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Sample records for random walks estimate

  1. Discriminative parameter estimation for random walks segmentation.

    PubMed

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

    2013-01-01

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

  2. Ant-inspired density estimation via random walks.

    PubMed

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

    2017-09-19

    Many ant species use distributed population density estimation in applications ranging from quorum sensing, to task allocation, to appraisal of enemy colony strength. It has been shown that ants estimate local population density by tracking encounter rates: The higher the density, the more often the ants bump into each other. We study distributed density estimation from a theoretical perspective. We prove that a group of anonymous agents randomly walking on a grid are able to estimate their density within a small multiplicative error in few steps by measuring their rates of encounter with other agents. Despite dependencies inherent in the fact that nearby agents may collide repeatedly (and, worse, cannot recognize when this happens), our bound nearly matches what would be required to estimate density by independently sampling grid locations. From a biological perspective, our work helps shed light on how ants and other social insects can obtain relatively accurate density estimates via encounter rates. From a technical perspective, our analysis provides tools for understanding complex dependencies in the collision probabilities of multiple random walks. We bound the strength of these dependencies using local mixing properties of the underlying graph. Our results extend beyond the grid to more general graphs, and we discuss applications to size estimation for social networks, density estimation for robot swarms, and random walk-based sampling for sensor networks.

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

    PubMed

    Liu, Risheng; Lin, Zhouchen; Su, Zhixun

    2014-11-01

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

  4. Quantum random walks without walking

    SciTech Connect

    Manouchehri, K.; Wang, J. B.

    2009-12-15

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

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

    PubMed Central

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

    2014-01-01

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

  6. Random walk designs for selecting pool sizes in group testing estimation with small samples.

    PubMed

    Haber, Gregory; Malinovsky, Yaakov

    2017-08-09

    Group testing estimation, which utilizes pooled rather than individual units for testing, has been an ongoing area of research for over six decades. While it is often argued that such methods can yield large savings in terms of resources and/or time, these benefits depend very much on the initial choice of pool sizes. In fact, when poor group sizes are used, the results can be much worse than those obtained using standard techniques. Tools for addressing this problem in the literature have been based on either large sample results or prior knowledge of the parameter being estimated, with little guidance when these assumptions are not met. In this paper, we introduce and study random walk designs for choosing pool sizes when only a small number of tests can be run and prior knowledge is vague. To illustrate these methods, application is made to the estimation of prevalence for two diseases among Australian chrysanthemum crops. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

    PubMed

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

    2013-02-27

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

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

    PubMed Central

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

    2013-01-01

    An actual account of the angle random walk (ARW) coefficients of gyros in the constant rate biased rate ring laser gyro (RLG) inertial navigation system (INS) is very important in practical engineering applications. However, no reported experimental work has dealt with the issue of characterizing the ARW of the constant rate biased RLG in the INS. To avoid the need for high cost precise calibration tables and complex measuring set-ups, the objective of this study is to present a cost-effective experimental approach to characterize the ARW of the gyros in the constant rate biased RLG INS. In the system, turntable dynamics and other external noises would inevitably contaminate the measured RLG data, leading to the question of isolation of such disturbances. A practical observation model of the gyros in the constant rate biased RLG INS was discussed, and an experimental method based on the fast orthogonal search (FOS) for the practical observation model to separate ARW error from the RLG measured data was proposed. Validity of the FOS-based method was checked by estimating the ARW coefficients of the mechanically dithered RLG under stationary and turntable rotation conditions. By utilizing the FOS-based method, the average ARW coefficient of the constant rate biased RLG in the postulate system is estimated. The experimental results show that the FOS-based method can achieve high denoising ability. This method estimate the ARW coefficients of the constant rate biased RLG in the postulate system accurately. The FOS-based method does not need precise calibration table with high cost and complex measuring set-up, and Statistical results of the tests will provide us references in engineering application of the constant rate biased RLG INS. PMID:23447008

  9. Quantum random walk polynomial and quantum random walk measure

    NASA Astrophysics Data System (ADS)

    Kang, Yuanbao; Wang, Caishi

    2014-05-01

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

  10. Fractional random walk lattice dynamics

    NASA Astrophysics Data System (ADS)

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

    2017-02-01

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

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

    NASA Astrophysics Data System (ADS)

    Montero, Miquel; Villarroel, Javier

    2016-09-01

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

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

    PubMed

    Montero, Miquel; Villarroel, Javier

    2016-09-01

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

  13. Random-walk enzymes

    PubMed Central

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

    2015-01-01

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

  14. Random-walk enzymes.

    PubMed

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

    2015-09-01

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

  15. Random-walk enzymes

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

  16. Estimating Genomic Distance from DNA Sequence Location in Cell Nuclei by a Random Walk Model

    NASA Astrophysics Data System (ADS)

    van den Engh, Ger; Sachs, Rainer; Trask, Barbara J.

    1992-09-01

    The folding of chromatin in interphase cell nuclei was studied by fluorescent in situ hybridization with pairs of unique DNA sequence probes. The sites of DNA sequences separated by 100 to 2000 kilobase pairs (kbp) are distributed in interphase chromatin according to a random walk model. This model provides the basis for calculating the spacing of sequences along the linear DNA molecule from interphase distance measurements. An interphase mapping strategy based on this model was tested with 13 probes from a 4-megabase pair (Mbp) region of chromosome 4 containing the Huntington disease locus. The results confirmed the locations of the probes and showed that the remaining gap in the published maps of this region is negligible in size. Interphase distance measurements should facilitate construction of chromosome maps with an average marker density of one per 100 kbp, approximately ten times greater than that achieved by hybridization to metaphase chromosomes.

  17. Estimating genomic distance from DNA sequence location in cell nuclei by a random walk model

    SciTech Connect

    Engh, G. van den; Trask, B.J. ); Sachs, R. )

    1992-09-04

    The folding of chromatin in interphase cell nuclei was studied by fluorescent in situ hybridization with pairs of unique DNA sequence probes. The sites of DNA sequences separated by 100 to 2000 kilobase pairs (kbp) are distributed in interphase chromatin according to a random walk model. This model provides the basis for calculating the spacing of sequences along the linear DNA molecule from interphase distance measurements. An interphase mapping strategy based on this model was tested with 13 probes from a 4-megabase pair (Mbp) region of chromosome 4 containing the Huntington disease locus. The results confirmed the locations of the probes and showed that the remaining gap in the published maps of this region is negligible in size. Interphase distance measurements should facilitate construction of chromosome maps with an average marker density of one per 100 kbp, approximately ten times greater than that achieved by hybridization to metaphase chromosomes.

  18. A relativistically covariant random walk

    NASA Astrophysics Data System (ADS)

    Almaguer, J.; Larralde, H.

    2007-08-01

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

  19. When Human Walking is a Random Walk

    NASA Astrophysics Data System (ADS)

    Hausdorff, J. M.

    1998-03-01

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

  20. Persistence of random walk records

    NASA Astrophysics Data System (ADS)

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

    2014-06-01

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

  1. Crossover from random walk to self-avoiding walk

    NASA Astrophysics Data System (ADS)

    Rieger, Jens

    1988-11-01

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

  2. Noisy continuous time random walks

    NASA Astrophysics Data System (ADS)

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

    2013-09-01

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

  3. On Convergent Probability of a Random Walk

    ERIC Educational Resources Information Center

    Lee, Y.-F.; Ching, W.-K.

    2006-01-01

    This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.

  4. On Convergent Probability of a Random Walk

    ERIC Educational Resources Information Center

    Lee, Y.-F.; Ching, W.-K.

    2006-01-01

    This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.

  5. Random walk with barriers

    PubMed Central

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

    2011-01-01

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

  6. Simulation of pedigree genotypes by random walks.

    PubMed Central

    Lange, K; Matthysse, S

    1989-01-01

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

  7. Random walks with similar transition probabilities

    NASA Astrophysics Data System (ADS)

    Schiefermayr, Klaus

    2003-04-01

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

  8. Quantum walks with random phase shifts

    SciTech Connect

    Kosik, Jozef; Buzek, Vladimir; Hillery, Mark

    2006-08-15

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

  9. Quantum random walks and decision making.

    PubMed

    Shankar, Karthik H

    2014-01-01

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

  10. Random recursive trees and the elephant random walk

    NASA Astrophysics Data System (ADS)

    Kürsten, Rüdiger

    2016-03-01

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

  11. Random walks on simplicial complexes and harmonics†

    PubMed Central

    Steenbergen, John

    2016-01-01

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

  12. Random walks in the history of life

    PubMed Central

    Cornette, James L.; Lieberman, Bruce S.

    2004-01-01

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

  13. Epidemic spreading driven by biased random walks

    NASA Astrophysics Data System (ADS)

    Pu, Cunlai; Li, Siyuan; Yang, Jian

    2015-08-01

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

  14. Random walk with chaotically driven bias

    NASA Astrophysics Data System (ADS)

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

    2016-12-01

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

  15. Random walk with chaotically driven bias.

    PubMed

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

    2016-12-08

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

  16. Random walk with chaotically driven bias

    PubMed Central

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

    2016-01-01

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

  17. Quantum random walks using quantum accelerator modes

    SciTech Connect

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

    2006-01-15

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

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

    NASA Astrophysics Data System (ADS)

    Li, Bin

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

  19. Random Walks and Branching Processes in Correlated Gaussian Environment

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

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

  20. From random walks to spin glasses

    NASA Astrophysics Data System (ADS)

    Derrida, B.

    1997-02-01

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

  1. Quantum random-walk search algorithm

    SciTech Connect

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

    2003-05-01

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

  2. Sunspot random walk and 22-year variation

    USGS Publications Warehouse

    Love, Jeffrey J.; Rigler, E. Joshua

    2012-01-01

    We examine two stochastic models for consistency with observed long-term secular trends in sunspot number and a faint, but semi-persistent, 22-yr signal: (1) a null hypothesis, a simple one-parameter random-walk model of sunspot-number cycle-to-cycle change, and, (2) an alternative hypothesis, a two-parameter random-walk model with an imposed 22-yr alternating amplitude. The observed secular trend in sunspots, seen from solar cycle 5 to 23, would not be an unlikely result of the accumulation of multiple random-walk steps. Statistical tests show that a 22-yr signal can be resolved in historical sunspot data; that is, the probability is low that it would be realized from random data. On the other hand, the 22-yr signal has a small amplitude compared to random variation, and so it has a relatively small effect on sunspot predictions. Many published predictions for cycle 24 sunspots fall within the dispersion of previous cycle-to-cycle sunspot differences. The probability is low that the Sun will, with the accumulation of random steps over the next few cycles, walk down to a Dalton-like minimum. Our models support published interpretations of sunspot secular variation and 22-yr variation resulting from cycle-to-cycle accumulation of dynamo-generated magnetic energy.

