely correlated to outdoor walking capacity and health-related quality of life in IC patients. Our data support the use of 6MWD for routine clinical evaluation of walking capacity in IC patients. Copyright © 2014 Society for Vascular Surgery. Published by Mosby, Inc. All rights reserved.
Excited random walk with periodic cookies
Kozma, Gady; Orenshtein, Tal; Shinkar, Igor
2016-08-01
In this paper we consider an excited random walk on $\\mathbb{Z}$ in identically piled periodic environment. This is a discrete time process on $\\mathbb{Z}$ defined by parameters $(p_1,\\dots p_M) \\in [0,1]^M$ for some positive integer $M$, where the walker upon the $i$-th visit to $z \\in \\mathbb{Z}$ moves to $z+1$ with probability $p_{i\\pmod M}$, and moves to $z-1$ with probability $1-p_{i \\pmod M}$. We give an explicit formula in terms of the parameters $(p_1,\\dots,p_M)$ which determines whether the walk is recurrent, transient to the left, or transient to the right. In particular, in the case that $\\frac{1}{M}\\sum_{i=1}^{M}p_{i}=\\frac {1}{2}$ all behaviors are possible, and may depend on the order of the $p_i$. Our framework allows us to reprove some known results on ERW with no additional effort.
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.
Hageman, David; Gommans, Lindy Nm; Scheltinga, Marc Rm; Teijink, Joep Aw
2017-02-01
Some believe that certain patients with intermittent claudication may be unsuitable for supervised exercise therapy (SET), based on the presence of comorbidities and the possibly increased risks. We conducted a systematic review (MEDLINE, EMBASE and CENTRAL) to summarize evidence on the potential influence of diabetes mellitus (DM) on the response to SET. Randomized and nonrandomized studies that investigated the effect of DM on walking distance after SET in patients with IC were included. Considered outcome measures were maximal, pain-free and functional walking distance (MWD, PFWD and FWD). Three articles met the inclusion criteria ( n = 845). In one study, MWD was 111 meters (128%) longer in the non-DM group compared to the DM group after 3 months of follow-up ( p = 0.056). In a second study, the non-DM group demonstrated a significant increase in PFWD (114 meters, p ⩽ 0.05) after 3 months of follow-up, whereas there was no statistically significant increase for the DM group (54 meters). On the contrary, the largest study of this review did not demonstrate any adverse effect of DM on MWD and FWD after SET. In conclusion, the data evaluating the effects of DM on SET were inadequate to determine if DM impairs the exercise response. While trends in the data do not suggest an impairment, they are not conclusive. Practitioners should consider this limitation when making clinical decisions.
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 ...
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
Global Optimization of Self Avoiding Random Walks using ...
African Journals Online (AJOL)
SARW) and evaluation of the simulated annealing (SA) optimization method in solving the Feyman problem which is an application of self ad voiding random walks. From the results of simulation, graphs of the shortest path among N randomly ...
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 (Ptraining period, Nordic walking training appeared more efficient than training without poles for increasing walk distance on the 6-min walk test for patients with ACS and PAOD. Copyright © 2017. Published by Elsevier Masson SAS.
A botanical compound, Padma 28, increases walking distance in stable intermittent claudication
DEFF Research Database (Denmark)
Drabaek, H; Mehlsen, J; Himmelstrup, H
1993-01-01
and by measurements of the pain-free and the maximal walking distance on a treadmill. The ankle pressure index (ankle systolic pressure/arm systolic pressure) was calculated. The group randomized to active treatment received two tablets bid containing 340 mg of a dried herbal mixture composed according to an ancient...
Ishihara, Tomoaki; Yamashita, Yasunobu; Takasaki, Naoko; Yamamoto, Shuhei; Hayashi, Erika; Tahara, Kayoko; Takenaga, Mitsuko; Yamakawa, Naoki; Ishihara, Tsutomu; Kasahara, Tadashi; Mizushima, Tohru
2013-08-01
Due to the low stability of lipid emulsions, a lipid emulsion of prostaglandin E1 (Lipo-PGE1 ) necessitates daily intravenous drip infusions. To overcome this issue, we developed nanoparticles containing PGE1 (Nano-PGE1 ). Nano-PGE1 showed a good sustained-release profile of PGE1 from the nanoparticles in vitro, which may permit a longer-lasting therapeutic effect to be achieved. We here examined the pharmacological activity of Nano-PGE1 in a rat experimental model of intermittent claudication induced by femoral artery ligation. The walking activity of the rat was tested on a rodent treadmill. Tissue levels of PGE1 were determined by enzyme immunoassay, and skeletal muscle angiogenesis (capillary growth) was monitored by immunohistochemical analysis. PGE1 could be detected in the lesion site one day after the intravenous administration of Nano-PGE1 but not of Lipo-PGE1 . An increased accumulation of Nano-PGE1 in the lesion site compared with control (unlesioned) site was also observed. The ligation procedure reduced the walking activity, which in turn was improved by a single administration of Nano-PGE1 but not of Lipo-PGE1 . The single administration of Nano-PGE1 also stimulated angiogenesis in the skeletal muscle around the ligated artery. The findings of this study suggest that Nano-PGE1 improves the walking activity of femoral artery-ligated rats through the accumulation and sustained release of PGE1 . © 2013 Royal Pharmaceutical Society.
Random walk in dynamically disordered chains: Poisson white noise disorder
International Nuclear Information System (INIS)
Hernandez-Garcia, E.; Pesquera, L.; Rodriguez, M.A.; San Miguel, M.
1989-01-01
Exact solutions are given for a variety of models of random walks in a chain with time-dependent disorder. Dynamic disorder is modeled by white Poisson noise. Models with site-independent (global) and site-dependent (local) disorder are considered. Results are described in terms of an affective random walk in a nondisordered medium. In the cases of global disorder the effective random walk contains multistep transitions, so that the continuous limit is not a diffusion process. In the cases of local disorder the effective process is equivalent to usual random walk in the absence of disorder but with slower diffusion. Difficulties associated with the continuous-limit representation of random walk in a disordered chain are discussed. In particular, the authors consider explicit cases in which taking the continuous limit and averaging over disorder sources do not commute
Temporal dynamics of recurrent airway symptoms and cellular random walk.
Suki, Béla; Frey, Urs
2003-11-01
Asthma is a complex chronic inflammatory disease of the small airways that has dramatically increased in prevalence in industrialized countries during the last decades. Risk factors for adult asthma have been related to the complex array of gene-environment interactions and exposure of the immune system to allergens in early childhood. In genetically predisposed subjects, continuous exposure to environmental agents such as allergens or infections can lead to recurrent airway symptoms characterized by recurrent episodes of airway inflammation and bronchoconstriction with clinical symptoms of cough, dyspnea, or wheezing. In this study, we report that the longterm temporal dynamics of recurrent airway symptoms in a population of unselected infants display a complex intermittent pattern and that the distribution of interepisode intervals follows a power law. We interpret the data by using a model of the dynamics of attack episodes in which an attack is triggered by an avalanche of airway constrictions. We map the dynamics of this model to the known problem of a random walk in the presence of an absorbing boundary in which the walker corresponds to the fluctuations in contractile state of airway smooth muscle cells. These findings may provide new insight into the mechanisms of otherwise unexplained symptom episodes.
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.
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
2017-02-09
Feb 9, 2017 ... Abstract. In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamil- tonians are generators of time translations. Then an attempt has been made to ...
Variational data assimilation using targetted random walks
Cotter, S. L.
2011-02-15
The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis. In either of these scenarios, it can be important to assess uncertainties in the assimilated state. Ideally, it is desirable to have complete information concerning the Bayesian posterior distribution for unknown state given data. We show that complete computational probing of this posterior distribution is now within the reach in the offline situation. We introduce a Markov chain-Monte Carlo (MCMC) method which enables us to directly sample from the Bayesian posterior distribution on the unknown functions of interest given observations. Since we are aware that these methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however, more sophisticated MCMC methods are available which exploit derivative information. For simplicity of exposition, we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number flow in a two-dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces. © 2011 John Wiley & Sons, Ltd.
Analytic results for asymmetric random walk with exponential transition probabilities
International Nuclear Information System (INIS)
Gutkowicz-Krusin, D.; Procaccia, I.; Ross, J.
1978-01-01
We present here exact analytic results for a random walk on a one-dimensional lattice with asymmetric, exponentially distributed jump probabilities. We derive the generating functions of such a walk for a perfect lattice and for a lattice with absorbing boundaries. We obtain solutions for some interesting moment properties, such as mean first passage time, drift velocity, dispersion, and branching ratio for absorption. The symmetric exponential walk is solved as a special case. The scaling of the mean first passage time with the size of the system for the exponentially distributed walk is determined by the symmetry and is independent of the range
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...
Random walks of cytoskeletal motors in open and closed compartments
Lipowsky, R.; Klumpp, S.
2001-01-01
Random walks of molecular motors, which bind to and unbind from cytoskeletal filaments, are studied theoretically. The bound and unbound motors undergo directed and nondirected motion, respectively. Motors in open compartments exhibit anomalous drift velocities. Motors in closed compartments
General discrete random walk with variable absorbing probabilities
van Uem, Theo
2009-01-01
We obtain expected number of arrivals, probability of arrival, absorption probabilities and expected time before absorption for a general discrete random walk with variable absorbing probabilities on a finite interval using Fibonacci numbers
Roerdink, J.B.T.M.; Shuler, K.E.
1985-01-01
The previously developed formalism for the calculation of asymptotic properties of multistate random walks is used to study random walks on several inhomogeneous periodic lattices, where the periodically repeated unit cell contains a number of inequivalent sites, as well as on lattices with a random
A New Random Walk for Replica Detection in WSNs.
Aalsalem, Mohammed Y; Khan, Wazir Zada; Saad, N M; Hossain, Md Shohrab; Atiquzzaman, Mohammed; Khan, Muhammad Khurram
2016-01-01
Wireless Sensor Networks (WSNs) are vulnerable to Node Replication attacks or Clone attacks. Among all the existing clone detection protocols in WSNs, RAWL shows the most promising results by employing Simple Random Walk (SRW). More recently, RAND outperforms RAWL by incorporating Network Division with SRW. Both RAND and RAWL have used SRW for random selection of witness nodes which is problematic because of frequently revisiting the previously passed nodes that leads to longer delays, high expenditures of energy with lower probability that witness nodes intersect. To circumvent this problem, we propose to employ a new kind of constrained random walk, namely Single Stage Memory Random Walk and present a distributed technique called SSRWND (Single Stage Memory Random Walk with Network Division). In SSRWND, single stage memory random walk is combined with network division aiming to decrease the communication and memory costs while keeping the detection probability higher. Through intensive simulations it is verified that SSRWND guarantees higher witness node security with moderate communication and memory overheads. SSRWND is expedient for security oriented application fields of WSNs like military and medical.
A New Random Walk for Replica Detection in WSNs.
Directory of Open Access Journals (Sweden)
Mohammed Y Aalsalem
Full Text Available Wireless Sensor Networks (WSNs are vulnerable to Node Replication attacks or Clone attacks. Among all the existing clone detection protocols in WSNs, RAWL shows the most promising results by employing Simple Random Walk (SRW. More recently, RAND outperforms RAWL by incorporating Network Division with SRW. Both RAND and RAWL have used SRW for random selection of witness nodes which is problematic because of frequently revisiting the previously passed nodes that leads to longer delays, high expenditures of energy with lower probability that witness nodes intersect. To circumvent this problem, we propose to employ a new kind of constrained random walk, namely Single Stage Memory Random Walk and present a distributed technique called SSRWND (Single Stage Memory Random Walk with Network Division. In SSRWND, single stage memory random walk is combined with network division aiming to decrease the communication and memory costs while keeping the detection probability higher. Through intensive simulations it is verified that SSRWND guarantees higher witness node security with moderate communication and memory overheads. SSRWND is expedient for security oriented application fields of WSNs like military and medical.
Intermittent Coronal Loop Oscillations by Random Energy Releases
Mendoza-Briceño, César A.; Erdélyi, Robert
2006-09-01
High-resolution observations by the SOHO and TRACE spacecraft have confirmed the existence of coronal loop oscillations and waves. In a recent work, Mendoza-Briceño et al. studied the heating response of coronal plasma to energy pulses randomly distributed in time and space along coronal loops. In this paper we focus on the oscillatory patterns and other features, such as cool gas blobs traveling along the loop, during the evolution of spatiotemporal randomly heated flux tubes in the corona. The nature of these oscillatory patterns is investigated using wavelet analysis. Periodic features, such as wave packets, with periods of 150-220, 500-600, and 800-1000 s are found. It is also found that the periods increase with the loop length and decrease with the length of the loop segments along which the pulses are injected. On the other hand, the randomly driven intermittent cool plasma blobs that propagate from one footpoint to the other are analyzed. Although plenty of coronal loop oscillations are detected by the cohort of the current high-resolution satellites, there are more controversial observational evidences about the predicted cold plasma blobs.
On Random Walks and Diffusions Related to Parrondo's Games
Pyke, R.
2002-01-01
In a series of papers, G. Harmer and D. Abbott study the behavior of random walks associated with games introduced in 1997 by J. M. R. Parrondo. These games illustrate an apparent paradox that random and deterministic mixtures of losing games may produce winning games. In this paper, classical cyclic random walks on the additive group of integers modulo $m$, a given integer, are used in a straightforward way to derive the strong law limits of a general class of games that contains the Parrond...
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.
TESTING OF BIST AND TURKDEX: RANDOM WALK AND MARKETEFFICIENCY
Directory of Open Access Journals (Sweden)
Gizay DAVER
2013-07-01
Full Text Available We implemented several parametric and non-parametrictests to investigaterandom walk hypothesis and market efficiency theorem for Turkey’s two mainmarkets, Turkish Derivatives Exchange andBorsaİst anbul(new name for İstanbulStock Exchange. 12/02/2007– 08/02/2013 period is our testing period and weuseddaily log returns. According to our findings in the very short term nullhypothesis of random walk is accepted.
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.
A generalized model via random walks for information filtering
International Nuclear Information System (INIS)
Ren, Zhuo-Ming; Kong, Yixiu; Shang, Ming-Sheng; Zhang, Yi-Cheng
2016-01-01
There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation. - Highlights: • We propose a generalized recommendation model employing the random walk dynamics. • The proposed model with single and hybrid of degree information is analyzed. • A strategy with the hybrid degree information improves precision of recommendation.
Post and a random-walk search mode
Martin, J. A.
1984-01-01
Multidisciplinary analysis often requires optimization of nonlinear systems that are subject to constraints. Trajectory optimization is one example of this situation. The Program to Optimize Simulated Trajectories (POST) was used successfully for a number of problems. The purpose is to describe POST and a new optimization approach that has been incorporated into it. Typical uses of POST will also be illustrated. The projected-gradient approach to optimization is the preferred option in POST and is discussed. A new approach to optimization, the random-walk approach, is described, and results with the random-walk approach are presented.
A strong invariance principle for the elephant random walk
Coletti, Cristian F.; Gava, Renato; Schütz, Gunter M.
2017-12-01
We consider a non-Markovian discrete-time random walk on {Z} with unbounded memory, called the elephant random walk (ERW). We prove a strong invariance principle for the ERW. More specifically, we prove that, under a suitable scaling and in the diffusive regime as well as at the critical value p_c=3/4 where the model is marginally superdiffusive, the ERW is almost surely well approximated by a Brownian motion. As a by-product of our result we get the law of iterated logarithm and the central limit theorem for the ERW.
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.
Navigation by anomalous random walks on complex networks
Weng, Tongfeng; Zhang, Jie; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan
2016-11-01
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks.
Computer Challenges: Random Walks in the Classroom.
Gamble, Andy
1982-01-01
Discusses a short computer program used in teaching the random (RND) function in the BASIC programming language. Focuses on the mathematical concepts involved in the program related to elementary probability. (JN)
Inference of random walk models to describe leukocyte migration
Jones, Phoebe J. M.; Sim, Aaron; Taylor, Harriet B.; Bugeon, Laurence; Dallman, Magaret J.; Pereira, Bernard; Stumpf, Michael P. H.; Liepe, Juliane
2015-12-01
While the majority of cells in an organism are static and remain relatively immobile in their tissue, migrating cells occur commonly during developmental processes and are crucial for a functioning immune response. The mode of migration has been described in terms of various types of random walks. To understand the details of the migratory behaviour we rely on mathematical models and their calibration to experimental data. Here we propose an approximate Bayesian inference scheme to calibrate a class of random walk models characterized by a specific, parametric particle re-orientation mechanism to observed trajectory data. We elaborate the concept of transition matrices (TMs) to detect random walk patterns and determine a statistic to quantify these TM to make them applicable for inference schemes. We apply the developed pipeline to in vivo trajectory data of macrophages and neutrophils, extracted from zebrafish that had undergone tail transection. We find that macrophage and neutrophils exhibit very distinct biased persistent random walk patterns, where the strengths of the persistence and bias are spatio-temporally regulated. Furthermore, the movement of macrophages is far less persistent than that of neutrophils in response to wounding.
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.
States recognition in random walk Markov chain via binary Entropy
Directory of Open Access Journals (Sweden)
Morteza Khodabin
2013-03-01
Full Text Available In this paper, a new method for specification of recurrence or transient of states in one and two dimensional simple random walk based on upper and lower bounds of {it r}-combinations from a set of m elements $(C^{m}_{r}$ via binary entropy is introduced.
The Random Walk Drainage Simulation Model as a Teaching Exercise
High, Colin; Richards, Paul
1972-01-01
Practical instructions about using the random walk drainage network simulation model as a teaching excercise are given and the results discussed. A source of directional bias in the resulting simulated drainage patterns is identified and given an interpretation in the terms of the model. Three points of educational value concerning the model are…
Limit distributions of random walks on stochastic matrices
Indian Academy of Sciences (India)
all 2 × 2 rank one stochastic matrices. We show that S(λ), the support of λ, consists of the end points of a countable number of disjoint open intervals and we have calculated the λ-measure of each such point. To the best of our knowledge, these results are new. Keywords. Random walk; stochastic matrices; limiting measure.
Stability of reaction fronts in random walk simulations
Nagy, Noemi; Izsak, F.
A model of propagating reaction fronts is given for simple autocatalytic reactions and the stability of the propagating reaction fronts are studied in several numerical experiments. The corresponding random walk simulations - extending of a recent algorithm - make possible the simultaneous treatment
Random 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.
Experimental Investigation of Percieved Risk in Random Walk Processes
Gneezy, U.; Das, J.W.M.
1996-01-01
The hypothesis that, on average, people accurately estimate probabilities in random walk processes is experimentally investigated.Individuals are confronted with a process that starts with $X, and in every stage either goes up or down by $1, with probabilities p and 1 - p respectively.For different
Averaging in SU(2) open quantum random walk
Clement, Ampadu
2014-03-01
We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.
Two particles' repelling random walks on the complete graph
Chen, Jun
2014-01-01
We consider two particles' repelling random walks on complete graphs. In this model, each particle has higher probability to visit the vertices which have been seldom visited by the other one. By a dynamical approach we prove that the two particles' occupation measure asymptotically has small joint support almost surely if the repulsion is strong enough.
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
2017-02-09
Feb 9, 2017 ... Abstract. In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for ... approach the effective Hamiltonian shows a clear dis- tinction between the two ...... of the results of the earlier work in the same direction in one dimension but differs ...
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.
Symmetry in stochasticity: Random walk models of large-scale ...
Indian Academy of Sciences (India)
This paper describes the insights gained from the excursion set approach, in which various questions about the phenomenology of large-scale structure formation can be mapped to problems associated with the ﬁrst crossing distribution of appropriately deﬁned barriers by random walks. Much of this is summarized in R K ...
Adaptive importance sampling of random walks on continuous state spaces
International Nuclear Information System (INIS)
Baggerly, K.; Cox, D.; Picard, R.
1998-01-01
The authors consider adaptive importance sampling for a random walk with scoring in a general state space. Conditions under which exponential convergence occurs to the zero-variance solution are reviewed. These results generalize previous work for finite, discrete state spaces in Kollman (1993) and in Kollman, Baggerly, Cox, and Picard (1996). This paper is intended for nonstatisticians and includes considerable explanatory material
Averaging in SU(2) open quantum random walk
International Nuclear Information System (INIS)
Ampadu Clement
2014-01-01
We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT
Renewal theory for perturbed random walks and similar processes
Iksanov, Alexander
2016-01-01
This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration. Being of major importance in modern probability theory, both theoretical and applied, these objects have been used to model various phenomena in the natural sciences as well as in insurance and finance. The book also presents the many significant results and efficient techniques and methods that have been worked out in the last decade. The first chapter is devoted to perturbed random walks and discusses their asymptotic behavior and various functionals pertaining to them, including supremum and first-passage time. The second chapter examines perpetuities, presenting results on continuity of their distributions and the existence of moments, as well as weak convergence of divergent perpetuities. Focusing on random processes with immigration, the third chapter investigates the existence of moments, describes long-time behavior and discusses limit theorems, both with and without scaling. Chapters fou...
Amnestically Induced Persistence in Random Walks
Cressoni, J. C.; da Silva, Marco Antonio Alves; Viswanathan, G. M.
2007-02-01
We study how the Hurst exponent α depends on the fraction f of the total time t remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walker’s position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimer’s disease and other dementias.
Pollen Grains, Random Walks and Einstein
Indian Academy of Sciences (India)
all the natural sciences, engineering, linguistics, finance, economics, and even the social sciences. ..... molecule in the system, and hence a randomly directed mean speed. V=J3k;r. (6). The collisions with the molecule ..... combined system of Brownian particles and molecules as a mixture of gases. Then the partial pressure ...
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.
Vibration driven random walk in a Chladni experiment
Energy Technology Data Exchange (ETDEWEB)
Grabec, Igor, E-mail: igor.grabec@amanova.si
2017-01-15
Drifting of sand particles bouncing on a vibrating membrane of a Chladni experiment is characterized statistically. Records of trajectories reveal that bounces are circularly distributed and random. The mean length of their horizontal displacement is approximately proportional to the vibration amplitude above the critical level and amounts about one fourth of the corresponding bounce height. For the description of horizontal drifting of particles a model of vibration driven random walk is proposed that yields a good agreement between experimental and numerically simulated data. - Highlights: • Bouncing of particles in the Chladni experiment is characterized statistically. • Statistical characteristics enable new modeling of Chladni pattern formation. • A new model of vibration driven random walk is introduced. • Good agreement between experimental and simulated data is demonstrated.
Random Walks and Diffusions on Graphs and Databases An Introduction
Blanchard, Philippe
2011-01-01
Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.
Random walks, critical phenomena, and triviality in quantum field theory
International Nuclear Information System (INIS)
Fernandez, R.; Froehlich, J.; Sokal, A.D.
1992-01-01
The subject of this book is equilibrium statistical mechanics - in particular the theory of critical phenomena - and quantum field theory. A general review of the theory of critical phenomena in spin systems, field theories, and random-walk and random-surface models is presented. Among the more technical topics treated in this book, the central theme is the use of random-walk representations as a tool to derive correlation inequalities. The consequences of these inequalities for critical-exponent theory and the triviality question in quantum field theory are expounded in detail. The book contains some previously unpublished results. It addresses both the researcher and the graduate student in modern statistical mechanics and quantum field theory. (orig.)
Spherically symmetric random walks. II. Dimensionally dependent critical behavior
International Nuclear Information System (INIS)
Bender, C.M.; Boettcher, S.; Meisinger, P.N.
1996-01-01
A recently developed model of random walks on a D-dimensional hyperspherical lattice, where D is not restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state distributions of random walkers are obtained for all dimensions D approx-gt 0 by solving a discrete eigenvalue problem. These distributions exhibit dimensionally dependent critical behavior as a function of the birth rate. This remarkably simple model exhibits a second-order phase transition with a universal, nontrivial critical exponent for all dimensions D approx-gt 0. copyright 1996 The American Physical Society
Vaes, Anouk W; Meijer, Kenneth; Delbressine, Jeannet M; Wiechert, Jozé; Willems, Paul; Wouters, Emiel F M; Franssen, Frits M E; Spruit, Martijn A
2015-08-01
Walking aids, such as rollator or draisine, improve mobility and functional exercise performance in individuals with chronic obstructive pulmonary disease (COPD) during an indoor 6-min walk test. However, this test does not reflect everyday walking, which is the most frequently reported problematic activity of daily life in individuals with COPD. To date, efficacy of walking aids during self-paced outdoor walking remains unknown. Therefore, we aimed to determine the efficacy of a rollator and draisine on self-paced outdoor walking in individuals with COPD. Fifteen individuals with COPD (68% men; age: 63 ± 8 years; forced expiratory volume in 1 s: 40 ± 14% predicted) performed three self-paced outdoor walking tests on two consecutive days: test 1 unaided, and tests 2 and 3 with rollator or draisine in random order. Participants had to walk as long as possible at their own pace. The test ended when participants needed to stop, with a maximum duration of 30 min. The use of rollator resulted in the highest walk distance and time (P walked significantly further and longer during an unaided test compared with a draisine aided test (P walking speed, fewer strides, greater stride length, and higher step and stride variability (P walk distance and time in individuals with moderate and advanced COPD and a poor functional exercise capacity, whereas the use of a draisine had a detrimental effect compared with unaided walking. © 2015 Asian Pacific Society of Respirology.
Angular Random Walk Estimation of a Time-Domain Switching Micromachined Gyroscope
2016-10-19
TECHNICAL DOCUMENT 3308 September 2016 Angular Random Walk Estimation of a Time-Domain Switching Micromachined Gyroscope Andrew B. Sabater Paul...angular random walk (ARW), bias instability, and scale factor instability. While there are methods to address issues with bias and scale factor...8 4. ANGULAR RANDOM WALK CHARACTERIZATION
Biasing the random walk of a molecular motor
Energy Technology Data Exchange (ETDEWEB)
Astumian, R Dean [Department of Physics, University of Maine, Orono, ME 04469-5709 (United States)
2005-11-30
Biomolecular motors are often described in mechanical terms, with analogy to cars, turbines, judo throws, levers, etc. It is important to remember however that because of their small size, and because of the aqueous environment in which molecular motors move, viscous drag and thermal noise dominate the inertial forces that drive macroscopic machines. The sequence of motions-conformational changes-by which a motor protein moves can best be described as a random walk, with transitions from one state to another occurring by thermal activation over energy barriers. In this paper I will address the question of how this random walk is biased by a non-equilibrium chemical reaction (ATP hydrolysis) so that the motor molecule moves preferentially (with almost unit certainty) in one direction, even when an external force is applied to drive it in the opposite direction. I will also discuss how these 'soft matter' motors can achieve thermodynamic efficiencies of nearly 100%.
Random walk theory applied to electron avalanche formation
Englert, G. W.
1974-01-01
Use of microscopic detail in random walk theory describing the initial formations of a large number of avalanches shows that concomitant electron transport coefficients quickly relax to equilibrium values. This enables the use of random walks having step sizes and probabilities based only on local electric field strengths and densities. 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 demonstrated for helium. Avalanche growth retardation followed by an abrupt growth augmentation as time proceeds is shown to be associated with the formation of regions of charge density extrema near the avalanche axis and within the axial distance covered by the electron swarm.
Aggregation is the key to succeed in random walks.
Hernandez-Suarez, Carlos M
2016-09-01
In a random walk (RW) in Z an individual starts at 0 and moves at discrete unitary steps to the right or left with respective probabilities p and 1-p. Assuming p > 1/2 and finite a, a > 1, the probability that state a will be reached before -a is Q(a, p) where Q(a, p) > p. Here we introduce the cooperative random walk (CRW) involving two individuals that move independently according to a RW each but dedicate a fraction of time θ to approach the other one unit. This simple strategy seems to be effective in increasing the expected number of individuals arriving to a first. We conjecture that this is a possible underlying mechanism for efficient animal migration under noisy conditions. Copyright © 2016 Elsevier Inc. All rights reserved.
Time domain random walks for hydrodynamic transport in heterogeneous media
Russian, Anna; Dentz, Marco; Gouze, Philippe
2016-05-01
We derive a general formulation of the time domain random walk (TDRW) approach to model the hydrodynamic transport of inert solutes in complex geometries and heterogeneous media. We demonstrate its formal equivalence with the discretized advection-dispersion equation and show that the TDRW is equivalent to a continuous time random walk (CTRW) characterized by space-dependent transition times and transition probabilities. The transition times are exponentially distributed. We discuss the implementation of different concentration boundary conditions and initial conditions as well as the occurrence of numerical dispersion. Furthermore, we propose an extension of the TDRW scheme to account for mobile-immobile multirate mass transfer. Finally, the proposed TDRW scheme is validated by comparison to analytical solutions for spatially homogeneous and heterogeneous transport scenarios.
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.
From elongated spanning trees to vicious random walks
Gorsky, A.; Nechaev, S.; Poghosyan, V. S.; Priezzhev, V. B.
2012-01-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of the paths are grouped in a fashion a $k$--leg watermelon. For large distance $r$ between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as $r^{-\
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.
Simulating intrafraction prostate motion with a random walk model.
Pommer, Tobias; Oh, Jung Hun; Munck Af Rosenschöld, Per; Deasy, Joseph O
2017-01-01
Prostate motion during radiation therapy (ie, intrafraction motion) can cause unwanted loss of radiation dose to the prostate and increased dose to the surrounding organs at risk. A compact but general statistical description of this motion could be useful for simulation of radiation therapy delivery or margin calculations. We investigated whether prostate motion could be modeled with a random walk model. Prostate motion recorded during 548 radiation therapy fractions in 17 patients was analyzed and used for input in a random walk prostate motion model. The recorded motion was categorized on the basis of whether any transient excursions (ie, rapid prostate motion in the anterior and superior direction followed by a return) occurred in the trace and transient motion. This was separately modeled as a large step in the anterior/superior direction followed by a returning large step. Random walk simulations were conducted with and without added artificial transient motion using either motion data from all observed traces or only traces without transient excursions as model input, respectively. A general estimate of motion was derived with reasonable agreement between simulated and observed traces, especially during the first 5 minutes of the excursion-free simulations. Simulated and observed diffusion coefficients agreed within 0.03, 0.2 and 0.3 mm 2 /min in the left/right, superior/inferior, and anterior/posterior directions, respectively. A rapid increase in variance at the start of observed traces was difficult to reproduce and seemed to represent the patient's need to adjust before treatment. This could be estimated somewhat using artificial transient motion. Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during
A Random Walk Phenomenon under an Interesting Stopping Rule
Chakraborty, S.
2007-01-01
In the simple one-dimensional random walk setup, a path is described as follows. Toss a coin. If the result is head, score +1 and move one step forward; otherwise score -1 and move one step backward. One is interested to know the position after a given number of steps. In this paper, once again a coin-tossing experiment is carried out. But this…
A Random Walk Test for Functional Time Series
Mingotti, Nicola; Lillo Rodríguez, Rosa Elvira; Romo Urroz, Juan
2015-01-01
In this paper we introduce a Random Walk test for Functional Autoregressive Processes of Order One. The test is non parametric, based on Bootstrap and Functional Principal Components. The power of the test is shown through an extensive Montecarlo simulation. We apply the test to two real dataset, Bitcoin prices and electrical energy consumption in France. The authors acknowledge financial support from the Spanish Ministry of Economy and Competition, research project ECO2012-38442.
Limit distributions of random walks on stochastic matrices
Indian Academy of Sciences (India)
condition that μm(P) > 0 for some positive integer m (as opposed to just 1, instead of m, considered in [1]), where μm is the ...... Limit distributions of random walks. 611. PROPOSITION 3.2. Let f be as introduced before Proposition 3.1. The probability distribution λ is the image of π by the map b ↦→ f (b). In other words, λ = ∑.
Continuous-Time Random Walks at All Times
Kolomeisky, Anatoly B.
2009-01-01
Continuous-time random walks (CTRW) play important role in understanding of a wide range of phenomena. However, most theoretical studies of these models concentrate only on stationary-state dynamics. We present a new theoretical approach, based on generalized master equations picture, that allowed us to obtain explicit expressions for Laplace transforms for all dynamic quantities for different CTRW models. This theoretical method leads to the effective description of CTRW at all times. Specif...
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.
Continuous time random walk in homogeneous porous media.
Jiang, Jianguo; Wu, Jichun
2013-12-01
Continuous time random walk (CTRW) has been successfully applied in the description of anomalous transport in porous media in recent years. We simulate solute transport in randomly packed spheres with the same diameter and use CTRW to analyze the simulated results. From analysis, we find that there exists weak anomalous transport in the approximately homogeneous porous media. The anomaly becomes more apparent with the increase of Pe. This conclusion consists with previous simulations in two-dimensional homogeneous media and experimental data. We also calculate the trapping probabilities of solute particles in stagnant regions, which could give a physically based explanation for this non-Gaussian behavior. © 2013.
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.
Social aggregation in pea aphids: experiment and random walk modeling.
Nilsen, Christa; Paige, John; Warner, Olivia; Mayhew, Benjamin; Sutley, Ryan; Lam, Matthew; Bernoff, Andrew J; Topaz, Chad M
2013-01-01
From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid's nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control.
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.
Dörenkamp, S; Mesters, E P E; Nijhuis-van der Sanden, M W G; Teijink, J A W; de Bie, R A; Hoogeboom, T J
2016-01-01
The aim of the present study was to assess the degree and impact of patient selection of patients with intermittent claudication undergoing supervised exercise therapy in Randomized Controlled Trials (RCTs) by describing commonly used exclusion criteria, and by comparing baseline characteristics and treatment response measured as improvement in maximum walking distance of patients included in RCTs and patients treated in standard care. We compared data from RCTs with unselected standard care data. First, we systematically reviewed RCTs that investigated the effect of supervised exercise therapy in patients with intermittent claudication. For each of the RCTs, we extracted and categorized the eligibility criteria and their justifications. To assess whether people in RCTs (n = 1,440) differed from patients treated in daily practice (n = 3,513), in terms of demographics, comorbidity and walking capacity, we assessed between group-differences using t-tests. To assess differences in treatment response, we compared walking distances at three and six months between groups using t-tests. Differences of ≥15% were set as a marker for a clinically relevant difference. All 20 included RCTs excluded large segments of patients with intermittent claudication. One-third of the RCTs eligibility criteria were justified. Despite, the numerous eligibility criteria, we found that baseline characteristics were largely comparable. A statistically significant and (borderline) clinically relevant difference in treatment response after three and six months between trial participants and standard care patients was found. Improvements in maximum walking distance after three and six months were significantly and clinically less in trial participants. The finding that baseline characteristics of patients included in RCTs and patients treated in standard care were comparable, may indicate that RCT eligibility criteria are used implicitly by professionals when referring patients to standard
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.
Aging Renewal Theory and Application to Random Walks
Directory of Open Access Journals (Sweden)
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.
Continuous-time random walks that alter environmental transport properties.
Angstmann, C; Henry, B I
2011-12-01
We consider continuous-time random walks (CTRWs) in which the walkers have a finite probability to alter the waiting-time and/or step-length transport properties of their environment, resulting in possibly transient anomalous diffusion. We refer to these CTRWs as transmogrifying continuous-time random walks (TCTRWs) to emphasize that they change the form of the transport properties of their environment, and in a possibly strange way. The particular case in which the CTRW waiting-time density has a finite probability to be permanently altered at a given site, following a visitation by a walker, is considered in detail. Master equations for the probability density function of transmogrifying random walkers are derived, and results are compared with Monte Carlo simulations. An interesting finding is that TCTRWs can generate transient subdiffusion or transient superdiffusion without invoking truncated or tempered power law densities for either the waiting times or the step lengths. The transient subdiffusion or transient superdiffusion arises in TCTRWs with Gaussian step-length densities and exponential waiting-time densities when the altered average waiting time is greater than or less than, respectively, the original average waiting time.
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
International Nuclear Information System (INIS)
Ben-Naim, E.; Daya, Z. A.; Vorobieff, P.; Ecke, R. E.
2001-01-01
We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard-core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with theoretical values
Universality in random-walk models with birth and death
International Nuclear Information System (INIS)
Bender, C.M.; Boettcher, S.; Meisinger, P.N.
1995-01-01
Models of random walks are considered in which walkers are born at one site and die at all other sites. Steady-state distributions of walkers exhibit dimensionally dependent critical behavior as a function of the birth rate. Exact analytical results for a hyperspherical lattice yield a second-order phase transition with a nontrivial critical exponent for all positive dimensions D≠2, 4. Numerical studies of hypercubic and fractal lattices indicate that these exact results are universal. This work elucidates the adsorption transition of polymers at curved interfaces. copyright 1995 The American Physical Society
Analytic method for calculating properties of random walks on networks
Goldhirsch, I.; Gefen, Y.
1986-01-01
A method for calculating the properties of discrete random walks on networks is presented. The method divides complex networks into simpler units whose contribution to the mean first-passage time is calculated. The simplified network is then further iterated. The method is demonstrated by calculating mean first-passage times on a segment, a segment with a single dangling bond, a segment with many dangling bonds, and a looplike structure. The results are analyzed and related to the applicability of the Einstein relation between conductance and diffusion.
Coordinated Search for a Random Walk Target Motion
El-Hadidy, Mohamed Abd Allah; Abou-Gabal, Hamdy M.
This paper presents the cooperation between two searchers at the origin to find a Random Walk moving target on the real line. No information is not available about the target’s position all the time. Rather than finding the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite, we show the existence of the optimal search strategy which minimizes this first meeting time. The effectiveness of this model is illustrated using a numerical example.
Random-walk topological transition revealed via electron counting
Engelhardt, G.; Benito, M.; Platero, G.; Schaller, G.; Brandes, T.
2017-12-01
The appearance of topological effects in systems exhibiting a nontrivial topological band structure strongly relies on the coherent wave nature of the equations of motion. Here, we reveal topological dynamics in a classical stochastic random walk version of the Su-Schrieffer-Heeger model with no relation to coherent wave dynamics. We explain that the commonly used topological invariant in the momentum space translates into an invariant in a counting-field space. This invariant gives rise to clear signatures of the topological phase in an associated escape time distribution.
Grid-free simulation of diffusion using random walk methods
Ghoniem, A. F.; Sherman, F. S.
1985-01-01
The simulation of the diffusion of a continuum field by the random walk (RW) displacement of a set of particles is considered. Elements of the gradients of the diffusive concentration are transported by computational particles. It is demonstrated that, by the use of concentration gradients in the RW process, statistical errors are reduced and each realization of the numerical solution is a representation of the exact solution. The algorithm is grid-free, and the computational elements move to follow the gradients; hence, the algorithm is self-adaptive, and uniform resolution is achieved for all times.
Time-delayed fronts from biased random walks
International Nuclear Information System (INIS)
Fort, Joaquim; Pujol, Toni
2007-01-01
We generalize a previous model of time-delayed reaction-diffusion fronts (Fort and Mendez 1999 Phys. Rev. Lett. 82 867) to allow for a bias in the microscopic random walk of particles or individuals. We also present a second model which takes the time order of events (diffusion and reproduction) into account. As an example, we apply them to the human invasion front across the USA in the 19th century. The corrections relative to the previous model are substantial. Our results are relevant to physical and biological systems with anisotropic fronts, including particle diffusion in disordered lattices, population invasions, the spread of epidemics, etc
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.
Integrable 2D Lorentzian gravity and random walks
Energy Technology Data Exchange (ETDEWEB)
Di Francesco, P. E-mail: philippe@spht.saclay.cea.fr; Guitter, E. E-mail: guitter@spht.saclay.cea.fr; Kristjansen, C. E-mail: kristjan@alf.nbi.dk
2000-02-21
We introduce and solve a family of discrete models of 2D Lorentzian gravity with higher curvature weight, which possess mutually commuting transfer matrices, and whose spectral parameter interpolates between flat and curved space-times. We further establish a one-to-one correspondence between Lorentzian triangulations and directed random walks. This gives a simple explanation why the Lorentzian triangulations have fractal dimension 2 and why the curvature model lies in the universality class of pure Lorentzian gravity. We also study integrable generalizations of the curvature model with arbitrary polygonal tiles. All of them are found to lie in the same universality class.
Continuous-time random walks at all times.
Kolomeisky, Anatoly B
2009-12-21
Continuous-time random walks (CTRW) play an important role in understanding of a wide range of phenomena. However, most theoretical studies of these models concentrate only on dynamics at long times. We present a new theoretical approach, based on generalized master equations picture, which allowed us to obtain explicit expressions for Laplace transforms for all dynamic quantities for different CTRW models. This theoretical method leads to the effective description of CTRW at all times. Specific calculations are performed for homogeneous, periodic models and for CTRW with irreversible detachments. The approach to stationary states for CTRW is analyzed. Our results are also used to analyze generalized fluctuations theorem.
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.
The Random Walk Model Based on Bipartite Network
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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
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.
Moving Image Signal Processing By Markovian Random Walk Approach
Ma, Yung-Lung; Ma, Chialo; Tu, Tsing-Yee
1988-07-01
A moving object recognition approach is presented in this paper. The motion of an object includes the linear or nonlinear translation and rotation. For a 3-D object, the images taken by a camera are in planar form. They are varied by different distances between camera and the object, variant angles and timing for taking pictures. However, the change rate among these images taken at different instant are logically related. The brightness level between any two neighbour string cells of machine digital scanning raster varies according to the Markovian random walk process. Thus, the direction and position of a moving object can be found by the variations of the cell random walk. The angles between a machine digital scanning raster and the edges of an object in a planar image are called pseudo-refractional angles. The variations of angles can be used as features for object recognition. Together with the Kolmogorov complexity program, the probability function of the process can be changed into a finite length of string arrays to simplify the recognition procedure. The distance between camera and the object can be measured by a radar or supersonic signal for military or industrial applications.
Real-Time Signal Processing By Markovian Random Walk Approach
Ma, Yung-Lung; Tu, Tsing-Yee; Ma, Chialo
1989-12-01
A moving object recognition approach is presented in this paper. The motion of an object includes the linear or nonlinear translation and rotation. For a 3-D object, the images taken by a camera are in planar form. They are varied by different distances between camera and the object, variant angles and timing for taking. pictures. However, the change rate among these images taken at different instant are logically related. The brightness level between any two neighbour string cells of machine digital scanning raster varies according to the Markovian random walk process. Thus, the direction and position of a moving object can be found by the variations of the cell random walk. The angles between a machine digital scanning raster and the edges of an object in a planar image are called pseudo-refractional angles. The variations of angles can be used as features for object recognition. Together with the Kolmogorov complexity program, the probability function of the process can be changed into a finite length of string arrays to simplify the recognition procedure. The distance between camera and the object can be measured by a radar or supersonic signal for military or industrial applications.
Continuous time random walks for the evolution of Lagrangian velocities
Dentz, Marco; Kang, Peter K.; Comolli, Alessandro; Le Borgne, Tanguy; Lester, Daniel R.
2016-11-01
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes the persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model the persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space-continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have nonstationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and nonstationary conditions. We provide explicit expressions for the Lagrangian velocity statistics and determine the behaviors of the mean particle velocity, velocity covariance, and particle dispersion. We find strong Lagrangian correlation and anomalous dispersion for velocity distributions that are tailed toward low velocities as well as marked differences depending on the initial conditions. The developed CTRW approach predicts the Lagrangian particle dynamics from an arbitrary initial condition based on the Eulerian velocity distribution and a characteristic correlation scale.
Random-walk simulation of the Schrodinger equation: H+3
International Nuclear Information System (INIS)
Anderson, J.B.
1975-01-01
A simple random-walk method for obtaining ab initio solutions of the Schrodinger equation is examined in its application to the case of the molecular ion H + 3 in the equilateral triangle configuration with side length R=1.66 bohr. The method, which is based on the similarity of the Schrodinger equation and the diffusion equation, involves the random movement of imaginary particles (psips) in electron configuration space subject to a variable chance of multiplication or disappearance. The computation requirements for high accuracy in determining energies of H + 3 are greater than those of existing LCAO--MO--SCF--CI methods. For more complex molecular systems the method may be competitive. (auth)
Influence of the random walk finite step on the first-passage probability
Klimenkova, Olga; Menshutin, Anton; Shchur, Lev
2018-01-01
A well known connection between first-passage probability of random walk and distribution of electrical potential described by Laplace equation is studied. We simulate random walk in the plane numerically as a discrete time process with fixed step length. We measure first-passage probability to touch the absorbing sphere of radius R in 2D. We found a regular deviation of the first-passage probability from the exact function, which we attribute to the finiteness of the random walk step.
Random Walks in Stock Exchange Prices and the Vienna Stock Exchange
Huber, Peter
1995-01-01
This paper uses the multiple variance ratio test procedure developed by Chow and Denning (1993) to test for a random walk of stock returns on the Austrian Stock Exchange. I find that with daily data the test rejects the random walk hypothesis at all conventional significance levels for each and every title and for both indeces tested. Individual shares, however, do seem to follow a random walk when weekly returns are considered, while the hypothesis is rejected for both indices. Dieser Art...
1986-02-04
M NRL Memorandum Report 5719 An Examination of Models of Relaxation in Complex Systems 1. Continuous Time Random Walk ( CTRW ) Models K. L. NGAI, R. W...Examination of Models of Relaxation in Complex Systems I. Continuous Time Random Walk ( CTRW ) Models E. PSRSONAL AUTHOR(S) Ntgi, K.L., Rendell. R.W...necessary and idenrify by block number) Models of relaxation in complex systemL based on the continuous time random walk ( CTRW ) formalism are examined on
Some Tests of Random Walk Hypothesis for Bulgarian Foreign Exchange Rates
Nikolai Gueorguiev
1993-01-01
The objective of this paper is to check if the exchange rate in newly emerged, relatively thin foreign exchange markets, follows a random walk pattern. The findings of the current study cast doubts on random walk presence in Bulgarian exchange rates against major international currencies. It turns out that the series of daily returns are stationary but correlated and therefore can be modelled better by higher-order ARIMA processes than by random walk.
Cognitive-Behavioral Therapy for Intermittent Explosive Disorder: A Pilot Randomized Clinical Trial
McCloskey, Michael S.; Noblett, Kurtis L.; Deffenbacher, Jerry L.; Gollan, Jackie K.; Coccaro, Emil F.
2008-01-01
No randomized clinical trials have evaluated the efficacy of psychotherapy for intermittent explosive disorder (IED). In the present study, the authors tested the efficacy of 12-week group and individual cognitive-behavioral therapies (adapted from J. L. Deffenbacher & M. McKay, 2000) by comparing them with a wait-list control in a randomized…
Koerkamp, Bas Groot; Spronk, Sandra; Stijnen, Theo; Hunink, M. G. Myriam
2010-01-01
The aim of this study is to design the optimal study comparing endovascular revascularization and supervised exercise training for patients with intermittent claudication and to demonstrate value of information (VOI) analysis of patient-level data from an economic randomized controlled trial to
Predicting genetic interactions with random walks on biological networks
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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
The average inter-crossing number of equilateral random walks and polygons
International Nuclear Information System (INIS)
Diao, Y; Dobay, A; Stasiak, A
2005-01-01
In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is a = 3ln2/8 ∼ 0.2599. In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance ρ apart and ρ is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of ρ. Our simulation result shows that the model in fact works very well for the entire range of ρ. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well
From elongated spanning trees to vicious random walks
Gorsky, A.; Nechaev, S.; Poghosyan, V. S.; Priezzhev, V. B.
2013-05-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of k paths (k is odd) along branches of trees or, equivalently, k loop-erased random walks. Starting and ending points of the paths are grouped such that they form a k-leg watermelon. For large distance r between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as r-ν log r with ν = (k2 - 1) / 2. Considering the spanning forest stretched along the meridian of this watermelon, we show that the two-dimensional k-leg loop-erased watermelon exponent ν is converting into the scaling exponent for the reunion probability (at a given point) of k (1 + 1)-dimensional vicious walkers, ν˜ =k2 / 2. At the end, we express the conjectures about the possible relation to integrable systems.
Fluid-fluid interfacial mobility from random walks
Barclay, Paul L.; Lukes, Jennifer R.
2017-12-01
Dual control volume grand canonical molecular dynamics is used to perform the first calculation of fluid-fluid interfacial mobilities. The mobility is calculated from one-dimensional random walks of the interface by relating the diffusion coefficient to the interfacial mobility. Three different calculation methods are employed: one using the interfacial position variance as a function of time, one using the mean-squared interfacial displacement, and one using the time-autocorrelation of the interfacial velocity. The mobility is calculated for two liquid-liquid interfaces and one liquid-vapor interface to examine the robustness of the methods. Excellent agreement between the three calculation methods is shown for all the three interfaces, indicating that any of them could be used to calculate the interfacial mobility.
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.
Complex networks: when random walk dynamics equals synchronization
International Nuclear Information System (INIS)
Kriener, Birgit; Anand, Lishma; Timme, Marc
2012-01-01
Synchrony prevalently emerges from the interactions of coupled dynamical units. For simple systems such as networks of phase oscillators, the asymptotic synchronization process is assumed to be equivalent to a Markov process that models standard diffusion or random walks on the same network topology. In this paper, we analytically derive the conditions for such equivalence for networks of pulse-coupled oscillators, which serve as models for neurons and pacemaker cells interacting by exchanging electric pulses or fireflies interacting via light flashes. We find that the pulse synchronization process is less simple, but there are classes of, e.g., network topologies that ensure equivalence. In particular, local dynamical operators are required to be doubly stochastic. These results provide a natural link between stochastic processes and deterministic synchronization on networks. Tools for analyzing diffusion (or, more generally, Markov processes) may now be transferred to pin down features of synchronization in networks of pulse-coupled units such as neural circuits. (paper)
Information filtering via biased random walk on coupled social network.
Nie, Da-Cheng; Zhang, Zi-Ke; Dong, Qiang; Sun, Chongjing; Fu, Yan
2014-01-01
The recommender systems have advanced a great deal in the past two decades. However, most researchers focus their attentions on mining the similarities among users or objects in recommender systems and overlook the social influence which plays an important role in users' purchase process. In this paper, we design a biased random walk algorithm on coupled social networks which gives recommendation results based on both social interests and users' preference. Numerical analyses on two real data sets, Epinions and Friendfeed, demonstrate the improvement of recommendation performance by taking social interests into account, and experimental results show that our algorithm can alleviate the user cold-start problem more effectively compared with the mass diffusion and user-based collaborative filtering methods.
Scattering quantum random-walk search with errors
International Nuclear Information System (INIS)
Gabris, A.; Kiss, T.; Jex, I.
2007-01-01
We analyze the realization of a quantum-walk search algorithm in a passive, linear optical network. The specific model enables us to consider the effect of realistic sources of noise and losses on the search efficiency. Photon loss uniform in all directions is shown to lead to the rescaling of search time. Deviation from directional uniformity leads to the enhancement of the search efficiency compared to uniform loss with the same average. In certain cases even increasing loss in some of the directions can improve search efficiency. We show that while we approach the classical limit of the general search algorithm by introducing random phase fluctuations, its utility for searching is lost. Using numerical methods, we found that for static phase errors the averaged search efficiency displays a damped oscillatory behavior that asymptotically tends to a nonzero value
From elongated spanning trees to vicious random walks
International Nuclear Information System (INIS)
Gorsky, A.; Nechaev, S.; Poghosyan, V.S.; Priezzhev, V.B.
2013-01-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of k paths (k is odd) along branches of trees or, equivalently, k loop-erased random walks. Starting and ending points of the paths are grouped such that they form a k-leg watermelon. For large distance r between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as r −ν logr with ν=(k 2 −1)/2. Considering the spanning forest stretched along the meridian of this watermelon, we show that the two-dimensional k-leg loop-erased watermelon exponent ν is converting into the scaling exponent for the reunion probability (at a given point) of k(1+1)-dimensional vicious walkers, ν -tilde= k 2 /2. At the end, we express the conjectures about the possible relation to integrable systems
Continuous Time Random Walk (CTRW) put to work
Scher, Harvey
2017-12-01
A personal history of the first applications of CTRW to the physics of transport and diffusion in disordered media is presented. The sequence of steps leading to the introduction of novel ψ(t), the probability density of particle-transfer times, without moments is briefly outlined. The key concept that emerged from those early applications is anomalous or non-Fickian transport. The latter involved spatial moments of the particle propagator with completely different time behavior, e.g., the mean ∝ tβ, 0 /σ = constant. With these results many puzzling experimental data were explained. The data ranged from electronic dynamics of amorphous films to chemical migration and interaction in the subsurface of the Earth. These were not anticipated results but a consequence of the CTRW with these special ψ(t). 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.
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.
Subdiffusion in time-averaged, confined random walks.
Neusius, Thomas; Sokolov, Igor M; Smith, Jeremy C
2009-07-01
Certain techniques characterizing diffusive processes, such as single-particle tracking or molecular dynamics simulation, provide time averages rather than ensemble averages. Whereas the ensemble-averaged mean-squared displacement (MSD) of an unbounded continuous time random walk (CTRW) with a broad distribution of waiting times exhibits subdiffusion, the time-averaged MSD, delta2, does not. We demonstrate that, in contrast to the unbounded CTRW, in which delta2 is linear in the lag time Delta, the time-averaged MSD of the CTRW of a walker confined to a finite volume is sublinear in Delta, i.e., for long lag times delta2 approximately Delta1-alpha. The present results permit the application of CTRW to interpret time-averaged experimental quantities.
A random walk in the land of precompound decay
International Nuclear Information System (INIS)
Akkermans, J.M.
1982-09-01
Several aspects of precompound-decay (preequilibrium) reactions, relevant for the application to fusion-reactor design, are considered. Preequilibrium angular distributions are discussed in the framework of the generalized exciton model. A critical discussion of the theory is given and various refinements are suggested. A comparison is made with experimental data on 14 MeV neutron-induced reactions for a large number of nuclides covering the whole mass range. The exciton model is further generalized to the description of multiparticle emission. Preequilibrium effects in multiple emission are investigated. Computational aspects of preequilibrium theory are examined whereby the exact solution for the mean exciton-state lifetimes is derived in closed form. A random-walk model of precompound decay is developed. The dynamics of the nuclear relaxation process and the fluctuations originating from its stochastic nature are studied in detail. Uncertainty calculations are presented for the exciton-state lifetimes and the emission cross-sections. (Auth.)
Oxygenation of the calf muscle during an incremental, intermittent walking exercise assessed by NIRS
Härtel, S.; Kutzner, C.; Schneider, D.; Grieger, S.; Neumaier, M.; Kohl-Bareis, M.
2011-07-01
We use near infrared spectroscopy (NIRS) for the non-invasive assessment of calf oxygenation during a new walking protocol in healthy subjects of different fitness levels. The protocol increases the exercise power by an increase of the skew rather than speed, and the incremental power steps are intermitted by a 30 s rest which serves for blood sampling. The NIRS measurement parameter of tissue oxygenation are discussed, and a high correlation of the oxygen saturation (tissue oxygenation index) difference between exercise and rest period with exercise power is observed. This difference parameter can be interpreted as strongly linked to blood flow rather than oxygenation. This finding is supported by comparison with spirometry data. The effect of training is discussed. The exercise protocol is suited for testing unfit, or older subjects and the data discussed here servers as a test for a larger trial with heart clinic patients.
A random walk approach to stochastic neutron transport
International Nuclear Information System (INIS)
Mulatier, Clelia de
2015-01-01
One of the key goals of nuclear reactor physics is to determine the distribution of the neutron population within a reactor core. This population indeed fluctuates due to the stochastic nature of the interactions of the neutrons with the nuclei of the surrounding medium: scattering, emission of neutrons from fission events and capture by nuclear absorption. Due to these physical mechanisms, the stochastic process performed by neutrons is a branching random walk. For most applications, the neutron population considered is very large, and all physical observables related to its behaviour, such as the heat production due to fissions, are well characterised by their average values. Generally, these mean quantities are governed by the classical neutron transport equation, called linear Boltzmann equation. During my PhD, using tools from branching random walks and anomalous diffusion, I have tackled two aspects of neutron transport that cannot be approached by the linear Boltzmann equation. First, thanks to the Feynman-Kac backward formalism, I have characterised the phenomenon of 'neutron clustering' that has been highlighted for low-density configuration of neutrons and results from strong fluctuations in space and time of the neutron population. Then, I focused on several properties of anomalous (non-exponential) transport, that can model neutron transport in strongly heterogeneous and disordered media, such as pebble-bed reactors. One of the novel aspects of this work is that problems are treated in the presence of boundaries. Indeed, even though real systems are finite (confined geometries), most of previously existing results were obtained for infinite systems. (author) [fr
Continuous Time Open Quantum Random Walks and Non-Markovian Lindblad Master Equations
Pellegrini, Clément
2014-02-01
A new type of quantum random walks, called Open Quantum Random Walks, has been developed and studied in Attal et al. (Open quantum random walks, preprint) and (Central limit theorems for open quantum random walks, preprint). In this article we present a natural continuous time extension of these Open Quantum Random Walks. This continuous time version is obtained by taking a continuous time limit of the discrete time Open Quantum Random Walks. This approximation procedure is based on some adaptation of Repeated Quantum Interactions Theory (Attal and Pautrat in Annales Henri Poincaré Physique Théorique 7:59-104, 2006) coupled with the use of correlated projectors (Breuer in Phys Rev A 75:022103, 2007). The limit evolutions obtained this way give rise to a particular type of quantum master equations. These equations appeared originally in the non-Markovian generalization of the Lindblad theory (Breuer in Phys Rev A 75:022103, 2007). We also investigate the continuous time limits of the quantum trajectories associated with Open Quantum Random Walks. We show that the limit evolutions in this context are described by jump stochastic differential equations. Finally we present a physical example which can be described in terms of Open Quantum Random Walks and their associated continuous time limits.
Random walk generated by random permutations of {1, 2, 3, ..., n + 1}
International Nuclear Information System (INIS)
Oshanin, G; Voituriez, R
2004-01-01
We study properties of a non-Markovian random walk X (n) l , l = 0, 1, 2, ..., n, evolving in discrete time l on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the rise-and-descent sequences characterizing random permutations π of [n + 1] = {1, 2, 3, ..., n + 1}. We determine exactly the probability of finding the end-point X n = X (n) n of the trajectory of such a permutation-generated random walk (PGRW) at site X, and show that in the limit n → ∞ it converges to a normal distribution with a smaller, compared to the conventional Polya random walk, diffusion coefficient. We formulate, as well, an auxiliary stochastic process whose distribution is identical to the distribution of the intermediate points X (n) l , l < n, which enables us to obtain the probability measure of different excursions and to define the asymptotic distribution of the number of 'turns' of the PGRW trajectories
Directory of Open Access Journals (Sweden)
Karen Wallman
2010-03-01
Full Text Available This study compared the effects of 12 weeks of caloric restriction and interval exercise (INT and caloric restriction and continuous aerobic exercise (CON on physiological outcomes in an obese population. Forty-four individuals (BMI > 30 kg·m-2 were randomised into the INT or CON group. Participant withdrawal resulted in 12 and 14 participants in the INT and CON groups, respectively. All participants were on a strict monitored diet. Exercise involved two 15-min bouts of walking performed on five days per week. Interval exercise consisted of a 2:1 min ratio of low-intensity (40-45% VO2peak and high- intensity (70-75% VO2peak exercise, while the CON group exercised between 50-55% VO2peak. Exercise duration and average intensity (%VO2peak were similar between groups. There were no significant differences (p > 0.05 between the two groups for any variable assessed apart from very low density lipoprotein (VLDL-C, which significantly decreased over time in the INT group only (p < 0.05, d = 1.03. Caloric restriction and interval exercise compared to caloric restriction and continuous aerobic exercise resulted in similar outcome measures apart from VLDL-C levels, which significantly improved in the INT group only
Exercise training for intermittent claudication.
McDermott, Mary M
2017-11-01
The objective of this study was to provide an overview of evidence regarding exercise therapies for patients with lower extremity peripheral artery disease (PAD). This manuscript summarizes the content of a lecture delivered as part of the 2016 Crawford Critical Issues Symposium. Multiple randomized clinical trials demonstrate that supervised treadmill exercise significantly improves treadmill walking performance in people with PAD and intermittent claudication symptoms. A meta-analysis of 25 randomized trials demonstrated a 180-meter increase in treadmill walking distance in response to supervised exercise interventions compared with a nonexercising control group. Supervised treadmill exercise has been inaccessible to many patients with PAD because of lack of medical insurance coverage. However, in 2017, the Centers for Medicare and Medicaid Services issued a decision memorandum to support health insurance coverage of 12 weeks of supervised treadmill exercise for patients with walking impairment due to PAD. Recent evidence also supports home-based walking exercise to improve walking performance in people with PAD. Effective home-exercise programs incorporate behavioral change interventions such as a remote coach, goal setting, and self-monitoring. Supervised treadmill exercise programs preferentially improve treadmill walking performance, whereas home-based walking exercise programs preferentially improve corridor walking, such as the 6-minute walk test. Clinical trial evidence also supports arm or leg ergometry exercise to improve walking endurance in people with PAD. Treadmill walking exercise appears superior to resistance training alone for improving walking endurance. Supervised treadmill exercise significantly improves treadmill walking performance in people with PAD by approximately 180 meters compared with no exercise. Recent evidence suggests that home-based exercise is also effective and preferentially improves over-ground walking performance, such as
Holahan, M; Abood, S; Hauptman, J; Koenigsknecht, C; Brown, A
2010-01-01
Malnutrition is a common problem in critically ill dogs and is associated with increased morbidity and mortality in human medicine. Enteral nutrition (EN) delivery methods have been evaluated in humans to determine which is most effective in achieving caloric goals. To compare continuous infusion and intermittent bolus feeding of EN in dogs admitted to a critical care unit. Fifty-four dogs admitted to the critical care unit and requiring nutritional support with a nasoenteric feeding tube. Prospective randomized clinical trial. Dogs were randomized to receive either continuous infusion (Group C) or intermittent bolus feeding (Group I) of liquid EN. The percentage of prescribed nutrition delivered (PPND) was calculated every 24 hours. Frequencies of gastrointestinal (GI), mechanical, and technical complications were recorded and gastric residual volumes (GRVs) were measured. PPND was significantly lower in Group C (98.4%) than Group I (100%). There was no significant difference in GI or mechanical complications, although Group C had a significantly higher rate of technical complications. GRVs did not differ significantly between Group C (3.1 mL/kg) and Group I (6.3 mL/kg) and were not correlated with the incidence of vomiting or regurgitation. There was a statistically significant difference in the PPND between continuously and intermittently fed dogs, but this difference is unlikely to be clinically relevant. Critically ill dogs can be successfully supported with either continuous infusion or intermittent bolus feeding of EN with few complications. Increased GRVs may not warrant termination of enteral feeding.
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.
Cosmic Rays in Intermittent Magnetic Fields
Energy Technology Data Exchange (ETDEWEB)
Shukurov, Anvar; Seta, Amit; Bushby, Paul J.; Wood, Toby S. [School of Mathematics and Statistics, Newcastle University, Newcastle Upon Tyne NE1 7RU (United Kingdom); Snodin, Andrew P., E-mail: a.seta1@ncl.ac.uk, E-mail: amitseta90@gmail.com [Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800 (Thailand)
2017-04-10
The propagation of cosmic rays in turbulent magnetic fields is a diffusive process driven by the scattering of the charged particles by random magnetic fluctuations. Such fields are usually highly intermittent, consisting of intense magnetic filaments and ribbons surrounded by weaker, unstructured fluctuations. Studies of cosmic-ray propagation have largely overlooked intermittency, instead adopting Gaussian random magnetic fields. Using test particle simulations, we calculate cosmic-ray diffusivity in intermittent, dynamo-generated magnetic fields. The results are compared with those obtained from non-intermittent magnetic fields having identical power spectra. The presence of magnetic intermittency significantly enhances cosmic-ray diffusion over a wide range of particle energies. We demonstrate that the results can be interpreted in terms of a correlated 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.
Continuous-time random walk approach to on-off diffusion
Energy Technology Data Exchange (ETDEWEB)
Miyazaki, Syuji; Harada, Tomohiro; Budiyono, Agung [Kyoto Univ., Graduate School of Informatics, Department of Applied Analysis and Complex Dynamical Systems, Kyoto (Japan)
2001-12-01
Statistical properties and scale invariances of on-off diffusion, which is an anomalous transport phenomenon caused by on-off intermittency, are studied on the basis of the continuous-time random walk (CTRW) approach. The anomalous production of heat is also analyzed. Scaling functions of the time evolution of the mean square displacement and the probability density function (PDF) of the position are analytically derived. It is found that there is a characteristic time separating two regimes of time intervals with different scaling laws for the PDF. In the interval that exists at times much smaller than the characteristic time, anomalous subdiffusion appears, which is followed by normal diffusion. In the earlier time interval, aside from the neighborhood of the origin, the PDF takes the form of a power law multiplied by a stretched exponential function, whereas in the later time interval, the PDF becomes a Gaussian. The results are compared with these model simulations. Good agreement between the theory and the simulation is obtained. (author)
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...
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.
Identifying diseases-related metabolites using random walk.
Hu, Yang; Zhao, Tianyi; Zhang, Ningyi; Zang, Tianyi; Zhang, Jun; Cheng, Liang
2018-04-11
Metabolites disrupted by abnormal state of human body are deemed as the effect of diseases. In comparison with the cause of diseases like genes, these markers are easier to be captured for the prevention and diagnosis of metabolic diseases. Currently, a large number of metabolic markers of diseases need to be explored, which drive us to do this work. The existing metabolite-disease associations were extracted from Human Metabolome Database (HMDB) using a text mining tool NCBO annotator as priori knowledge. Next we calculated the similarity of a pair-wise metabolites based on the similarity of disease sets of them. Then, all the similarities of metabolite pairs were utilized for constructing a weighted metabolite association network (WMAN). Subsequently, the network was utilized for predicting novel metabolic markers of diseases using random walk. Totally, 604 metabolites and 228 diseases were extracted from HMDB. From 604 metabolites, 453 metabolites are selected to construct the WMAN, where each metabolite is deemed as a node, and the similarity of two metabolites as the weight of the edge linking them. The performance of the network is validated using the leave one out method. As a result, the high area under the receiver operating characteristic curve (AUC) (0.7048) is achieved. The further case studies for identifying novel metabolites of diabetes mellitus were validated in the recent studies. In this paper, we presented a novel method for prioritizing metabolite-disease pairs. The superior performance validates its reliability for exploring novel metabolic markers of diseases.
From elongated spanning trees to vicious random walks
Energy Technology Data Exchange (ETDEWEB)
Gorsky, A. [ITEP, B. Cheryomushkinskaya 25, 117218 Moscow (Russian Federation); Nechaev, S., E-mail: nechaev@lptms.u-psud.fr [LPTMS, Université Paris Sud, 91405 Orsay Cedex (France); P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 119991 Moscow (Russian Federation); Poghosyan, V.S. [Institute for Informatics and Automation Problems NAS of Armenia, 375044 Yerevan (Armenia); Priezzhev, V.B. [Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)
2013-05-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of k paths (k is odd) along branches of trees or, equivalently, k loop-erased random walks. Starting and ending points of the paths are grouped such that they form a k-leg watermelon. For large distance r between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as r{sup −ν}logr with ν=(k{sup 2}−1)/2. Considering the spanning forest stretched along the meridian of this watermelon, we show that the two-dimensional k-leg loop-erased watermelon exponent ν is converting into the scaling exponent for the reunion probability (at a given point) of k(1+1)-dimensional vicious walkers, ν{sup -tilde=}k{sup 2}/2. At the end, we express the conjectures about the possible relation to integrable systems.