  3. Sunspot random walk and 22-year variation

    NASA Astrophysics Data System (ADS)

    Love, Jeffrey J.; Rigler, E. Joshua

    2012-05-01

    We examine two stochastic models for consistency with observed long-term secular trends in sunspot number and a faint, but semi-persistent, 22-yr signal: (1) a null hypothesis, a simple one-parameter log-normal random-walk model of sunspot-number cycle-to-cycle change, and, (2) an alternative hypothesis, a two-parameter random-walk model with an imposed 22-yr alternating amplitude. The observed secular trend in sunspots, seen from solar cycle 5 to 23, would not be an unlikely result of the accumulation of multiple random-walk steps. Statistical tests show that a 22-yr signal can be resolved in historical sunspot data; that is, the probability is low that it would be realized from random data. On the other hand, the 22-yr signal has a small amplitude compared to random variation, and so it has a relatively small effect on sunspot predictions. Many published predictions for cycle 24 sunspots fall within the dispersion of previous cycle-to-cycle sunspot differences. The probability is low that the Sun will, with the accumulation of random steps over the next few cycles, walk down to a Dalton-like minimum. Our models support published interpretations of sunspot secular variation and 22-yr variation resulting from cycle-to-cycle accumulation of dynamo-generated magnetic energy.

  4. Convergence of quantum random walks with decoherence

    SciTech Connect

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

    2011-10-15

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

  5. Quantum Random Walks with General Particle States

    NASA Astrophysics Data System (ADS)

    Belton, Alexander C. R.

    2014-06-01

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

  6. Random Walk Weakly Attracted to a Wall

    NASA Astrophysics Data System (ADS)

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

    2008-10-01

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

  7. Random walk centrality for temporal networks

    NASA Astrophysics Data System (ADS)

    Rocha, Luis E. C.; Masuda, Naoki

    2014-06-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

  9. Random walk of passive tracers among randomly moving obstacles.

    PubMed

    Gori, Matteo; Donato, Irene; Floriani, Elena; Nardecchia, Ilaria; Pettini, Marco

    2016-04-14

    This study is mainly motivated by the need of understanding how the diffusion behavior of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target. By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle among randomly moving and interacting obstacles. The relevant physical quantity which is worked out is the diffusion coefficient of the passive tracer which is computed as a function of the average inter-obstacles distance. The results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its motion can be considerably slowed down.

  10. A Random Walk on a Circular Path

    ERIC Educational Resources Information Center

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

    2005-01-01

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

  11. A Random Walk on a Circular Path

    ERIC Educational Resources Information Center

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

    2005-01-01

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

  12. Random Walk Method for Potential Problems

    NASA Technical Reports Server (NTRS)

    Krishnamurthy, T.; Raju, I. S.

    2002-01-01

    A local Random Walk Method (RWM) for potential problems governed by Lapalace's and Paragon's equations is developed for two- and three-dimensional problems. The RWM is implemented and demonstrated in a multiprocessor parallel environment on a Beowulf cluster of computers. A speed gain of 16 is achieved as the number of processors is increased from 1 to 23.

  13. Random walk centrality in interconnected multilayer networks

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  14. An invariance property of diffusive random walks

    NASA Astrophysics Data System (ADS)

    Blanco, S.; Fournier, R.

    2003-01-01

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

  15. Do we really need a large number of particles to simulate bimolecular reactive transport with random walk methods? A kernel density estimation approach

    NASA Astrophysics Data System (ADS)

    Rahbaralam, Maryam; Fernàndez-Garcia, Daniel; Sanchez-Vila, Xavier

    2015-12-01

    Random walk particle tracking methods are a computationally efficient family of methods to solve reactive transport problems. While the number of particles in most realistic applications is in the order of 106-109, the number of reactive molecules even in diluted systems might be in the order of fractions of the Avogadro number. Thus, each particle actually represents a group of potentially reactive molecules. The use of a low number of particles may result not only in loss of accuracy, but also may lead to an improper reproduction of the mixing process, limited by diffusion. Recent works have used this effect as a proxy to model incomplete mixing in porous media. In this work, we propose using a Kernel Density Estimation (KDE) of the concentrations that allows getting the expected results for a well-mixed solution with a limited number of particles. The idea consists of treating each particle as a sample drawn from the pool of molecules that it represents; this way, the actual location of a tracked particle is seen as a sample drawn from the density function of the location of molecules represented by that given particle, rigorously represented by a kernel density function. The probability of reaction can be obtained by combining the kernels associated to two potentially reactive particles. We demonstrate that the observed deviation in the reaction vs time curves in numerical experiments reported in the literature could be attributed to the statistical method used to reconstruct concentrations (fixed particle support) from discrete particle distributions, and not to the occurrence of true incomplete mixing. We further explore the evolution of the kernel size with time, linking it to the diffusion process. Our results show that KDEs are powerful tools to improve computational efficiency and robustness in reactive transport simulations, and indicates that incomplete mixing in diluted systems should be modeled based on alternative mechanistic models and not on a

  16. A Random Walk Picture of Basketball

    NASA Astrophysics Data System (ADS)

    Gabel, Alan; Redner, Sidney

    2012-02-01

    We analyze NBA basketball play-by-play data and found that scoring is well described by a weakly-biased, anti-persistent, continuous-time random walk. The time between successive scoring events follows an exponential distribution, with little memory between events. We account for a wide variety of statistical properties of scoring, such as the distribution of the score difference between opponents and the fraction of game time that one team is in the lead.

  17. Random walks on generalized Koch networks

    NASA Astrophysics Data System (ADS)

    Sun, Weigang

    2013-10-01

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

  18. Lattice Boltzmann simulation of solute transport in heterogeneous porous media with conduits to estimate macroscopic continuous time random walk model parameters

    SciTech Connect

    Anwar, S.; Cortis, A.; Sukop, M.

    2008-10-20

    Lattice Boltzmann models simulate solute transport in porous media traversed by conduits. Resulting solute breakthrough curves are fitted with Continuous Time Random Walk models. Porous media are simulated by damping flow inertia and, when the damping is large enough, a Darcy's Law solution instead of the Navier-Stokes solution normally provided by the lattice Boltzmann model is obtained. Anisotropic dispersion is incorporated using a direction-dependent relaxation time. Our particular interest is to simulate transport processes outside the applicability of the standard Advection-Dispersion Equation (ADE) including eddy mixing in conduits. The ADE fails to adequately fit any of these breakthrough curves.

  19. Fragment formation in biased random walks

    NASA Astrophysics Data System (ADS)

    Ramola, Kabir

    2008-10-01

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

  20. Generalized ruin problems and asynchronous random walks

    NASA Astrophysics Data System (ADS)

    Abad, E.

    2005-07-01

    We consider a gambling game with two different kinds of trials and compute the duration of the game (averaged over all possible initial capitals of the players) by a mapping of the problem to a 1D lattice walk of two particles reacting upon encounter. The relative frequency of the trials is governed by the synchronicity parameter p of the random walk. The duration of the game is given by the mean time to reaction, which turns out to display a different behavior for even and odd lattices, i.e. this quantity is monotonic in p for odd lattices and non-monotonic for even lattices. In the game picture, this implies that the players minimize the duration of the game by restricting themselves to one type of trial if their joint capital is odd, otherwise a non-symmetric mixture of both trials is needed.

  1. Walking pattern classification and walking distance estimation algorithms using gait phase information.

    PubMed

    Wang, Jeen-Shing; Lin, Che-Wei; Yang, Ya-Ting C; Ho, Yu-Jen

    2012-10-01

    This paper presents a walking pattern classification and a walking distance estimation algorithm using gait phase information. A gait phase information retrieval algorithm was developed to analyze the duration of the phases in a gait cycle (i.e., stance, push-off, swing, and heel-strike phases). Based on the gait phase information, a decision tree based on the relations between gait phases was constructed for classifying three different walking patterns (level walking, walking upstairs, and walking downstairs). Gait phase information was also used for developing a walking distance estimation algorithm. The walking distance estimation algorithm consists of the processes of step count and step length estimation. The proposed walking pattern classification and walking distance estimation algorithm have been validated by a series of experiments. The accuracy of the proposed walking pattern classification was 98.87%, 95.45%, and 95.00% for level walking, walking upstairs, and walking downstairs, respectively. The accuracy of the proposed walking distance estimation algorithm was 96.42% over a walking distance.

  2. Random Walks in Model Brain Tissue

    NASA Astrophysics Data System (ADS)

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

    2011-03-01

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

  3. Scalable networks for discrete quantum random walks

    SciTech Connect

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

    2005-09-15

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

  4. Molecular motors: thermodynamics and the random walk.

    PubMed Central

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

    2001-01-01

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

  5. Excursion set theory for correlated random walks

    NASA Astrophysics Data System (ADS)

    Farahi, Arya; Benson, Andrew J.

    2013-08-01

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

  6. Random walk with random resetting to the maximum position

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

    We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability r , and with probability (1 -r ) , it undergoes symmetric random walk, i.e., it hops to one of its neighboring sites, with equal probability (1 -r )/2 . For r =0 , it reduces to a standard random walk whose typical distance grows as √{n } for large n . In the presence of a nonzero resetting rate 0

  7. The Not-so-Random Drunkard's Walk

    ERIC Educational Resources Information Center

    Ehrhardt, George

    2013-01-01

    This dataset contains the results of a quasi-experiment, testing Karl Pearson's "drunkard's walk" analogy for an abstract random walk. Inspired by the alternate hypothesis that drunkards stumble to the side of their dominant hand, it includes data on intoxicated test subjects walking a 10' line. Variables include: the…

  8. The Not-so-Random Drunkard's Walk

    ERIC Educational Resources Information Center

    Ehrhardt, George

    2013-01-01

    This dataset contains the results of a quasi-experiment, testing Karl Pearson's "drunkard's walk" analogy for an abstract random walk. Inspired by the alternate hypothesis that drunkards stumble to the side of their dominant hand, it includes data on intoxicated test subjects walking a 10' line. Variables include: the…

  9. Gait recognition and walking exercise intensity estimation.

    PubMed

    Lin, Bor-Shing; Liu, Yu-Ting; Yu, Chu; Jan, Gene Eu; Hsiao, Bo-Tang

    2014-04-04

    Cardiovascular patients consult doctors for advice regarding regular exercise, whereas obese patients must self-manage their weight. Because a system for permanently monitoring and tracking patients' exercise intensities and workouts is necessary, a system for recognizing gait and estimating walking exercise intensity was proposed. For gait recognition analysis, αβ filters were used to improve the recognition of athletic attitude. Furthermore, empirical mode decomposition (EMD) was used to filter the noise of patients' attitude to acquire the Fourier transform energy spectrum. Linear discriminant analysis was then applied to this energy spectrum for training and recognition. When the gait or motion was recognized, the walking exercise intensity was estimated. In addition, this study addressed the correlation between inertia and exercise intensity by using the residual function of the EMD and quadratic approximation to filter the effect of the baseline drift integral of the acceleration sensor. The increase in the determination coefficient of the regression equation from 0.55 to 0.81 proved that the accuracy of the method for estimating walking exercise intensity proposed by Kurihara was improved in this study.

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

    SciTech Connect

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

    2010-06-15

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

  11. Random walk with priorities in communicationlike networks

    NASA Astrophysics Data System (ADS)

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

    2013-08-01

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

  12. Background Extraction Using Random Walk Image Fusion.

    PubMed

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

    2016-12-23

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

  13. Lazy random walks for superpixel segmentation.

    PubMed

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

    2014-04-01

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

  14. Homogeneous Superpixels from Markov Random Walks

    NASA Astrophysics Data System (ADS)

    Perbet, Frank; Stenger, Björn; Maki, Atsuto

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

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

    PubMed Central

    Nilsen, Christa; Paige, John; Warner, Olivia; Mayhew, Benjamin; Sutley, Ryan; Lam, Matthew; Bernoff, Andrew J.; Topaz, Chad M.

    2013-01-01

    From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid's nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control. PMID:24376691

  16. Social aggregation in pea aphids: experiment and random walk modeling.

    PubMed

    Nilsen, Christa; Paige, John; Warner, Olivia; Mayhew, Benjamin; Sutley, Ryan; Lam, Matthew; Bernoff, Andrew J; Topaz, Chad M

    2013-01-01

    From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid's nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control.

  17. FRACTAL DIMENSION RESULTS FOR CONTINUOUS TIME RANDOM WALKS

    PubMed Central

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

    2013-01-01

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

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

    PubMed Central

    2015-01-01

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

  19. Phenomenological picture of fluctuations in branching random walks.

    PubMed

    Mueller, A H; Munier, S

    2014-10-01

    We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the 1/sqrt[t] correction to the average position of the rightmost particle of a branching random walk for large times t≫1, computed by Ebert and Van Saarloos, as fluctuations on top of the mean-field approximation of this process with a Brunet-Derrida cutoff at the tip that simulates discreteness. Our analytical formulas successfully compare to numerical simulations of a particular model of a branching random walk.

  20. Phenomenological picture of fluctuations in branching random walks

    NASA Astrophysics Data System (ADS)

    Mueller, A. H.; Munier, S.

    2014-10-01

    We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the 1 /√{t } correction to the average position of the rightmost particle of a branching random walk for large times t ≫1 , computed by Ebert and Van Saarloos, as fluctuations on top of the mean-field approximation of this process with a Brunet-Derrida cutoff at the tip that simulates discreteness. Our analytical formulas successfully compare to numerical simulations of a particular model of a branching random walk.

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

    NASA Astrophysics Data System (ADS)

    Shchur, Lev N.; Butera, Paolo

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

  2. Zero Range Process and Multi-Dimensional Random Walks

    NASA Astrophysics Data System (ADS)

    Bogoliubov, Nicolay M.; Malyshev, Cyril

    2017-07-01

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

  3. Random walks on real metro systems

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  4. ISWI remodels nucleosomes through a random walk.

    PubMed

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

    2014-07-15

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

  5. ISWI Remodels Nucleosomes through a Random Walk

    PubMed Central

    2015-01-01

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

  6. Random walks in directed modular networks

    NASA Astrophysics Data System (ADS)

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

    2014-12-01

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

  7. Random-walk model of homologous recombination

    NASA Astrophysics Data System (ADS)

    Fujitani, Youhei; Kobayashi, Ichizo

    1995-12-01

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

  8. IMU-based ambulatory walking speed estimation in constrained treadmill and overground walking.

    PubMed

    Yang, Shuozhi; Li, Qingguo

    2012-01-01

    This study evaluated the performance of a walking speed estimation system based on using an inertial measurement unit (IMU), a combination of accelerometers and gyroscopes. The walking speed estimation algorithm segments the walking sequence into individual stride cycles (two steps) based on the inverted pendulum-like behaviour of the stance leg during walking and it integrates the angular velocity and linear accelerations of the shank to determine the displacement of each stride. The evaluation was performed in both treadmill and overground walking experiments with various constraints on walking speed, step length and step frequency to provide a relatively comprehensive assessment of the system. Promising results were obtained in providing accurate and consistent walking speed/step length estimation in different walking conditions. An overall percentage root mean squared error (%RMSE) of 4.2 and 4.0% was achieved in treadmill and overground walking experiments, respectively. With an increasing interest in understanding human walking biomechanics, the IMU-based ambulatory system could provide a useful walking speed/step length measurement/control tool for constrained walking studies.

  9. MFPT calculation for random walks in inhomogeneous networks

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-04-01

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

  11. Scaling random walks on arbitrary sets

    NASA Astrophysics Data System (ADS)

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

    1999-01-01

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

  12. Biased random walks on Kleinberg's spatial networks

    NASA Astrophysics Data System (ADS)

    Pan, Gui-Jun; Niu, Rui-Wu

    2016-12-01

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

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

    NASA Astrophysics Data System (ADS)

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

    1984-06-01

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

  14. Superdiffusive Dispersals Impart the Geometry of Underlying Random Walks

    NASA Astrophysics Data System (ADS)

    Zaburdaev, V.; Fouxon, I.; Denisov, S.; Barkai, E.

    2016-12-01

    It is recognized now that a variety of real-life phenomena ranging from diffusion of cold atoms to the motion of humans exhibit dispersal faster than normal diffusion. Lévy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive Lévy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

  15. A scaling law for random walks on networks

    PubMed Central

    Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

    2014-01-01

    The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics. PMID:25311870

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

    NASA Astrophysics Data System (ADS)

    Sabir, Behlool; Santhanam, M. S.

    2014-09-01

    The study of record statistics of correlated series in physics, such as random walks, is gaining momentum, and several analytical results have been obtained in the past few years. In this work, we study the record statistics of correlated empirical data for which random walk models have relevance. We obtain results for the records statistics of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent α lying in the range 1.5≤α≤1.8. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that obtained from empirical stock data.

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

    PubMed

    Sabir, Behlool; Santhanam, M S

    2014-09-01

    The study of record statistics of correlated series in physics, such as random walks, is gaining momentum, and several analytical results have been obtained in the past few years. In this work, we study the record statistics of correlated empirical data for which random walk models have relevance. We obtain results for the records statistics of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent α lying in the range 1.5≤α≤1.8. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that obtained from empirical stock data.

  18. A scaling law for random walks on networks

    NASA Astrophysics Data System (ADS)

    Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

    2014-10-01

    The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

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

    SciTech Connect

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

    2012-10-15

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

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

    NASA Astrophysics Data System (ADS)

    Berrones, Arturo; Larralde, Hernán

    2001-03-01

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

  1. Lévy random walks on multiplex networks

    PubMed Central

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

    2016-01-01

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

  2. Lévy random walks on multiplex networks

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

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

  3. Visual estimation of travel distance during walking.

    PubMed

    Lappe, Markus; Frenz, Harald

    2009-12-01

    The optic flow generated in the eyes during self-motion provides an important control signal for direction and speed of self-motion, and can be used to track the distance that has been traveled. The use of vision for these behavioral tasks can be studied in isolation in virtual reality setups, in which self-motion is merely simulated, and in which the visual motion can be controlled independently of other sensory cues. In such experiments it was found that the estimation of the travel distance of a simulated movement shows characteristic errors, sometimes overestimating and sometimes underestimating the true travel distance. These errors can be explained by a leaky path integration model. To test whether this model also holds for actual self-motion in the real world we studied walking distance perception in an open field with tasks similar to those previously used in virtual environments. We show that similar errors occur in the estimation of travel distance in the real world as in virtual environment, and that they are consistent with the leaky integration model.

  4. Superstatistical analysis and modelling of heterogeneous random walks.

    PubMed

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

    2015-06-25

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

  5. Superstatistical analysis and modelling of heterogeneous random walks

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

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

  6. Superstatistical analysis and modelling of heterogeneous random walks

    PubMed Central

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

    2015-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

  8. Aerobic treadmill plus Bobath walking training improves walking in subacute stroke: a randomized controlled trial.

    PubMed

    Eich, H-J; Mach, H; Werner, C; Hesse, S

    2004-09-01

    To evaluate the immediate and long-term effects of aerobic treadmill plus Bobath walking training in subacute stroke survivors compared with Bobath walking training alone. Randomized controlled trial. Rehabilitation unit. Fifty patients, first-time supratentorial stroke, stroke interval less than six weeks, Barthel Index (0-100) from 50 to 80, able to walk a minimum distance of 12 m with either intermittent help or stand-by while walking, cardiovascular stable, minimum 50 W in the bicycle ergometry, randomly allocated to two groups, A and B. Group A 30 min of treadmill training, harness secured and minimally supported according to patients' needs, and 30 min of physiotherapy, every workday for six weeks, speed and inclination of the treadmill were adjusted to achieve a heart rate of HR: (Hrmax-HRrest)*0.6+HRrest; in group B 60 min of daily physiotherapy for six weeks. Primary outcome variables were the absolute improvement of walking velocity (m/s) and capacity (m), secondary were gross motor function including walking ability (score out of 13) and walking quality (score out of 41), blindly assessed before and after the intervention, and at follow-up three months later. Patients tolerated the aerobic training well with no side-effects, significantly greater improvement of walking velocity and capacity both at study end (p =0.001 versus p =0.002) and at follow-up (p <0.001 versus p <0.001) in the experimental group. Between weeks 0 and 6, the experimental group improved walking speed and capacity by a mean of.31 m/s and 91 m, the control group by a mean of 0.16 m/s and 56 m. Between weeks 0 and 18, the experimental group improved walking speed and capacity by a mean of 0.36 m/s and 111 m, the control group by a mean of 0.15 m/s and 57 m. Gross motor function and walking quality did not differ at any time. Aerobic treadmill plus Bobath walking training in moderately affected stroke patients was better than Bobath walking training alone with respect to the improvement

  9. A New Family of Solvable Pearson-Dirichlet Random Walks

    NASA Astrophysics Data System (ADS)

    Le Caër, Gérard

    2011-07-01

    An n-step Pearson-Gamma random walk in ℝ d starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations. The gamma distribution of each step length has a shape parameter q>0. Constrained random walks of n steps in ℝ d are obtained from the latter walks by imposing that the sum of the step lengths is equal to a fixed value. Simple closed-form expressions were obtained in particular for the distribution of the endpoint of such constrained walks for any d≥ d 0 and any n≥2 when q is either q = d/2 - 1 ( d 0=3) or q= d-1 ( d 0=2) (Le Caër in J. Stat. Phys. 140:728-751, 2010). When the total walk length is chosen, without loss of generality, to be equal to 1, then the constrained step lengths have a Dirichlet distribution whose parameters are all equal to q and the associated walk is thus named a Pearson-Dirichlet random walk. The density of the endpoint position of a n-step planar walk of this type ( n≥2), with q= d=2, was shown recently to be a weighted mixture of 1+ floor( n/2) endpoint densities of planar Pearson-Dirichlet walks with q=1 (Beghin and Orsingher in Stochastics 82:201-229, 2010). The previous result is generalized to any walk space dimension and any number of steps n≥2 when the parameter of the Pearson-Dirichlet random walk is q= d>1. We rely on the connection between an unconstrained random walk and a constrained one, which have both the same n and the same q= d, to obtain a closed-form expression of the endpoint density. The latter is a weighted mixture of 1+ floor( n/2) densities with simple forms, equivalently expressed as a product of a power and a Gauss hypergeometric function. The weights are products of factors which depends both on d and n and Bessel numbers independent of d.