Determinantal Martingales and Correlations of Noncolliding Random Walks
Katori, Makoto
2015-04-01
We study the noncolliding random walk (RW), which is a particle system of one-dimensional, simple and symmetric RWs starting from distinct even sites and conditioned never to collide with each other. When the number of particles is finite, , this discrete process is constructed as an -transform of absorbing RW in the -dimensional Weyl chamber. We consider Fujita's polynomial martingales of RW with time-dependent coefficients and express them by introducing a complex Markov process. It is a complexification of RW, in which independent increments of its imaginary part are in the hyperbolic secant distribution, and it gives a discrete-time conformal martingale. The -transform is represented by a determinant of the matrix, whose entries are all polynomial martingales. From this determinantal-martingale representation (DMR) of the process, we prove that the noncolliding RW is determinantal for any initial configuration with , and determine the correlation kernel as a function of initial configuration. We show that noncolliding RWs started at infinite-particle configurations having equidistant spacing are well-defined as determinantal processes and give DMRs for them. Tracing the relaxation phenomena shown by these infinite-particle systems, we obtain a family of equilibrium processes parameterized by particle density, which are determinantal with the discrete analogues of the extended sine-kernel of Dyson's Brownian motion model with . Following Donsker's invariance principle, convergence of noncolliding RWs to the Dyson model is also discussed.
Continuous-time random walk with correlated waiting times.
Chechkin, Aleksei V; Hofmann, Michael; Sokolov, Igor M
2009-09-01
Based on the Langevin description of the continuous time random walk (CTRW), we consider a generalization of CTRW in which the waiting times between the subsequent jumps are correlated. We discuss the cases of exponential and slowly decaying persistent power-law correlations between the waiting times as two generic examples and obtain the corresponding mean squared displacements as functions of time. In the case of exponential-type correlations the (sub)diffusion at short times is slower than in the absence of correlations. At long times the behavior of the mean squared displacement is the same as in uncorrelated CTRW. For power-law correlations we find subdiffusion characterized by the same exponent at all times, which appears to be smaller than the one in uncorrelated CTRW. Interestingly, in the limiting case of an extremely long power-law correlations, the (sub)diffusion exponent does not tend to zero, but is bounded from below by the subdiffusion exponent corresponding to a short-time behavior in the case of exponential correlations.
Anomalous transport in turbulent plasmas and continuous time random walks
Energy Technology Data Exchange (ETDEWEB)
Balescu, R. [Association Euratom-Etat Belge pour la Fusion, Physique Statistique et Plasmas, Universite Libre de Bruxelles, Campus Plaine, Code Postal 231, Boulevard du Triomphe, 1050 Bruxelles (Belgium)
1995-05-01
The possibility of a model of anomalous transport problems in a turbulent plasma by a purely stochastic process is investigated. The theory of continuous time random walks (CTRW`s) is briefly reviewed. It is shown that a particular class, called the standard long tail CTRW`s is of special interest for the description of subdiffusive transport. Its evolution is described by a non-Markovian diffusion equation that is constructed in such a way as to yield exact values for all the moments of the density profile. The concept of a CTRW model is compared to an exact solution of a simple test problem: transport of charged particles in a fluctuating magnetic field in the limit of infinite perpendicular correlation length. Although the well-known behavior of the mean square displacement proportional to {ital t}{sup 1/2} is easily recovered, the exact density profile cannot be modeled by a CTRW. However, the quasilinear approximation of the kinetic equation has the form of a non-Markovian diffusion equation and can thus be generated by a CTRW.
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.
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.
Transport behavior of coupled continuous-time random walks.
Dentz, Marco; Scher, Harvey; Holder, Devora; Berkowitz, Brian
2008-10-01
The origin of anomalous or non-Fickian transport in disordered media is the broad spectrum of transition rates intrinsic to these systems. A system that contains within it heterogeneities over multiple length scales is geological formations. The continuous time random walk (CTRW) framework, which has been demonstrated to be an effective means to model non-Fickian transport features in these systems and to have predictive capacities, has at its core this full spectrum represented as a joint probability density psi(s,t) of random space time displacements (s,t) . Transport in a random fracture network (RFN) has been calculated with a coupled psi(s,t) and has subsequently been shown to be approximated well by a decoupled form psi(s,t)=F(s)psi(t) . The latter form has been used extensively to model non-Fickian transport in conjunction with a velocity distribution Phi(xi),xi identical with 1v, where v is the velocity magnitude. The power-law behavior of psi(t) proportional to (-1-beta), which determines non-Fickian transport, derives from the large xi dependence of Phi(xi) . In this study we use numerical CTRW simulations to explore the expanded transport phenomena derived from a coupled psi(s,t) . Specifically, we introduce the features of a power-law dependence in the s distribution with different Phi(xi) distributions (including a constant v) coupled by t=s(xi) . Unlike Lévy flights in this coupled scenario the spatial moments of the plumes are well defined. The shapes of the plumes depend on the entire Phi(xi) distribution, i.e., both small and large xi dependence; there is a competition between long displacements (which depend on the small xi dependence) and large time events (which depend on a power law for large xi). These features give rise to an enhanced range of transport behavior with a broader scope of applications, e.g., to correlated migrations in a RFN and in heterogeneous permeability fields. The approximation to the decoupled case is investigated as a
Transduction on Directed Graphs via Absorbing Random Walks.
De, Jaydeep; Zhang, Xiaowei; Lin, Feng; Cheng, Li
2017-08-11
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications.Different from existing research efforts that either only deal with undirected graphs or circumvent directionality by means of symmetrization, we propose a novel random walk approach on directed graphs using absorbing Markov chains, which can be regarded as maximizing the accumulated expected number of visits from the unlabeled transient states. Our algorithm is simple, easy to implement, and works with large-scale graphs on binary, multiclass, and multi-label prediction problems. Moreover, it is capable of preserving the graph structure even when the input graph is sparse and changes over time, as well as retaining weak signals presented in the directed edges. We present its intimate connections to a number of existing methods, including graph kernels, graph Laplacian based methods, and interestingly, spanning forest of graphs. Its computational complexity and the generalization error are also studied. Empirically our algorithm is systematically evaluated on a wide range of applications, where it has shown to perform competitively comparing to a suite of state-of-the-art methods. In particular, our algorithm is shown to work exceptionally well with large sparse directed graphs with e.g. millions of nodes and tens of millions of edges, where it significantly outperforms other state-of-the-art methods. In the dynamic graph setting involving insertion or deletion of nodes and edge-weight changes over time, it also allows efficient online updates that produce the same results as of the batch update counterparts.
The First Order Correction to the Exit Distribution for Some Random Walks
Kennedy, Tom
2016-07-01
We study three different random walk models on several two-dimensional lattices by Monte Carlo simulations. One is the usual nearest neighbor random walk. Another is the nearest neighbor random walk which is not allowed to backtrack. The final model is the smart kinetic walk. For all three of these models the distribution of the point where the walk exits a simply connected domain D in the plane converges weakly to harmonic measure on partial D as the lattice spacing δ → 0. Let ω (0,\\cdot ;D) be harmonic measure for D, and let ω _δ (0,\\cdot ;D) be the discrete harmonic measure for one of the random walk models. Our definition of the random walk models is unusual in that we average over the orientation of the lattice with respect to the domain. We are interested in the limit of (ω _δ (0,\\cdot ;D)- ω (0,\\cdot ;D))/δ . Our Monte Carlo simulations of the three models lead to the conjecture that this limit equals c_{M,L} ρ _D(z) times Lebesgue measure with respect to arc length along the boundary, where the function ρ _D(z) depends on the domain, but not on the model or lattice, and the constant c_{M,L} depends on the model and on the lattice, but not on the domain. So there is a form of universality for this first order correction. We also give an explicit formula for the conjectured density ρ _D.
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.
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...
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.
Mathematical conversations multicolor problems, problems in the theory of numbers, and random walks
Dynkin, E B
2006-01-01
Comprises Multicolor Problems, dealing with map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; Random Walks, addressing basic problems in probability theory. 1963 edition.
A Realization of a Quasi-Random Walk for Atoms in Time-Dependent Optical Potentials
Directory of Open Access Journals (Sweden)
Torsten Hinkel
2015-09-01
Full Text Available We consider the time dependent dynamics of an atom in a two-color pumped cavity, longitudinally through a side mirror and transversally via direct driving of the atomic dipole. The beating of the two driving frequencies leads to a time dependent effective optical potential that forces the atom into a non-trivial motion, strongly resembling a discrete random walk behavior between lattice sites. We provide both numerical and analytical analysis of such a quasi-random walk behavior.
Origins and applications of the Montroll-Weiss continuous time random walk
Shlesinger, Michael F.
2017-05-01
The Continuous Time Random Walk (CTRW) was introduced by Montroll and Weiss in 1965 in a purely mathematical paper. Its antecedents and later applications beginning in 1973 are discussed, especially for the case of fractal time where the mean waiting time between jumps is infinite. Contribution to the Topical Issue: "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
All-time dynamics of continuous-time random walks on complex networks
Teimouri, Hamid; Kolomeisky, Anatoly B.
2012-01-01
The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social and economic sciences. Recently, several theoretical approaches have been developed that allowed to analyze explicitly dynamics of CTRW at all times, which is critically important for understanding mechanisms of underlying phenomena. However, theoretical analysis has been done mostly for...
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.
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.
Scaling Properties of Field-Induced Superdiffusion in Continuous Time Random Walks
Burioni, R.; Gradenigo, G.; Sarracino, A.; Vezzani, A.; Vulpiani, A.
2014-10-01
We consider a broad class of Continuous Time Random Walks (CTRW) with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a Lévy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.
Abdel-Aziem, Amr A; El-Basatiny, Heba My
2017-06-01
To compare the effects of backward walking training and forward walking training on spatiotemporal gait parameters, and gross motor function measures in children with cerebral palsy. Randomized controlled clinical trial. Physical therapy clinics. A total of 30 children with hemiparetic cerebral palsy of both sexes (10 to 14 years of age, classified as I or II by gross motor function classification system) participated in this study. They were randomly assigned into two equal groups. Both groups received a conventional physical therapy program for 12 successive weeks (three sessions per week). The experimental group additionally received (25 min) backward walking training. The control group additionally received (25 min) forward walking training. Baseline, posttreatment, and follow-up assessment for spatiotemporal gait parameters and gross motor functions were evaluated by using three dimensional gait analysis system and gross motor function measures. There was a significant improvement in step length, walking velocity, cadence, stance phase, and swing phase percentage and gross motor function measures (Dimensions D and E) of the experimental group (0.55 ±0.16, 0.53 ±0.19, 121.73 ±2.89, 54.73 ±1.67, 44.40 ±1.40, 90.20 ±6.44, 82.47 ±12.82), respectively, than the control group (0.39 ±0.13, 0.46 ±0.20, 125.80 ±2.96, 50.27 ±1.62, 49.47 ±1.55, 82.47 ±7.05, 80.47 ±12.61), respectively, ( p cerebral palsy.
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.
Continuous-time random walk and parametric subordination in fractional diffusion
Energy Technology Data Exchange (ETDEWEB)
Gorenflo, Rudolf [Department of Mathematics and Informatics, Free University of Berlin, Arnimallee 3, D-14195 Berlin (Germany); Mainardi, Francesco [Department of Physics, University of Bologna and INFN, Via Irnerio 46, I-40126 Bologna (Italy)]. E-mail: mainardi@bo.infn.it; Vivoli, Alessandro [Department of Physics, University of Bologna and INFN, Via Irnerio 46, I-40126 Bologna (Italy)
2007-10-15
The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW) is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW itself. We treat the CTRW as a combination of a random walk on the axis of physical time with a random walk in space, both walks happening in discrete operational time. In the continuum limit, we obtain a (generally non-Markovian) diffusion process governed by a space-time fractional diffusion equation. The essential assumption is that the probabilities for waiting times and jump-widths behave asymptotically like powers with negative exponents related to the orders of the fractional derivatives. By what we call parametric subordination, applied to a combination of a Markov process with a positively oriented Levy process, we generate and display sample paths for some special cases.
Quasi-steady-state analysis of two-dimensional random intermittent search processes
Bressloff, Paul C.
2011-06-01
We use perturbation methods to analyze a two-dimensional random intermittent search process, in which a searcher alternates between a diffusive search phase and a ballistic movement phase whose velocity direction is random. A hidden target is introduced within a rectangular domain with reflecting boundaries. If the searcher moves within range of the target and is in the search phase, it has a chance of detecting the target. A quasi-steady-state analysis is applied to the corresponding Chapman-Kolmogorov equation. This generates a reduced Fokker-Planck description of the search process involving a nonzero drift term and an anisotropic diffusion tensor. In the case of a uniform direction distribution, for which there is zero drift, and isotropic diffusion, we use the method of matched asymptotics to compute the mean first passage time (MFPT) to the target, under the assumption that the detection range of the target is much smaller than the size of the domain. We show that an optimal search strategy exists, consistent with previous studies of intermittent search in a radially symmetric domain that were based on a decoupling or moment closure approximation. We also show how the decoupling approximation can break down in the case of biased search processes. Finally, we analyze the MFPT in the case of anisotropic diffusion and find that anisotropy can be useful when the searcher starts from a fixed location. © 2011 American Physical Society.
Central limit theorem and related results for the elephant random walk
Coletti, Cristian F.; Gava, Renato; Schütz, Gunter M.
2017-05-01
We study the so-called elephant random walk (ERW) which is a non-Markovian discrete-time random walk on ℤ with unbounded memory which exhibits a phase transition from a diffusive to superdiffusive behavior. We prove a law of large numbers and a central limit theorem. Remarkably the central limit theorem applies not only to the diffusive regime but also to the phase transition point which is superdiffusive. Inside the superdiffusive regime, the ERW converges to a non-degenerate random variable which is not normal. We also obtain explicit expressions for the correlations of increments of the ERW.
Kolokoltsov, Vassili N.
2007-01-01
Functional limit theorem for continuous-time random walks (CTRW) are found in general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional dynamics. Probabilistic interpretation of generalized fractional evolution is given in terms of the random time change (subordination) by means of hitting times processes.
Tribby, Calvin P; Miller, Harvey J; Brown, Barbara B; Werner, Carol M; Smith, Ken R
2017-11-01
Walking is a form of active transportation with numerous benefits, including better health outcomes, lower environmental impacts and stronger communities. Understanding built environmental associations with walking behavior is a key step towards identifying design features that support walking. Human mobility data available through GPS receivers and cell phones, combined with high resolution walkability data, provide a rich source of georeferenced data for analyzing environmental associations with walking behavior. However, traditional techniques such as route choice models have difficulty with highly dimensioned data. This paper develops a novel combination of a data-driven technique with route choice modeling for leveraging walkability audits. Using data from a study in Salt Lake City, Utah, USA, we apply the data-driven technique of random forests to select variables for use in walking route choice models. We estimate data-driven route choice models and theory-driven models based on predefined walkability dimensions. Results indicate that the random forest technique selects variables that dramatically improve goodness of fit of walking route choice models relative to models based on predefined walkability dimensions. We compare the theory-driven and data-driven walking route choice models based on interpretability and policy relevance.
DEFF Research Database (Denmark)
Tagbor, Harry; Cairns, Matthew; Bojang, Kalifa
2015-01-01
BACKGROUND: The efficacy of intermittent preventive treatment for malaria with sulfadoxine-pyrimethamine (IPTp-SP) in pregnancy is threatened in parts of Africa by the emergence and spread of resistance to SP. Intermittent screening with a rapid diagnostic test (RDT) and treatment of positive wom...... receiving cotrimoxazole prophylaxis in whom SP is contraindicated. TRIAL REGISTRATION: ClinicalTrials.gov NCT01084213 Pan African Clinical trials Registry PACT201202000272122....... (ISTp) is an alternative approach. METHODS AND FINDINGS: An open, individually randomized, non-inferiority trial of IPTp-SP versus ISTp was conducted in 5,354 primi- or secundigravidae in four West African countries with a low prevalence of resistance to SP (The Gambia, Mali, Burkina Faso and Ghana...
Convex hulls of random walks in higher dimensions: A large-deviation study
Schawe, Hendrik; Hartmann, Alexander K.; Majumdar, Satya N.
2017-12-01
The distribution of the hypervolume V and surface ∂ V of convex hulls of (multiple) random walks in higher dimensions are determined numerically, especially containing probabilities far smaller than P =10-1000 to estimate large deviation properties. For arbitrary dimensions and large walk lengths T , we suggest a scaling behavior of the distribution with the length of the walk T similar to the two-dimensional case and behavior of the distributions in the tails. We underpin both with numerical data in d =3 and d =4 dimensions. Further, we confirm the analytically known means of those distributions and calculate their variances for large T .
International Nuclear Information System (INIS)
Kiskis, J.; Narayanan, R.; Vranas, P.
1993-01-01
The authors study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments, the authors show that the critical exponent v describing the vanishing of the physical mass at the critical point is equal to v θ /d w , where d w is the Hausdorff dimension of the walk, and v θ = var-phi, where var-phi is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is var-phi/v for O(N) models. 3 refs
Walking improves sleep in individuals with cancer: a meta-analysis of randomized, controlled trials.
Chiu, Hsiao-Yean; Huang, Hui-Chuan; Chen, Pin-Yuan; Hou, Wen-Hsuan; Tsai, Pei-Shan
2015-03-01
To evaluate the effectiveness of walking exercise on sleep in people with cancer. Databases searched included China Knowledge Resource Integrated Database, CINAHL®, Cochrane Central Register of Controlled Trials, EMBASE, PsycINFO®, PubMed, Wanfang Data, and Web of Science. Nine randomized, controlled trials involving 599 patients were included. Most of the studies used moderate-intensity walking exercise. Overall, walking exercise significantly improved sleep in people with cancer (Hedges' g = –0.52). Moderator analyses showed that walking exercise alone and walking exercise combined with other forms of interventions yielded comparable effects on sleep improvement, and that the effect size did not differ among participants who were at different stages of cancer. The effect sizes for studies involving individuals with breast cancer and for studies including individuals with other types of cancer were similar. Moderate-intensity walking exercise is effective in improving sleep in individuals with cancer. The authors' findings support the inclusion of walking exercise into the multimodal approaches to managing sleep in people with cancer. Healthcare providers must convey the benefits of walking exercise to individuals with cancer who are suffering from sleep problems.
Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications
Directory of Open Access Journals (Sweden)
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.
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...... simulations depend, each of which lead to radically different macro-scale dynamics as expressed in their corresponding Fokker-Planck equations. In addition, diffusivity is not a unique parameter describing a random walk and its corresponding Fokker-Planck equation. Spatially varying translation speed and turn...
A connection between a system of random walks and rumor transmission
Lebensztayn, E.; Rodriguez, P. M.
2013-12-01
We establish a relationship between the phenomenon of rumor transmission on a population and a probabilistic model of interacting particles on the complete graph. More precisely, we consider variations of the Maki-Thompson epidemic model and the “frog model” of random walks, which were introduced in the scientific literature independently and in different contexts. We analyze the Markov chains which describe these models, and show a coupling between them. Our connection shows how the propagation of a rumor in a closed homogeneously mixing population can be described by a system of random walks on the complete graph. Additionally, we discuss further applications of the random walk model which are relevant to the modeling of different biological dynamics.
Gale, Ella M; Johns, Marcus A; Wirawan, Remigius H; Scott, Janet L
2017-07-21
Polysaccharides, such as cellulose, are often processed by dissolution in solvent mixtures, e.g. an ionic liquid (IL) combined with a dipolar aprotic co-solvent (CS) that the polymer does not dissolve in. A multi-walker, discrete-time, discrete-space 1-dimensional random walk can be applied to model solvation of a polymer in a multi-component solvent mixture. The number of IL pairs in a solvent mixture and the number of solvent shells formable, x, is associated with n, the model time-step, and N, the number of random walkers. The mean number of distinct sites visited is proportional to the amount of polymer soluble in a solution. By also fitting a polynomial regression model to the data, we can associate the random walk terms with chemical interactions between components and probe where the system deviates from a 1-D random walk. The 'frustration' between solvents shells is given as ln x in the random walk model and as a negative IL:IL interaction term in the regression model. This frustration appears in regime II of the random walk model (high volume fractions of IL) where walkers interfere with each other, and the system tends to its limiting behaviour. In the low concentration regime, (regime I) the solvent shells do not interact, and the system depends only on IL and CS terms. In both models (and both regimes), the system is almost entirely controlled by the volume available to solvation shells, and thus is a counting/space-filling problem, where the molar volume of the CS is important. Small deviations are observed when there is an IL-CS interaction. The use of two models, built on separate approaches, confirm these findings, demonstrating that this is a real effect and offering a route to identifying such systems. Specifically, the majority of CSs - such as dimethylformide - follow the random walk model, whilst 1-methylimidazole, dimethyl sulfoxide, 1,3-dimethyl-2-imidazolidinone and tetramethylurea offer a CS-mediated improvement and propylene carbonate
DEFF Research Database (Denmark)
Momsen, A H; Jensen, M B; Norager, C B
2010-01-01
Intermittent claudication is a disabling symptom of peripheral arterial disease for which few medical treatments are available. This study investigated the effect of caffeine on physical capacity in patients with intermittent claudication.......Intermittent claudication is a disabling symptom of peripheral arterial disease for which few medical treatments are available. This study investigated the effect of caffeine on physical capacity in patients with intermittent claudication....
Reliable H∞ control of discrete-time systems against random intermittent faults
Tao, Yuan; Shen, Dong; Fang, Mengqi; Wang, Youqing
2016-07-01
A passive fault-tolerant control strategy is proposed for systems subject to a novel kind of intermittent fault, which is described by a Bernoulli distributed random variable. Three cases of fault location are considered, namely, sensor fault, actuator fault, and both sensor and actuator faults. The dynamic feedback controllers are designed not only to stabilise the fault-free system, but also to guarantee an acceptable performance of the faulty system. The robust H∞ performance index is used to evaluate the effectiveness of the proposed control scheme. In terms of linear matrix inequality, the sufficient conditions of the existence of controllers are given. An illustrative example indicates the effectiveness of the proposed fault-tolerant control method.
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.
Quenched Sub-Exponential Tail Estimates for One-Dimensional Random Walk in Random Environment
Gantert, Nina; Zeitouni, Ofer
Suppose that the integers are assigned i.i.d. random variables {ωx} (taking values in the unit interval), which serve as an environment. This environment defines a random walk {Xn} (called a RWRE) which, when at x, moves one step to the right with probability ωx, and one step to the left with probability 1- ωx. Solomon (1975) determined the almost-sure asymptotic speed vα (=rate of escape) of a RWRE. Greven and den Hollander (1994) have proved a large deviation principle for Xn /n, conditional upon the environment, with deterministic rate function. For certain environment distributions where the drifts 2 ωx-1 can take both positive and negative values, their rate function vanisheson an interval (0,vα). We find the rate of decay on this interval and prove it is a stretched exponential of appropriate exponent, that is the absolute value of the log of the probability that the empirical mean Xn /n is smaller than v, v∈ (0,vα), behaves roughly like a fractional power of n. The annealed estimates of Dembo, Peres and Zeitouni (1996) play a crucial role in the proof. We also deal with the case of positive and zero drifts, and prove there a quenched decay of the form .
Novel pseudo-random number generator based on quantum random walks
Yang, Yu-Guang; Zhao, Qian-Qian
2016-02-01
In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.
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.
A random-walk model for pore pressure accumulation in marine soils
DEFF Research Database (Denmark)
Sumer, B. Mutlu; Cheng, Niang-Sheng
1999-01-01
A numerical random-walk model has been developed for the pore-water pressure. The model is based on the analogy between the variation of the pore pressure and the diffusion process of any passive quantity such as concentration. The pore pressure in the former process is analogous to the concentra......A numerical random-walk model has been developed for the pore-water pressure. The model is based on the analogy between the variation of the pore pressure and the diffusion process of any passive quantity such as concentration. The pore pressure in the former process is analogous...
Random Walks for Synthetic Aperture Radar Image Fusion in Framelet Domain.
Yang, Xiaoyuan; Wang, Jingkai; Zhu, Ridong
2017-08-30
A new framelet-based random walks (RW) method is presented for synthetic aperture radar (SAR) image fusion, including SAR-visible images, SAR-infrared images and Multiband SAR images. In this method, we build a novel random walks model based on the statistical characteristics of framelet coefficients to fuse the high-frequency and low-frequency coefficients. This model converts the fusion problem to estimate the probability of each framelet coefficient being assigned each input image. Experimental results show that the proposed approach improves the contrast while preserves the edges simultaneously, and outperforms many traditional and state-of-the-art fusion techniques in both qualitative and quantitative analysis.
Is walking a random walk? Evidence for long-range correlations in stride interval of human gait
Hausdorff, Jeffrey M.; Peng, C.-K.; Ladin, Zvi; Wei, Jeanne Y.; Goldberger, Ary L.
1995-01-01
Complex fluctuation of unknown origin appear in the normal gait pattern. These fluctuations might be described as being (1) uncorrelated white noise, (2) short-range correlations, or (3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that sucessfully accounts for the experimentally observed long-range correlations.
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
Emergence of an optimal search strategy from a simple random walk.
Sakiyama, Tomoko; Gunji, Yukio-Pegio
2013-09-06
In reports addressing animal foraging strategies, it has been stated that Lévy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths.
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...... is increasing in the popularity/media coverage of the celebrity in question, and is larger for stocks that are more affected by investor sentiment. Overall, my findings are consistent with the lab research on the affect management model, which maintains that incidental negative affect promotes risk....../environmental factors, and market liquidity, I find that the death of popular and beloved celebrities is immediately followed by a 16 basis point increase in stock returns, which is consistent with a rise in the net demand for risky instruments. I also find evidence that the size of this celebrity-death effect...
Fritschi, Juliette O; Brown, Wendy J; van Uffelen, Jannique G Z
2014-04-17
Physical activity is associated with better physical and mental health in older adults. Pole walking is a form of walking which may have additional health benefits in older adults, because of the addition of hand held poles, and consequent upper limb involvement. However, few studies have examined the potential additional effects of pole walking on physical and psychosocial health in older adults compared with walking. The aim of this study is to compare the effect of a pole walking program with the effects of a walking program, on physical and psychosocial wellbeing, in older adults in assisted living facilities. Sixty men and women from assisted living communities over 65 years will be recruited from senior retirement facilities and randomized into a group based, pole walking program, or walking program. The pole walking group will use the Exerstrider method of pole walking. Total duration of the programs is 12 weeks, with three sessions per week, building from 20 minute to 30 minute sessions.The primary outcome is physical function, as measured by items from the Seniors Fitness Test and hand grip strength. Secondary outcomes include, physical activity levels, sedentary behaviour, joint pain, and quality of life. All outcomes will be assessed before and after the programs, using valid and reliable measures. The study will add to the evidence base for the effects of pole walking, compared with walking, on physical and psychosocial health and physical function, in healthy older adults. This will improve understanding about the feasibility of pole walking programs and its specific benefits in this population. Australian New Zealand Clinical Trials Registry ACTRN12612001127897.
Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki
2018-03-01
We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2}). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3}) and the level sets of the Gaussian free field ({d≥ 3}). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.
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.
Regularity of the Speed of Biased Random Walk in a One-Dimensional Percolation Model
Gantert, Nina; Meiners, Matthias; Müller, Sebastian
2018-03-01
We consider biased random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. Axelson-Fisk and Häggström established for this model a phase transition for the asymptotic linear speed \\overline{v} of the walk. Namely, there exists some critical value λ c>0 such that \\overline{v}>0 if λ \\in (0,λ c) and \\overline{v}=0 if λ ≥ λ c. We show that the speed \\overline{v} is continuous in λ on (0,∞) and differentiable on (0,λ c/2). Moreover, we characterize the derivative as a covariance. For the proof of the differentiability of \\overline{v} on (0,λ c/2), we require and prove a central limit theorem for the biased random walk. Additionally, we prove that the central limit theorem fails to hold for λ ≥ λ c/2.
Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs
International Nuclear Information System (INIS)
Salimi, S.; Jafarizadeh, M. A.
2009-01-01
In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product Cayley graphs (complete cycle, complete K n , charter and n-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as t → ∞ but for quantum state is not always satisfied. (general)
Pandey, Ambarish; Banerjee, Subhash; Ngo, Christian; Mody, Purav; Marso, Steven P; Brilakis, Emmanouil S; Armstrong, Ehrin J; Giri, Jay; Bonaca, Marc P; Pradhan, Aruna; Bavry, Anthony A; Kumbhani, Dharam J
2017-04-10
The authors performed a meta-analysis of randomized controlled trials to compare the efficacy of initial endovascular treatment with or without supervised exercise training (SET) versus SET alone in patients with intermittent claudication. Current guidelines recommend SET as the initial treatment modality for patients with intermittent claudication, in addition to optimal medical therapy. The role of endovascular therapy as primary treatment for claudication has been controversial. The primary outcome was treadmill-measured maximal walk distance at the end of follow-up. Secondary outcomes included resting ankle brachial index (ABI) and treadmill-measured ischemic claudication distance on follow-up. Risk of revascularization or amputations was also compared. Pooled estimates of the difference in outcomes between endovascular therapy with or without SET and SET-only groups were calculated using fixed and random effects models. A total of 987 patients from 7 trials were included. In pooled analysis, compared with SET only (reference group), patients that underwent combined endovascular therapy and SET had significantly higher maximum walk distance (standardized mean difference 0.79 [95% confidence interval (CI): 0.18 to 1.39]; weighted mean difference 98.9 [95% CI: 31.4 to 166.4 feet], and lower risk of revascularization or amputation (odds ratio 0.19 [95% CI: (0.09 to 0.40]; p < 0.0001, number needed to treat = 8) over a median follow-up of 12.4 months. By contrast, revascularization was not associated with significant improvement in exercise capacity or risk of future revascularization or amputation, compared with SET alone. Follow-up ABI was significantly higher among patients that underwent endovascular therapy with or without SET as compared with SET alone. Compared with initial SET only, endovascular therapy in combination with SET is associated with significant improvement in total walking distance, ABI, and risk of future revascularization or amputation. By
Nordic Walking and chronic low back pain: design of a randomized clinical trial
Directory of Open Access Journals (Sweden)
Hartvigsen Jan
2006-10-01
Full Text Available Abstract Background Low Back Pain is a major public health problem all over the western world. Active approaches including exercise in the treatment of low back pain results in better outcomes for patients, but it is not known exactly which types of back exercises are most beneficial or whether general physical activity provide similar benefits. Nordic Walking is a popular and fast growing type of exercise in Northern Europe. Initial studies have demonstrated that persons performing Nordic Walking are able to exercise longer and harder compared to normal walking thereby increasing their cardiovascular metabolism. Until now no studies have been performed to investigate whether Nordic Walking has beneficial effects in relation to low back pain. The primary aim of this study is to investigate whether supervised Nordic Walking can reduce pain and improve function in a population of chronic low back pain patients when compared to unsupervised Nordic Walking and advice to stay active. In addition we investigate whether there is an increase in the cardiovascular metabolism in persons performing supervised Nordic Walking compared to persons who are advised to stay active. Finally, we investigate whether there is a difference in compliance between persons receiving supervised Nordic Walking and persons doing unsupervised Nordic Walking. Methods One hundred and fifty patients with low back pain for at least eight weeks and referred to a specialized secondary sector outpatient back pain clinic are included in the study. After completion of the standard back centre treatment patients are randomized into one of three groups: A Nordic Walking twice a week for eight weeks under supervision of a specially trained instructor; B Unsupervised Nordic Walking for eight weeks after one training session with an instructor; C A one hour motivational talk including advice to stay active. Outcome measures are pain, function, overall health, cardiovascular ability and
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
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.
Cai, Bingjing; Wang, Haiying; Zheng, Huiru; Wang, Hui
2015-01-01
Systematic identification of protein complexes from protein-protein interaction networks (PPIs) is an important application of data mining in life science. Over the past decades, various new clustering techniques have been developed based on modelling PPIs as binary relations. Non-binary information of co-complex relations (prey/bait) in PPIs data derived from tandem affinity purification/mass spectrometry (TAP-MS) experiments has been unfairly disregarded. In this paper, we propose a Biased Random Walk based algorithm for detecting protein complexes from TAP-MS data, resulting in the random walk with restarting baits (RWRB). RWRB is developed based on Random walk with restart. The main contribution of RWRB is the incorporation of co-complex relations in TAP-MS PPI networks into the clustering process, by implementing a new restarting strategy during the process of random walk. Through experimentation on un-weighted and weighted TAP-MS data sets, we validated biological significance of our results by mapping them to manually curated complexes. Results showed that, by incorporating non-binary, co-membership information, significant improvement has been achieved in terms of both statistical measurements and biological relevance. Better accuracy demonstrates that the proposed method outperformed several state-of-the-art clustering algorithms for the detection of protein complexes in TAP-MS data.
Energy difference space random walk to achieve fast free energy calculations.
Min, Donghong; Yang, Wei
2008-05-21
A method is proposed to efficiently obtain free energy differences. In the present algorithm, free energy calculations proceed by the realization of an energy difference space random walk. Thereby, this algorithm can greatly improve the sampling of the regions in phase space where target states overlap.
Seah, Choon Sen; Kasim, Shahreen; Fudzee, Mohd Farhan Md; Law Tze Ping, Jeffrey Mark; Mohamad, Mohd Saberi; Saedudin, Rd Rohmat; Ismail, Mohd Arfian
2017-12-01
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.
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.
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...
A Coupled Continuous Time Random Walk Approach For Transport in Highly Heterogeneous Porous Media
Dentz, M.; Scher, H.; Holder, D.; Berkowitz, B.
2008-12-01
We present a coupled continuous time random walk (CTRW) approach as an effective model for transport in highly heterogeneous media. This approach models solute transport by a coupled system of Langevin equations for random movements in the spatial and temporal domains. Motivated by transport in random fracture networks, here we consider a model that is characterized by given distributions of transition lengths (fracture length) and velocities. Thus, transition lengths and times are intrinsically related. Fracture length and velocity define the transition time. A maximum transition time is given by the diffusion time over the fracture length. Diffusion into the matrix can be modeled explicitly by a distribution of retention times. We study spatial distributions, and effective apparent transport coefficients as well as first arrival time distributions for a series of scenarios. The scaling behavior of such a fully coupled walk is different from the one observed in uncoupled walks. We investigate the competition between long jumps and long waiting times in this fully coupled continuous time random walk and determine scaling laws for the spatial moments of concentration.
National Research Council Canada - National Science Library
Durrett, Richard; Kesten, Harry; Spitzer, Frank
1991-01-01
..., made the transparency used in the printing process. STUDENTS OF FRANK SPITZERSTUDENTS OF FRANK SPITZER 1957 J. W. Lamperti, On the asymptotic behavior of recurrent and almostrecurrent events. 1964 W. W. Whitman, Some strong laws for random walks and Brownian motion. 1965 J. C. Mineka, The existence and uniqueness of positive solutions to the Wien...
Czech Academy of Sciences Publication Activity Database
Wiesner, Ivo; Wiesnerová, Dana
2010-01-01
Roč. 54, č. 2 (2010), s. 353-356 ISSN 0006-3134 R&D Projects: GA AV ČR 1QS500510566 Institutional research plan: CEZ:AV0Z50510513 Keywords : begonia germplasm identification * random walk * primary sequence analysis Subject RIV: EB - Genetics ; Molecular Biology Impact factor: 1.582, year: 2010
Approximation of quantum Lévy processes by quantum random walks
Indian Academy of Sciences (India)
Introduction. The note is concerned with investigating convergence of random walks on quantum groups to quantum Lévy processes. The theory of the latter is a natural noncommutative coun- terpart of the theory of classical Lévy processes on groups [Hey]. It has been initiated in. [ASW] and further extensively developed by ...
The invariant measure of random walks in the quarter-plane: respresentation in geometric terms
Chen, Y.; Boucherie, Richardus J.; Goseling, Jasper
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these linear combinations such that the resulting measure may
The supremuim of a negative drift random walk with dependent heavy-tailed steps
Mikosch, T; Smorodnitsky, G
Many important probabilistic models in queuing theory, insurance and finance deal with partial sums of a negative mean stationary process (a negative drift random walk), and the law of the supremum of such a process is used to calculate, depending on the context, the ruin probability, the steady
Do exchange rates follow random walks? A variance ratio test of the ...
African Journals Online (AJOL)
The random-walk hypothesis in foreign-exchange rates market is one of the most researched areas, particularly in developed economies. However, emerging markets in sub-Saharan Africa have received little attention in this regard. This study applies Lo and MacKinlay's (1988) conventional variance ratio test and Wright's ...
Martingale convergence and the functional equation in the multi-type branching random walk
Kyprianou, A.E.; Rahimzadeh Sani, A.
2000-01-01
A generalization of Biggins Martingale Convergence Theorem is proved for the multitype branching random walk The proof appeals to modern techniques involving the construction of sizebiased measures on the space of marked trees generated by the branching process As a simple conse quence we obtain
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...... of the CTRW theory. (C) 2008 Elsevier B.V. All rights reserved....
On the relationship between multiple porosity models and continuous time random walk
Nordbotten, Jan Martin; Vasilyev, Leonid
2010-01-01
We derive a multiple porosity model based on the continuous time random walk model (CTRW). In particular, we show how the parameters of the multiple porosity models relate to the transition probability function which is at the heart of the CTRW formulation. A simple example is included to illustrate the results.
The random walk of a drilling laser beam
Anthony, T. R.
1980-01-01
The disregistry of holes drilled with a pulse laser beam in 330-micron-thick single-crystal silicon-on-sapphire wafers is examined. The exit positions of the holes were displaced from the hole entrance positions on the opposing face of the wafer, and this random displacement increased with the number of laser pulses required. A model in which the bottom of the drill hole experiences small random displacements during each laser pulse is used to describe the experimental observations. It is shown that the average random displacement caused by each pulse is only a few percent of the hole diameter and can be reduced by using as few laser pulses as necessary while avoiding the cracking and spalling of the wafer that occur with a hole drilled with a single pulse.
Random intermittent search and the tug-of-war model of motor-driven transport
Newby, Jay
2010-04-16
We formulate the \\'tug-of-war\\' model of microtubule cargo transport by multiple molecular motors as an intermittent random search for a hidden target. A motor complex consisting of multiple molecular motors with opposing directional preference is modeled using a discrete Markov process. The motors randomly pull each other off of the microtubule so that the state of the motor complex is determined by the number of bound motors. The tug-of-war model prescribes the state transition rates and corresponding cargo velocities in terms of experimentally measured physical parameters. We add space to the resulting Chapman-Kolmogorov (CK) equation so that we can consider delivery of the cargo to a hidden target at an unknown location along the microtubule track. The target represents some subcellular compartment such as a synapse in a neuron\\'s dendrites, and target delivery is modeled as a simple absorption process. Using a quasi-steady-state (QSS) reduction technique we calculate analytical approximations of the mean first passage time (MFPT) to find the target. We show that there exists an optimal adenosine triphosphate (ATP) concentration that minimizes the MFPT for two different cases: (i) the motor complex is composed of equal numbers of kinesin motors bound to two different microtubules (symmetric tug-of-war model) and (ii) the motor complex is composed of different numbers of kinesin and dynein motors bound to a single microtubule (asymmetric tug-of-war model). © 2010 IOP Publishing Ltd.
Effective speed and agility conditioning methodology for random intermittent dynamic type sports.
Bloomfield, Jonathan; Polman, Remco; O'Donoghue, Peter; McNaughton, Lars
2007-11-01
Different coaching methods are often used to improve performance. This study compared the effectiveness of 2 methodologies for speed and agility conditioning for random, intermittent, and dynamic activity sports (e.g., soccer, tennis, hockey, basketball, rugby, and netball) and the necessity for specialized coaching equipment. Two groups were delivered either a programmed method (PC) or a random method (RC) of conditioning with a third group receiving no conditioning (NC). PC participants used the speed, agility, quickness (SAQ) conditioning method, and RC participants played supervised small-sided soccer games. PC was also subdivided into 2 groups where participants either used specialized SAQ equipment or no equipment. A total of 46 (25 males and 21 females) untrained participants received (mean +/- SD) 12.2 +/- 2.1 hours of physical conditioning over 6 weeks between a battery of speed and agility parameter field tests. Two-way analysis of variance results indicated that both conditioning groups showed a significant decrease in body mass and body mass index, although PC achieved significantly greater improvements on acceleration, deceleration, leg power, dynamic balance, and the overall summation of % increases when compared to RC and NC (p speed and agility parameters; however, this study found that specialized SAQ equipment was not a requirement to observe significant improvements. Further research is required to establish whether these benefits transfer to sport-specific tasks as well as to the underlying mechanisms resulting in improved performance.
Elavsky, Steriani; McAuley, Edward
2007-01-01
To examine the effects of walking and yoga on multidimensional self-esteem and roles played by self-efficacy, body composition, and physical activity (PA) in changes in esteem. Four-month randomized controlled exercise trial with three arms: walking, yoga, and control. Previously low-active middle-aged women (n=164; M age = 49.9; SD = 3.6). Structured and supervised walking program meeting three times per week for I hour and supervised yoga program meeting twice per week for 90 minutes. Body composition, fitness assessment, and battery of psychologic measures. Panel analysis within a structural equation modeling framework using Mplus 3.0. The walking and yoga interventions failed to enhance global or physical self-esteem but improved subdomain esteem relative to physical condition and strength (for walking) and body attractiveness (for both walking and yoga). Over time the effects of PA, self-efficacy, and body fat on changes in physical self-esteem and global esteem were mediated by changes in physical condition and body attractiveness subdomain esteem. Women reporting greater levels of self-efficacy and PA with lower body fat also reported greater enhancements in subdomain esteem. These results provide support for the hierarchic and multidimensional nature of self-esteem and indicate that middle-aged women may enhance certain aspects of physical self-esteem by participating in PA.
On the genealogy of branching random walks and of directed polymers
Derrida, Bernard; Mottishaw, Peter
2016-08-01
It is well known that the mean-field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite-size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks.
Brownian Motion Problem: Random Walk and Beyond -RE ...
Indian Academy of Sciences (India)
by their continuous bombardment by the surrounding molecules of much smaller size (Figure 1). This effect .... of continuous impacts of the randomly moving surround- ing molecules of the fluid (the 'npise'); (ii) these ..... ually increasing range of values due to integration and, thus, keeping it alive. Consequently, the observed ...
Directory of Open Access Journals (Sweden)
Burton Nicola W
2009-07-01
Full Text Available Abstract Background Interventions designed to increase workplace physical activity may not automatically reduce high volumes of sitting, a behaviour independently linked to chronic diseases such as obesity and type II diabetes. This study compared the impact two different walking strategies had on step counts and reported sitting times. Methods Participants were white-collar university employees (n = 179; age 41.3 ± 10.1 years; 141 women, who volunteered and undertook a standardised ten-week intervention at three sites. Pre-intervention step counts (Yamax SW-200 and self-reported sitting times were measured over five consecutive workdays. Using pre-intervention step counts, employees at each site were randomly allocated to a control group (n = 60; maintain normal behaviour, a route-based walking group (n = 60; at least 10 minutes sustained walking each workday or an incidental walking group (n = 59; walking in workday tasks. Workday step counts and reported sitting times were re-assessed at the beginning, mid- and endpoint of intervention and group mean± SD steps/day and reported sitting times for pre-intervention and intervention measurement points compared using a mixed factorial ANOVA; paired sample-t-tests were used for follow-up, simple effect analyses. Results A significant interactive effect (F = 3.5; p t = 3.9, p t = 2.5, p Conclusion Compared to controls, both route and incidental walking increased physical activity in white-collar employees. Our data suggests that workplace walking, particularly through incidental movement, also has the potential to decrease employee sitting times, but there is a need for on-going research using concurrent and objective measures of sitting, standing and walking.
Perlmutter, M.
1973-01-01
Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks.
Koschate, J; Drescher, U; Thieschäfer, L; Heine, O; Baum, K; Hoffmann, U
2016-12-01
This study aims to compare cardiorespiratory kinetics as a response to a standardised work rate protocol with pseudo-random binary sequences between cycling and walking in young healthy subjects. Muscular and pulmonary oxygen uptake (V̇O 2 ) kinetics as well as heart rate kinetics were expected to be similar for walking and cycling. Cardiac data and V̇O 2 of 23 healthy young subjects were measured in response to pseudo-random binary sequences. Kinetics were assessed applying time series analysis. Higher maxima of cross-correlation functions between work rate and the respective parameter indicate faster kinetics responses. Muscular V̇O 2 kinetics were estimated from heart rate and pulmonary V̇O 2 using a circulatory model. Muscular (walking vs. cycling [mean±SD in arbitrary units]: 0.40±0.08 vs. 0.41±0.08) and pulmonary V̇O 2 kinetics (0.35±0.06 vs. 0.35±0.06) were not different, although the time courses of the cross-correlation functions of pulmonary V̇O 2 showed unexpected biphasic responses. Heart rate kinetics (0.50±0.14 vs. 0.40±0.14; P=0.017) was faster for walking. Regarding the biphasic cross-correlation functions of pulmonary V̇O 2 during walking, the assessment of muscular V̇O 2 kinetics via pseudo-random binary sequences requires a circulatory model to account for cardio-dynamic distortions. Faster heart rate kinetics for walking should be considered by comparing results from cycle and treadmill ergometry. © Georg Thieme Verlag KG Stuttgart · New York.
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
Random walk of motor planning in task-irrelevant dimensions.
van Beers, Robert J; Brenner, Eli; Smeets, Jeroen B J
2013-02-01
The movements that we make are variable. It is well established that at least a part of this variability is caused by noise in central motor planning. Here, we studied how the random effects of planning noise translate into changes in motor planning. Are the random effects independently added to a constant mean end point, or do they accumulate over movements? To distinguish between these possibilities, we examined repeated, discrete movements in various tasks in which the motor output could be decomposed into a task-relevant and a task-irrelevant component. We found in all tasks that the task-irrelevant component had a positive lag 1 autocorrelation, suggesting that the random effects of planning noise accumulate over movements. In contrast, the task-relevant component always had a lag 1 autocorrelation close to zero, which can be explained by effective trial-by-trial correction of motor planning on the basis of observed motor errors. Accumulation of the effects of planning noise is consistent with current insights into the stochastic nature of synaptic plasticity. It leads to motor exploration, which may subserve motor learning and performance optimization.
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.
Limit theorems for random walks on a strip in subdiffusive regimes
International Nuclear Information System (INIS)
Dolgopyat, D; Goldsheid, I
2013-01-01
We study the asymptotic behaviour of occupation times of a transient random walk (RW) in a quenched random environment (RE) on a strip in a subdiffusive regime. The asymptotic behaviour of hitting times, which is a more traditional object of study, is exactly the same. As a particular case, we solve a long standing problem of describing the asymptotic behaviour of a RW with bounded jumps on a one-dimensional lattice. Our technique results from the development of ideas from our previous work (Dolgopyat and Goldsheid 2012 Commun. Math. Phys. 315 241–77) on the simple RWs in RE and those used in Bolthausen and Goldsheid (2000 Commun. Math. Phys. 214 429–47; 2008 Commun. Math. Phys. 278 253–88) and Goldsheid (2008 Probab. Theory Relat. Fields 141 471–511) for the study of random walks on a strip. (paper)
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.
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...
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.
Conformal invariance self-avoiding walks in the plane or on a random surface
International Nuclear Information System (INIS)
Duplantier, B.
1988-01-01
The two-dimensional (2D) properties of polymers embedded in a solvent, are studied. They are modeled on a lattice by self-avoiding walks. The polymer properties either in the plane with a fixed metric, or on a random 2D surface, where the metric has critical fluctuations, are considered. In the scope of the work, the following topics are discussed: the watermelon topology; the O(n) model and Coulomb gas technique; the model and critical behaviours of polymers on a two-dimensional random lattice; the conformal invariance in a random surface and higher topologies
Corley, B T; Carroll, R W; Hall, R M; Weatherall, M; Parry-Strong, A; Krebs, J D
2018-05-01
To establish whether the risk of hypoglycaemia is greater with 2 consecutive days of very-low-calorie diet compared with 2 non-consecutive days of very-low-calorie diet in people with Type 2 diabetes. This was a non-blinded randomized parallel group interventional trial of intermittent fasting in adults. The participants had a BMI of 30-45 kg/m 2 , Type 2 diabetes treated with metformin and/or hypoglycaemic medications and an HbA 1c concentration of 50-86 mmol/mol (6.7-10%). The participants followed a 2092-2510-kJ diet on 2 days per week for 12 weeks. A total of 41 participants were randomized 1:1 to consecutive (n=19) or non-consecutive (n=22) day fasts, of whom 37 (n=18 and n=19, respectively) were included in the final analysis. The primary outcome was difference in the rate of hypoglycaemia between the two study arms. Secondary outcomes included change in diet, quality of life, weight, lipid, glucose and HbA 1c levels, and liver function. The mean hypoglycaemia rate was 1.4 events over 12 weeks. Fasting increased the rate of hypoglycaemia despite medication reduction (RR 2.05, 95% CI 1.17 to 3.52). There was no difference between fasting on consecutive days and fasting on non-consecutive days (RR 1.54, 95% CI 0.35 to 6.11). Improvements in weight, HbA 1c , fasting glucose and quality of life were experienced by participants in both arms. In individuals with Type 2 diabetes on hypoglycaemic medications, fasting of any type increased the rate of hypoglycaemia. With education and medication reduction, fewer than expected hypoglycaemic events occurred. Although it was not possible to determine whether fasting on consecutive days increased the risk of hypoglycaemia, an acceptable rate was observed in both arms. © 2018 Diabetes UK.
Yang, Jheng-Dao; Tam, Ka-Wai; Huang, Tsai-Wei; Huang, Shih-Wei; Liou, Tsan-Hon; Chen, Hung-Chou
2017-07-01
A meta-analysis. The aim of this study was to perform a comprehensive search of current literature and conduct a meta-analysis of randomized controlled trials (RCTs) to assess the neck pain relieving effect of intermittent cervical traction (ICT). Neck pain is a common and disabling problem with a high prevalence in general population. It causes a considerable burden on the health care system with a substantial expenditure. ICT is a common component of physical therapy for neck pain in the outpatient clinic. However, the evidence regarding the effectiveness of ICT for neck pain is insufficient. Data were obtained from the PubMed, Cochrane Library, Embase, and Scopus databases from the database inception date to July 02, 2016. RCTs reporting the effects of ICT on neck pain, including those comparing the effects of ICT with those of a placebo treatment, were included. Two reviewers independently reviewed the studies, conducted a risk of bias assessment, and extracted data. The data were pooled in a meta-analysis by using a random-effects model. The meta-analysis included seven RCTs. The results indicated that patients who received ICT for neck pain had significantly lower pain scores than those receiving placebos did immediately after treatment (standardized mean difference = -0.26, 95% confidence interval = -0.46 to -0.07). The pain scores during the follow-up period and the neck disability index scores immediately after treatment and during the follow-up period did not differ significantly. ICT may have a short-term neck pain-relieving effect. Some risks of bias were noted in the included studies, reducing the evidence level of this meta-analysis. Additional high-quality RCTs are required to clarify the long-term effects of ICT on neck pain. 1.
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.
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......-tailed distribution of quantities that provide the spatio-temporal coupling in the random-walk process. As an illustration, we present the dielectric permittivity spectra of several butanediol isomers....
Intra-fraction motion of the prostate is a random walk.
Ballhausen, H; Li, M; Hegemann, N-S; Ganswindt, U; Belka, C
2015-01-21
A random walk model for intra-fraction motion has been proposed, where at each step the prostate moves a small amount from its current position in a random direction. Online tracking data from perineal ultrasound is used to validate or reject this model against alternatives. Intra-fraction motion of a prostate was recorded by 4D ultrasound (Elekta Clarity system) during 84 fractions of external beam radiotherapy of six patients. In total, the center of the prostate was tracked for 8 h in intervals of 4 s. Maximum likelihood model parameters were fitted to the data. The null hypothesis of a random walk was tested with the Dickey-Fuller test. The null hypothesis of stationarity was tested by the Kwiatkowski-Phillips-Schmidt-Shin test. The increase of variance in prostate position over time and the variability in motility between fractions were analyzed. Intra-fraction motion of the prostate was best described as a stochastic process with an auto-correlation coefficient of ρ = 0.92 ± 0.13. The random walk hypothesis (ρ = 1) could not be rejected (p = 0.27). The static noise hypothesis (ρ = 0) was rejected (p random walk and neither static (like inter-fraction setup errors) nor stationary (like a cyclic motion such as breathing, for example). The prostate tends to drift away from the isocenter during a fraction, and this variance increases with time, such that shorter fractions are beneficial to the problem of intra-fraction motion. As a consequence, fixed safety margins (which would over-compensate at the beginning and under-compensate at the end of a fraction) cannot optimally account for intra-fraction motion. Instead, online tracking and position correction on-the-fly should be considered as the preferred approach to counter intra-fraction motion.
Random and directed walk-based top-(k) queries in wireless sensor networks.
Fu, Jun-Song; Liu, Yun
2015-05-26
In wireless sensor networks, filter-based top- query approaches are the state-of-the-art solutions and have been extensively researched in the literature, however, they are very sensitive to the network parameters, including the size of the network, dynamics of the sensors' readings and declines in the overall range of all the readings. In this work, a random walk-based top- query approach called RWTQ and a directed walk-based top- query approach called DWTQ are proposed. At the beginning of a top- query, one or several tokens are sent to the specific node(s) in the network by the base station. Then, each token walks in the network independently to record and process the readings in a random or directed way. A strategy of choosing the "right" way in DWTQ is carefully designed for the token(s) to arrive at the high-value regions as soon as possible. When designing the walking strategy for DWTQ, the spatial correlations of the readings are also considered. Theoretical analysis and simulation results indicate that RWTQ and DWTQ both are very robust against these parameters discussed previously. In addition, DWTQ outperforms TAG, FILA and EXTOK in transmission cost, energy consumption and network lifetime.
International Nuclear Information System (INIS)
Musho, M.K.; Kozak, J.J.
1984-01-01
A method is presented for calculating exactly the relative width (sigma 2 )/sup 1/2// , the skewness γ 1 , and the kurtosis γ 2 characterizing the probability distribution function for three random-walk models of diffusion-controlled processes. For processes in which a diffusing coreactant A reacts irreversibly with a target molecule B situated at a reaction center, three models are considered. The first is the traditional one of an unbiased, nearest-neighbor random walk on a d-dimensional periodic/confining lattice with traps; the second involves the consideration of unbiased, non-nearest-neigh bor (i.e., variable-step length) walks on the same d-dimensional lattice; and, the third deals with the case of a biased, nearest-neighbor walk on a d-dimensional lattice (wherein a walker experiences a potential centered at the deep trap site of the lattice). Our method, which has been described in detail elsewhere [P.A. Politowicz and J. J. Kozak, Phys. Rev. B 28, 5549 (1983)] is based on the use of group theoretic arguments within the framework of the theory of finite Markov processes
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.
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...... and a principle for selection of a unique bounded solution is formulated. Fundamental solutions are obtained and compared with the results of direct simulation of the random walks. (c) 2006 Elsevier B.V. All rights reserved....
All-time dynamics of continuous-time random walks on complex networks.
Teimouri, Hamid; Kolomeisky, Anatoly B
2013-02-28
The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social, and economic sciences. Recently, several theoretical approaches have been developed that allowed to analyze explicitly dynamics of CTRW at all times, which is critically important for understanding mechanisms of underlying phenomena. However, theoretical analysis has been done mostly for systems with a simple geometry. Here we extend the original method based on generalized master equations to analyze all-time dynamics of CTRW models on complex networks. Specific calculations are performed for models on lattices with branches and for models on coupled parallel-chain lattices. Exact expressions for velocities and dispersions are obtained. Generalized fluctuations theorems for CTRW models on complex networks are discussed.
The continuous time random walk, still trendy: fifty-year history, state of art and outlook
Kutner, Ryszard; Masoliver, Jaume
2017-03-01
In this article we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism, the numerous modifications permitted by its flexibility, its various applications, and the promising perspectives in the various fields of knowledge. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We focused on a pivotal role of CTRWs mainly in anomalous stochastic processes discovered in physics and beyond. This article plays the role of an extended announcement of the Eur. Phys. J. B Special Issue [ctrw-50-years-on">http://epjb.epj.org/open-calls-for-papers/123-epj-b/1090-ctrw-50-years-on] containing articles which show incredible possibilities of the CTRWs. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Ferrer, Leopoldo E; Romero, David J; Vásquez, Oscar I; Matute, Ednna C; Van de Velde, Marc
2017-11-01
Continuous epidural infusion and programmed intermittent epidural boluses are analgesic techniques routinely used for pain relief in laboring women. We aimed to assess both techniques and compare them with respect to labor analgesia and obstetric outcomes. After Institutional Review Board approval, 132 laboring women aged between 18 and 45 years were randomized to epidural analgesia of 10 mL of a mixture of 0.1% bupivacaine plus 2 µg/mL of fentanyl either by programmed intermittent boluses or continuous infusion (66 per group). Primary outcome was quality of analgesia. Secondary outcomes were duration of labor, total drug dose used, maternal satisfaction, sensory level, motor block level, presence of unilateral motor block, hemodynamics, side effects, mode of delivery, and newborn outcome. Patients in the programmed intermittent epidural boluses group received statistically less drug dose than those with continuous epidural infusion (24.9 vs 34.4 mL bupivacaine; P = 0.01). There was no difference between groups regarding pain control, characteristics of block, hemodynamics, side effects, and Apgar scores. Our study evidenced a lower anesthetic consumption in the programmed intermittent boluses group with similar labor analgesic control, and obstetric and newborn outcomes in both groups.
Englert, G. W.
1971-01-01
A model of the random walk is formulated to allow a simple computing procedure to replace the difficult problem of solution of the Fokker-Planck equation. The step sizes and probabilities of taking steps in the various directions are expressed in terms of Fokker-Planck coefficients. Application is made to many particle systems with Coulomb interactions. The relaxation of a highly peaked velocity distribution of particles to equilibrium conditions is illustrated.
Inferring new indications for approved drugs via random walk on drug-disease heterogenous networks.
Liu, Hui; Song, Yinglong; Guan, Jihong; Luo, Libo; Zhuang, Ziheng
2016-12-23
Since traditional drug research and development is often time-consuming and high-risk, there is an increasing interest in establishing new medical indications for approved drugs, referred to as drug repositioning, which provides a relatively low-cost and high-efficiency approach for drug discovery. With the explosive growth of large-scale biochemical and phenotypic data, drug repositioning holds great potential for precision medicine in the post-genomic era. It is urgent to develop rational and systematic approaches to predict new indications for approved drugs on a large scale. In this paper, we propose the two-pass random walks with restart on a heterogenous network, TP-NRWRH for short, to predict new indications for approved drugs. Rather than random walk on bipartite network, we integrated the drug-drug similarity network, disease-disease similarity network and known drug-disease association network into one heterogenous network, on which the two-pass random walks with restart is implemented. We have conducted performance evaluation on two datasets of drug-disease associations, and the results show that our method has higher performance than six existing methods. A case study on the Alzheimer's disease showed that nine of top 10 predicted drugs have been approved or investigational for neurodegenerative diseases. The experimental results show that our method achieves state-of-the-art performance in predicting new indications for approved drugs. We proposed a two-pass random walk with restart on the drug-disease heterogeneous network, referred to as TP-NRWRH, to predict new indications for approved drugs. Performance evaluation on two independent datasets showed that TP-NRWRH achieved higher performance than six existing methods on 10-fold cross validations. The case study on the Alzheimer's disease showed that nine of top 10 predicted drugs have been approved or are investigational for neurodegenerative diseases. The results show that our method achieves state
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
Biased random walk on critical Galton-Watson trees conditioned to survive
Croydon, David A.; Fribergh, Alexander; Kumagai, Takashi
2012-01-01
We consider the biased random walk on a critical Galton–Watson tree conditioned to survive, and confirm that this model with trapping belongs to the same universality class as certain one-dimensional trapping models with slowly-varying tails. Indeed, in each of these two settings, we establish closely-related functional limit theorems involving an extremal process and also demonstrate extremal aging occurs.
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.
Application of continuous time random walks to transport in porous media
Energy Technology Data Exchange (ETDEWEB)
Margolin, G.; Berkowitz, B.
2000-04-27
The behavior of chemical species as they migrate through heterogeneous porous media is considered. The so-called anomalous transport patterns frequently measured in these materials are quantified in the framework of a continuous time random walk (CTRW) formalism. The physical basis for application of the CTRW is discussed, and new solutions for the first passage time distribution are presented to cover the entire range of transport behaviors. Application of these solutions to analysis of experimental data is also discussed.
Kullgren, Jeffrey T.; Harkins, Kristin A.; Bellamy, Scarlett L.; Gonzales, Amy; Tao, Yuanyuan; Zhu, Jingsan; Volpp, Kevin G.; Asch, David A.; Heisler, Michele; Karlawish, Jason
2014-01-01
Background: Financial incentives and peer networks could be delivered through eHealth technologies to encourage older adults to walk more. Methods: We conducted a 24-week randomized trial in which 92 older adults with a computer and Internet access received a pedometer, daily walking goals, and weekly feedback on goal achievement. Participants…
Random Walk Based Segmentation for the Prostate on 3D Transrectal Ultrasound Images.
Ma, Ling; Guo, Rongrong; Tian, Zhiqiang; Venkataraman, Rajesh; Sarkar, Saradwata; Liu, Xiabi; Nieh, Peter T; Master, Viraj V; Schuster, David M; Fei, Baowei
2016-02-27
This paper proposes a new semi-automatic segmentation method for the prostate on 3D transrectal ultrasound images (TRUS) by combining the region and classification information. We use a random walk algorithm to express the region information efficiently and flexibly because it can avoid segmentation leakage and shrinking bias. We further use the decision tree as the classifier to distinguish the prostate from the non-prostate tissue because of its fast speed and superior performance, especially for a binary classification problem. Our segmentation algorithm is initialized with the user roughly marking the prostate and non-prostate points on the mid-gland slice which are fitted into an ellipse for obtaining more points. Based on these fitted seed points, we run the random walk algorithm to segment the prostate on the mid-gland slice. The segmented contour and the information from the decision tree classification are combined to determine the initial seed points for the other slices. The random walk algorithm is then used to segment the prostate on the adjacent slice. We propagate the process until all slices are segmented. The segmentation method was tested in 32 3D transrectal ultrasound images. Manual segmentation by a radiologist serves as the gold standard for the validation. The experimental results show that the proposed method achieved a Dice similarity coefficient of 91.37±0.05%. The segmentation method can be applied to 3D ultrasound-guided prostate biopsy and other applications.
Distributed clone detection in static wireless sensor networks: random walk with network division.
Directory of Open Access Journals (Sweden)
Wazir Zada Khan
Full Text Available Wireless Sensor Networks (WSNs are vulnerable to clone attacks or node replication attacks as they are deployed in hostile and unattended environments where they are deprived of physical protection, lacking physical tamper-resistance of sensor nodes. As a result, an adversary can easily capture and compromise sensor nodes and after replicating them, he inserts arbitrary number of clones/replicas into the network. If these clones are not efficiently detected, an adversary can be further capable to mount a wide variety of internal attacks which can emasculate the various protocols and sensor applications. Several solutions have been proposed in the literature to address the crucial problem of clone detection, which are not satisfactory as they suffer from some serious drawbacks. In this paper we propose a novel distributed solution called Random Walk with Network Division (RWND for the detection of node replication attack in static WSNs which is based on claimer-reporter-witness framework and combines a simple random walk with network division. RWND detects clone(s by following a claimer-reporter-witness framework and a random walk is employed within each area for the selection of witness nodes. Splitting the network into levels and areas makes clone detection more efficient and the high security of witness nodes is ensured with moderate communication and memory overheads. Our simulation results show that RWND outperforms the existing witness node based strategies with moderate communication and memory overheads.
Distributed clone detection in static wireless sensor networks: random walk with network division.
Khan, Wazir Zada; Aalsalem, Mohammed Y; Saad, N M
2015-01-01
Wireless Sensor Networks (WSNs) are vulnerable to clone attacks or node replication attacks as they are deployed in hostile and unattended environments where they are deprived of physical protection, lacking physical tamper-resistance of sensor nodes. As a result, an adversary can easily capture and compromise sensor nodes and after replicating them, he inserts arbitrary number of clones/replicas into the network. If these clones are not efficiently detected, an adversary can be further capable to mount a wide variety of internal attacks which can emasculate the various protocols and sensor applications. Several solutions have been proposed in the literature to address the crucial problem of clone detection, which are not satisfactory as they suffer from some serious drawbacks. In this paper we propose a novel distributed solution called Random Walk with Network Division (RWND) for the detection of node replication attack in static WSNs which is based on claimer-reporter-witness framework and combines a simple random walk with network division. RWND detects clone(s) by following a claimer-reporter-witness framework and a random walk is employed within each area for the selection of witness nodes. Splitting the network into levels and areas makes clone detection more efficient and the high security of witness nodes is ensured with moderate communication and memory overheads. Our simulation results show that RWND outperforms the existing witness node based strategies with moderate communication and memory overheads.
Hierarchical random walks in trace fossils and the origin of optimal search behavior.
Sims, David W; Reynolds, Andrew M; Humphries, Nicolas E; Southall, Emily J; Wearmouth, Victoria J; Metcalfe, Brett; Twitchett, Richard J
2014-07-29
Efficient searching is crucial for timely location of food and other resources. Recent studies show that diverse living animals use a theoretically optimal scale-free random search for sparse resources known as a Lévy walk, but little is known of the origins and evolution of foraging behavior and the search strategies of extinct organisms. Here, using simulations of self-avoiding trace fossil trails, we show that randomly introduced strophotaxis (U-turns)--initiated by obstructions such as self-trail avoidance or innate cueing--leads to random looping patterns with clustering across increasing scales that is consistent with the presence of Lévy walks. This predicts that optimal Lévy searches may emerge from simple behaviors observed in fossil trails. We then analyzed fossilized trails of benthic marine organisms by using a novel path analysis technique and find the first evidence, to our knowledge, of Lévy-like search strategies in extinct animals. Our results show that simple search behaviors of extinct animals in heterogeneous environments give rise to hierarchically nested Brownian walk clusters that converge to optimal Lévy patterns. Primary productivity collapse and large-scale food scarcity characterizing mass extinctions evident in the fossil record may have triggered adaptation of optimal Lévy-like searches. The findings suggest that Lévy-like behavior has been used by foragers since at least the Eocene but may have a more ancient origin, which might explain recent widespread observations of such patterns among modern taxa.
Fedotov, Sergei; Korabel, Nickolay
2015-12-01
We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bimodal aggregation.
Fedotov, Sergei; Korabel, Nickolay
2015-12-01
We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bimodal aggregation.
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.
Parrondo-like behavior in continuous-time random walks with memory.
Montero, Miquel
2011-11-01
The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.
Exact probability distribution function for multifractal random walk models of stocks
Saakian, D. B.; Martirosyan, A.; Hu, Chin-Kun; Struzik, Z. R.
2011-07-01
We investigate the multifractal random walk (MRW) model, popular in the modelling of stock fluctuations in the financial market. The exact probability distribution function (PDF) is derived by employing methods proposed in the derivation of correlation functions in string theory, including the analytical extension of Selberg integrals. We show that the recent results by Y. V. Fyodorov, P. Le Doussal and A. Rosso obtained with the logarithmic Random Energy Model (REM) model are sufficient to derive exact formulas for the PDF of the log returns in the MRW model.