  10. A New Random Walk for Replica Detection in WSNs

    PubMed Central

    Aalsalem, Mohammed Y.; Saad, N. M.; Hossain, Md. Shohrab; Atiquzzaman, Mohammed; Khan, Muhammad Khurram

    2016-01-01

    Wireless Sensor Networks (WSNs) are vulnerable to Node Replication attacks or Clone attacks. Among all the existing clone detection protocols in WSNs, RAWL shows the most promising results by employing Simple Random Walk (SRW). More recently, RAND outperforms RAWL by incorporating Network Division with SRW. Both RAND and RAWL have used SRW for random selection of witness nodes which is problematic because of frequently revisiting the previously passed nodes that leads to longer delays, high expenditures of energy with lower probability that witness nodes intersect. To circumvent this problem, we propose to employ a new kind of constrained random walk, namely Single Stage Memory Random Walk and present a distributed technique called SSRWND (Single Stage Memory Random Walk with Network Division). In SSRWND, single stage memory random walk is combined with network division aiming to decrease the communication and memory costs while keeping the detection probability higher. Through intensive simulations it is verified that SSRWND guarantees higher witness node security with moderate communication and memory overheads. SSRWND is expedient for security oriented application fields of WSNs like military and medical. PMID:27409082

  11. Quantum random walks do not need a coin toss

    SciTech Connect

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

    2005-03-01

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

  12. Current-reinforced random walks for constructing transport networks

    PubMed Central

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

    2013-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Yan, Jiayong; Liu, Hong; Cui, Yaoyao

    2014-04-01

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

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

    NASA Astrophysics Data System (ADS)

    Herzenberg, Caroline

    2012-03-01

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

  15. Validation of Walk Score for estimating access to walkable amenities.

    PubMed

    Carr, Lucas J; Dunsiger, Shira I; Marcus, Bess H

    2011-11-01

    Proximity to walkable destinations or amenities is thought to influence physical activity behaviour. Previous efforts attempting to calculate neighbourhood walkability have relied on self-report or time-intensive and costly measures. Walk Score is a novel and publicly available website that estimates neighbourhood walkability based on proximity to 13 amenity categories (eg, grocery stores, coffee shops, restaurants, bars, movie theatres, schools, parks, libraries, book stores, fitness centres, drug stores, hardware stores, clothing/music stores). The purpose of this study is to test the validity and reliability of Walk Score for estimating access to objectively measured walkable amenities. Walk Scores of 379 residential/non-residential addresses in Rhode Island were manually calculated. Geographic information systems (GIS) was used to objectively measure 4194 walkable amenities in the 13 Walk Score categories. GIS data were aggregated from publicly available data sources. Sums of amenities within each category were matched to address data, and Pearson correlations were calculated between the category sums and address Walk Scores. Significant correlations were identified between Walk Score and all categories of aggregated walkable destinations within a 1-mile buffer of the 379 residential and non-residential addresses. Test-retest reliability correlation coefficients for a subsample of 100 addresses were 1.0. These results support Walk Score as a reliable and valid measure of estimating access to walkable amenities. Walk Score may be a convenient and inexpensive option for researchers interested in exploring the relationship between access to walkable amenities and health behaviours such as physical activity.

  16. Feature Learning Based Random Walk for Liver Segmentation

    PubMed Central

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

    2016-01-01

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

  17. Stride Counting in Human Walking and Walking Distance Estimation Using Insole Sensors

    PubMed Central

    Truong, Phuc Huu; Lee, Jinwook; Kwon, Ae-Ran; Jeong, Gu-Min

    2016-01-01

    This paper proposes a novel method of estimating walking distance based on a precise counting of walking strides using insole sensors. We use an inertial triaxial accelerometer and eight pressure sensors installed in the insole of a shoe to record walkers’ movement data. The data is then transmitted to a smartphone to filter out noise and determine stance and swing phases. Based on phase information, we count the number of strides traveled and estimate the movement distance. To evaluate the accuracy of the proposed method, we created two walking databases on seven healthy participants and tested the proposed method. The first database, which is called the short distance database, consists of collected data from all seven healthy subjects walking on a 16 m distance. The second one, named the long distance database, is constructed from walking data of three healthy subjects who have participated in the short database for an 89 m distance. The experimental results show that the proposed method performs walking distance estimation accurately with the mean error rates of 4.8% and 3.1% for the short and long distance databases, respectively. Moreover, the maximum difference of the swing phase determination with respect to time is 0.08 s and 0.06 s for starting and stopping points of swing phases, respectively. Therefore, the stride counting method provides a highly precise result when subjects walk. PMID:27271634

  18. Solving Schroedinger's equation using random walks

    NASA Astrophysics Data System (ADS)

    Aspuru-Guzik, Alan

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

  19. Navigation by anomalous random walks on complex networks

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

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

  20. Navigation by anomalous random walks on complex networks

    PubMed Central

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

    2016-01-01

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

  1. Treadmill motor current value based walk phase estimation.

    PubMed

    Ohki, Eiichi; Nakashima, Yasutaka; Ando, Takeshi; Fujie, Masakatsu G

    2009-01-01

    We have developed a gait rehabilitation robot for hemiplegic patients using the treadmill. A walk phase, which includes time balance of stance and swing legs, is one of the most basic indexes to evaluate patients' gait. In addition, the walking phase is one of the indexes to control our robotic rehabilitation system. However, conventional methods to measure the walk phase require another system such as the foot switch and force plate. In this paper, an original algorithm to estimate the walk phase of a person on a treadmill using only the current value of DC motor to control the treadmill velocity is proposed. This algorithm was verified by experiments on five healthy subjects, and the walk phase of four subjects could be estimated in 0.2 (s) errors. However, the algorithm had erroneously identified a period of time in the stance phase as swing phase time when little body weight loaded on the subject's leg. Because a period of time with little body weight to affected leg is often observed in a hemiplegic walk, the proposed algorithm might fail to properly estimate the walk phase of hemiplegic patients. However, this algorithm could be used to estimate the time when body weight is loaded on patient legs, and thus could be used as a new quantitative evaluation index.

  2. Inference of random walk models to describe leukocyte migration

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  3. Protein localization prediction using random walks on graphs

    PubMed Central

    2013-01-01

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

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

    SciTech Connect

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

    1998-11-01

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

  5. Amnestically Induced Persistence in Random Walks

    NASA Astrophysics Data System (ADS)

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

    2007-02-01

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

  6. Amnestically induced persistence in random walks.

    PubMed

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

    2007-02-16

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

  7. Vibration driven random walk in a Chladni experiment

    NASA Astrophysics Data System (ADS)

    Grabec, Igor

    2017-01-01

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

  8. Random walks models with intermediate fractional diffusion asymptotics

    NASA Astrophysics Data System (ADS)

    Saichev, Alexander I.; Utkin, Sergei G.

    2004-05-01

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

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

    NASA Astrophysics Data System (ADS)

    Asztalos, Andrea

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

  10. Homogeneous Open Quantum Random Walks on a Lattice

    NASA Astrophysics Data System (ADS)

    Carbone, Raffaella; Pautrat, Yan

    2015-09-01

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

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

    SciTech Connect

    Maire, Sylvain; Simon, Martin

    2015-12-15

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

  12. An Analysis of Random-Walk Cuckoo Hashing

    NASA Astrophysics Data System (ADS)

    Frieze, Alan; Melsted, Páll; Mitzenmacher, Michael

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

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

    NASA Astrophysics Data System (ADS)

    Santha, Miklos

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

  14. Sub-Markov Random Walk for Image Segmentation.

    PubMed

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

    2016-02-01

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

  15. IS QUASAR OPTICAL VARIABILITY A DAMPED RANDOM WALK?

    SciTech Connect

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

    2013-03-10

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

  16. Random Walks and Effective Optical Depth in Relativistic Flow

    NASA Astrophysics Data System (ADS)

    Shibata, Sanshiro; Tominaga, Nozomu; Tanaka, Masaomi

    2014-05-01

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

  17. An effective Hamiltonian approach to quantum random walk

    NASA Astrophysics Data System (ADS)

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

    2017-03-01

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

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

    SciTech Connect

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

    2007-05-15

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

  19. Random walk after the big bang

    SciTech Connect

    Mijic, M. )

    1990-10-15

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

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

    PubMed

    Schwarz, W

    1989-01-01

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

  1. A generalized model via random walks for information filtering

    NASA Astrophysics Data System (ADS)

    Ren, Zhuo-Ming; Kong, Yixiu; Shang, Ming-Sheng; Zhang, Yi-Cheng

    2016-08-01

    There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation.

  2. Statistical Modeling of Robotic Random Walks on Different Terrain

    NASA Astrophysics Data System (ADS)

    Naylor, Austin; Kinnaman, Laura

    Issues of public safety, especially with crowd dynamics and pedestrian movement, have been modeled by physicists using methods from statistical mechanics over the last few years. Complex decision making of humans moving on different terrains can be modeled using random walks (RW) and correlated random walks (CRW). The effect of different terrains, such as a constant increasing slope, on RW and CRW was explored. LEGO robots were programmed to make RW and CRW with uniform step sizes. Level ground tests demonstrated that the robots had the expected step size distribution and correlation angles (for CRW). The mean square displacement was calculated for each RW and CRW on different terrains and matched expected trends. The step size distribution was determined to change based on the terrain; theoretical predictions for the step size distribution were made for various simple terrains. It's Dr. Laura Kinnaman, not sure where to put the Prefix.