Combs-Miller, Stephanie A; Kalpathi Parameswaran, Anu; Colburn, Dawn; Ertel, Tara; Harmeyer, Amanda; Tucker, Lindsay; Schmid, Arlene A
2014-09-01
To compare the effects of body weight-supported treadmill training and overground walking training when matched for task and dose (duration/frequency/intensity) on improving walking function, activity, and participation after stroke. Single-blind, pilot randomized controlled trial with three-month follow-up. University and community settings. A convenience sample of participants (N = 20) at least six months post-stroke and able to walk independently were recruited. Thirty-minute walking interventions (body weight-supported treadmill training or overground walking training) were administered five times a week for two weeks. Intensity was monitored with the Borg Rating of Perceived Exertion Scale at five-minute increments to maintain a moderate training intensity. Walking speed (comfortable/fast 10-meter walk), walking endurance (6-minute walk), spatiotemporal symmetry, and the ICF Measure of Participation and ACTivity were assessed before, immediately after, and three months following the intervention. The overground walking training group demonstrated significantly greater improvements in comfortable walking speed compared with the body weight-supported treadmill training group immediately (change of 0.11 m/s vs. 0.06 m/s, respectively; p = 0.047) and three months (change of 0.14 m/s vs. 0.08 m/s, respectively; p = 0.029) after training. Only the overground walking training group significantly improved comfortable walking speed (p = 0.001), aspects of gait symmetry (p = 0.032), and activity (p = 0.003) immediately after training. Gains were maintained at the three-month follow-up (p training was more beneficial than body weight-supported treadmill training at improving self-selected walking speed for the participants in this study. © The Author(s) 2014.
Filling of a Poisson trap by a population of random intermittent searchers
Bressloff, Paul C.
2012-03-01
We extend the continuum theory of random intermittent search processes to the case of N independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi-infinite track. Each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state. We assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process. The hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target; the particle is removed from the system after delivering its cargo. As a further generalization of previous models, we assume that up to n successive particles can find the target and deliver its cargo. Assuming that the rate of target detection scales as 1/N, we show that there exists a well-defined mean-field limit N→ in which the stochastic model reduces to a deterministic system of linear reaction-hyperbolic equations for the concentrations of particles in each of the internal states. These equations decouple from the stochastic process associated with filling the target with cargo. The latter can be modeled as a Poisson process in which the time-dependent rate of filling λ(t) depends on the concentration of stationary particles within the target domain. Hence, we refer to the target as a Poisson trap. We analyze the efficiency of filling the Poisson trap with n particles in terms of the waiting time density f n(t). The latter is determined by the integrated Poisson rate μ(t)=0tλ(s)ds, which in turn depends on the solution to the reaction-hyperbolic equations. We obtain an approximate solution for the particle concentrations by reducing the system of reaction-hyperbolic equations to a scalar advection-diffusion equation using a quasisteady-state analysis. We compare our analytical results for the
A novel Random Walk algorithm with Compulsive Evolution for heat exchanger network synthesis
International Nuclear Information System (INIS)
Xiao, Yuan; Cui, Guomin
2017-01-01
Highlights: • A novel Random Walk Algorithm with Compulsive Evolution is proposed for HENS. • A simple and feasible evolution strategy is presented in RWCE algorithm. • The integer and continuous variables of HEN are optimized simultaneously in RWCE. • RWCE is demonstrated a relatively strong global search ability in HEN optimization. - Abstract: The heat exchanger network (HEN) synthesis can be characterized as highly combinatorial, nonlinear and nonconvex, contributing to unmanageable computational time and a challenge in identifying the global optimal network design. Stochastic methods are robust and show a powerful global optimizing ability. Based on the common characteristic of different stochastic methods, namely randomness, a novel Random Walk algorithm with Compulsive Evolution (RWCE) is proposed to achieve the best possible total annual cost of heat exchanger network with the relatively simple and feasible evolution strategy. A population of heat exchanger networks is first randomly initialized. Next, the heat load of heat exchanger for each individual is randomly expanded or contracted in order to optimize both the integer and continuous variables simultaneously and to obtain the lowest total annual cost. Besides, when individuals approach to local optima, there is a certain probability for them to compulsively accept the imperfect networks in order to keep the population diversity and ability of global optimization. The presented method is then applied to heat exchanger network synthesis cases from the literature to compare the best results published. RWCE consistently has a lower computed total annual cost compared to previously published results.
Stability of a Random Walk Model for Fruiting Body Aggregation in M. xanthus
McKenzie-Smith, G. C.; Schüttler, H. B.; Cotter, C.; Shimkets, L.
2015-03-01
Myxococcus xanthus exhibits the social starvation behavior of aggregation into a fruiting body containing myxospores able to survive harsh conditions. During fruiting body aggregation, individual bacteria follow random walk paths determined by randomly selected runtimes, turning angles, and speeds. We have simulated this behavior in terms of a continuous-time random walk (CTRW) model, re-formulated as a system of integral equations, describing the angle-resolved cell density, R(r, t, θ), at position r and cell orientation angle θ at time t, and angle-integrated ambient cell density ρ(r, t). By way of a linear stability analysis, we investigated whether a uniform cell density R0 will be unstable for a small non-uniform density perturbation δR(r, t, θ). Such instability indicates aggregate formation, whereas stability indicates absence of aggregation. We show that a broadening of CTRW distributions of the random speed and/or random runtimes strongly favors aggregation. We also show that, in the limit of slowly-varying (long-wavelength) density perturbations, the time-dependent linear density response can be approximated by a drift-diffusion model for which we calculate diffusion and drift coefficients as functions of the CTRW model parameters. Funded by the Fungal Genomics and Computational Biology REU at UGA.
Solvable continuous-time random walk model of the motion of tracer particles through porous media
Fouxon, Itzhak; Holzner, Markus
2016-08-01
We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015), 10.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ , length l , and velocity v . We solve our model with independent l and v . The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α . Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α , ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ . Universality of tracer diffusion in the porous medium is considered.
Effects of vacusac in intermittent claudication
DEFF Research Database (Denmark)
Himmelstrup, H; Himmelstrup, Bodil; Mehlsen, J
1991-01-01
The effect of a new physical treatment modality, Vacusac, was tested on a group of patients with stable intermittent claudication. Twenty-two patients with a median age of 65 years and a median duration of intermittent claudication of 5 years were randomized to either active or placebo treatments....... Seventeen patients completed the study. The effect of treatment was quantified by measurements of systemic and peripheral systolic blood pressures and by measurements of the pain-free and the maximal walking distance on a treadmill. The ankle pressure index (ankle systolic pressure/arm systolic pressure......) and toe pressure index (toe systolic pressure/arm systolic pressure) were calculated. After 25 active treatments, administered over a period of 2 months, the patients allocated to this group attained a significant increase in the pain-free walking distance from 54 m (24-107 m) to 99 m (30-420 m) (P less...
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
DEFF Research Database (Denmark)
Oxlund, J; Clausen, A H; Venø, S
2018-01-01
BACKGROUND: Ultrasound-guided interscalene nerve block with ropivacaine as local anesthetic agent given as boluses or continuous infusion is the preferred pain management after major shoulder surgery. The use of automated intermittent boluses has been shown to be superior to continuous infusion....... Patients were allocated to either automated intermittent boluses with 16 mg ropivacaine every 2 h combined with patient-controlled administration or to a conventional regimen of continuous infusion of 8 mg/h (4 ml/h) of ropivacaine combined with patient controlled administration (2 ml, lockout time 30 min......). Pain (Visual Analog Scale, VAS) was assessed every 8 h postoperatively. RESULTS: Fifty-seven patients completed the study, 29 in the continuous infusion group and 28 in the automated intermittent bolus group. Shoulder arthroplasty was performed in 49 (86%) of the cases. There were no significant...
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.
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.
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% (Puse of the HESWO as an alternative support for paraplegic walking. Copyright © 2017. Published by Elsevier B.V.
Directory of Open Access Journals (Sweden)
Dixon H
2017-04-01
Full Text Available Helen Dixon,1 Catherine E Baker,2 Julien S Baker,3 Susan Dewhurst,4 Lawrence D Hayes4 1School of Human Sciences, London Metropolitan University, London, 2English Institute of Sport, Bisham Abbey National Sports Center, Buckinghamshire, 3Institute of Clinical Exercise and Health Science, University of the West of Scotland, Hamilton, 4Department of Medical and Sport Sciences, University of Cumbria, Lancaster, UK Abstract: This study investigated the effect of sodium bicarbonate (NaHCO3– ingestion on the Yo-Yo intermittent recovery test 1 (IR1. We tested the hypothesis that acute ingestion of NaHCO3– would increase blood lactate concentrations [BLa], enhance performance, and reduce rating of perceived exertion (RPE in the Yo-Yo IR1. Eight recreationally active males (N=8, age: 26±4 yr, height: 178±6 cm, body mass: 82±10 kg participated in the Yo-Yo IR1 on two separate occasions, separated by 1 wk, in a randomized crossover design. Following familiarization, during seated rest, participants’ pretest [BLa] was taken, and participants then consumed either a placebo of 0.3 g·kg–1 body weight sodium chloride or 0.3 g·kg–1 body weight NaHCO3–. Sixty minutes postingestion, a standardized warm-up preceded the Yo-Yo IR1. Upon completion, postexercise [BLa] (mmol·L–1, RPE (arbitrary units and Yo-Yo IR1 time to fatigue (s were recorded. Paired t-test revealed a small but significant improvement in Yo-Yo IR1 performance under the NaHCO3– condition (610±267 sec, compared to the placebo condition (556±259 sec; p=0.01; Cohen’s d=0.20. [BLa] increased more under the NaHCO3– condition (1.6±0.7 to 17.5±5.2 mmol·L–1; p<0.001; Cohen’s d=4.29, compared to the placebo condition (2.0±0.7 to 11.5±5.0 mmol·L–1; p=0.001; Cohen’s d=2.66. Postexercise RPE was not significantly different between conditions. The results of this study suggest that acute NaHCO3– ingestion improves Yo-Yo IR1 performance without altering RPE, likely
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
Taniguchi, Chie; Sato, Chifumi
2016-10-01
We examined the effects of home-based walking on sedentary Japanese women's pregnancy outcomes and mood. A randomized controlled trial was conducted, involving 118 women aged 22-36 years. Participants were randomly assigned to walking intervention (n = 60) or control (n = 58) groups. The walking group was instructed to walk briskly for 30 min, three times weekly from 30 weeks' gestation until delivery. Both groups counted their daily steps using pedometers. Pregnancy and delivery outcomes were assessed, participants completed the Profile of Mood States, and we used the intention-to-treat principle. Groups showed no differences regarding pregnancy or delivery outcomes. The walking group exhibited decreased scores on the depression-dejection and confusion subscales of the Profile of Mood States. Five of the 54 women in the intervention group who remained in the study (9.2%) completed 100% of the prescribed walking program; 32 (59.3%) women completed 80% or more. Unsupervised walking improves sedentary pregnant women's mood, indicating that regular walking during pregnancy should be promoted in this group. © 2016 John Wiley & Sons Australia, Ltd.
Makharia, Govind K; Ghoshal, Uday C; Ramakrishna, Balakrishnan S; Agnihotri, Abhishek; Ahuja, Vineet; Chowdhury, Sudipta Dhar; Gupta, Siddhartha Datta; Mechenro, John; Mishra, Asha; Mishra, Asha; Pathak, Manish K; Pandey, Ravinder M; Sharma, Raju; Sharma, Surendra K
2015-09-01
The duration of treatment of gastrointestinal tuberculosis continues to be a matter of debate. The World Health Organization advocates intermittent directly observed short-course therapy (DOTs), but there is a lack of data of its efficacy in abdominal tuberculosis. We therefore conducted a multicenter randomized controlled trial to compare 6 months and 9 months of antituberculosis therapy using DOTs. One hundred ninety-seven patients with abdominal tuberculosis (gastrointestinal, 154; peritoneal, 40; mixed, 3) were randomized to receive 6 months (n = 104) or 9 months (n = 93) of antituberculosis therapy using intermittent directly observed therapy. Patients were followed up 1 year after completion of treatment to assess recurrence. Patients were evaluated for primary endpoint (complete clinical response, partial response, and no response) and secondary endpoint (recurrence of the disease at the end of 1 year of follow-up). Baseline characteristics were similar between the 2 randomized groups. There was no difference between the 6-month group and 9-month group in the complete clinical response rate on per-protocol analysis (91.5% vs 90.8%; P = .88) or intent-to-treat analysis (75% vs 75.8%; P = .89). Only 1 patient in the 9-month group and no patients in the 6-month group had recurrence of disease. Side effects occurred in 21 (21.3%) and 16 (18.2%) patients in the 6-month and 9-month groups, respectively. There was no difference in efficacy of antituberculosis therapy delivered for either 6 months or 9 months in either gastrointestinal or peritoneal tuberculosis, confirming the efficacy of intermittent directly observed therapy. NCT01124929. © The Author 2015. Published by Oxford University Press on behalf of the Infectious Diseases Society of America. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Applications of a general random-walk theory for confined diffusion.
Calvo-Muñoz, Elisa M; Selvan, Myvizhi Esai; Xiong, Ruichang; Ojha, Madhusudan; Keffer, David J; Nicholson, Donald M; Egami, Takeshi
2011-01-01
A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.
Continuous time random walks for non-local radial solute transport
Dentz, Marco; Kang, Peter K.; Le Borgne, Tanguy
2015-08-01
This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile-immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection-dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer
Directory of Open Access Journals (Sweden)
Joana Nunes
Full Text Available Abstract Background: There is evidence that administration of a programmed intermittent epidural bolus (PIEB compared to continuous epidural infusion (CEI leads to greater analgesia efficacy and maternal satisfaction with decreased anesthetic interventions. Methods: In this study, 166 women with viable pregnancies were included. After an epidural loading dose of 10 mL with Ropivacaine 0.16% plus Sufentanil 10 µg, parturient were randomly assigned to one of three regimens: A - Ropivacaine 0.15% plus Sufentanil 0.2 µg/mL solution as continuous epidural infusion (5 mL/h, beginning immediately after the initial bolus; B - Ropivacaine 0.1% plus Sufentanil 0.2 µg/mL as programmed intermittent epidural bolus and C - Same solution as group A as programmed intermittent epidural bolus. PIEB regimens were programmed as 10 mL/h starting 60 min after the initial bolus. Rescue boluses of 5 mL of the same solution were administered, with the infusion pump. We evaluated maternal satisfaction using a verbal numeric scale from 0 to 10. We also evaluated adverse, maternal and neonatal outcomes. Results: We analyzed 130 pregnants (A = 60; B = 33; C = 37. The median verbal numeric scale for maternal satisfaction was 8.8 in group A; 8.6 in group B and 8.6 in group C (p = 0.83. We found a higher caesarean delivery rate in group A (56.7%; p = 0.02. No differences in motor block, instrumental delivery rate and neonatal outcomes were observed. Conclusions: Maintenance of epidural analgesia with programmed intermittent epidural bolus is associated with a reduced incidence of caesarean delivery with equally high maternal satisfaction and no adverse outcomes.
Nunes, Joana; Nunes, Sara; Veiga, Mariano; Cortez, Mara; Seifert, Isabel
2016-01-01
There is evidence that administration of a programmed intermittent epidural bolus (PIEB) compared to continuous epidural infusion (CEI) leads to greater analgesia efficacy and maternal satisfaction with decreased anesthetic interventions. In this study, 166 women with viable pregnancies were included. After an epidural loading dose of 10mL with Ropivacaine 0.16% plus Sufentanil 10μg, parturient were randomly assigned to one of three regimens: A - Ropivacaine 0.15% plus Sufentanil 0.2μg/mL solution as continuous epidural infusion (5mL/h, beginning immediately after the initial bolus); B - Ropivacaine 0.1% plus Sufentanil 0.2μg/mL as programmed intermittent epidural bolus and C - Same solution as group A as programmed intermittent epidural bolus. PIEB regimens were programmed as 10mL/h starting 60min after the initial bolus. Rescue boluses of 5mL of the same solution were administered, with the infusion pump. We evaluated maternal satisfaction using a verbal numeric scale from 0 to 10. We also evaluated adverse, maternal and neonatal outcomes. We analyzed 130 pregnants (A=60; B=33; C=37). The median verbal numeric scale for maternal satisfaction was 8.8 in group A; 8.6 in group B and 8.6 in group C (p=0.83). We found a higher caesarean delivery rate in group A (56.7%; p=0.02). No differences in motor block, instrumental delivery rate and neonatal outcomes were observed. Maintenance of epidural analgesia with programmed intermittent epidural bolus is associated with a reduced incidence of caesarean delivery with equally high maternal satisfaction and no adverse outcomes. Copyright © 2015 Sociedade Brasileira de Anestesiologia. Published by Elsevier Editora Ltda. All rights reserved.
Rote, Aubrianne E; Klos, Lori A; Brondino, Michael J; Harley, Amy E; Swartz, Ann M
2015-06-16
Facebook may be a useful tool to provide a social support group to encourage increases in physical activity. This study examines the efficacy of a Facebook social support group to increase steps/day in young women. Female college freshmen (N = 63) were randomized to one of two 8-week interventions: a Facebook Social Support Group (n = 32) or a Standard Walking Intervention (n = 31). Participants in both groups received weekly step goals and tracked steps/day with a pedometer. Women in the Facebook Social Support Group were also enrolled in a Facebook group and asked to post information about their steps/day and provide feedback to one another. Women in both intervention arms significantly increased steps/day pre- to postintervention (F(8,425) = 94.43, P Facebook Social Support Group increased steps/day significantly more (F(1,138) = 11.34, P Facebook to offer a social support group to increase physical activity in young women. Women in the Facebook Social Support Group increased walking by approximately 1.5 miles/day more than women in the Standard Walking Intervention which, if maintained, could have a profound impact on their future health.
Scaling Law for Photon Transmission through Optically Turbid Slabs Based on Random Walk Theory
Directory of Open Access Journals (Sweden)
Xuesong Li
2012-03-01
Full Text Available Past work has demonstrated the value of a random walk theory (RWT to solve multiple-scattering problems arising in numerous contexts. This paper’s goal is to investigate the application range of the RWT using Monte Carlo simulations and extending it to anisotropic media using scaling laws. Meanwhile, this paper also reiterates rules for converting RWT formulas to real physical dimensions, and corrects some errors which appear in an earlier publication. The RWT theory, validated by the Monte Carlo simulations and combined with the scaling law, is expected to be useful to study multiple scattering and to greatly reduce the computation cost.
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
International Nuclear Information System (INIS)
Lu Dawei; Peng Xinhua; Du Jiangfeng; Zhu Jing; Zou Ping; Yu Yihua; Zhang Shanmin; Chen Qun
2010-01-01
An important quantum search algorithm based on the quantum random walk performs an oracle search on a database of N items with O(√(phN)) calls, yielding a speedup similar to the Grover quantum search algorithm. The algorithm was implemented on a quantum information processor of three-qubit liquid-crystal nuclear magnetic resonance (NMR) in the case of finding 1 out of 4, and the diagonal elements' tomography of all the final density matrices was completed with comprehensible one-dimensional NMR spectra. The experimental results agree well with the theoretical predictions.
Neutral cometary atmospheres. I - An average random walk model for photodissociation in comets
Combi, M. R.; Delsemme, A. H.
1980-01-01
A method for constructing physically realistic photochemical models, taking into account the isotropic ejection of dissociated molecular fragments as well as radiation pressure acceleration, has been developed using Monte Carlo techniques. The effect of the isotropic ejection, as opposed to the radial motion arbitrarily assumed in Haser's model, is adequately described by a simple average random walk model. It is shown that measured radial (Haser) scale lengths are in fact only lower limits to a range of possible true scale lengths for a given brightness profile, which explains the current discrepancies between observed scale lengths and those predicted by photochemistry.
A boundary element-Random walk model of mass transport in groundwater
Kemblowski, M.
1986-01-01
A boundary element solution to the convective mass transport in groundwater is presented. This solution produces a continuous velocity field and reduces the amount of data preparation time and bookkeeping. By combining this solution and the random walk procedure, a convective-dispersive mass transport model is obtained. This model may be easily used to simulate groundwater contamination problems. The accuracy of the boundary element model has been verified by reproducing the analytical solution to a two-dimensional convective mass transport problem. The method was also used to simulate a convective-dispersive problem. ?? 1986.
Complete corrected diffusion approximations for the maximum of a random walk
Blanchet, Jose; Glynn, Peter
2006-01-01
Consider a random walk $(S_n:n\\geq0)$ with drift $-\\mu$ and $S_0=0$. Assuming that the increments have exponential moments, negative mean, and are strongly nonlattice, we provide a complete asymptotic expansion (in powers of $\\mu>0$) that corrects the diffusion approximation of the all time maximum $M=\\max_{n\\geq0}S_n$. Our results extend both the first-order correction of Siegmund [Adv. in Appl. Probab. 11 (1979) 701--719] and the full asymptotic expansion provided in the Gaussian case by Ch...
Doubly charmed baryon mass and wave function through a random walks method
Kerbikov, B. O.
2018-02-01
The mass and the wave function of doubly charmed Ξ cc ++(ccu) baryon are evaluated using Green Function Monte Carlo method to solve the three-body problem with Cornell potential. The mass of Ξ cc ++with spin 1/2 is in a good agreement with the LHCb value. Simulation of the wave function by random walks resulted in a configuration of the quark-diquark type. The radius of Ξ cc ++is much larger than the size needed for a large isospin splitting. The prediction for the Ω cc mass is presented.
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.
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.
Non-Markovian random walks and nonlinear reactions: subdiffusion and propagating fronts.
Fedotov, Sergei
2010-01-01
The main aim of the paper is to incorporate the nonlinear kinetic term into non-Markovian transport equations described by a continuous time random walk (CTRW) with nonexponential waiting time distributions. We consider three different CTRW models with reactions. We derive nonlinear Master equations for the mesoscopic density of reacting particles corresponding to CTRW with arbitrary jump and waiting time distributions. We apply these equations to the problem of front propagation in the reaction-transport systems with Kolmogorov-Petrovskii-Piskunov kinetics and anomalous diffusion. We have found an explicit expression for the speed of a propagating front in the case of subdiffusive transport.
Multi-point Distribution Function for the Continuous Time Random Walk
Barkai, E.; Sokolov, I. M.
2007-01-01
We derive an explicit expression for the Fourier-Laplace transform of the two-point distribution function $p(x_1,t_1;x_2,t_2)$ of a continuous time random walk (CTRW), thus generalizing the result of Montroll and Weiss for the single point distribution function $p(x_1,t_1)$. The multi-point distribution function has a structure of a convolution of the Montroll-Weiss CTRW and the aging CTRW single point distribution functions. The correlation function $$ for the biased CTRW process is found. T...
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.
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
Simulation of a directed random-walk model: the effect of pseudo-random-number correlations
Shchur, L. N.; Heringa, J. R.; Blöte, H. W. J.
1996-01-01
We investigate the mechanism that leads to systematic deviations in cluster Monte Carlo simulations when correlated pseudo-random numbers are used. We present a simple model, which enables an analysis of the effects due to correlations in several types of pseudo-random-number sequences. This model provides qualitative understanding of the bias mechanism in a class of cluster Monte Carlo algorithms.
Maruyama, Yutaka
2017-09-01
In this paper, we show that diffusion phenomena in three-dimensional discontinuous media can be described as a random walk by two simple interface-correction methods, namely step-balance and fictitious-velocity corrections, which are completely different in a physical picture but equivalent in that the continuity of the random walk at interfaces is considered. In both corrections, asymmetric interface permeability of a random walker, which comes from ensuring the continuity, causes apparent confinement of the walker in higher-diffusivity layers for benchmark tests on heat diffusion in two-phase multilayered systems. Effective thermal conductivities (walker diffusivities) computed from the trajectories are in excellent agreement with the series and parallel conduction formulas, indicating the equivalence of the two corrections and the importance of ensuring the continuity of a random walk at interfaces.
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...... 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.......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...
Khan, Rehan Ramzan; Awan, Waqar Ahmad; Rashid, Sajid; Masood, Tahir
2017-01-01
To compare the effectiveness of intermittent cervical Traction in sitting vs. supine position for the management of cervical radiculopathy. A randomized clinical trial was done to compare pain and disability modification of cervical radiculopathy patients by using cervical traction in sitting and supine positions. Forty patients (males and females aged between 18-60 years with chronic cervical radiculopathy) were recruited for the trial. Participants were randomized into two homogeneous groups by dice method. The Group-A (n=20) received 3-weeks of intermittent cervical traction in sitting position along with Transcutaneous Electric Nerve Stimulation (TENS) and hot pack. The Group-B (n=20) received the same treatment except the intermittent cervical traction that was applied in supine position. Participants were assessed two times: at baseline (week 0) and at the termination of rehabilitation (week 3). Neck disability index was used to collect the data before and after the treatment. The mean age of the patients was 43.15±8.99 vs. 48.80±6.89 years in Group-A vs. Group-B respectively. Mean (±S.D.) weight of the patients was 74.75±12.11 vs. 74.60±11.24 kg in Group-A vs. Group-B respectively. Mean Neck Disability Index score at start of treatment was 30.30±7.46 vs. 30.75±7.85 in Group-A and Group-B respectively. There was a significant difference in Group-A and Group-B regarding aggregate NDI score at the end of treatment (19.45±7.12 vs. 11.05±4.40; pcervical traction as compared to sitting position for the management of cervical radiculopathy comparing post interventional NDI score.
Directory of Open Access Journals (Sweden)
Alessandra de Souza Miranda
2013-06-01
Full Text Available CONTEXT: Over the past few years, several clinical trials have been performed to analyze the effects of exercise training on walking ability in patients with intermittent claudication (IC. However, it remains unclear which type of physical exercise provides the maximum benefits in terms of walking ability. OBJECTIVE: To analyze, by means of a meta-analysis, the effects of walking and strength training on the walking capacity in patients with IC. METHODS: Papers analyzing the effects of walking and strength training programs in patients with IC were browsed on the Medline, Lilacs, and Cochrane databases. Randomized clinical trials scoring >4 on the Physiotherapy Evidence Database (PEDro scale and assessing claudication distance (CD and total walking distance (TWD were included in the review. RESULTS: Walking and strength training yielded increases in CD and TWD (P < 0.05. However, walking training yielded greater increases than strength training (P = 0.02. CONCLUSION: Walking and strength training improve walking capacity in patients with IC. However, greater improvements in TWD are obtained with walking training.
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...
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.
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.
IRWRLDA: improved random walk with restart for lncRNA-disease association prediction.
Chen, Xing; You, Zhu-Hong; Yan, Gui-Ying; Gong, Dun-Wei
2016-09-06
In recent years, accumulating evidences have shown that the dysregulations of lncRNAs are associated with a wide range of human diseases. It is necessary and feasible to analyze known lncRNA-disease associations, predict potential lncRNA-disease associations, and provide the most possible lncRNA-disease pairs for experimental validation. Considering the limitations of traditional Random Walk with Restart (RWR), the model of Improved Random Walk with Restart for LncRNA-Disease Association prediction (IRWRLDA) was developed to predict novel lncRNA-disease associations by integrating known lncRNA-disease associations, disease semantic similarity, and various lncRNA similarity measures. The novelty of IRWRLDA lies in the incorporation of lncRNA expression similarity and disease semantic similarity to set the initial probability vector of the RWR. Therefore, IRWRLDA could be applied to diseases without any known related lncRNAs. IRWRLDA significantly improved previous classical models with reliable AUCs of 0.7242 and 0.7872 in two known lncRNA-disease association datasets downloaded from the lncRNADisease database, respectively. Further case studies of colon cancer and leukemia were implemented for IRWRLDA and 60% of lncRNAs in the top 10 prediction lists have been confirmed by recent experimental reports.
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.
Flow-deformed conformations of entangled polymers as persistent random walks
Shnidman, Yitzhak
2007-03-01
Modeling interfacial phenomena in polymer fluids requires resolution of chain conformations on the Kuhn length scale. If the chains are at thermodynamic equilibrium, or undergo flow deformation in the unentangled regime, this is accomplished by representing chain conformations as Wiener (uncorrelated) random walks. When entangled chains are deformed by flow, stretching and orientation of chain strands between successive entanglements entails inertial, as well as diffusive, aspects in the anisotropic propagation model for strand conformation. This is best captured by a persistent (correlated) random walk at constant speed, which is a second-order Markov process governed by the initial probabilities and the scattering rates for the velocities. We present here a generalized Green-Kubo relation linking these parameters to the second moment of the strand's end-to-end distance. The latter evolves according to an approximate differential equation coupling local flow deformation rate with strand stretching and orientation, which relax on distinct time scales [G. Marrucci and G. Ianniruberto, Phil. Trans. R. Soc. Lond. A 361, 677 (2003)]. The proposed relation provides a cornerstone for a new entangled version of our dynamic self-consistent field theory, that thus far has been limited to unentangled inhomogeneous polymer fluids [M. Mihajlovic, T. S. Lo, and Y. Shnidman, Phys. Rev. E 72, 041801 (2005)].
Mendoza, Jason A; Watson, Kathy; Baranowski, Tom; Nicklas, Theresa A; Uscanga, Doris K; Hanfling, Marcus J
2011-09-01
To evaluate the impact of a "walking school bus" program on children's rates of active commuting to school and physical activity. We conducted a pilot cluster randomized controlled trial among 4th-graders from 8 schools in Houston, Texas (N = 149). Random allocation to treatment or control conditions was at the school level. Study staff walked with children to and from school up to 5 days/week. Outcomes were measured the week before (time 1) and during weeks 4 and 5 of the intervention (time 2). The main outcome was the weekly rate of active commuting, and a secondary outcome was moderate-to-vigorous physical activity. Covariates included sociodemographics, distance from home to school, neighborhood safety, child BMI z score, parent self-efficacy/outcome expectations, and child self-efficacy for active commuting. A mixed-model repeated measures regression accounted for clustering by school, and stepwise procedures with backward elimination of nonsignificant covariates were used to identify significant predictors. Intervention children increased active commuting (mean ± SD) from 23.8% ± 9.2% (time 1) to 54% ± 9.2% (time 2), whereas control subjects decreased from 40.2% ± 8.9% (time 1) to 32.6% ± 8.9% (time 2) (P school and daily moderate-to-vigorous physical activity.
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.
Navigational efficiency in a biased and correlated random walk model of individual animal movement.
Bailey, Joseph D; Wallis, Jamie; Codling, Edward A
2018-01-01
Understanding how an individual animal is able to navigate through its environment is a key question in movement ecology that can give insight into observed movement patterns and the mechanisms behind them. Efficiency of navigation is important for behavioral processes at a range of different spatio-temporal scales, including foraging and migration. Random walk models provide a standard framework for modeling individual animal movement and navigation. Here we consider a vector-weighted biased and correlated random walk (BCRW) model for directed movement (taxis), where external navigation cues are balanced with forward persistence. We derive a mathematical approximation of the expected navigational efficiency for any BCRW of this form and confirm the model predictions using simulations. We demonstrate how the navigational efficiency is related to the weighting given to forward persistence and external navigation cues, and highlight the counter-intuitive result that for low (but realistic) levels of error on forward persistence, a higher navigational efficiency is achieved by giving more weighting to this indirect navigation cue rather than direct navigational cues. We discuss and interpret the relevance of these results for understanding animal movement and navigation strategies. © 2017 by the Ecological Society of America.
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.
Geometrical aspects of quantum walks on random two-dimensional structures.
Anishchenko, Anastasiia; Blumen, Alexander; Mülken, Oliver
2013-12-01
We study the transport properties of continuous-time quantum walks (CTQWs) over finite two-dimensional structures with a given number of randomly placed bonds and with different aspect ratios (ARs). Here, we focus on the transport from, say, the left side to the right side of the structure where absorbing sites are placed. We do so by analyzing the long-time average of the survival probability of CTQWs. We compare the results to the classical continuous-time random walk case (CTRW). For small ARs (landscape configurations) we observe only small differences between the quantum and the classical transport properties, i.e., roughly the same number of bonds is needed to facilitate the transport. However, with increasing ARs (portrait configurations) a much larger number of bonds is needed in the CTQW case than in the CTRW case. While for CTRWs the number of bonds needed decreases when going from small ARs to large ARs, for CTQWs this number is large for small ARs, has a minimum for the square configuration, and increases again for increasing ARs. We explain our findings by analyzing the average eigenstates of the corresponding structures: The participation ratios allow us to distinguish between localized and nonlocalized (average) eigenstates. In particular, for large ARs we find for CTQWs that the eigenstates are localized for bond numbers exceeding the bond numbers needed to facilitate transport in the CTRW case. Thus, a rather large number of bonds is needed in order for quantum transport to be efficient for large ARs.
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 the dislocation lines are within narrowly confined spaces. Frame-by-frame analysis of digitized video sequences recorded at different temperatures for the same inclusion attached to a nearly horizontal dislocation illustrates the two types of movement. The step lengths parallel to the dislocation increase rapidly...... with increasing temperature while the step lengths in the transverse movement only display a weak temperature dependence. A detailed statistical analysis of the inclusion trajectories documents that both patterns of movement are random. The activation enthalpy of the one-dimensional movement parallel...... 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...
Asymptotic results for the semi-Markovian random walk with delay
International Nuclear Information System (INIS)
Khaniyev, T.A.; Aliyev, R.T.
2006-12-01
In this study, the semi-Markovian random walk with a discrete interference of chance (X(t) ) is considered and under some weak assumptions the ergodicity of this process is discussed. Characteristic function of the ergodic distribution of X(t) is expressed by means of the probability characteristics of the boundary functionals (N,S N ). Some exact formulas for first and second moments of ergodic distribution of the process X(t) are obtained when the random variable ζ 1 - s, which is describing a discrete interference of chance, has Gamma distribution on the interval [0, ∞) with parameter (α,λ) . Based on these results, the asymptotic expansions with three terms for the first two moments of the ergodic distribution of the process X(t) are obtained, as λ → 0. (author)
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.
Oakley, C; Spafford, C; Beard, J D
2017-05-01
The objective of this study was to collect 1 year follow-up information on walking distance, speed, compliance, and cost in patients with intermittent claudication who took part in a previously reported 12 week randomised clinical trial of a home exercise programme augmented with Nordic pole walking versus controls who walked normally. A second objective was to look at quality of life and ankle brachial pressure indices (ABPIs) after a 12 week augmented home exercise programme. Thirty-two of the 38 patients who completed the original trial were followed-up after 6 and 12 months. Frequency, duration, speed, and distance of walking were recorded using diaries and pedometers. A new observational cohort of 29 patients was recruited to the same augmented home exercise programme. ABPIs, walking improvement, and quality of life questionnaire were recorded at baseline and 12 weeks (end of the programme). Both groups in the follow-up study continued to improve their walking distance and speed over the following year. Compliance was excellent: 98% of the augmented group were still walking with poles at both 6 and 12 months, while 74% of the control group were still walking at the same point. The augmented group increased their mean walking distance to 17.5 km by 12 months, with a mean speed of 4.2 km/hour. The control group only increased their mean walking distance from 4.2 km to 5.6 km, and speed to 3.3 km/hour. Repeated ANOVA showed the results to be highly significant (p = .002). The 21/29 patients who completed the observational study showed a statistically significant increase in resting ABPIs from baseline (mean ± SD 0.75 ± 0.12) to week 12 (mean ± SD 0.85 ± 0.12) (t = (20) -8.89, p = .000 [two-tailed]). All their walking improvement and quality of life parameters improved significantly (p = .002 or less in the six categories) over the same period and their mean health scores improved by 79%. Following a 12 week augmented home exercise
Pedometer-driven Walking for Chronic Low Back Pain A Feasibility Randomized Controlled Trial
McDonough, Suzanne M.; Tully, Mark A.; Boyd, Adele; O’Connor, Seán R.; Kerr, Daniel P.; O’Neill, Siobhán M.; Delitto, Antony; Bradbury, Ian; Tudor-Locke, Catrine; Baxter, George David; Hurley, Deirdre A.
2016-01-01
Objectives To evaluate the feasibility of an RCT of a pedometer driven walking program and education/advice to remain active compared with education/advice only for treatment of chronic low back pain (CLBP). Methods Fifty-seven participants with CLBP recruited from primary care were randomly allocated to either: (1) education/advice (E, n=17) or (2) education/advice plus an 8-week pedometer driven walking program (EWP, n=40). Step targets, actual daily step counts, and adverse events were recorded in a walking diary over the 8 weeks of intervention for the EWP group only. All other outcomes (eg, functional disability using the Oswestry Disability Questionnaire (ODQ), pain scores, physical activity (PA) measurement etc.) were recorded at baseline, week 9 (immediately post intervention), and 6 months in both groups. Results The recruitment rate was 22% and the dropout rate was lower than anticipated (13% to 18% at 6 mo). Adherence with the EWP was high, 93% (n=37/40) walked for ≥6 weeks, and increased their steps/day (mean absolute increase in steps/d, 2776, 95% confidence interval [CI], 1996–3557) by 59% (95% CI, 40.73%–76.25%) from baseline. Mean percentage adherence with weekly step targets was 70% (95% CI, 62%–77%). Eight (20%) minor-related adverse events were observed in 13% (5/40) of the participants. The EWP group participants demonstrated an 8.2% point improvement (95% CI, −13 to −3.4) on the ODQ at 6 months compared with 1.6% points (95% CI, –9.3 to 6.1) for the E group (between group d=0.44). There was also a larger mean improvement in pain (d=0.4) and a larger increase in PA (d=0.59) at 6 months in EWP. Discussion This preliminary study demonstrated that a main RCT is feasible. EWP was safe and produced a real increase in walking; CLBP function and pain improved, and participants perceived a greater improvement in their PA levels. These improvements require confirmation in a fully powered RCT. PMID:23446066
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 ...... 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......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...
Ageing first passage time density in continuous time random walks and quenched energy landscapes
Krüsemann, Henning; Godec, Aljaž; Metzler, Ralf
2015-07-01
We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function \\psi (t)≃ {t}-1-α (0≤slant α ≤slant 2). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time ta, the time elapsed between its preparation and the start of the observation. Subdiffusive ageing CTRWs with 0\\lt α \\lt 1 describe systems such as charge carriers in amorphous semiconducters, tracer dispersion in geological and biological systems, or the dynamics of blinking quantum dots. We derive the exact forms of the first passage time density for an ageing subdiffusive CTRW in the semi-infinite, confined, and biased case, finding different scaling regimes for weakly, intermediately, and strongly aged systems: these regimes, with different scaling laws, are also found when the scaling exponent is in the range 1\\lt α \\lt 2, for sufficiently long ta. We compare our results with the ageing motion of a test particle in a quenched energy landscape. We test our theoretical results in the quenched landscape against simulations: only when the bias is strong enough, the correlations from returning to previously visited sites become insignificant and the results approach the ageing CTRW results. With small bias or without bias, the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found, reflecting the build-up of correlations in the quenched landscape.
International Nuclear Information System (INIS)
Mirinejad, M.; Yaghoubi, A.R.; Azarfarin, R.
2007-01-01
The aim of this study was to compare continuous infusion and intermittent bolus administration of cisatracurium (CA) with respect to total intraoperative dose and time of recovery from neuromuscular blockade after cardiac surgery. From June 2005 to April 2006 sixty patients who undergoing coronary bypass graft and valve replacement surgery were randomized to receive either intermittent bolus (Group A, n=30) or continuous infusion (Group B, n=30) of CA in Madni heart center in Tabriz, Iran.Total intraoperative dose of CA and time to trainoffour (TOF) ratio=0.8 after operation were measured. Anesthesia technique in two groups was the same. Intensity of neuromuscular blockade maintained on one TOF twitch response of adductor pollicis during operation. Mean received dose of CA was 32.8+-20.6 meu/kg/hr in Group A and 89.7+-39.4 meu/kg/hr in Group B (p=0.003). Total intraoperative dose of CA was 23.6+-4.9 mg in Group A and 39.2+-10.1 mg in Group B (p=0.001). Spontaneous recovery from neuromuscular blockade in ICU (TOF ratio=0.8) was reached in 43.8+-9.2 min in Group A, and 64.2+-15.1 min in Group B (p=0.0001). Intubation time in ICU was not significantly different (Group A=8.3+-5.1 hrs vs. Group B=10.2+-6.2 hrs, p=0.256). Intermittent bolus administration of cisatracurium in cardiac surgery with cardiopulmonary bypass used lower intraoperative dose and gave shorter postoperative recovery time as compared to continuous infusion. (author)
Ellery, Adam J; Baker, Ruth E; Simpson, Matthew J
2015-11-24
Random walk models are often used to interpret experimental observations of the motion of biological cells and molecules. A key aim in applying a random walk model to mimic an in vitro experiment is to estimate the Fickian diffusivity (or Fickian diffusion coefficient), D. However, many in vivo experiments are complicated by the fact that the motion of cells and molecules is hindered by the presence of obstacles. Crowded transport processes have been modeled using repeated stochastic simulations in which a motile agent undergoes a random walk on a lattice that is populated by immobile obstacles. Early studies considered the most straightforward case in which the motile agent and the obstacles are the same size. More recent studies considered stochastic random walk simulations describing the motion of an agent through an environment populated by obstacles of different shapes and sizes. Here, we build on previous simulation studies by analyzing a general class of lattice-based random walk models with agents and obstacles of various shapes and sizes. Our analysis provides exact calculations of the Fickian diffusivity, allowing us to draw conclusions about the role of the size, shape and density of the obstacles, as well as examining the role of the size and shape of the motile agent. Since our analysis is exact, we calculate D directly without the need for random walk simulations. In summary, we find that the shape, size and density of obstacles has a major influence on the exact Fickian diffusivity. Furthermore, our results indicate that the difference in diffusivity for symmetric and asymmetric obstacles is significant.
Høyer, Ellen; Jahnsen, Reidun; Stanghelle, Johan Kvalvik; Strand, Liv Inger
2012-01-01
Treadmill training with body weight support (TTBWS) for relearning walking ability after brain damage is an approach under current investigation. Efficiency of this method beyond traditional training is lacking evidence, especially in patients needing walking assistance after stroke. The objective of this study was to investigate change in walking and transfer abilities, comparing TTBWS with traditional walking training. A single-blinded, randomized controlled trial was conducted. Sixty patients referred for multi-disciplinary primary rehabilitation were assigned into one of two intervention groups, one received 30 sessions of TTBWS plus traditional training, the other traditional training alone. Daily training was 1 hr. Outcome measures were Functional Ambulation Categories (FAC), Walking, Functional Independence Measure (FIM); shorter transfer and stairs, 10 m and 6-min walk tests. Substantial improvements in walking and transfer were shown within both groups after 5 and 11 weeks of intervention. Overall no statistical significant differences were found between the groups, but 12 of 17 physical measures tended to show improvements in favour of the treadmill approach. Both training strategies provided significant improvements in the tested activities, suggesting that similar outcomes can be obtained in the two modalities by systematic, intensive and goal directed training.
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
Directory of Open Access Journals (Sweden)
Jila Agah
2014-01-01
Full Text Available Background. Entonox (N2O2 which is an inhalational gas for relieving labor pain is commonly used intermittently; however some women are interested in continuous breathing in face mask. So we decided to compare the complications induced by two methods to find out whether it is safe to permit the mothers to use Entonox continuously or not. Patients and Methods. This randomized clinical trial was performed in Mobini Hospital, Sabzevar, Iran. 50 parturients used Entonox intermittently and 50 cases used it continuously during labor. Then obstetrical outcomes were analyzed in two groups by spss 17 software, t-test, and Chi2 while P<0.05 was considered significant. Results. This study showed the mean duration of second stage of labor had no significant difference (P=0.3. Perineal laceration was less in continuous group significantly (P=0.04. Assisted vaginal birth was not different significantly (P=0.4. Uterine atony had no significant difference in two groups (P=0.2. Maternal collaboration in pushing and satisfaction were higher in continuous group significantly (P=0.03, (P<0.0001. Apgar score of neonates at first and fifth minute was acceptable and not different significantly in two groups (P=0.3. Conclusions. Our study demonstrated continuous method is also safe. So, it seems reasonable to set mothers free to choose the desired method of Entonox usage.
Abad, E; Yuste, S B; Lindenberg, Katja
2010-03-01
Starting from a continuous-time random-walk (CTRW) model of particles that may evanesce as they walk, our goal is to arrive at macroscopic integrodifferential equations for the probability density for a particle to be found at point r at time t given that it started its walk from r_{0} at time t=0 . The passage from the CTRW to an integrodifferential equation is well understood when the particles are not evanescent. Depending on the distribution of stepping times and distances, one arrives at standard macroscopic equations that may be "normal" (diffusion) or "anomalous" (subdiffusion and/or superdiffusion). The macroscopic description becomes considerably more complicated and not particularly intuitive if the particles can die during their walk. While such equations have been derived for specific cases, e.g., for location-independent exponential evanescence, we present a more general derivation valid under less stringent constraints than those found in the current literature.
A random-walk model for pore pressure accumulation in marine soils
DEFF Research Database (Denmark)
Sumer, B. Mutlu; Cheng, Niang-Sheng
1999-01-01
A numerical random-walk model has been developed for the pore-water pressure. The model is based on the analogy between the variation of the pore pressure and the diffusion process of any passive quantity such as concentration. The pore pressure in the former process is analogous...... to the concentration in the latter. In the simulation, particles are released in the soil, and followed as they travel through the statistical field variables. The model has been validated (1) against the Terzaghi consolidation process, and (2) against the process where the pore pressure builds up under progressive...... waves. The model will apparently enable the researcher to handle complex geometries (such as a pipeline buried in a soil) relatively easily. Early results with regard to the latter example, namely the buildup of pore pressure around a buried pipeline subject to a progressive wave, are encouraging....
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.
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.
International Nuclear Information System (INIS)
Ni Xiaohui; Jiang Zhiqiang; Zhou Weixing
2009-01-01
The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.
A random walk description of the heterogeneous glassy dynamics of attracting colloids
Energy Technology Data Exchange (ETDEWEB)
Chaudhuri, Pinaki; Berthier, Ludovic; Kob, Walter [Laboratoire des Colloides, Verres et Nanomateriaux, UMR 5587, Universite Montpellier II and CNRS, 34095 Montpellier (France); Gao Yongxiang; Kilfoil, Maria [Department of Physics, McGill University, Montreal, H3A 2T8 (Canada)], E-mail: berthier@lcvn.univ-montp2.fr
2008-06-18
We study the heterogeneous dynamics of attractive colloidal particles close to the gel transition using confocal microscopy experiments combined with a theoretical statistical analysis. We focus on single particle dynamics and show that the self-part of the van Hove distribution function is not the Gaussian expected for a Fickian process, but that it reflects instead the existence, at any given time, of colloids with widely different mobilities. Our confocal microscopy measurements can be described well by a simple analytical model based on a conventional continuous time random walk picture, as already found for several other glassy materials. In particular, the theory successfully accounts for the presence of broad tails in the van Hove distributions that exhibit exponential, rather than Gaussian, decay at large distance.
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.
Magnetic field line random walk in two-dimensional dynamical turbulence
Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.
2017-08-01
The field line random walk (FLRW) of magnetic turbulence is one of the important topics in plasma physics and astrophysics. In this article, by using the field line tracing method, the mean square displacement (MSD) of FLRW is calculated on all possible length scales for pure two-dimensional turbulence with the damping dynamical model. We demonstrate that in order to describe FLRW with the damping dynamical model, a new dimensionless quantity R is needed to be introduced. On different length scales, dimensionless MSD shows different relationships with the dimensionless quantity R. Although the temporal effect affects the MSD of FLRW and even changes regimes of FLRW, it does not affect the relationship between the dimensionless MSD and dimensionless quantity R on all possible length scales.
Modelling large-particle diffusion in porous media as anisotropic continuous-time random walk
Amitai, Shahar; Blumenfeld, Raphael
We test the fidelity of modelling diffusion of finite-size particles in porous media by continuous-time random walk (CTRW), where the step-size and waiting-time distributions of the former, Pl and Pt, are used as input to the latter. As the particle size is increased, the diffusion undergoes a transition from normal to anomalous. We find that, based only on Pl and Pt, CTRW does not predict correctly this transition. We show that the discrepancy is due to the change in effective connectivity (topology) of the porous media with increasing particle size. We propose a method to capture this within the CTRW model by adding anisotropy. This adjustment yields good agreement with the simulated diffusion process, making it possible to use CTRW, with all its advantages, to model diffusion of any finite size particle in confined geometries.
Energy Technology Data Exchange (ETDEWEB)
van Milligen, B. Ph. [Asociacion EURATOM-CIEMAT; Calvo, Ivan [CIEMAT, Madrid; Sanchez, Raul [ORNL
2008-01-01
The present work studies continuous time random walks (CTRWs) in a finite domain. A broad class of boundary conditions, of which absorbing and reflecting boundaries are particular cases, is considered. It is shown how any CTRW in this class can be mapped to a CTRW in an infinite domain. This may allow applying well-known techniques for infinite CTRWs to the problem of obtaining the fluid limit for finite domain CTRWs, where the fluid limit (or hydrodynamic limit) refers to the partial differential equation describing the long time and large distance behavior of the system. As an illustration, the fluid limit equation and its propagator are obtained explicitly in the case of purely reflecting boundaries. We also derive the modification of the Riemann-Liouville fractional differential operators implementing the reflecting boundary conditions.
V-Langevin equations, continuous time random walks and fractional diffusion
Energy Technology Data Exchange (ETDEWEB)
Balescu, R. [Association Euratom-Etat Belge, Universite Libre de Bruxelles, CP 231, Campus Plaine ULB, Bd du Triomphe, 1050 Brussels (Belgium)
2007-10-15
The following question is addressed: under what conditions can a strange diffusive process, defined by a semi-dynamical V-Langevin equation or its associated hybrid kinetic equation (HKE), be described by an equivalent purely stochastic process, defined by a continuous time random walk (CTRW) or by a fractional differential equation (FDE)? More specifically, does there exist a class of V-Langevin equations with long-range (algebraic) velocity temporal correlation, that leads to a time-fractional superdiffusive process? The answer is always affirmative in one dimension. It is always negative in two dimensions: any algebraically decaying temporal velocity correlation (with a Gaussian spatial correlation) produces a normal diffusive process. General conditions relating the diffusive nature of the process to the temporal exponent of the Lagrangian velocity correlation (in Corrsin approximation) are derived. It is shown that a bifurcation occurs as the latter parameter is varied. Above that bifurcation value the process is always diffusive.
Energy Technology Data Exchange (ETDEWEB)
Milligen, B Ph van; Calvo, I [Asociacion EURATOM-CIEMAT para Fusion, Avda. Complutense 22, 28040 Madrid (Spain); Sanchez, R [Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)], E-mail: boudewijn.vanmilligen@ciemat.es
2008-05-30
The present work studies continuous time random walks (CTRWs) in a finite domain. A broad class of boundary conditions, of which absorbing and reflecting boundaries are particular cases, is considered. It is shown how any CTRW in this class can be mapped to a CTRW in an infinite domain. This may allow applying well-known techniques for infinite CTRWs to the problem of obtaining the fluid limit for finite domain CTRWs, where the fluid limit (or hydrodynamic limit) refers to the partial differential equation describing the long time and large distance behaviour of the system. As an illustration, the fluid limit equation and its propagator are obtained explicitly in the case of purely reflecting boundaries. We also derive the modification of the Riemann-Liouville fractional differential operators implementing the reflecting boundary conditions.
Efficiency analysis of diffusion on T-fractals in the sense of random walks.
Peng, Junhao; Xu, Guoai
2014-04-07
Efficiently controlling the diffusion process is crucial in the study of diffusion problem in complex systems. In the sense of random walks with a single trap, mean trapping time (MTT) and mean diffusing time (MDT) are good measures of trapping efficiency and diffusion efficiency, respectively. They both vary with the location of the node. In this paper, we analyze the effects of node's location on trapping efficiency and diffusion efficiency of T-fractals measured by MTT and MDT. First, we provide methods to calculate the MTT for any target node and the MDT for any source node of T-fractals. The methods can also be used to calculate the mean first-passage time between any pair of nodes. Then, using the MTT and the MDT as the measure of trapping efficiency and diffusion efficiency, respectively, we compare the trapping efficiency and diffusion efficiency among all nodes of T-fractal and find the best (or worst) trapping sites and the best (or worst) diffusing sites. Our results show that the hub node of T-fractal is the best trapping site, but it is also the worst diffusing site; and that the three boundary nodes are the worst trapping sites, but they are also the best diffusing sites. Comparing the maximum of MTT and MDT with their minimums, we find that the maximum of MTT is almost 6 times of the minimum of MTT and the maximum of MDT is almost equal to the minimum for MDT. Thus, the location of target node has large effect on the trapping efficiency, but the location of source node almost has no effect on diffusion efficiency. We also simulate random walks on T-fractals, whose results are consistent with the derived results.
The Walking School Bus and Children's Physical Activity: A Pilot Cluster Randomized Controlled Trial
Watson, Kathy; Baranowski, Tom; Nicklas, Theresa A.; Uscanga, Doris K.; Hanfling, Marcus J.
2011-01-01
OBJECTIVE: To evaluate the impact of a “walking school bus” program on children's rates of active commuting to school and physical activity. METHODS: We conducted a pilot cluster randomized controlled trial among 4th-graders from 8 schools in Houston, Texas (N = 149). Random allocation to treatment or control conditions was at the school level. Study staff walked with children to and from school up to 5 days/week. Outcomes were measured the week before (time 1) and during weeks 4 and 5 of the intervention (time 2). The main outcome was the weekly rate of active commuting, and a secondary outcome was moderate-to-vigorous physical activity. Covariates included sociodemographics, distance from home to school, neighborhood safety, child BMI z score, parent self-efficacy/outcome expectations, and child self-efficacy for active commuting. A mixed-model repeated measures regression accounted for clustering by school, and stepwise procedures with backward elimination of nonsignificant covariates were used to identify significant predictors. RESULTS: Intervention children increased active commuting (mean ± SD) from 23.8% ± 9.2% (time 1) to 54% ± 9.2% (time 2), whereas control subjects decreased from 40.2% ± 8.9% (time 1) to 32.6% ± 8.9% (time 2) (P < .0001). Intervention children increased their minutes of daily moderate-to-vigorous physical activity from 46.6 ± 4.5 (time 1) to 48.8 ± 4.5 (time 2), whereas control children decreased from 46.1 ± 4.3 (time 1) to 41.3 ± 4.3 (time 2) (P = .029). CONCLUSIONS: The program improved children's active commuting to school and daily moderate-to-vigorous physical activity. PMID:21859920
SU-F-BRD-09: A Random Walk Model Algorithm for Proton Dose Calculation
International Nuclear Information System (INIS)
Yao, W; Farr, J
2015-01-01
Purpose: To develop a random walk model algorithm for calculating proton dose with balanced computation burden and accuracy. Methods: Random walk (RW) model is sometimes referred to as a density Monte Carlo (MC) simulation. In MC proton dose calculation, the use of Gaussian angular distribution of protons due to multiple Coulomb scatter (MCS) is convenient, but in RW the use of Gaussian angular distribution requires an extremely large computation and memory. Thus, our RW model adopts spatial distribution from the angular one to accelerate the computation and to decrease the memory usage. From the physics and comparison with the MC simulations, we have determined and analytically expressed those critical variables affecting the dose accuracy in our RW model. Results: Besides those variables such as MCS, stopping power, energy spectrum after energy absorption etc., which have been extensively discussed in literature, the following variables were found to be critical in our RW model: (1) inverse squared law that can significantly reduce the computation burden and memory, (2) non-Gaussian spatial distribution after MCS, and (3) the mean direction of scatters at each voxel. In comparison to MC results, taken as reference, for a water phantom irradiated by mono-energetic proton beams from 75 MeV to 221.28 MeV, the gamma test pass rate was 100% for the 2%/2mm/10% criterion. For a highly heterogeneous phantom consisting of water embedded by a 10 cm cortical bone and a 10 cm lung in the Bragg peak region of the proton beam, the gamma test pass rate was greater than 98% for the 3%/3mm/10% criterion. Conclusion: We have determined key variables in our RW model for proton dose calculation. Compared with commercial pencil beam algorithms, our RW model much improves the dose accuracy in heterogeneous regions, and is about 10 times faster than MC simulations
Avrachenkov, Konstantin; Borkar, Vivek S; Kadavankandy, Arun; Sreedharan, Jithin K
2018-01-01
In the framework of network sampling, random walk (RW) based estimation techniques provide many pragmatic solutions while uncovering the unknown network as little as possible. Despite several theoretical advances in this area, RW based sampling techniques usually make a strong assumption that the samples are in stationary regime, and hence are impelled to leave out the samples collected during the burn-in period. This work proposes two sampling schemes without burn-in time constraint to estimate the average of an arbitrary function defined on the network nodes, for example, the average age of users in a social network. The central idea of the algorithms lies in exploiting regeneration of RWs at revisits to an aggregated super-node or to a set of nodes, and in strategies to enhance the frequency of such regenerations either by contracting the graph or by making the hitting set larger. Our first algorithm, which is based on reinforcement learning (RL), uses stochastic approximation to derive an estimator. This method can be seen as intermediate between purely stochastic Markov chain Monte Carlo iterations and deterministic relative value iterations. The second algorithm, which we call the Ratio with Tours (RT)-estimator, is a modified form of respondent-driven sampling (RDS) that accommodates the idea of regeneration. We study the methods via simulations on real networks. We observe that the trajectories of RL-estimator are much more stable than those of standard random walk based estimation procedures, and its error performance is comparable to that of respondent-driven sampling (RDS) which has a smaller asymptotic variance than many other estimators. Simulation studies also show that the mean squared error of RT-estimator decays much faster than that of RDS with time. The newly developed RW based estimators (RL- and RT-estimators) allow to avoid burn-in period, provide better control of stability along the sample path, and overall reduce the estimation time. Our
First-passage times in multiscale random walks: The impact of movement scales on search efficiency
Campos, Daniel; Bartumeus, Frederic; Raposo, E. P.; Méndez, Vicenç
2015-11-01
An efficient searcher needs to balance properly the trade-off between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free Lévy search strategies. Here we study multiscale random walks as an approximation to the scale-free case and derive the exact expressions for their mean-first-passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the situation in which both nearby and faraway targets are available to the searcher, so the exploration-exploitation trade-off does not have a trivial solution. For this situation, we prove that the combination of only two movement scales is able to outperform both ballistic and Lévy strategies. This two-scale strategy involves an optimal discrimination between the nearby and faraway targets which is only possible by adjusting the range of values of the two movement scales to the typical distances between encounters. So, this optimization necessarily requires some prior information (albeit crude) about target distances or distributions. Furthermore, we found that the incorporation of additional (three, four, …) movement scales and its adjustment to target distances does not improve further the search efficiency. This allows us to claim that optimal random search strategies arise through the informed combination of only two walk scales (related to the exploitative and the explorative scales, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through Lévy paths (or, equivalently, through a hierarchical combination of multiple scales).
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.
Fluid limit of the continuous-time random walk with general Levy jump distribution functions
Energy Technology Data Exchange (ETDEWEB)
Cartea, A. [Birbeck College, University of London; Del-Castillo-Negrete, Diego B [ORNL
2007-01-01
The continuous time random walk (CTRW) is a natural generalization of the Brownian random walk that allows the incorporation of waiting time distributions psi(t) and general jump distribution functions eta(x). There are two well-known fluid limits of this model in the uncoupled case. For exponential decaying waiting times and Gaussian jump distribution functions the fluid limit leads to the diffusion equation. On the other hand, for algebraic decaying waiting times psi similar to t(-(1+beta)) and algebraic decaying jump distributions eta similar to x(-(1+alpha)) corresponding to Levy stable processes, the fluid limit leads to the fractional diffusion equation of order alpha in space and order beta in time. However, these are two special cases of a wider class of models. Here we consider the CTRW for the most general Levy stochastic processes in the Levy-Khintchine representation for the jump distribution function and obtain an integrodifferential equation describing the dynamics in the fluid limit. The resulting equation contains as special cases the regular and the fractional diffusion equations. As an application we consider the case of CTRWs with exponentially truncated Levy jump distribution functions. In this case the fluid limit leads to a transport equation with exponentially truncated fractional derivatives which describes the interplay between memory, long jumps, and truncation effects in the intermediate asymptotic regime. The dynamics exhibits a transition from superdiffusion to subdiffusion with the crossover time scaling as tau(c)similar to lambda(-alpha/beta), where 1/lambda is the truncation length scale. The asymptotic behavior of the propagator (Green's function) of the truncated fractional equation exhibits a transition from algebraic decay for t <
Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach
Comolli, Alessandro; Dentz, Marco
2017-09-01
We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy's law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in
Continuous Time Random Walks and the Causes of Non-Fickian Transport in Heterogeneous Media
Dentz, M.; Le Borgne, T.; Kang, P. K.
2015-12-01
Solute transport in heterogeneous porous media is in generalnon-Fickian, this means it shows behaviors that do not conform toadvection-dispersion models characterized by constant equivalent transportparameters. The causes for such behaviors are manifold, while their quantitative relation to large scale non-Fickian transport is often not known. We address the questions of (i) how different heterogeneity and microscale transport mechanisms manifest in large scale transport behavior, (ii) which are their impacts on anomalous solute dispersion, and (iii) how they can be quantified in terms of large scale dynamics. We focus here on the roles of medium and flow heterogeneity, mass transfer between mobile and immobile zones, as well as spatially variable retardation properties on large scale anomalous transport. Starting from the different microscale heterogeneity and transport dynamics, we use a stochastic modeling approach to coarse grain and average particle transport in a Lagrangian modeling framework, and quantify the large scale particle dynamics in terms of continuous time random walks (CTRW). The large scale particle movements are characterized in terms of a random space increment, which can be related to the heterogeneity structure and geometry, and a random time increment, which is quantified in terms of the heterogeneity distribution. We present the CTRW models resulting from the differentheterogeneity scenarios and analyze their transport signatures in terms of solute dispersion and breakthrough curves.
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...
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 0random walk. From these analytical results we establish a generalization of Polya’s recurrence theorem for fractional random walks on d-dimensional infinite lattices: The fractional random walk is transient for dimensions d > α (recurrent for d≤slantα ) of the lattice. As a consequence, for 0random walk is transient for all lattice dimensions d=1, 2, .. and in the range 1≤slantα walk is transient only for lattice dimensions d≥slant 3 . The generalization of Polya’s recurrence theorem remains valid for the class of random walks with Lévy flight asymptotics for long-range steps. We also analyze the mean first passage probabilities, mean residence times, mean first passage times and global mean first passage times (Kemeny constant) for the fractional random walk. For an infinite 1D lattice (infinite ring) we obtain for the transient regime 0random walk is generated by the non-diagonality of the fractional Laplacian matrix with Lévy-type heavy tailed inverse power law decay for the probability of long-range moves. This non-local and asymptotic behavior of the fractional random walk introduces small-world properties with the emergence of Lévy flights on large (infinite) lattices.
Kamienkowski, Juan E.; Pashler, Harold; Dehaene, Stanislas; Sigman, Mariano
2011-01-01
Does extensive practice reduce or eliminate central interference in dual-task processing? We explored the reorganization of task architecture with practice by combining interference analysis (delays in dual-task experiment) and random-walk models of decision making (measuring the decision and non-decision contributions to RT). The main delay…
An Application of the Random Walk Model to Proper Motions of Coronal Bright Points from SDO Data
Czech Academy of Sciences Publication Activity Database
Skokić, Ivica; Sudar, D.; Saar, S.H.; Brajša, R.; Poljančić-Beljan, I.
2016-01-01
Roč. 40, č. 1 (2016), s. 23-28 ISSN 1845-8319. [Hvar Astrophysical Colloquium /14./. Hvar, 26.09.2016-30.09.2016] EU Projects: European Commission(XE) 312495 - SOLARNET Institutional support: RVO:67985815 Keywords : Sun * coronal bright points * random walk Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics
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=
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).…
Kottink, A.I.R.; Kottink, Anke I.; Hermens, Hermanus J.; Nene, A.V.; Tenniglo, Martinus Johannes Bernardus; van der Aa, Hans E.; Buschman, H.P.J.; IJzerman, Maarten Joost
Objective To determine the effect of a new implantable 2-channel peroneal nerve stimulator on walking speed and daily activities, in comparison with the usual treatment in chronic stroke survivors with a drop foot. Design Randomized controlled trial. Setting All subjects were measured 5 times in the
Random walks with statistical shape prior for cochlea and inner ear segmentation in micro-CT images
DEFF Research Database (Denmark)
Ruiz Pujadas, Esmeralda; Piella, Gemma; Kjer, Hans Martin
2017-01-01
-CT cochlear images using random walks, where a region term estimated by a Gaussian mixture model is combined with a shape prior initially obtained by a statistical shape model (SSM). The region term can then take advantage of the high contrast between the background and foreground, while the shape prior...
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…
Czech Academy of Sciences Publication Activity Database
Šolc, Milan
2005-01-01
Roč. 219, č. 8 (2005), s. 1185-1189 ISSN 0942-9352 Institutional research plan: CEZ:AV0Z40320502 Keywords : random walk * fluctuation * chemical equilibrum Subject RIV: CA - Inorganic Chemistry Impact factor: 1.161, year: 2005
Stavrakis, Stavros; Stoner, Julie A; Kardokus, Joel; Garabelli, Paul J; Po, Sunny S; Lazzara, Ralph
2017-01-01
We hypothesized that intermittent anticoagulation based on daily rhythm monitoring using the novel oral anticoagulants (NOACs) is feasible and safe among patients with paroxysmal atrial fibrillation (AF). Patients with paroxysmal AF and ≥1 risk factors for stroke were randomized to either intermittent or continuous anticoagulation. Those in the intermittent group were instructed to transmit a daily ECG using an iPhone-based rhythm monitoring device. If AF was detected, patients received one of the NOACs for 48 h-1 week. Patients who failed to transmit an ECG for three consecutive days or more than 7 days total were crossed over to continuous anticoagulation. Patients in the continuous group received one of the NOACs. Fifty-eight patients were randomized to either intermittent (n = 29) or continuous anticoagulation (n = 29). Over a median follow-up of 20 months, 20 patients in the intermittent group failed to submit a daily ECG at least once (median three failed submissions). Four patients (14 %) crossed over to continuous anticoagulation due to failure to submit an ECG for three consecutive days. One stroke (continuous group) occurred during the study. Major bleeding occurred in two patients in the continuous and one patient in the intermittent group, after crossing over to continuous anticoagulation. In a prespecified per-protocol analysis, gastrointestinal bleeding was more frequent in the continuous group (16 vs. 0 %; p = 0.047). Intermittent anticoagulation based on daily rhythm monitoring is feasible and may decrease bleeding in low-risk patients with paroxysmal AF. A larger trial, adequately powered to detect clinical outcomes, is warranted.
Brach, Jennifer S; Van Swearingen, Jessie M; Perera, Subashan; Wert, David M; Studenski, Stephanie
2013-11-01
To compare the effect of motor learning with that of standard exercise on measures of mobility and perceived function and disability. Single-blind randomized trial. University research center. Older adults (n = 40) with a mean age of 77.1 ± 6.0, normal walking speed (≥ 1.0 m/s), and impaired motor skills (Figure of 8 walk time >8 seconds). The motor learning program incorporated goal-oriented stepping and walking to promote timing and coordination within the phases of the gait cycle. The standard program employed endurance training by treadmill walking. Both included strength training and were offered twice weekly for 1 hour for 12 weeks. Primary outcomes were mobility performance (gait efficiency, motor skill in walking, gait speed, walking endurance); secondary outcomes were perceived function and disability (Late-Life Function and Disability Instrument). Thirty-eight of 40 participants completed the trial (motor learning, n = 18; standard, n = 20). The motor learning group improved more than the standard group in gait speed (0.13 vs 0.05 m/s, P = .008) and motor skill (-2.2 vs -0.89 seconds, P endurance (28.3 and 22.9 m, P = .14). Changes in gait efficiency and perceived function and disability were not different between the groups (P > .10). In older adults with subclinical gait dysfunction, motor learning exercise improved some parameters of mobility performance more than standard exercise. © 2013, Copyright the Authors Journal compilation © 2013, The American Geriatrics Society.