  3. The random walk of tracers through river catchments

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Atreyee

    2012-08-01

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

  4. Random Walk on the High-Dimensional IIC

    NASA Astrophysics Data System (ADS)

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

    2014-07-01

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

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

    PubMed

    Hernandez-Suarez, Carlos M

    2016-09-01

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

  6. Universal properties of branching random walks in confined geometries

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

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

  7. Reheating-volume measure for random-walk inflation

    SciTech Connect

    Winitzki, Sergei

    2008-09-15

    The recently proposed 'reheating-volume' (RV) measure promises to solve the long-standing problem of extracting probabilistic predictions from cosmological multiverse scenarios involving eternal inflation. I give a detailed description of the new measure and its applications to generic models of eternal inflation of random-walk type. For those models I derive a general formula for RV-regulated probability distributions that is suitable for numerical computations. I show that the results of the RV cutoff in random-walk type models are always gauge invariant and independent of the initial conditions at the beginning of inflation. In a toy model where equal-time cutoffs lead to the 'youngness paradox', the RV cutoff yields unbiased results that are distinct from previously proposed measures.

  8. A random walk in physical biology

    NASA Astrophysics Data System (ADS)

    Peterson, Eric Lee

    Biology as a scientific discipline is becoming evermore quantitative as tools become available to probe living systems on every scale from the macro to the micro and now even to the nanoscale. In quantitative biology the challenge is to understand the living world in an in vivo context, where it is often difficult for simple theoretical models to connect with the full richness and complexity of the observed data. Computational models and simulations offer a way to bridge the gap between simple theoretical models and real biological systems; towards that aspiration are presented in this thesis three case studies in applying computational models that may give insight into native biological structures.The first is concerned with soluble proteins; proteins, like DNA, are linear polymers written in a twenty-letter "language" of amino acids. Despite the astronomical number of possible proteins sequences, a great amount of similarity is observed among the folded structures of globular proteins. One useful way of discovering similar sequences is to align their sequences, as done e.g. by the popular BLAST program. By clustering together amino acids and reducing the alphabet that proteins are written in to fewer than twenty letters, we find that pairwise sequence alignments are actually more sensitive to proteins with similar structures.The second case study is concerned with the measurement of forces applied to a membrane. We demonstrate a general method for extracting the forces applied to a fluid lipid bilayer of arbitrary shape and show that the subpiconewton forces applied by optical tweezers to vesicles can be accurately measured in this way.In the third and final case study we examine the forces between proteins in a lipid bilayer membrane. Due to the bending of the membrane surrounding them, such proteins feel mutually attractive forces which can help them to self-organize and act in concert. These finding are relevant at the areal densities estimated for membrane

  9. A Random Walk Phenomenon under an Interesting Stopping Rule

    ERIC Educational Resources Information Center

    Chakraborty, S.

    2007-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

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

  11. A Random Walk Phenomenon under an Interesting Stopping Rule

    ERIC Educational Resources Information Center

    Chakraborty, S.

    2007-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Petritis, Dimitri

    2016-08-01

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

  13. Random walk of microswimmers: puller and pusher cases

    NASA Astrophysics Data System (ADS)

    Rafai, Salima; Peyla, Philippe; Dyfcom Team

    2014-11-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2010-11-01

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

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

    NASA Astrophysics Data System (ADS)

    Sarkar, Purnamrita; Moore, Andrew W.

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

  16. Theory of continuum random walks and application to chemotaxis

    NASA Astrophysics Data System (ADS)

    Schnitzer, Mark J.

    1993-10-01

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

  17. Correlated Random Walks with a Finite Memory Range

    NASA Astrophysics Data System (ADS)

    Bidaux, Roger; Boccara, Nino

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

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

    NASA Astrophysics Data System (ADS)

    Ampadu, Clement

    2013-04-01

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

  19. Asymptotic behaviour of random walks with correlated temporal structure

    PubMed Central

    Magdziarz, Marcin; Szczotka, Władysław; Żebrowski, Piotr

    2013-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Athreya, Siva; Drewitz, Alexander; Sun, Rongfeng

    2017-03-01

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

  1. RANDOM WALKS AND EFFECTIVE OPTICAL DEPTH IN RELATIVISTIC FLOW

    SciTech Connect

    Shibata, Sanshiro; Tominaga, Nozomu; Tanaka, Masaomi

    2014-05-20

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

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

    PubMed

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

    2014-05-01

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

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

    SciTech Connect

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

    2014-12-15

    Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the history information arise naturally as geometrical degrees of freedom on the lattice.

  4. Conditioned random walks and interaction-driven condensation

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

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

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

    PubMed Central

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

    2012-01-01

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

  6. Tests of the random walk hypothesis for financial data

    NASA Astrophysics Data System (ADS)

    Nakamura, Tomomichi; Small, Michael

    2007-04-01

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

  7. First Passage Time for Random Walks in Heterogeneous Networks

    NASA Astrophysics Data System (ADS)

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

    2012-08-01

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

  8. Characteristic times of biased random walks on complex networks

    NASA Astrophysics Data System (ADS)

    Bonaventura, Moreno; Nicosia, Vincenzo; Latora, Vito

    2014-01-01

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

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

    PubMed

    Angstmann, C; Henry, B I

    2011-12-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

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

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

    SciTech Connect

    Mazzolo, Alain Zoia, Andrea

    2014-08-01

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

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

    PubMed

    Bonaventura, Moreno; Nicosia, Vincenzo; Latora, Vito

    2014-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Grassberger, Peter

    2017-07-01

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

  14. A random walk to stochastic diffusion through spreadsheet analysis

    NASA Astrophysics Data System (ADS)

    Brazzle, Bob

    2013-11-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-06-01

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

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

    SciTech Connect

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

    2013-11-15

    In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the number of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.

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

    NASA Astrophysics Data System (ADS)

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

    2015-01-01

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

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

    PubMed

    Wang, Peng; Mu, Hailin

    2011-01-01

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

  19. Parsimonious Continuous Time Random Walk Models and Kurtosis for Diffusion in Magnetic Resonance of Biological Tissue

    NASA Astrophysics Data System (ADS)

    Ingo, Carson; Sui, Yi; Chen, Yufen; Parrish, Todd; Webb, Andrew; Ronen, Itamar

    2015-03-01

    In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.

  20. Record statistics of a strongly correlated time series: random walks and Lévy flights

    NASA Astrophysics Data System (ADS)

    Godrèche, Claude; Majumdar, Satya N.; Schehr, Grégory

    2017-08-01

    We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few years, it was indeed realized that random walks are a very useful ‘laboratory’ to test the effects of correlations on the record statistics. We start with the simple one-dimensional random walk with symmetric jumps (both continuous and discrete) and discuss in detail the statistics of the number of records, as well as of the ages of the records, i.e. the lapses of time between two successive record breaking events. Then we review the results that were obtained for a wide variety of random walk models, including random walks with a linear drift, continuous time random walks, constrained random walks (like the random walk bridge) and the case of multiple independent random walkers. Finally, we discuss further observables related to records, like the record increments, as well as some questions raised by physical applications of record statistics, like the effects of measurement error and noise.

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

    PubMed

    Zhang, Zhongzhi; Li, Huan; Sheng, Yibin

    2014-12-12

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

  2. Effects of reciprocity on random walks in weighted networks

    PubMed Central

    Zhang, Zhongzhi; Li, Huan; Sheng, Yibin

    2014-01-01

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

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

    PubMed Central

    2014-01-01

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

  4. Cochlea segmentation using iterated random walks with shape prior

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

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

    SciTech Connect

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

    2014-04-10

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

  6. Combinatorial approximation algorithms for MAXCUT using random walks.

    SciTech Connect

    Seshadhri, Comandur; Kale, Satyen

    2010-11-01

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

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

    NASA Astrophysics Data System (ADS)

    Chakrabarti, Arnab; Chakraborty, Ipsita; Bhattacharyya, Rangeet

    2016-05-01

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

  8. Ergodic transitions in continuous-time random walks

    NASA Astrophysics Data System (ADS)

    Saa, Alberto; Venegeroles, Roberto

    2010-09-01

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

  9. Statistics of largest loops in a random walk

    NASA Astrophysics Data System (ADS)

    Ertas, Deniz; Kantor, Yacov

    1997-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Lavenda, B. H.

    2004-02-01

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

  11. Estimating mood variation from MPF of EMG during walking.

    PubMed

    Kinase, Yuta; Venture, Gentiane

    2013-01-01

    The information on the mood included in behavior is classified into nonverbal information, and is included in behavior without necessarily being based on the intention of an agent. Consequently, it is considered that we can estimate the mood from the measurement of the behavior. In this work, we estimate the mood from the surface electromyogram (EMG) information of the muscles of the upper limb during walking. Identification of emotion and mood using EMG information has been done with a variety of methods until now. In addition, it is known that human walking includes information that is specific to the individual and be affected by mood. Therefore, it is thought that the EMG analysis of walking is effective in the identification of human mood. In this work, we made a subject walk in the various mood states and answer psychological tests that measure the mood. We use two types of tasks (music listening and numerical calculation) for evoking different moods. Statistical features of EMG signals are calculated using Fast Fourier Transform (FFT) and Principal Component Analysis (PCA). These statistical features are related with psychological test scores, using regression analysis. In this paper, we have shown the statistical significance of the linear model to predict the variation of mood based on the information on the variation in MPF of EMG data of the muscles of the upper limb during walking with different moods. This shows the validity of such a mapping. However, since the interpretability of the model is still low, it cannot be said that the model is able to accurately represent the mood variation. Creating a model with high accuracy is a key issue in the future.

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

    NASA Astrophysics Data System (ADS)

    Abramson, Joshua Simon

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

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

    SciTech Connect

    Stadje, W.

    1988-05-01

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

  14. Estimation of detection thresholds for redirected walking techniques.

    PubMed

    Steinicke, Frank; Bruder, Gerd; Jerald, Jason; Frenz, Harald; Lappe, Markus

    2010-01-01

    In immersive virtual environments (IVEs), users can control their virtual viewpoint by moving their tracked head and walking through the real world. Usually, movements in the real world are mapped one-to-one to virtual camera motions. With redirection techniques, the virtual camera is manipulated by applying gains to user motion so that the virtual world moves differently than the real world. Thus, users can walk through large-scale IVEs while physically remaining in a reasonably small workspace. In psychophysical experiments with a two-alternative forced-choice task, we have quantified how much humans can unknowingly be redirected on physical paths that are different from the visually perceived paths. We tested 12 subjects in three different experiments: (E1) discrimination between virtual and physical rotations, (E2) discrimination between virtual and physical straightforward movements, and (E3) discrimination of path curvature. In experiment E1, subjects performed rotations with different gains, and then had to choose whether the visually perceived rotation was smaller or greater than the physical rotation. In experiment E2, subjects chose whether the physical walk was shorter or longer than the visually perceived scaled travel distance. In experiment E3, subjects estimate the path curvature when walking a curved path in the real world while the visual display shows a straight path in the virtual world. Our results show that users can be turned physically about 49 percent more or 20 percent less than the perceived virtual rotation, distances can be downscaled by 14 percent and upscaled by 26 percent, and users can be redirected on a circular arc with a radius greater than 22 m while they believe that they are walking straight.

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

    PubMed

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

    2001-12-15

    We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases. Stochastic modeling of the gait rhythm dynamics, based on transitions between different "neural centers", reproduces distinctive statistical properties of the gait pattern. By tuning one model parameter, the hopping (transition) range, the model can describe alterations in gait dynamics from childhood to adulthood including a decrease in the correlation and volatility exponents with maturation.

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

    NASA Astrophysics Data System (ADS)

    Hausdorff, Jeffrey M.; Ashkenazy, Yosef; Peng, Chang-K.; Ivanov, Plamen Ch.; Stanley, H. Eugene; Goldberger, Ary L.

    2001-12-01

    We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases. Stochastic modeling of the gait rhythm dynamics, based on transitions between different “neural centers”, reproduces distinctive statistical properties of the gait pattern. By tuning one model parameter, the hopping (transition) range, the model can describe alterations in gait dynamics from childhood to adulthood - including a decrease in the correlation and volatility exponents with maturation.

  17. Empirical scaling of the length of the longest increasing subsequences of random walks

    NASA Astrophysics Data System (ADS)

    Mendonça, J. Ricardo G.

    2017-02-01

    We provide Monte Carlo estimates of the scaling of the length L n of the longest increasing subsequences of n-step random walks for several different distributions of step lengths, short and heavy-tailed. Our simulations indicate that, barring possible logarithmic corrections, {{L}n}∼ {{n}θ} with the leading scaling exponent 0.60≲ θ ≲ 0.69 for the heavy-tailed distributions of step lengths examined, with values increasing as the distribution becomes more heavy-tailed, and θ ≃ 0.57 for distributions of finite variance, irrespective of the particular distribution. The results are consistent with existing rigorous bounds for θ, although in a somewhat surprising manner. For random walks with step lengths of finite variance, we conjecture that the correct asymptotic behavior of L n is given by \\sqrt{n}\\ln n , and also propose the form for the subleading asymptotics. The distribution of L n was found to follow a simple scaling form with scaling functions that vary with θ. Accordingly, when the step lengths are of finite variance they seem to be universal. The nature of this scaling remains unclear, since we lack a working model, microscopic or hydrodynamic, for the behavior of the length of the longest increasing subsequences of random walks.

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

    NASA Astrophysics Data System (ADS)

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

    2017-09-01

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

  19. A Branching Random Walk Seen from the Tip

    NASA Astrophysics Data System (ADS)

    Brunet, Éric; Derrida, Bernard

    2011-05-01

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

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

    PubMed

    Rosvall, Martin; Bergstrom, Carl T

    2008-01-29

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

  1. First-passage properties of bursty random walks

    NASA Astrophysics Data System (ADS)

    Volovik, D.; Redner, S.

    2010-06-01

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

  2. Random walks for spike-timing-dependent plasticity

    NASA Astrophysics Data System (ADS)

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

    2004-08-01

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

  3. Random walks on activity-driven networks with attractiveness

    NASA Astrophysics Data System (ADS)

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

    2017-05-01

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

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

    PubMed

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

    2014-01-01

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

  5. Subdiffusion in time-averaged, confined random walks

    NASA Astrophysics Data System (ADS)

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

    2009-07-01

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

  6. Complex networks: when random walk dynamics equals synchronization

    NASA Astrophysics Data System (ADS)

    Kriener, Birgit; Anand, Lishma; Timme, Marc

    2012-09-01

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

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

    SciTech Connect

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

    2016-04-18

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

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

    PubMed

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

    2013-03-01

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

  9. Knots and Random Walks in Vibrated Granular Chains

    NASA Astrophysics Data System (ADS)

    Ben-Naim, Eli

    2002-03-01

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

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

    PubMed Central

    Dong, Qiang; Fu, Yan

    2014-01-01

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

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

    PubMed

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

    2003-08-01

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

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

    SciTech Connect

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

    2016-04-18

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

  13. Composition of many spins, random walks and statistics

    NASA Astrophysics Data System (ADS)

    Polychronakos, Alexios P.; Sfetsos, Konstantinos

    2016-12-01

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

  14. Correlated continuous time random walk and option pricing

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

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

    SciTech Connect

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

    2000-04-11

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

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

    PubMed

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

    2017-03-01

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

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

    PubMed

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

    2003-11-01

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

  18. Treadmill training improves overground walking economy in Parkinson's disease: a randomized, controlled pilot study.

    PubMed

    Fernández-Del-Olmo, Miguel Angel; Sanchez, Jose Andres; Bello, Olalla; Lopez-Alonso, Virginia; Márquez, Gonzalo; Morenilla, Luis; Castro, Xabier; Giraldez, Manolo; Santos-García, Diego

    2014-01-01

    Gait disturbances are one of the principal and most incapacitating symptoms of Parkinson's disease (PD). In addition, walking economy is impaired in PD patients and could contribute to excess fatigue in this population. An important number of studies have shown that treadmill training can improve kinematic parameters in PD patients. However, the effects of treadmill and overground walking on the walking economy remain unknown. The goal of this study was to explore the walking economy changes in response to a treadmill and an overground training program, as well as the differences in the walking economy during treadmill and overground walking. Twenty-two mild PD patients were randomly assigned to a treadmill or overground training group. The training program consisted of 5 weeks (3 sessions/week). We evaluated the energy expenditure of overground walking, before and after each of the training programs. The energy expenditure of treadmill walking (before the program) was also evaluated. The treadmill, but not the overground training program, lead to an improvement in the walking economy (the rate of oxygen consumed per distance during overground walking at a preferred speed) in PD patients. In addition, walking on a treadmill required more energy expenditure compared with overground walking at the same speed. This study provides evidence that in mild PD patients, treadmill training is more beneficial compared with that of walking overground, leading to a greater improvement in the walking economy. This finding is of clinical importance for the therapeutic administration of exercise in PD.

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

    PubMed Central

    Fernández-del-Olmo, Miguel Angel; Sanchez, Jose Andres; Bello, Olalla; Lopez-Alonso, Virginia; Márquez, Gonzalo; Morenilla, Luis; Castro, Xabier; Giraldez, Manolo; Santos-García, Diego

    2014-01-01

    Gait disturbances are one of the principal and most incapacitating symptoms of Parkinson’s disease (PD). In addition, walking economy is impaired in PD patients and could contribute to excess fatigue in this population. An important number of studies have shown that treadmill training can improve kinematic parameters in PD patients. However, the effects of treadmill and overground walking on the walking economy remain unknown. The goal of this study was to explore the walking economy changes in response to a treadmill and an overground training program, as well as the differences in the walking economy during treadmill and overground walking. Twenty-two mild PD patients were randomly assigned to a treadmill or overground training group. The training program consisted of 5 weeks (3 sessions/week). We evaluated the energy expenditure of overground walking, before and after each of the training programs. The energy expenditure of treadmill walking (before the program) was also evaluated. The treadmill, but not the overground training program, lead to an improvement in the walking economy (the rate of oxygen consumed per distance during overground walking at a preferred speed) in PD patients. In addition, walking on a treadmill required more energy expenditure compared with overground walking at the same speed. This study provides evidence that in mild PD patients, treadmill training is more beneficial compared with that of walking overground, leading to a greater improvement in the walking economy. This finding is of clinical importance for the therapeutic administration of exercise in PD. PMID:25309510

  20. Quantum random walks on congested lattices and the effect of dephasing

    PubMed Central

    Motes, Keith R.; Gilchrist, Alexei; Rohde, Peter P.

    2016-01-01

    We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled on lattices that contain static defects which reverse the walker’s direction. We implement a dephasing process after each step which allows us to smoothly interpolate between classical and quantum random walks as well as study the effect of dephasing on the quantum walk. Our key results show that a quantum walker escapes a finite boundary dramatically faster than a classical walker and that this advantage remains in the presence of heavily congested lattices. PMID:26812924

  1. Unbinding of mutually avoiding random walks and two-dimensional quantum gravity

    NASA Astrophysics Data System (ADS)

    Carlon, Enrico; Baiesi, Marco

    2004-12-01

    We analyze the unbinding transition for a two-dimensional lattice polymer in which the constituent strands are mutually avoiding random walks. At low temperatures the strands are bound and form a single self-avoiding walk. We show that unbinding in this model is a strong first order transition. The entropic exponents associated with denaturated loops and end-segment distributions show sharp differences at the transition point and in the high temperature phase. Their values can be deduced from some exact arguments relying on a conformal mapping of copolymer networks into a fluctuating geometry, i.e., in the presence of quantum gravity. An excellent agreement between analytical and numerical estimates is observed for all cases analyzed.

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

    NASA Astrophysics Data System (ADS)

    Pellegrini, Clément

    2014-02-01

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

  3. The development of an estimation model for energy expenditure during water walking by acceleration and walking speed.

    PubMed

    Kaneda, Koichi; Ohgi, Yuji; Tanaka, Chiaki; Burkett, Brendan

    2014-01-01

    The aim of this study was to develop an estimation equation for energy expenditure during water walking based on the acceleration and walking speed. Cross-validation study. Fifty participants, males (n=29, age: 27-73) and females (n=21, age: 33-70) volunteered for this study. Based on their physical condition water walking was conducted at three self-selected walking speeds from a range of: 20, 25, 30, 35 and 40 m/min. Energy expenditure during each trial was calculated. During water walking, an accelerometer was attached to the occipital region and recorded three-dimensional accelerations at 100 Hz. A stopwatch was used for timing the participant's walking speed. The estimation model for energy expenditure included three components; (i) resting metabolic rate, (ii) internal energy expenditure for moving participants' body, and (iii) external energy expenditure due to water drag force. When comparing the measured and estimated energy expenditure with the acceleration data being the third component of the estimation model, high correlation coefficients were found in both male (r=0.73) and female (r=0.77) groups. When walking speeds were applied to the third component of the model, higher correlation coefficients were found (r=0.82 in male and r=0.88 in female). Good agreements of the developed estimation model were found in both methods, regardless of gender. This study developed a valid estimation model for energy expenditure during water walking by using head acceleration and walking speed. Copyright © 2013 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.