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 Markov random walk under constraint for discovering overlapping communities in complex networks
International Nuclear Information System (INIS)
Jin, Di; Yang, Bo; Liu, Dayou; He, Dongxiao; Liu, Jie; Baquero, Carlos
2011-01-01
The detection of overlapping communities in complex networks has motivated recent research in relevant fields. Aiming to address this problem, we propose a Markov-dynamics-based algorithm, called UEOC, which means 'unfold and extract overlapping communities'. In UEOC, when identifying each natural community that overlaps, a Markov random walk method combined with a constraint strategy, which is based on the corresponding annealed network (degree conserving random network), is performed to unfold the community. Then, a cutoff criterion with the aid of a local community function, called conductance, which can be thought of as the ratio between the number of edges inside the community and those leaving it, is presented to extract this emerged community from the entire network. The UEOC algorithm depends on only one parameter whose value can be easily set, and it requires no prior knowledge of the hidden community structures. The proposed UEOC has been evaluated both on synthetic benchmarks and on some real-world networks, and has been compared with a set of competing algorithms. The experimental result has shown that UEOC is highly effective and efficient for discovering overlapping communities
Random Walk on a Perturbation of the Infinitely-Fast Mixing Interchange Process
Salvi, Michele; Simenhaus, François
2018-03-01
We consider a random walk in dimension d≥1 in a dynamic random environment evolving as an interchange process with rate γ >0 . We prove that, if we choose γ large enough, almost surely the empirical velocity of the walker X_t/t eventually lies in an arbitrary small ball around the annealed drift. This statement is thus a perturbation of the case γ =+∞ where the environment is refreshed between each step of the walker. We extend three-way part of the results of Huveneers and Simenhaus (Electron J Probab 20(105):42, 2015), where the environment was given by the 1-dimensional exclusion process: (i) We deal with any dimension d≥1 ; (ii) We treat the much more general interchange process, where each particle carries a transition vector chosen according to an arbitrary law μ ; (iii) We show that X_t/t is not only in the same direction of the annealed drift, but that it is also close to it.
Movements of Rana catesbeiana tadpoles in weak current flows resemble a directed random walk.
Schmidt, Brian P; Knowles, Jeffrey M; Simmons, Andrea Megela
2011-07-15
Current flow is an important biological stimulus for larval anuran amphibians, but little is known about how it is perceived. We quantified behavioral responses to controlled water flow in the bullfrog tadpole (Rana catesbeiana) at developmental stages prior to metamorphic climax, and examined the contribution of a functioning lateral line system to these behaviors. Tadpoles at these developmental stages show a significant preference for the sides and bottom of a flow tank. In response to water flow at three different rates, they exhibit a significant, time-dependent tendency to move downstream, away from the source of the flow, and to remain in areas where flow is minimized. The consistency of these behaviors at all tested flow rates suggests that the animals are not simply passively pushed by the current; instead, they actively swim away from the current source. Tadpoles do not exhibit positive rheotaxis towards the source of the flow at any flow rate but as a group are randomly oriented. Treatment with cobalt chloride, a known blocker of superficial neuromast function, significantly reduces the tendency to move downstream, but does not alter the preference for the sides and bottom of the tank. Tadpoles' movements under flow are consistent with a model of locomotion based on a directed random walk.
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.
Range walk error correction and modeling on Pseudo-random photon counting system
Shen, Shanshan; Chen, Qian; He, Weiji
2017-08-01
Signal to noise ratio and depth accuracy are modeled for the pseudo-random ranging system with two random processes. The theoretical results, developed herein, capture the effects of code length and signal energy fluctuation are shown to agree with Monte Carlo simulation measurements. First, the SNR is developed as a function of the code length. Using Geiger-mode avalanche photodiodes (GMAPDs), longer code length is proven to reduce the noise effect and improve SNR. Second, the Cramer-Rao lower bound on range accuracy is derived to justify that longer code length can bring better range accuracy. Combined with the SNR model and CRLB model, it is manifested that the range accuracy can be improved by increasing the code length to reduce the noise-induced error. Third, the Cramer-Rao lower bound on range accuracy is shown to converge to the previously published theories and introduce the Gauss range walk model to range accuracy. Experimental tests also converge to the presented boundary model in this paper. It has been proven that depth error caused by the fluctuation of the number of detected photon counts in the laser echo pulse leads to the depth drift of Time Point Spread Function (TPSF). Finally, numerical fitting function is used to determine the relationship between the depth error and the photon counting ratio. Depth error due to different echo energy is calibrated so that the corrected depth accuracy is improved to 1cm.
Transmembrane protein CD93 diffuses by a continuous time random walk.
Goiko, Maria; de Bruyn, John; Heit, Bryan
Molecular motion within the cell membrane is a poorly-defined process. In this study, we characterized the diffusion of the transmembrane protein CD93. By careful analysis of the dependence of the ensemble-averaged mean squared displacement (EA-MSD, r2) on time t and the ensemble-averaged, time-averaged MSD (EA-TAMSD, δ2) on lag time τ and total measurement time T, we showed that the motion of CD93 is well-described by a continuous-time random walk (CTRW). CD93 tracks were acquired using single particle tracking. The tracks were classified as confined or free, and the behavior of the MSD analyzed. EA-MSDs of both populations grew non-linearly with t, indicative of anomalous diffusion. Their EA-TAMSDs were found to depend on both τ and T, indicating non-ergodicity. Free molecules had r2 tα and δ2 (τ /T 1 - α) , with α 0 . 5 , consistent with a CTRW. Mean maximal excursion analysis supported this result. Confined CD93 had r2 t0 and δ2 (τ / T) α , with α 0 . 3 , consistent with a confined CTRW. CTRWs are described by a series of random jumps interspersed with power-law distributed waiting times, and may arise due to the interactions of CD93 with the endocytic machinery. NSERC.
Optimal intermittent search strategies: smelling the prey
International Nuclear Information System (INIS)
Revelli, J A; Wio, H S; Rojo, F; Budde, C E
2010-01-01
We study the kinetics of the search of a single fixed target by a searcher/walker that performs an intermittent random walk, characterized by different states of motion. In addition, we assume that the walker has the ability to detect the scent left by the prey/target in its surroundings. Our results, in agreement with intuition, indicate that the prey's survival probability could be strongly reduced (increased) if the predator is attracted (or repelled) by the trace left by the prey. We have also found that, for a positive trace (the predator is guided towards the prey), increasing the inhomogeneity's size reduces the prey's survival probability, while the optimal value of α (the parameter that regulates intermittency) ceases to exist. The agreement between theory and numerical simulations is excellent.
Directory of Open Access Journals (Sweden)
Raphael Mendes Ritti-Dias
2009-02-01
Full Text Available FUNDAMENTO: O Walking Impairment Questionnaire (WIQ tem sido utilizado para a obtenção de informações sobre a percepção de locomoção dos indivíduos com claudicação intermitente (CI. Entretanto, esse questionário ainda não foi traduzido para o idioma português, o que limita sua utilização em amostra brasileira. OBJETIVO: Traduzir e verificar a validade e reprodutibilidade do WIQ em brasileiros com CI. MÉTODOS: Participaram deste estudo 42 indivíduos com CI, diagnosticados pelo índice tornozelo-braço FUNDAMENTO: El Walking Impairment Questionnaire (WIQ se utiliza para la obtención de informaciones sobre la percepción de locomoción de los individuos con claudicación intermitente (CI. No obstante, este cuestionario aún no ha sido traducido al portugués, lo que limita su utilización en muestra brasileña. OBJETIVO: Traducir y verificar la validez y reproducibilidad del WIQ en brasileños con CI. MÉTODOS: Participaron en este estudio 42 individuos con CI, diagnosticados por el índice tobillo-brazo BACKGROUND: The Walking Impairment Questionnaire (WIQ has been used to evaluate walking impairment in subjects with intermittent claudication (IC. However, this questionnaire has yet to be translated to Brazilian Portuguese, which limits its use in Brazilian subjects. OBJECTIVE: To translate and analyze the validity and reliability of WIQ in Brazilian subjects with IC. METHODS: Forty-two patients with IC, determined by the ankle-brachial index < 0.90, participated in the study. After translation and re-translation, carried out by two independent translators, the construct validity of the WIQ was analyzed by correlating the WIQ scores with the Medical Outcome Study Questionnaire Short Form 36 (SF-36 scores and the physical fitness performance (treadmill and strength tests. The reliability was analyzed with a 7-day interval between two questionnaire applications. RESULTS: Significant correlations between the WIQ domains and the SF
Johansson, Kerstin; Greis, Gunvor; Johansson, Birgit; Grundtmann, Agneta; Pahlby, Yvonne; Törn, Solveig; Axelberg, Hanna; Carlsson, Petrea
2013-02-01
Polyvinyl chloride (PVC) is commonly used as a catheter material in catheters for clean intermittent catheterization (CIC) but, owing mainly to environmental concerns, a PVC-free material has been proposed. The objective of this study was to compare patients' tolerability for catheters made of PVC and a newly developed PVC-free material. This was a prospective, randomized, crossover study in 104 male patients with maintained urethra sensibility who practised CIC. The patients evaluated in a randomized order a PVC and a PVC-free LoFric® catheter after 1 week's use of each. The material properties and tolerability, i.e. reported perceived discomfort, of each catheter were compared and adverse events documented. Twenty-nine (28%) and 15 (14%) patients reported discomfort when using the PVC catheter and the PVC-free LoFric catheter, respectively. A comparison showed that five patients (5%) reported discomfort with the PVC-free and not with the PVC catheter, and 19 patients (18%) reported discomfort with the PVC and not with the PVC-free catheter (p = 0.0066). Forty patients reported a total of 91 adverse events, of which the most common were discomfort in terms of pain, a burning sensation and bleeding. Generally low discomfort rates were reported in the study population, suggesting a high tolerance for CIC with catheters of both the PVC and the PVC-free materials. The lowest discomfort was, however, found when CIC was performed using the PVC-free LoFric catheter.
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。...
Lee, Kyoung O; Holmes, Thomas W; Calderon, Adan F; Gardner, Robin P
2012-05-01
Using a Monte Carlo (MC) simulation, random walks were used for pebble tracking in a two-dimensional geometry in the presence of a biased gravity field. We investigated the effect of viscosity damping in the presence of random Gaussian fluctuations. The particle tracks were generated by Molecular Dynamics (MD) simulation for a Pebble Bed Reactor. The MD simulations were conducted in the interaction of noncohesive Hertz-Mindlin theory where the random walk MC simulation has a correlation with the MD simulation. This treatment can easily be extended to include the generation of transient gamma-ray spectra from a single pebble that contains a radioactive tracer. Then the inverse analysis thereof could be made to determine the uncertainty of the realistic measurement of transient positions of that pebble by any given radiation detection system designed for that purpose. Copyright Â© 2011 Elsevier Ltd. All rights reserved.
2013-01-01
Background Regaining independent ambulation is the top priority for individuals recovering from stroke. Thus, physical rehabilitation post-stroke should focus on improving walking function and endurance. However, the amount of walking completed by individuals with stroke attending rehabilitation is far below that required for independent community ambulation. There has been increased interest in accelerometer-based monitoring of walking post-stroke. Walking monitoring could be integrated within the goal-setting process for those with ambulation goals in rehabilitation. The feedback from these devices can be downloaded to a computer to produce reports. The purpose of this study is to determine the effect of accelerometer-based feedback of daily walking activity during rehabilitation on the frequency and duration of walking post-stroke. Methods Participants will be randomly assigned to one of two groups: feedback or no feedback. Participants will wear accelerometers daily during in- and out-patient rehabilitation and, for participants in the feedback group, the participants’ treating physiotherapist will receive regular reports of walking activity. The primary outcome measures are the amount of daily walking completed, as measured using the accelerometers, and spatio-temporal characteristics of walking (e.g. walking speed). We will also examine goal attainment, satisfaction with progress towards goals, stroke self-efficacy, and community-integration. Discussion Increased walking activity during rehabilitation is expected to improve walking function and community re-integration following discharge. In addition, a focus on altering walking behaviour within the rehabilitation setting may lead to altered behaviour and increased activity patterns after discharge. Trial registration ClinicalTrials.gov NCT01521234 PMID:23865593
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.
A Non-Lévy Random Walk in Chacma Baboons: What Does It Mean?
Sueur, Cédric
2011-01-01
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...
Kravtsov, V E; Yevtushenko, O M; Snajberk, P; Cuevas, E
2012-08-01
We employ the method of virial expansion to compute the retarded density correlation function (generalized diffusion propagator) in the critical random matrix ensemble in the limit of strong multifractality. We find that the long-range nature of the Hamiltonian is a common root of both multifractality and Lévy flights, which show up in the power-law intermediate- and long-distance behaviors, respectively, of the density correlation function. We review certain models of classical random walks on fractals and show the similarity of the density correlation function in them to that for the quantum problem described by the random critical long-range Hamiltonians.
Jung, Kyeong-Man; Bang, Dae-Hyouk
2017-02-01
[Purpose] To investigate the effects of inspiratory muscle training on respiratory capacity and walking ability in subacute stroke patients. [Subjects and Methods] The subjects were randomly assigned to an experimental group (n=6) or a control group (n=6). Patients in the experimental group received inspiratory muscle training for 30 minutes (six sets of five-minutes) and traditional physical therapy once a day, five days a week, for four weeks. The control group received aerobic exercise for 30 minutes and traditional physical therapy for 30 minutes a day, five days a week, for four weeks. [Results] After the intervention, both groups showed significant improvements in the forced vital capacity, forced expiratory volume in one second, 10-meter walking test, and six-minute walking test over the baseline results. There were significant between-group differences for the forced vital capacity, forced expiratory volume in one second, and six-minute walking test. No statistically significant differences were observed for measures of saturation pulse oximetry oxygen and 10-meter walking test between the groups. [Conclusion] These findings gave some indications that inspiratory muscle training may benefit in patients with subacute stroke, and it is feasible to be included in rehabilitation program with this population.
Ikenaga, Masahiro; Yamada, Yosuke; Kose, Yujiro; Morimura, Kazuhiro; Higaki, Yasuki; Kiyonaga, Akira; Tanaka, Hiroaki
2017-01-01
We developed a short-interval, low-intensity, slow-jogging (SJ) program consisting of sets of 1 min of SJ at walking speed and 1 min of walking. We aimed to examine the effects of an easily performed SJ program on skeletal muscle, fat infiltration, and fitness in older adults. A total of 81 community-dwelling, independent, older adults (70.8 ± 4.0 years) were randomly assigned to the SJ or control group. The SJ group participants were encouraged to perform 90 min of SJ at their anaerobic threshold (AT) intensity and 90 min of walking intermittently per week. Aerobic capacity at the AT and sit-to-stand (STS) scores were measured. Intracellular water (ICW) in the legs was assessed by segmental multi-frequency bioelectrical impedance analysis. Subcutaneous (SAT) and intermuscular (IMAT) adipose tissue and muscle cross-sectional area (CSA) were measured at the mid-thigh using computed tomography. A total of 75 participants (37 SJ group, 38 controls) completed the 12-week intervention. The AT and STS improved in the SJ group compared with the controls (AT 15.7 vs. 4.9 %, p < 0.01; STS 12.9 vs. 4.5 %, p < 0.05). ICW in the upper leg increased only in the SJ group (9.7 %, p < 0.05). SAT and IMAT were significantly decreased only in the SJ group (p < 0.01). The 12-week SJ program was easily performed by older adults with low skeletal muscle mass, improved aerobic capacity, muscle function, and muscle composition in older adults.
Directory of Open Access Journals (Sweden)
Badara Cisse
Full Text Available BACKGROUND: The long terminal half life of piperaquine makes it suitable for intermittent preventive treatment for malaria but no studies of its use for prevention have been done in Africa. We did a cluster randomized trial to determine whether piperaquine in combination with either dihydroartemisin (DHA or sulfadoxine-pyrimethamine (SP is as effective, and better tolerated, than SP plus amodiaquine (AQ, when used for intermittent preventive treatment in children delivered by community health workers in a rural area of Senegal. METHODS: Treatments were delivered to children 3-59 months of age in their homes once per month during the transmission season by community health workers. 33 health workers, each covering about 60 children, were randomized to deliver either SP+AQ, DHA+PQ or SP+PQ. Primary endpoints were the incidence of attacks of clinical malaria, and the incidence of adverse events. RESULTS: 1893 children were enrolled. Coverage of monthly rounds and compliance with daily doses was similar in all groups; 90% of children received at least 2 monthly doses. Piperaquine combinations were better tolerated than SP+AQ with a significantly lower risk of common, mild adverse events. 103 episodes of clinical malaria were recorded during the course of the trial. 68 children had malaria with parasitaemia >3000/microL, 29/671 (4.3% in the SP+AQ group, compared with 22/604 (3.6% in the DHA+PQ group (risk difference 0.47%, 95%CI -2.3%,+3.3%, and 17/618 (2.8% in the SP+PQ group (risk difference 1.2%, 95%CI -1.3%,+3.6%. Prevalences of parasitaemia and the proportion of children carrying Pfdhfr and Pfdhps mutations associated with resistance to SP were very low in all groups at the end of the transmission season. CONCLUSIONS: Seasonal IPT with SP+PQ in children is highly effective and well tolerated; the combination of two long-acting drugs is likely to impede the emergence of resistant parasites. TRIAL REGISTRATION: ClinicalTrials.gov NCT00529620.
Essential Protein Detection by Random Walk on Weighted Protein-Protein Interaction Networks.
Xu, Bin; Guan, Jihong; Wang, Yang; Wang, Zewei
2017-05-12
Essential proteins are critical to the development and survival of cells. Identification of essential proteins is helpful for understanding the minimal set of required genes in a living cell and for designing new drugs. To detect essential proteins, various computational methods have been proposed based on protein-protein interaction (PPI) networks. However, protein interaction data obtained by highthroughput experiments usually contain high false positives, which negatively impacts the accuracy of essential protein detection. Moreover, most existing studies focused on the local information of proteins in PPI networks, while ignoring the influence of indirect protein interactions on essentiality. In this paper, we propose a novel method, called Essentiality Ranking (EssRank in short), to boost the accuracy of essential protein detection. To deal with the inaccuracy of PPI data, confidence scores of interactions are evaluated by integrating various biological information. Weighted edge clustering coefficient (WECC), considering both interaction confidence scores and network topology, is proposed to calculate edge weights in PPI networks. The weight of each node is evaluated by the sum of WECC values of its linking edges. A random walk method, making use of both direct and indirect protein interactions, is then employed to calculate protein essentiality iteratively. Experimental results on the yeast PPI network show that EssRank outperforms most existing methods, including the most commonly-used centrality measures (SC, DC, BC, CC, IC, EC), topology based methods (DMNC and NC) and the data integrating method IEW.
Fluctuations around equilibrium laws in ergodic continuous-time random walks.
Schulz, Johannes H P; Barkai, Eli
2015-06-01
We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.
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.
Network Location-Aware Service Recommendation with Random Walk in Cyber-Physical Systems
Directory of Open Access Journals (Sweden)
Yuyu Yin
2017-09-01
Full Text Available 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.
Jafarnezhadgero, Amir Ali; Majlesi, Mahdi; Etemadi, Hojat; Robertson, D G E
2018-02-21
Previous studies have demonstrated increased medial stresses in knee varus alignment. Selecting a suitable treatment strategy for individuals with knee malalignment should be a priority. We aimed to investigate the effects of a 16-week corrective exercise continuum (CEC) program on 3-D joint angles of the dominant and non-dominant lower limbs in children with genu varus during walking. Overall, 28 male children with genu varus (age range 9-14 years) volunteered to participate in this study. They were randomly divided into 2 equal groups (experimental and control). The participants of the experimental group received CEC for 16 weeks. 3-D gait analysis involved using a Vicon Motion System. Paired and independent sample t-tests were used for within- and between-group comparisons, respectively. For the experimental group, comparison of pre- and post-test joint kinematics of the dominant lower limb revealed that CEC decreased the peak ankle dorsiflexion angle by 26% (P=0.020), peak foot internal rotation angle by 53% (P=0.001), peak knee internal rotation angle by 40% (P=0.011), peak hip abduction by 47% (P=0.010), and peak hip external rotation angle by 60% (P=0.001). In contrast, peak knee external rotation angle of the dominant limb was increased after the training program by 46% (P=0.044). For the non-dominant lower limb, CEC decreased the peak ankle inversion by 63% (Pvarus. Copyright © 2018 Elsevier Masson SAS. All rights reserved.
Path statistics, memory, and coarse-graining of continuous-time random walks on networks
Manhart, Michael; Kion-Crosby, Willow; Morozov, Alexandre V.
2015-12-01
Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs.
Prioritizing disease-causing microbes based on random walking on the heterogeneous network.
Shen, Xianjun; Chen, Yao; Jiang, Xingpeng; Hu, Xiaohua; He, Tingting; Yang, Jincai
2017-07-15
As we all know, the microbiota show remarkable variability within individuals. At the same time, those microorganisms living in the human body play a very important role in our health and disease, so the identification of the relationships between microbes and diseases will contribute to better understanding of microbes interactions, mechanism of functions. However, the microbial data which are obtained through the related technical sequencing is too much, but the known associations between the diseases and microbes are very less. In bioinformatics, many researchers choose the network topology analysis to solve these problems. Inspired by this idea, we proposed a new method for prioritization of candidate microbes to predict potential disease-microbe association. First of all, we connected the disease network and microbe network based on the known disease-microbe relationships information to construct a heterogeneous network, then we extended the random walk to the heterogeneous network, and used leave-one-out cross-validation and ROC curve to evaluate the method. In conclusion, the algorithm could be effective to disclose some potential associations between diseases and microbes that cannot be found by microbe network or disease network only. Furthermore, we studied three representative diseases, Type 2 diabetes, Asthma and Psoriasis, and finally presented the potential microbes associated with these diseases by ranking candidate disease-causing microbes, respectively. We confirmed that the discovery of the new associations will be a good clinical solution for disease mechanism understanding, diagnosis and therapy. Copyright © 2017 Elsevier Inc. All rights reserved.
Li, JiaRui; Chen, Lei; Wang, ShaoPeng; Zhang, YuHang; Kong, XiangYin; Huang, Tao; Cai, Yu-Dong
2018-02-01
Epigenetic regulation has long been recognized as a significant factor in various biological processes, such as development, transcriptional regulation, spermatogenesis, and chromosome stabilization. Epigenetic alterations lead to many human diseases, including cancer, depression, autism, and immune system defects. Although efforts have been made to identify epigenetic regulators, it remains a challenge to systematically uncover all the components of the epigenetic regulation in the genome level using experimental approaches. The advances of constructing protein-protein interaction (PPI) networks provide an excellent opportunity to identify novel epigenetic factors computationally in the genome level. In this study, we identified potential epigenetic factors by using a computational method that applied the random walk with restart (RWR) algorithm on a protein-protein interaction (PPI) network using reported epigenetic factors as seed nodes. False positives were identified by their specific roles in the PPI network or by a low-confidence interaction and a weak functional relationship with epigenetic regulators. After filtering out the false positives, 26 candidate epigenetic factors were finally accessed. According to previous studies, 22 of these are thought to be involved in epigenetic regulation, suggesting the robustness of our method. Our study provides a novel computational approach which successfully identified 26 potential epigenetic factors, paving the way on deepening our understandings on the epigenetic mechanism.
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
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.
The rotation of photospheric magnetic fields: A random walk transport model
Wang, Y. -M.; Sheeley, N. R., Jr.
1994-01-01
In an earlier study of solar differential rotation, we showed that the transport of magnetic flux across latitudes acts to establish quasi-stationary patterns, therby accounting for the observed rigid rotation of the large-scale photospheric field. In that paper, the effect of supergranular convection was represented by a continuum diffusion, limiting the applicability of the calculations to large spatial scales. Here we extend the model to scales comparable to that of the supergranulation itself by replacing the diffusive transport with a discrete random walk process. Rotation curves are derived by cross-correlating the simulated photospheric field maps for a variety of time lags and spatial resolutions. When the lag between maps is relatively short less than or approximately = 15 days), the midlatitude correlation functions show two distinct components: a broad feature associated with the large-scale unipolar patterns and a narrow feature originating from small magnetic structures encompossing from one to several supergranular cells. By fitting the broad component we obtain the rigid rotation profile of the patterns, whereas by fitting the narrow component, we recover the differential rate of the photospheric plasma itself. For time lags of 1 month or greater, only the broad feature associated with the long-lived patterns remains clearly identifiable in the simulations.
Calibration of Discrete Random Walk (DRW) Model via G.I Taylor's Dispersion Theory
Javaherchi, Teymour; Aliseda, Alberto
2012-11-01
Prediction of particle dispersion in turbulent flows is still an important challenge with many applications to environmental, as well as industrial, fluid mechanics. Several models of dispersion have been developed to predict particle trajectories and their relative velocities, in combination with a RANS-based simulation of the background flow. The interaction of the particles with the velocity fluctuations at different turbulent scales represents a significant difficulty in generalizing the models to the wide range of flows where they are used. We focus our attention on the Discrete Random Walk (DRW) model applied to flow in a channel, particularly to the selection of eddies lifetimes as realizations of a Poisson distribution with a mean value proportional to κ / ɛ . We present a general method to determine the constant of this proportionality by matching the DRW model dispersion predictions for fluid element and particle dispersion to G.I Taylor's classical dispersion theory. This model parameter is critical to the magnitude of predicted dispersion. A case study of its influence on sedimentation of suspended particles in a tidal channel with an array of Marine Hydrokinetic (MHK) turbines highlights the dependency of results on this time scale parameter. Support from US DOE through the Northwest National Marine Renewable Energy Center, a UW-OSU partnership.
McIntire, Eliot J B; Rompré, Ghislain; Severns, Paul M
2013-05-01
Animals in fragmented landscapes have a major challenge to move between high-quality habitat patches through lower-quality matrix. Two current mechanistic hypotheses that describe the movement used by animals outside of their preferred patches (e.g., high-quality habitat or home range) are the biased, correlated random walk (BCRW) and the foray loop (FL). There is also a variant of FL with directed movement (FLdm). While these have been most extensively tested on butterflies, they have never been tested simultaneously with data across a whole metapopulation and over multiple generations, two key scales for population dynamics. Using the pattern-oriented approach, we compare support for these competing hypotheses with a spatially explicit individual-based simulation model on an 11-year dataset that follows 12 patches of the federally endangered Fender's blue butterfly (Plebejus icarioides fenderi) in Oregon's Willamette Valley. BCRW and medium-scale FL and FLdm scenarios predicted the annual total metapopulation size for ≥ 9 of 12 patches as well as patch extinctions. The key difference, however, was that the FL scenarios predicted patch colonizations and persistence poorly, failing to adequately capture movement dynamics; BCRW and one FLdm scenario predicted the observed patch colonization and persistence with reasonable probabilities. This one FLdm scenario, however, had larger prediction intervals. BCRW, the biologically simplest and thus most parsimonious movement hypothesis, performed consistently well across all nine different tests, resulting in the highest quality metapopulation predictions for butterfly conservation.
Continuous time random walk analysis of solute transport in fractured porous media
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Cortis, Andrea; Cortis, Andrea; Birkholzer, Jens
2008-06-01
The objective of this work is to discuss solute transport phenomena in fractured porous media, where the macroscopic transport of contaminants in the highly permeable interconnected fractures can be strongly affected by solute exchange with the porous rock matrix. We are interested in a wide range of rock types, with matrix hydraulic conductivities varying from almost impermeable (e.g., granites) to somewhat permeable (e.g., porous sandstones). In the first case, molecular diffusion is the only transport process causing the transfer of contaminants between the fractures and the matrix blocks. In the second case, additional solute transfer occurs as a result of a combination of advective and dispersive transport mechanisms, with considerable impact on the macroscopic transport behavior. We start our study by conducting numerical tracer experiments employing a discrete (microscopic) representation of fractures and matrix. Using the discrete simulations as a surrogate for the 'correct' transport behavior, we then evaluate the accuracy of macroscopic (continuum) approaches in comparison with the discrete results. However, instead of using dual-continuum models, which are quite often used to account for this type of heterogeneity, we develop a macroscopic model based on the Continuous Time Random Walk (CTRW) framework, which characterizes the interaction between the fractured and porous rock domains by using a probability distribution function of residence times. A parametric study of how CTRW parameters evolve is presented, describing transport as a function of the hydraulic conductivity ratio between fractured and porous domains.
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Geiger, S.; Cortis, A.; Birkholzer, J.T.
2010-04-01
Solute transport in fractured porous media is typically 'non-Fickian'; that is, it is characterized by early breakthrough and long tailing and by nonlinear growth of the Green function-centered second moment. This behavior is due to the effects of (1) multirate diffusion occurring between the highly permeable fracture network and the low-permeability rock matrix, (2) a wide range of advection rates in the fractures and, possibly, the matrix as well, and (3) a range of path lengths. As a consequence, prediction of solute transport processes at the macroscale represents a formidable challenge. Classical dual-porosity (or mobile-immobile) approaches in conjunction with an advection-dispersion equation and macroscopic dispersivity commonly fail to predict breakthrough of fractured porous media accurately. It was recently demonstrated that the continuous time random walk (CTRW) method can be used as a generalized upscaling approach. Here we extend this work and use results from high-resolution finite element-finite volume-based simulations of solute transport in an outcrop analogue of a naturally fractured reservoir to calibrate the CTRW method by extracting a distribution of retention times. This procedure allows us to predict breakthrough at other model locations accurately and to gain significant insight into the nature of the fracture-matrix interaction in naturally fractured porous reservoirs with geologically realistic fracture geometries.
From medium heterogeneity to flow and transport: A time-domain random walk approach
Hakoun, V.; Comolli, A.; Dentz, M.
2017-12-01
The prediction of flow and transport processes in heterogeneous porous media is based on the qualitative and quantitative understanding of the interplay between 1) spatial variability of hydraulic conductivity, 2) groundwater flow and 3) solute transport. Using a stochastic modeling approach, we study this interplay through direct numerical simulations of Darcy flow and advective transport in heterogeneous media. First, we study flow in correlated hydraulic permeability fields and shed light on the relationship between the statistics of log-hydraulic conductivity, a medium attribute, and the flow statistics. Second, we determine relationships between Eulerian and Lagrangian velocity statistics, this means, between flow and transport attributes. We show how Lagrangian statistics and thus transport behaviors such as late particle arrival times are influenced by the medium heterogeneity on one hand and the initial particle velocities on the other. We find that equidistantly sampled Lagrangian velocities can be described by a Markov process that evolves on the characteristic heterogeneity length scale. We employ a stochastic relaxation model for the equidistantly sampled particle velocities, which is parametrized by the velocity correlation length. This description results in a time-domain random walk model for the particle motion, whose spatial transitions are characterized by the velocity correlation length and temporal transitions by the particle velocities. This approach relates the statistical medium and flow properties to large scale transport, and allows for conditioning on the initial particle velocities and thus to the medium properties in the injection region. The approach is tested against direct numerical simulations.
Angular random walk limited by Rayleigh backscattering in resonator fiber optic gyros.
Jiang, Zhiguo; Hu, Zongfu; Fu, Changsong
2017-12-01
This paper is concerned with the angular random walk (ARW) limited by Rayleigh backscattering in the resonator fiber optic gyro (RFOG) with a light source of arbitrary temporal coherence. First, a model of Rayleigh backscattering noise in RFOGs is established to predict the fluctuation characteristics of backscattered intensity and interference intensity. Next, the formula for the ARW limited by Rayleigh backscattering is derived, and the requirement of carrier suppression level is calculated to make sure the ARW is limited by the detector's shot noise rather than Rayleigh scattering noise. Finally, the influences of the cavity length, the linewidth, and the finesse on the ARW limited by Rayleigh backscattering are investigated. The results predict that the influence of the cavity length L and the laser linewidth Δυ L on the ARW is dominantly related to the factor e -2πΔυ L n e L/c , and under the finesse 88, the best ARW is obtained when there is a relation L·Δυ L ≈4×10 5 m·Hz.
Backward jump continuous-time random walk: An application to market trading
Gubiec, Tomasz; Kutner, Ryszard
2010-10-01
The backward jump modification of the continuous-time random walk model or the version of the model driven by the negative feedback was herein derived for spatiotemporal continuum in the context of a share price evolution on a stock exchange. In the frame of the model, we described stochastic evolution of a typical share price on a stock exchange with a moderate liquidity within a high-frequency time scale. The model was validated by satisfactory agreement of the theoretical velocity autocorrelation function with its empirical counterpart obtained for the continuous quotation. This agreement is mainly a result of a sharp backward correlation found and considered in this article. This correlation is a reminiscence of such a bid-ask bounce phenomenon where backward price jump has the same or almost the same length as preceding jump. We suggested that this correlation dominated the dynamics of the stock market with moderate liquidity. Although assumptions of the model were inspired by the market high-frequency empirical data, its potential applications extend beyond the financial market, for instance, to the field covered by the Le Chatelier-Braun principle of contrariness.