  4. Accuracy of a low-cost global positioning system receiver for estimating grade during outdoor walking.

    PubMed

    de Müllenheim, Pierre-Yves; Chaudru, Ségolène; Gernigon, Marie; Mahé, Guillaume; Bickert, Sandrine; Prioux, Jacques; Noury-Desvaux, Bénédicte; Le Faucheur, Alexis

    2016-09-21

    The aim of this study was to assess, for the first time, the accuracy of a low-cost global positioning system (GPS) receiver for estimating grade during outdoor walking. Thirty subjects completed outdoor walks (2.0, 3.5 and 5.0 km · h(-1)) in three randomized conditions: 1/level walking on a 0.0% grade; 2/graded (uphill and downhill) walking on a 3.4% grade; and 3/on a 10.4% grade. Subjects were equipped with a GPS receiver (DG100, GlobalSat Technology Corp., Taiwan; ~US$75). The GPS receiver was set to record at 1 Hz and its antenna was placed on the right shoulder. Grade was calculated from GPS speed and altitude data (grade  =  altitude variation/travelled distance  ×  100). Two methods were used for the grade calculation: one using uncorrected altitude data given by the GPS receiver and another one using corrected altitude data obtained using map projection software (CartoExploreur, version 3.11.0, build 2.6.6.22, Bayo Ltd, Appoigny, France, ~US$35). Linear regression of GPS-estimated versus actual grade with R (2) coefficients, bias with 95% limits of agreement (±95% LoA), and typical error of the estimate with 95% confidence interval (TEE (95% CI)) were computed to assess the accuracy of the GPS receiver. 444 walking periods were performed. Using uncorrected altitude data, we obtained: R (2)  =  0.88 (p  <  0.001), bias  =  0.0  ±  6.6%, TEE between 1.9 (1.7-2.2)% and 4.2 (3.6-4.9)% according to the grade level. Using corrected altitude data, we obtained: R (2)  =  0.98 (p  <  0.001), bias  =  0.2  ±  1.9%, TEE between 0.2 (0.2-0.3)% and 1.0 (0.9-1.2)% according to the grade level. The low-cost GPS receiver used was weakly accurate for estimating grade during outdoor walking when using uncorrected altitude data. However, the accuracy was greatly improved when using corrected altitude data. This study supports the potential interest of using GPS for estimating energy

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

    PubMed

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

    2017-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

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

  7. Ranking Competitors Using Degree-Neutralized Random Walks

    PubMed Central

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

    2014-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-05-01

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

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

    PubMed

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

    2015-05-01

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

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

    PubMed Central

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

    2013-01-01

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

  11. Monotonic continuous-time random walks with drift and stochastic reset events

    NASA Astrophysics Data System (ADS)

    Montero, Miquel; Villarroel, Javier

    2013-01-01

    In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

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

    PubMed Central

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

    2009-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Corwin, Ivan; Gu, Yu

    2017-01-01

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

  14. Random walk approach for dispersive transport in pipe networks

    NASA Astrophysics Data System (ADS)

    Sämann, Robert; Graf, Thomas; Neuweiler, Insa

    2016-04-01

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

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

    SciTech Connect

    Balescu, R.

    1995-05-01

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

  16. Electron avalanche structure determined by random walk theory

    NASA Technical Reports Server (NTRS)

    Englert, G. W.

    1973-01-01

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

  17. Stochastic calculus for uncoupled continuous-time random walks

    NASA Astrophysics Data System (ADS)

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

    2009-06-01

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

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

    NASA Astrophysics Data System (ADS)

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

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

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

    PubMed

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

    2009-06-01

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

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

    DOE PAGES

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

    2016-04-18

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

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

    PubMed

    Sendova-Franks, Ana B; Van Lent, Jan

    2002-07-21

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

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

    NASA Astrophysics Data System (ADS)

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

    2010-01-01

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

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

    PubMed Central

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

    2014-01-01

    Background Multi-channel surface functional electrical stimulation (FES) for walking has been used to improve voluntary walking and balance in individuals with spinal cord injury (SCI). Objective To investigate short- and long-term benefits of 16 weeks of thrice-weekly FES-assisted walking program, while ambulating on a body weight support treadmill and harness system, versus a non-FES exercise program, on improvements in gait and balance in individuals with chronic incomplete traumatic SCI, in a randomized controlled trial design. Methods Individuals with traumatic and chronic (≥18 months) motor incomplete SCI (level C2 to T12, American Spinal Cord Injury Association Impairment Scale C or D) were recruited from an outpatient SCI rehabilitation hospital, and randomized to FES-assisted walking therapy (intervention group) or aerobic and resistance training program (control group). Outcomes were assessed at baseline, and after 4, 6, and 12 months. Gait, balance, spasticity, and functional measures were collected. Results Spinal cord independence measure (SCIM) mobility sub-score improved over time in the intervention group compared with the control group (baseline/12 months: 17.27/21.33 vs. 19.09/17.36, respectively). On all other outcome measures the intervention and control groups had similar improvements. Irrespective of group allocation walking speed, endurance, and balance during ambulation all improved upon completion of therapy, and majority of participants retained these gains at long-term follow-ups. Conclusions Task-oriented training improves walking ability in individuals with incomplete SCI, even in the chronic stage. Further randomized controlled trials, involving a large number of participants are needed, to verify if FES-assisted treadmill training is superior to aerobic and strength training. PMID:25229735

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

    PubMed

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

    2014-09-01

    Multi-channel surface functional electrical stimulation (FES) for walking has been used to improve voluntary walking and balance in individuals with spinal cord injury (SCI). To investigate short- and long-term benefits of 16 weeks of thrice-weekly FES-assisted walking program, while ambulating on a body weight support treadmill and harness system, versus a non-FES exercise program, on improvements in gait and balance in individuals with chronic incomplete traumatic SCI, in a randomized controlled trial design. Individuals with traumatic and chronic (≥18 months) motor incomplete SCI (level C2 to T12, American Spinal Cord Injury Association Impairment Scale C or D) were recruited from an outpatient SCI rehabilitation hospital, and randomized to FES-assisted walking therapy (intervention group) or aerobic and resistance training program (control group). Outcomes were assessed at baseline, and after 4, 6, and 12 months. Gait, balance, spasticity, and functional measures were collected. Spinal cord independence measure (SCIM) mobility sub-score improved over time in the intervention group compared with the control group (baseline/12 months: 17.27/21.33 vs. 19.09/17.36, respectively). On all other outcome measures the intervention and control groups had similar improvements. Irrespective of group allocation walking speed, endurance, and balance during ambulation all improved upon completion of therapy, and majority of participants retained these gains at long-term follow-ups. Task-oriented training improves walking ability in individuals with incomplete SCI, even in the chronic stage. Further randomized controlled trials, involving a large number of participants are needed, to verify if FES-assisted treadmill training is superior to aerobic and strength training.

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

    DOE PAGES

    Rudinger, Kenneth; Gamble, John King; Bach, Eric; ...

    2013-07-01

    Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erencesmore » in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.« less

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

    SciTech Connect

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

    2013-07-01

    Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erences in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.

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

    PubMed

    Klotzsch, Stephan; Binder, Martin; Händel, Falk

    2017-01-01

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

  8. Ambulatory estimation of center of mass displacement during walking.

    PubMed

    Schepers, H Martin; van Asseldonk, Edwin H F; Buurke, Jaap H; Veltink, Peter H

    2009-04-01

    The center of mass (CoM) and the center of pressure (CoP) are two variables that are crucial in assessing energy expenditure and stability of human walking. The purpose of this study is to estimate the CoM displacement continuously using an ambulatory measurement system. The measurement system consists of instrumented shoes with 6 DOF force/moment sensors beneath the heels and the forefeet. Moreover, two inertial sensors are rigidly attached to the force/moment sensors for the estimation of position and orientation. The estimation of CoM displacement is achieved by fusing low-pass filtered CoP data with high-pass filtered double integrated CoM acceleration, both estimated using the instrumented shoes. Optimal cutoff frequencies for the low-pass and high-pass filters appeared to be 0.2 Hz for the horizontal direction and 0.5 Hz for the vertical direction. The CoM estimation using this ambulatory measurement system was compared to CoM estimation using an optical reference system based on the segmental kinematics method. The rms difference of each component of the CoM displacement averaged over a hundred trials obtained from seven stroke patients was ( 0.020 +/-0.007 ) m (mean +/- standard deviation) for the forward x-direction, ( 0.013 +/-0.005) m for the lateral y-direction, and ( 0.007 +/-0.001) m for the upward z-direction. Based on the results presented in this study, it is concluded that the instrumented shoe concept allows accurate and continuous estimation of CoM displacement under ambulatory conditions.

  9. A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian

    NASA Astrophysics Data System (ADS)

    Rösler, Margit; Voit, Michael

    2015-02-01

    We consider compact Grassmann manifolds G/K over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type BC. From an explicit integral representation of these polynomials we deduce a sharp Mehler-Heine formula, that is an approximation of the Heckman-Opdam polynomials in terms of Bessel functions, with a precise estimate on the error term. This result is used to derive a central limit theorem for random walks on the semi-lattice parametrizing the dual of G/K, which are constructed by successive decompositions of tensor powers of spherical representations of G. The limit is the distribution of a Laguerre ensemble in random matrix theory. Most results of this paper are established for a larger continuous set of multiplicity parameters beyond the group cases.

  10. Exact and approximate graph matching using random walks.

    PubMed

    Gori, Marco; Maggini, Marco; Sarti, Lorenzo

    2005-07-01

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

  11. A Pearson Random Walk with Steps of Uniform Orientation and Dirichlet Distributed Lengths

    NASA Astrophysics Data System (ADS)

    Le Caër, Gérard

    2010-08-01

    A constrained diffusive random walk of n steps in ℝ d and a random flight in ℝ d , which are equivalent, were investigated independently in recent papers (J. Stat. Phys. 127:813, 2007; J. Theor. Probab. 20:769, 2007, and J. Stat. Phys. 131:1039, 2008). The n steps of the walk are independent and identically distributed random vectors of exponential length and uniform orientation. Conditioned on the sum of their lengths being equal to a given value l, closed-form expressions for the distribution of the endpoint of the walk were obtained altogether for any n for d=1,2,4. Uniform distributions of the endpoint inside a ball of radius l were evidenced for a walk of three steps in 2D and of two steps in 4D. The previous walk is generalized by considering step lengths which have independent and identical gamma distributions with a shape parameter q>0. Given the total walk length being equal to 1, the step lengths have a Dirichlet distribution whose parameters are all equal to q. The walk and the flight above correspond to q=1. Simple analytical expressions are obtained for any d≥2 and n≥2 for the endpoint distributions of two families of walks whose q are integers or half-integers which depend solely on d. These endpoint distributions have a simple geometrical interpretation. Expressed for a two-step planar walk whose q=1, it means that the distribution of the endpoint on a disc of radius 1 is identical to the distribution of the projection on the disc of a point M uniformly distributed over the surface of the 3D unit sphere. Five additional walks, with a uniform distribution of the endpoint in the inside of a ball, are found from known finite integrals of products of powers and Bessel functions of the first kind. They include four different walks in ℝ3, two of two steps and two of three steps, and one walk of two steps in ℝ4. Pearson-Liouville random walks, obtained by distributing the total lengths of the previous Pearson-Dirichlet walks according to some

  12. Covering Ground: Movement Patterns and Random Walk Behavior in Aquilonastra anomala Sea Stars.

    PubMed

    Lohmann, Amanda C; Evangelista, Dennis; Waldrop, Lindsay D; Mah, Christopher L; Hedrick, Tyson L

    2016-10-01

    The paths animals take while moving through their environments affect their likelihood of encountering food and other resources; thus, models of foraging behavior abound. To collect movement data appropriate for comparison with these models, we used time-lapse photography to track movements of a small, hardy, and easy-to-obtain organism, Aquilonastra anomala sea stars. We recorded the sea stars in a tank over many hours, with and without a food cue. With food present, they covered less distance, as predicted by theory; this strategy would allow them to remain near food. We then compared the paths of the sea stars to three common models of animal movement: Brownian motion, Lévy walks, and correlated random walks; we found that the sea stars' movements most closely resembled a correlated random walk. Additionally, we compared the search performance of models of Brownian motion, a Lévy walk, and a correlated random walk to that of a model based on the sea stars' movements. We found that the behavior of the modeled sea star walk was similar to that of the modeled correlated random walk and the Brownian motion model, but that the sea star walk was slightly more likely than the other walks to find targets at intermediate distances. While organisms are unlikely to follow an idealized random walk in all details, our data suggest that comparing the effectiveness of an organism's paths to those from theory can give insight into the organism's actual movement strategy. Finally, automated optical tracking of invertebrates proved feasible, and A. anomala was revealed to be a tractable, 2D-movement study system.