Learning by random walks in the weight space of the Ising perceptron
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Huang, Haiping; Zhou, Haijun
2010-01-01
Several variants of a stochastic local search process for constructing the synaptic weights of an Ising perceptron are studied. In this process, binary patterns are sequentially presented to the Ising perceptron and are then learned as the synaptic weight configuration is modified through a chain of single- or double-weight flips within the compatible weight configuration space of the earlier learned patterns. This process is able to reach a storage capacity of α≈0.63 for pattern length N = 101 and α≈0.41 for N = 1001. If in addition a relearning process is exploited, the learning performance is further improved to a storage capacity of α≈0.80 for N = 101 and α≈0.42 for N = 1001. We found that, for a given learning task, the solutions constructed by the random walk learning process are separated by a typical Hamming distance, which decreases with the constraint density α of the learning task; at a fixed value of α, the width of the Hamming distance distribution decreases with N
Langevin formulation of a subdiffusive continuous-time random walk in physical time
Cairoli, Andrea; Baule, Adrian
2015-07-01
Systems living in complex nonequilibrated environments often exhibit subdiffusion characterized by a sublinear power-law scaling of the mean square displacement. One of the most common models to describe such subdiffusive dynamics is the continuous-time random walk (CTRW). Stochastic trajectories of a CTRW can be described in terms of the subordination of a normal diffusive process by an inverse Lévy-stable process. Here, we propose an equivalent Langevin formulation of a force-free CTRW without subordination. By introducing a different type of non-Gaussian noise, we are able to express the CTRW dynamics in terms of a single Langevin equation in physical time with additive noise. We derive the full multipoint statistics of this noise and compare it with the scaled Brownian motion (SBM), an alternative stochastic model describing subdiffusive dynamics. Interestingly, these two noises are identical up to the second order correlation functions, but different in the higher order statistics. We extend our formalism to general waiting time distributions and force fields and compare our results with those of the SBM. In the presence of external forces, our proposed noise generates a different class of stochastic processes, resembling a CTRW but with forces acting at all times.
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.
Dispersion in porous media, continuous-time random walks, and percolation.
Sahimi, Muhammad
2012-01-01
A promising approach to the modeling of anomalous (non-Gaussian) dispersion in flow through heterogeneous porous media is the continuous-time random walk (CTRW) method. In such a formula on the waiting time distribution ψ(t) is usually assumed to be given by ψ(t)∼t-1-α, with α fitted to the experimental data. The exponent α is also related to the power-law growth of the mean-square displacement of the solute with the time t ∼ tζ. Invoking percolation and using a scaling analysis, we relate α to the geometrical exponents of percolation (ν, β, and βB) as well as the exponents μ and e that characterize the power-law behavior of the effective conductivity and permeability of porous media near the percolation threshold. We then explain the cause of the nonuniversality of α in terms of the nonuniversality of μ and e in continuum systems, and in percolation models with long-range correlations, and propose bounds for it. The results are consistent with the experimental data, both at the laboratory and field scales.
D Fluid Deformation and Mixing via a Continuous Time Random Walk
Lester, D. R.; Dentz, M.; Le Borgne, T.; de Barros, F.
2015-12-01
Fluid stretching and deformation as quantified by the fluid deformation gradient tensor directly controls mixing of diffusive species in both chaotic and non-chaotic, 2D and 3D flows at the pore- and Darcy scales. Indeed, recent advances [LeBorgne et. al. PRL, 110, 204501, 2013] in the prediction of mixing and scalar dissipation require the distribution of fluid deformation rates as quantitative inputs. However, these measures are often difficult to link to medium properties or statistical heterogeneity controls. To advance this problem, we present a novel Continuous Time Random Walk (CTRW) to model stochastic evolution of the 3D fluid deformation tensor in a Protean (streamline) coordinate frame. This approach allows topological constraints imposed by the flow kinematics to be naturally obeyed, and furthermore flow features that generate non-Fickian transport can be clearly elucidated. For simple flows, this framework allows the distribution of deformation rates (and hence mixing) to be expressed in terms of heterogenenity controls, and for more complex flows, this approach clearly identifies what flow features govern anomalous transport and how their statistics can be measured as model inputs.
Natural Organic Matter Transport Modeling with a Continuous Time Random Walk Approach.
McInnis, Daniel P; Bolster, Diogo; Maurice, Patricia A
2014-02-01
In transport experiments through columns packed with naturally Fe/Al oxide-coated quartz sand, breakthrough curves (BTCs) of natural organic matter (NOM) displayed strong and persistent power law tailing that could not be described by the classical advection-dispersion equation. Tailing was not observed in BTCs for a nonreactive tracer (sulforhodamine B); therefore, the anomalous transport is attributed to diverse adsorptive behavior of the polydisperse NOM sample rather than to physical heterogeneity of the porous medium. NOM BTC tailing became more pronounced with decreases in pH and increases in ionic strength, conditions previously shown to be associated with enhanced preferential adsorption of intermediate to high molecular weight NOM components. Drawing from previous work on anomalous solute transport, we develop an approach to model NOM transport within the framework of a continuous time random walk (CTRW) and show that under all conditions examined, the CTRW model is able to capture tailing of NOM BTCs by accounting for differences in transport rates of NOM fractions through a distribution of effective retardation factors. These results demonstrate the importance of considering effects of adsorptive fractionation on NOM mobility, and illustrate the ability of the CTRW model to describe transport of a multicomponent solute.
Continuous-time random walk for open systems: fluctuation theorems and counting statistics.
Esposito, Massimiliano; Lindenberg, Katja
2008-05-01
We consider continuous-time random walks (CTRW) for open systems that exchange energy and matter with multiple reservoirs. Each waiting time distribution (WTD) for times between steps is characterized by a positive parameter alpha , which is set to alpha=1 if it decays at least as fast as t{-2} at long times and therefore has a finite first moment. A WTD with alphaCTRW. However, R can be identified as a trajectory entropy change only if the WTDs have alpha=1 and satisfy separability (also called "direction time independence"). For nonseparable WTDs with alpha=1 , R can only be identified as a trajectory entropy change at long times, and a fluctuation theorem for the entropy change then only holds at long times. For WTDs with 0
Life and Death of Stationary Linear Response in Anomalous Continuous Time Random Walk Dynamics
Igor, Goychuk
2014-10-01
Linear theory of stationary response in systems at thermal equilibrium requires to find equilibrium correlation function of unperturbed responding system. Studies of the response of the systems exhibiting anomalously slow dynamics are often based on the continuous time random walk description (CTRW) with divergent mean waiting times. The bulk of the literature on anomalous response contains linear response functions like one by Cole-Cole calculated from such a CTRW theory and applied to systems at thermal equilibrium. Here we show within a fairly simple and general model that for the systems with divergent mean waiting times the stationary response at thermal equilibrium is absent, in accordance with some recent studies. The absence of such stationary response (or dying to zero non-stationary response in aging experiments) would confirm CTRW with divergent mean waiting times as underlying physical relaxation mechanism, but reject it otherwise. We show that the absence of stationary response is closely related to the breaking of ergodicity of the corresponding dynamical variable. As an important new result, we derive a generalized Cole-Cole response within ergodic CTRW dynamics with finite waiting time. Moreover, we provide a physically reasonable explanation of the origin and wide presence of 1/f noise in condensed matter for ergodic dynamics close to normal, rather than strongly deviating.
Occupation times and ergodicity breaking in biased continuous time random walks
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Bel, Golan; Barkai, Eli [Physics Department, Bar-Ilan University, Ramat-Gan 52900 (Israel)
2005-12-14
Continuous time random walk (CTRW) models are widely used to model diffusion in condensed matter. There are two classes of such models, distinguished by the convergence or divergence of the mean waiting time. Systems with finite average sojourn time are ergodic and thus Boltzmann-Gibbs statistics can be applied. We investigate the statistical properties of CTRW models with infinite average sojourn time; in particular, the occupation time probability density function is obtained. It is shown that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point exhibits bimodal U or trimodal W shape, related to the arcsine law. The key points are as follows. (a) In a CTRW with finite or infinite mean waiting time, the distribution of the number of visits on a lattice point is determined by the probability that a member of an ensemble of particles in equilibrium occupies the lattice point. (b) The asymmetry parameter of the probability distribution function of occupation times is related to the Boltzmann probability and to the partition function. (c) The ensemble average is given by Boltzmann-Gibbs statistics for either finite or infinite mean sojourn time, when detailed balance conditions hold. (d) A non-ergodic generalization of the Boltzmann-Gibbs statistical mechanics for systems with infinite mean sojourn time is found.
MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD
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Sonsrettee, W.; Ruffolo, D.; Snodin, A. P.; Wongpan, P. [Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400 (Thailand); Subedi, P.; Matthaeus, W. H. [Bartol Research Institute, University of Delaware, Newark, DE 19716 (United States); Chuychai, P., E-mail: bturbulence@gmail.com, E-mail: david.ruf@mahidol.ac.th, E-mail: andrew.snodin@gmail.com, E-mail: pat.wongpan@postgrad.otago.ac.nz, E-mail: piyanate@gmail.com, E-mail: prasub@udel.edu, E-mail: whm@udel.edu [Thailand Center of Excellence in Physics, CHE, Ministry of Education, Bangkok 10400 (Thailand)
2015-01-01
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B {sub 0})(ℓ{sub ∥}/ℓ ) for rms magnetic fluctuation b, large-scale mean field B {sub 0}, and parallel and perpendicular coherence scales ℓ{sub ∥} and ℓ , respectively. Here we examine the FLRW when R → ∞ by taking B {sub 0} → 0 for finite b{sub z} (fluctuation component along B {sub 0}), which differs from the well-studied route with b{sub z} = 0 or b{sub z} << B {sub 0} as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B {sub 0} = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k {sup –1} or k {sup –2} moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B {sub 0} → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.
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Lim Ming Han
Full Text Available 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.
Modzelewski, Romain; Janvresse, Elise; de la Rue, Thierry; Vera, Pierre
2010-06-01
A Random Walk (RW) algorithm was designed to quantify the level of diffuse heterogeneous perfusion in brain SPECT images in patients suffering from systemic brain disease or from drug-induced therapy. The goal of the present paper is to understand the behavior of the RW method on different kinds of images (extrinsic parameters) and also to understand how to choose the right parameters of the RW (intrinsic parameters) depending on the image characteristics (i.e. SPECT images). "Extrinsic parameters" are related to the image characteristics (level/size of defect and diffuse heterogeneity) and "intrinsic" parameters are related to the parameters of the method (number (N(rw)) and length of walk (L(rw)), temperature (T) and slowing parameter (S)). Two successive studies were conducted to test the influence of these parameters on the RW result. In the first study, calibrated checkerboard images are used to test the influence of "extrinsic parameters" (i.e. image characteristics) on the RW result (R-value). The R-value was tested as a function of (i) the size of black & white (B&W) squares simulating the size of a cortical defect, (ii) the intensity level gaps between the B&W squares simulating the intensity of the cortical defect and (iii) intensity (=variance) of noise, simulating the diffuse heterogeneity. The second study was constructed with simulated representative brain SPECT images, to test the "intrinsic" parameters. The R-value was tested regarding the influence of four parameters: S, T, N(rw) and L(rw). The third study is constructed so as to see if the classification by diffuse heterogeneity of real brain SPECT images is the same if it's made by senior clinicians or by RW algorithm. Study 1: the RW was strongly influenced by all the characteristics of the images. Moreover, these characteristics interact with each other. The RW is influenced most by diffuse heterogeneity, then by intensity and finally by the size of a defect. Study 2: N(rw) and L(rw) values of
A non-Lévy random walk in chacma baboons: what does it mean?
Sueur, Cédric
2011-01-13
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.
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.
Schapowal, Andreas
2005-06-01
Intermittent allergic rhinitis (IAR) causes patients distress and impairs their work performance and quality of life. A variety of medicines are used by sufferers whose anguish frequently leads to trying new treatments, increasingly from herbal sources. Prospective, randomized, double-blind, parallel group comparison study of Butterbur extract (Ze 339; 8 mg total petasine; one tablet thrice-daily), fexofenadine (Telfast 180, one tablet once-daily) and placebo in 330 patients. Protocol and analysis were according to the latest guidelines on new treatments for allergic rhinitis. The primary efficacy variable was a change in symptoms from baseline to endpoint during daytime. The secondary efficacy variables were: (a) as per primary variable (evening/night); (b) Physician's global assessment; (c) Responder rates. Safety was closely monitored. Both active treatments were individually significantly superior to placebo (p<0.001) in improving symptoms of IAR, while there were no differences between the two active treatments (p=0.37). Superiority to placebo was similarly shown during the evening/night (p<0.001), by physicians' own assessment and by responder rates. Both treatments were well tolerated. Butterbur Ze 339 and Fexofenadine are comparably efficacious relative to placebo. Despite being a herbal drug, Butterbur Ze 339 has now been subject to a series of well controlled trials and should be considered as an alternative treatment for IAR. Copyright (c) 2005 John Wiley & Sons, Ltd.
Bell, David C; Erbaugh, Elizabeth B; Serrano, Tabitha; Dayton-Shotts, Cheryl A; Montoya, Isaac D
2017-02-01
Both random walk and respondent-driven sampling (RDS) exploit social networks and may reduce biases introduced by earlier methods for sampling from hidden populations. Although RDS has become much more widely used by social researchers than random walk (RW), there has been little discussion of the tradeoffs in choosing RDS over RW. This paper compares experiences of implementing RW and RDS to recruit drug users to a network-based study in Houston, Texas. Both recruitment methods were implemented over comparable periods of time, with the same population, by the same research staff. RDS methods recruited more participants with less strain on staff. However, participants recruited through RW were more forthcoming than RDS participants in helping to recruit members of their social networks. Findings indicate that, dependent upon study goals, researchers' choice of design may influence participant recruitment, participant commitment, and impact on staff, factors that may in turn affect overall study success. Copyright © 2016 Elsevier Inc. All rights reserved.
Effect of intermittent PTH treatment on plasma glucose in osteoporosis: A randomized trial.
D'Amelio, Patrizia; Sassi, Francesca; Buondonno, Ilaria; Spertino, Elena; Tamone, Cristina; Piano, Simonetta; Zugna, Daniela; Richiardi, Lorenzo; Isaia, Giovanni Carlo
2015-07-01
We investigated the effect of bone turnover on glucose homeostasis, fat distribution and adipokine production during anabolic treatment with PTH. This is a parallel, randomized controlled, open label, trial. The randomization was done by computer generated tables to allocate treatments. Forty-six postmenopausal osteoporotic non-diabetic women were assigned to treatment with calcium and colecalcipherol with (24) or without (22) PTH 1-84. Patients were recalled after 3, 6, 12 and 18 months of treatment and markers of bone turnover, glucose metabolism, adipokine secretion and fat distribution were analyzed. Markers of bone turnover and adipokines were measured by ELISA. Glucose metabolism was evaluated by an oral glucose load test and insulin resistance and secretion were calculated. Fat and lean mass were evaluated by anthropometric measures. The effect of treatment on measured variables was analyzed by repeated measure test, and its effect on glucose was also evaluated by mediation analysis after correction for possible confounders. Twenty patients in the calcium and vitamin D groups and 19 in the group treated with PTH 1-84 completed the study. There were no significance adverse events. Treatment with PTH increases osteocalcin, both total (OC) and undercarboxylated (uOC), and decreases blood glucose, without influence on insulin secretion, resistance and pancreatic β cell function. Treatment with PTH does not influence fat distribution and adipokine production. The results of the mediation analyses suggest a total effect of PTH on blood glucose, moderately mediated by OC and to a less extent by uOC. Here we suggest that treatment with PTH influences glucose metabolism partially through its effect on bone turnover, without influence on insulin secretion, resistance, pancreatic β cell function and fat mass. Copyright © 2015 Elsevier Inc. All rights reserved.
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.
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Haroldo Valetin Ribeiro
2012-03-01
Full Text Available We investigate how it is possible to obtain different diffusive regimes from the Continuous Time Random Walk (CTRW approach performing suitable changes for the waiting time and jumping distributions in order to get two or more regimes for the same diffusive process. We also obtain diffusion-like equations related to these processes and investigate the connection of the results with anomalous diffusion.
Random Walk and Graph Cut for Co-Segmentation of Lung Tumor on PET-CT Images.
Ju, Wei; Xiang, Dehui; Xiang, Deihui; Zhang, Bin; Wang, Lirong; Kopriva, Ivica; Chen, Xinjian
2015-12-01
Accurate lung tumor delineation plays an important role in radiotherapy treatment planning. Since the lung tumor has poor boundary in positron emission tomography (PET) images and low contrast in computed tomography (CT) images, segmentation of tumor in the PET and CT images is a challenging task. In this paper, we effectively integrate the two modalities by making fully use of the superior contrast of PET images and superior spatial resolution of CT images. Random walk and graph cut method is integrated to solve the segmentation problem, in which random walk is utilized as an initialization tool to provide object seeds for graph cut segmentation on the PET and CT images. The co-segmentation problem is formulated as an energy minimization problem which is solved by max-flow/min-cut method. A graph, including two sub-graphs and a special link, is constructed, in which one sub-graph is for the PET and another is for CT, and the special link encodes a context term which penalizes the difference of the tumor segmentation on the two modalities. To fully utilize the characteristics of PET and CT images, a novel energy representation is devised. For the PET, a downhill cost and a 3D derivative cost are proposed. For the CT, a shape penalty cost is integrated into the energy function which helps to constrain the tumor region during the segmentation. We validate our algorithm on a data set which consists of 18 PET-CT images. The experimental results indicate that the proposed method is superior to the graph cut method solely using the PET or CT is more accurate compared with the random walk method, random walk co-segmentation method, and non-improved graph cut method.
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.
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Godrèche, Claude
2017-01-01
The probability distribution of the longest interval between two zeros of a simple random walk starting and ending at the origin, and of its continuum limit, the Brownian bridge, was analysed in the past by Rosén and Wendel, then extended by the latter to stable processes. We recover and extend these results using simple concepts of renewal theory, which allows to revisit past and recent works of the physics literature. (paper)
Bisquert, Juan
2003-07-04
We investigate the macroscopic diffusion of carriers in the multiple-trapping (MT) regime, in relation with electron transport in nanoscaled heterogeneous systems, and we describe the differences, as well as the similarities, between MT and the continuous-time random walk (CTRW). Diffusion of free carriers in MT can be expressed as a generalized continuity equation based on fractional time derivatives, while the CTRW model for diffusive transport generalizes the constitutive equation for the carrier flux.
Recchia, Stephen
Kevlar is the most common high-end plastic filament yarn used in body armor, tire reinforcement, and wear resistant applications. Kevlar is a trade name for an aramid fiber. These are fibers in which the chain molecules are highly oriented along the fiber axis, so the strength of the chemical bond can be exploited. The bulk material is extruded into filaments that are bound together into yarn, which may be chorded with other materials as in car tires, woven into a fabric, or layered in an epoxy to make composite panels. The high tensile strength to low weight ratio makes this material ideal for designs that decrease weight and inertia, such as automobile tires, body panels, and body armor. For designs that use Kevlar, increasing the strength, or tenacity, to weight ratio would improve performance or reduce cost of all products that are based on this material. This thesis computationally and experimentally investigates the tenacity and stiffness of Kevlar yarns with varying twist ratios. The test boundary conditions were replicated with a geometrically accurate finite element model, resulting in a customized code that can reproduce tortuous filaments in a yarn was developed. The solid model geometry capturing filament tortuosity was implemented through a random walk method of axial geometry creation. A finite element analysis successfully recreated the yarn strength and stiffness dependency observed during the tests. The physics applied in the finite element model was reproduced in an analytical equation that was able to predict the failure strength and strain dependency of twist ratio. The analytical solution can be employed to optimize yarn design for high strength applications.
Systematic Angle Random Walk Estimation of the Constant Rate Biased Ring Laser Gyro
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Guohu Feng
2013-02-01
Full Text Available An actual account of the angle random walk (ARW coefficients of gyros in the constant rate biased rate ring laser gyro (RLG inertial navigation system (INS is very important in practical engineering applications. However, no reported experimental work has dealt with the issue of characterizing the ARW of the constant rate biased RLG in the INS. To avoid the need for high cost precise calibration tables and complex measuring set-ups, the objective of this study is to present a cost-effective experimental approach to characterize the ARW of the gyros in the constant rate biased RLG INS. In the system, turntable dynamics and other external noises would inevitably contaminate the measured RLG data, leading to the question of isolation of such disturbances. A practical observation model of the gyros in the constant rate biased RLG INS was discussed, and an experimental method based on the fast orthogonal search (FOS for the practical observation model to separate ARW error from the RLG measured data was proposed. Validity of the FOS-based method was checked by estimating the ARW coefficients of the mechanically dithered RLG under stationary and turntable rotation conditions. By utilizing the FOS-based method, the average ARW coefficient of the constant rate biased RLG in the postulate system is estimated. The experimental results show that the FOS-based method can achieve high denoising ability. This method estimate the ARW coefficients of the constant rate biased RLG in the postulate system accurately. The FOS-based method does not need precise calibration table with high cost and complex measuring set-up, and Statistical results of the tests will provide us references in engineering application of the constant rate biased RLG INS.
Continuous time random walk model better describes the tailing of atrazine transport in soil.
Deng, Jiancai; Jiang, Xin; Zhang, Xiaoxian; Hu, Weiping; Crawford, John W
2008-05-01
Contaminant transport in soils is complicated and involves some physical and chemical nonequilibrium processes. In this research, the soil column displacement experiments of Cl(-) and atrazine under different flow velocities were carried out. The data sets of Cl(-) transport in sandy loam fitted to the convection dispersion equation (CDE) and the two-region model (TRM) indicated that the effects of physical nonequilibrium process produced by immobile water on the breakthrough curves (BTCs) of Cl(-) and atrazine transport through the repacking soil columns were negligible. The two-site model (TSM) and the continuous time random walk (CTRW) were also used to fit atrazine transport behavior at the flow rate of 19.86 cm h(-1). The CTRW convincingly captured the full evolution of atrazine BTC in the soil column, especially for the part of long tailing. However, the TSM failed to characterize the tailing of atrazine BTC in the soil column. The calculated fraction of equilibrium sorption sites, F, ranging from 0.78 to 0.80 for all flow rates suggested the contribution of nonequilibrium sorption sites to the asymmetry of atrazine BTCs. Furthermore, the data sets for the flow rates of 6.68 cm h(-1) and 32.81 cm h(-1) were predicted by the TSM and the CTRW. As to the flow rate of 6.68 cm h(-1), the CTRW predicted the entire BTC of atrazine transport better than the TSM did. For the flow rate of 32.81 cm h(-1), the CTRW characterized the late part of the tail better, while the TSM failed to predict the tailings of atrazine BTC.
Application of continuous time random walk theory to nonequilibrium transport in soil.
Li, Na; Ren, Li
2009-09-01
Continuous time random walk (CTRW) formulations have been demonstrated to provide a general and effective approach that quantifies the behavior of solute transport in heterogeneous media in field, laboratory, and numerical experiments. In this paper we first apply the CTRW approach to describe the sorbing solute transport in soils under chemical (or) and physical nonequilibrium conditions by curve-fitting. Results show that the theoretical solutions are in a good agreement with the experimental measurements. In case that CTRW parameters cannot be determined directly or easily, an alternative method is then proposed for estimating such parameters independently of the breakthrough curve data to be simulated. We conduct numerical experiments with artificial data sets generated by the HYDRUS-1D model for a wide range of pore water velocities (upsilon) and retardation factors (R) to investigate the relationship between CTRW parameters for a sorbing solute and these two quantities (upsilon, R) that can be directly measured in independent experiments. A series of best-fitting regression equations are then developed from the artificial data sets, which can be easily used as an estimation or prediction model to assess the transport of sorbing solutes under steady flow conditions through soil. Several literature data sets of pesticides are used to validate these relationships. The results show reasonable performance in most cases, thus indicating that our method could provide an alternative way to effectively predict sorbing solute transport in soils. While the regression relationships presented are obtained under certain flow and sorption conditions, the methodology of our study is general and may be extended to predict solute transport in soils under different flow and sorption conditions.
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.
The stochastic dynamics of intermittent porescale particle motion
Dentz, Marco; Morales, Veronica; Puyguiraud, Alexandre; Gouze, Philippe; Willmann, Matthias; Holzner, Markus
2017-04-01
Numerical and experimental data for porescale particle dynamics show intermittent patterns in Lagrangian velocities and accelerations, which manifest in long time intervals of low and short durations of high velocities [1, 2]. This phenomenon is due to the spatial persistence of particle velocities on characteristic heterogeneity length scales. In order to systematically quantify these behaviors and extract the stochastic dynamics of particle motion, we focus on the analysis of Lagrangian velocities sampled equidistantly along trajectories [3]. This method removes the intermittency observed under isochrone sampling. The space-Lagrangian velocity series can be quantified by a Markov process that is continuous in distance along streamline. It is fully parameterized in terms of the flux-weighted Eulerian velocity PDF and the characteristic pore-length. The resulting stochastic particle motion describes a continuous time random walk (CTRW). This approach allows for the process based interpretation of experimental and numerical porescale velocity, acceleration and displacement data. It provides a framework for the characterization and upscaling of particle transport and dispersion from the pore to the Darcy-scale based on the medium geometry and Eulerian flow attributes. [1] P. De Anna, T. Le Borgne, M. Dentz, A.M. Tartakovsky, D. Bolster, and P. Davy, "Flow intermittency, dispersion, and correlated continuous time random walks in porous media," Phys. Rev. Lett. 110, 184502 (2013). [2] M. Holzner, V. L. Morales, M. Willmann, and M. Dentz, "Intermittent Lagrangian velocities and accelerations in three- dimensional porous medium flow," Phys. Rev. E 92, 013015 (2015). [3] M. Dentz, P. K. Kang, A. Comolli, T. Le Borgne, and D. R. Lester, "Continuous time random walks for the evolution of Lagrangian velocities," Phys. Rev. Fluids (2016).
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). The intervention consisted of 12 weeks functional PRE circuit training, for 3 times a week. Main outcome measures were walking ability and participation. Secondary outcomes were muscle strength and anaerobic muscle power. Possible adverse outcomes were spasticity and passive range of motion (ROM). Muscle strength increased significantly in the training group compared to the control group, but walking ability, participation and anaerobic muscle power did not change. Spasticity and ROM remained unchanged, except for a significant decrease in rectus femoris length in the intervention group. It is concluded that twelve weeks of functional PRE-training does not improve walking ability, despite improved muscle strength. Copyright © 2011 Elsevier Ltd. All rights reserved.
Løppenthin, Katrine; Esbensen, Bente Appel; Jennum, Poul; Østergaard, Mikkel; Christensen, Jesper Frank; Thomsen, Tanja; Bech, Julie Schjerbech; Midtgaard, Julie
2014-02-21
Poor sleep is prevalent in patients with systemic inflammatory disorders, including rheumatoid arthritis, and, in addition to fatigue, pain, depression and inflammation, is associated with an increased risk of co-morbidity and all-cause mortality. Whereas non-pharmacological interventions in patients with rheumatoid arthritis have been shown to reduce pain and fatigue, no randomized controlled trials have examined the effect of non-pharmacological interventions on improvement of sleep in patients with rheumatoid arthritis. The aim of this trial was to evaluate the efficacy of an intermittent aerobic exercise intervention on sleep, assessed both objectively and subjectively in patients with rheumatoid arthritis. A randomized controlled trial including 44 patients with rheumatoid arthritis randomly assigned to an exercise training intervention or to a control group. The intervention consists of 18 session intermittent aerobic exercise training on a bicycle ergometer three times a week. Patients are evaluated according to objective changes in sleep as measured by polysomnography (primary outcome). Secondary outcomes include changes in subjective sleep quality and sleep disturbances, fatigue, pain, depressive symptoms, physical function, health-related quality of life and cardiorespiratory fitness. This trial will provide evidence of the effect of intermittent aerobic exercise on the improvement of sleep in patients with rheumatoid arthritis, which is considered important in promotion of health and well-being. As such, the trial meets a currently unmet need for the provision of non-pharmacological treatment initiatives of poor sleep in patients with rheumatoid arthritis. ClinicalTrials.gov Identifier: NCT01966835.
Continuous-time random-walk model for anomalous diffusion in expanding media
Le Vot, F.; Abad, E.; Yuste, S. B.
2017-09-01
Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium
Alghadir, Ahmad; Anwer, Shahnawaz
2016-04-12
Walking, a closed kinetic chain (CKC) activity, is widely used in knee rehabilitation as it allows early weight bearing and movement. It has been suggested that retro-walking may provide additional benefits beyond those experienced by forward-walking. The present study will investigate the effect of retro- and forward-walking on quadriceps muscle strength, pain, function, balance and mobility in knee Osteoarthritis (OA) subjects. Sixty-nine participants with knee OA will be recruited from the outpatient department in this randomized controlled trial. The participants will be randomly assigned to one of three groups; retro walking, forward walking or control group. The training program will be 3 days/week for 6 weeks. In addition, all the participants will receive a standard physiotherapy training program. An independent assessor blinded to group assignment will measure quadriceps muscle strength, knee pain intensity, functional disability, and mobility at baseline and 6 weeks after training. The results of this study will enhance our understanding on the therapeutic effects of walking (retro- or forward-walking) in knee OA. The findings from this study will help determine whether retro- or forward-walking or both are effective in the rehabilitation of subjects with knee OA. Controlled Trials ISRCTN12850845, Registered 26 January 2015.
Nagata, Chie; Tanabe, Hiroshi; Takakura, Satoshi; Narui, Chikage; Saito, Motoaki; Yanaihara, Nozomu; Okamoto, Aikou
2015-09-01
The aim of this study was to compare the efficacy and safety of enoxaparin and intermittent pneumatic compression (IPC) for venous thromboembolism (VTE) prevention in Japanese surgical patients with gynecologic malignancy. Patients ≥ 40 years old undergoing major surgery for gynecologic malignancy without preoperative VTE were included. Written informed consent was obtained. Enrolled patients received IPC immediately before surgery. After surgery, they were randomly assigned to either an enoxaparin group or an IPC-alone group. The enoxaparin group received enoxaparin injection (20 mg, subcutaneous, every 12 h) from postoperative day 2 to 8. IPC was discontinued after the first injection. In the IPC-alone group, IPC was continued until full ambulation. The primary end-point was incidence of VTE, including pulmonary embolism and deep vein thrombosis, regardless of symptoms. An interim analysis was to be conducted when the first 30 patients had completed the study protocol. A Data and Safety Monitoring Board was established for making recommendation on the continuation or termination of the study based on the interim results. At the time of the interim analysis, six cases of VTE were found: five in the IPC-alone group and one in the enoxaparin group (Fisher's exact test, P = 0.08). Three patients in the IPC-alone group developed pulmonary embolism, but none in the enoxaparin group did so (Fisher's exact test, P = 0.10). The study was terminated following the Data and Safety Monitoring Board's recommendation. Enoxaparin might have lowered the risk of VTE among surgical patients with gynecologic malignancy. Further studies are necessary to confirm this. © 2015 Japan Society of Obstetrics and Gynecology.
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.
2014-01-01
Background 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). Methods/design 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. Discussion The first data gathered have allowed us to identify the
Eisenlohr-Moul, Tory A; Girdler, Susan S; Johnson, Jacqueline L; Schmidt, Peter J; Rubinow, David R
2017-10-01
Although traditionally dosed combined oral contraceptives (COCs) (21 days of active pills, 7 days of inactive pills) have not been demonstrated as superior to placebo for the treatment of premenstrual dysphoria (PMD), some randomized controlled trials (RCTs) indicate that oral contraceptives administered with a shortened or eliminated hormone-free interval are superior to placebo. However, results of such trials are mixed, and no existing studies have directly compared continuous and intermittent dosing schedules of the same oral contraceptive. The present study compared placebo, intermittent dosing of oral contraceptives, and continuous dosing of contraceptives for the treatment of PMD. Fifty-five women with prospectively confirmed PMD completed a three-arm, RCT in which they were randomized to 3 months of placebo (n = 22), intermittent drospirenone/ethinyl estradiol dosed on a 21-7 schedule (n = 17), or continuous drospirenone/estradiol (n = 16) following a baseline assessment month. All three groups demonstrated similar, robust reductions in premenstrual symptoms over time. A marked placebo response was observed. The study fails to replicate a uniquely beneficial effect of continuous COC on PMD. Additional work is needed to understand the psychosocial context bolstering the placebo response in women with PMD. © 2017 Wiley Periodicals, Inc.
Oliveira, R.; Bijeljic, B.; Blunt, M. J.; Colbourne, A.; Sederman, A. J.; Mantle, M. D.; Gladden, L. F.
2017-12-01
Mixing and reactive processes have a large impact on the viability of enhanced oil and gas recovery projects that involve acid stimulation and CO2 injection. To achieve a successful design of the injection schemes an accurate understanding of the interplay between pore structure, flow and reactive transport is necessary. Dependent on transport and reactive conditions, this complex coupling can also be dependent on initial rock heterogeneity across a variety of scales. To address these issues, we devise a new method to study transport and reactive flow in porous media at multiple scales. The transport model is based on an efficient Particle Tracking Method based on Continuous Time Random Walks (CTRW-PTM) on a lattice. Transport is modelled using an algorithm described in Rhodes and Blunt (2006) and Srinivasan et al. (2010); this model is expanded to enable for reactive flow predictions in subsurface rock undergoing a first-order fluid/solid chemical reaction. The reaction-induced alteration in fluid/solid interface is accommodated in the model through changes in porosity and flow field, leading to time dependent transport characteristics in the form of transit time distributions which account for rock heterogeneity change. This also enables the study of concentration profiles at the scale of interest. Firstly, we validate transport model by comparing the probability of molecular displacement (propagators) measured by Nuclear Magnetic Resonance (NMR) with our modelled predictions for concentration profiles. The experimental propagators for three different porous media of increasing complexity, a beadpack, a Bentheimer sandstone and a Portland carbonate, show a good agreement with the model. Next, we capture the time evolution of the propagators distribution in a reactive flow experiment, where hydrochloric acid is injected into a limestone rock. We analyse the time-evolving non-Fickian signatures for the transport during reactive flow and observe an increase in
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
Avelino, Patrick Roberto; Nascimento, Lucas R; Menezes, Kênia K P; Scianni, Aline A; Ada, Louise; Teixeira-Salmela, Luci F
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.
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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.