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

    PubMed

    Vickers, Mathew; Schwarzkopf, Lin

    2016-04-01

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

  14. Origins and applications of the Montroll-Weiss continuous time random walk

    NASA Astrophysics Data System (ADS)

    Shlesinger, Michael F.

    2017-05-01

    The Continuous Time Random Walk (CTRW) was introduced by Montroll and Weiss in 1965 in a purely mathematical paper. Its antecedents and later applications beginning in 1973 are discussed, especially for the case of fractal time where the mean waiting time between jumps is infinite. Contribution to the Topical Issue: "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

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

    NASA Astrophysics Data System (ADS)

    Ovchinnikov, M. N.

    2017-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Millett, K. C.

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

  17. Branching random walk with step size coming from a power law

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Ayan; Subhra Hazra, Rajat; Roy, Parthanil

    2015-09-01

    In their seminal work, Brunet and Derrida made predictions on the random point configurations associated with branching random walks. We shall discuss the limiting behavior of such point configurations when the displacement random variables come from a power law. In particular, we establish that two prediction of remains valid in this setup and investigate various other issues mentioned in their paper.

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

    PubMed Central

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

    2017-01-01

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

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

    PubMed

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

    2017-01-01

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

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

    PubMed

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

    2009-10-01

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

  1. Slope estimation during normal walking using a shank-mounted inertial sensor.

    PubMed

    López, Antonio M; Álvarez, Diego; González, Rafael C; Álvarez, Juan C

    2012-01-01

    In this paper we propose an approach for the estimation of the slope of the walking surface during normal walking using a body-worn sensor composed of a biaxial accelerometer and a uniaxial gyroscope attached to the shank. It builds upon a state of the art technique that was successfully used to estimate the walking velocity from walking stride data, but did not work when used to estimate the slope of the walking surface. As claimed by the authors, the reason was that it did not take into account the actual inclination of the shank of the stance leg at the beginning of the stride (mid stance). In this paper, inspired by the biomechanical characteristics of human walking, we propose to solve this issue by using the accelerometer as a tilt sensor, assuming that at mid stance it is only measuring the gravity acceleration. Results from a set of experiments involving several users walking at different inclinations on a treadmill confirm the feasibility of our approach. A statistical analysis of slope estimations shows in first instance that the technique is capable of distinguishing the different slopes of the walking surface for every subject. It reports a global RMS error (per-unit difference between actual and estimated inclination of the walking surface for each stride identified in the experiments) of 0.05 and this can be reduced to 0.03 with subject-specific calibration and post processing procedures by means of averaging techniques.

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

    PubMed

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

    2003-11-01

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

  3. Random walk study of electron motion in helium in crossed electromagnetic fields

    NASA Technical Reports Server (NTRS)

    Englert, G. W.

    1972-01-01

    Random walk theory, previously adapted to electron motion in the presence of an electric field, is extended to include a transverse magnetic field. In principle, the random walk approach avoids mathematical complexity and concomitant simplifying assumptions and permits determination of energy distributions and transport coefficients within the accuracy of available collisional cross section data. Application is made to a weakly ionized helium gas. Time of relaxation of electron energy distribution, determined by the random walk, is described by simple expressions based on energy exchange between the electron and an effective electric field. The restrictive effect of the magnetic field on electron motion, which increases the required number of collisions per walk to reach a terminal steady state condition, as well as the effect of the magnetic field on electron transport coefficients and mean energy can be quite adequately described by expressions involving only the Hall parameter.

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

    NASA Astrophysics Data System (ADS)

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

    1992-12-01

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

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

    PubMed Central

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

    2014-01-01

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

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

    PubMed

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

    2017-06-01

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

  7. 2D trajectory estimation during free walking using a tiptoe-mounted inertial sensor.

    PubMed

    Sagawa, Koichi; Ohkubo, Kensuke

    2015-07-16

    An estimation method for a two-dimensional walking trajectory during free walking, such as forward walking, side stepping and backward walking, was investigated using a tiptoe-mounted inertial sensor. The horizontal trajectory of the toe-tip is obtained by double integration of toe-tip acceleration during the moving phase in which the sensor is rotated before foot-off or after foot-contact, in addition to the swing phase. Special functions that determine the optimum moving phase as the integral duration in every one step are developed statistically using the gait cycle and the resultant angular velocity of dorsi/planter flexion, pronation/supination and inversion/eversion so that the difference between the estimated trajectory and actual one gives a minimum value during free walking with several cadences. To develop the functions, twenty healthy volunteers participated in free walking experiments in which subjects performed forward walking, side stepping to the right, side stepping to the left, and backward walking at 39 m down a straight corridor with several predetermined cadences. To confirm the effect of the developed functions, five healthy subjects participated in the free walking experiment in which each subject performed free walking with different velocities of normal, fast, and slow based on their own assessment in a square course with 7 m side. The experimentally obtained results of free walking with a combination of forward walking, backward walking, and side stepping indicate that the proposed method produces walking trajectory with high precision compared with the constant threshold method which determines swing phase using the size of the angular velocity. Copyright © 2015 Elsevier Ltd. All rights reserved.

  8. Sedimentary bed evolution as a mean-reverting random walk: Implications for tracer statistics

    NASA Astrophysics Data System (ADS)

    Martin, Raleigh L.; Purohit, Prashant K.; Jerolmack, Douglas J.

    2014-09-01

    Sediment tracers are increasingly employed to estimate bed load transport and landscape evolution rates. Tracer trajectories are dominated by periods of immobility ("waiting times") as they are buried and reexcavated in the stochastically evolving river bed. Here we model bed evolution as a random walk with mean-reverting tendency (Ornstein-Uhlenbeck process) originating from the restoring effect of erosion and deposition. The Ornstein-Uhlenbeck model contains two parameters, a and b, related to the particle feed rate and range of bed elevation fluctuations, respectively. Observations of bed evolution in flume experiments agree with model predictions; in particular, the model reproduces the asymptotic t-1 tail in the tracer waiting time exceedance probability distribution. This waiting time distribution is similar to that inferred for tracers in natural gravel streams and avalanching rice piles, indicating applicability of the Ornstein-Uhlenbeck mean-reverting model to many disordered transport systems with tracer burial and excavation.

  9. Walking speed estimation using a shank-mounted inertial measurement unit.

    PubMed

    Li, Q; Young, M; Naing, V; Donelan, J M

    2010-05-28

    We studied the feasibility of estimating walking speed using a shank-mounted inertial measurement unit. Our approach took advantage of the inverted pendulum-like behavior of the stance leg during walking to identify a new method for dividing up walking into individual stride cycles and estimating the initial conditions for the direct integration of the accelerometer and gyroscope signals. To test its accuracy, we compared speed estimates to known values during walking overground and on a treadmill. The speed estimation method worked well across treadmill speeds and slopes yielding a root mean square speed estimation error of only 7%. It also worked well during overground walking with a 4% error in the estimated travel distance. This accuracy is comparable to that achieved from foot-mounted sensors, providing an alternative in sensor positioning for walking speed estimation. Shank mounted sensors may be of great benefit for estimating speed in walking with abnormal foot motion and for the embedded control of knee-mounted devices such as prostheses and energy harvesters.

  10. Estimating daily walking distance of captive African elephants using an accelerometer.

    PubMed

    Rothwell, Emily S; Bercovitch, Fred B; Andrews, Jeff R M; Anderson, Matthew J

    2011-01-01

    Two central concerns for elephant husbandry and management are whether zoological enclosures are appropriately sized and the degree to which naturalistic exercise and activity are observed in such enclosures. In order to address these issues, accurate data on the daily walking distance of elephants both in situ and ex situ are necessary. We used an accelerometer, a pedometer that measures step count and activity level, to estimate walking distance in African elephants (Loxodonta africana) at the San Diego Zoo's Wild Animal Park. The accelerometer was worn simultaneously with a GPS unit that recorded actual walking distance. Estimates of walking distance were extrapolated from the accelerometer and compared with actual distances determined by GPS data. The accelerometer was found to overestimate step count, and subsequently walking distance, by including false counts of steps. Extrapolating walking distance based upon stride length measurements did not match actual GPS walking distance. However, activity level output from the accelerometer significantly correlated with actual GPS walking distance. In addition, we report that the rate of movement is comparable to that reported in other zoological settings. We provide a linear regression equation that can be utilized by other institutions to estimate daily walking distance of elephants in their collection who are outfitted with accelerometers.

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

    NASA Astrophysics Data System (ADS)

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

    1994-09-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2017-05-01

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

  13. The Walking School Bus and children's physical activity: A pilot cluster randomized controlled trial

    USDA-ARS?s Scientific Manuscript database

    To evaluate the impact of a "walking school bus" program on children's rates of active commuting to school and physical activity. We conducted a pilot cluster randomized controlled trial among 4th-graders from 8 schools in Houston, Texas (N = 149). Random allocation to treatment or control condition...

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

    PubMed

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

    2015-03-01

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


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

    NASA Astrophysics Data System (ADS)

    van Megen, W.

    2006-01-01

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

  16. Use of Accelerometer-Based Feedback of Walking Activity for Appraising Progress With Walking-Related Goals in Inpatient Stroke Rehabilitation: A Randomized Controlled Trial.

    PubMed

    Mansfield, Avril; Wong, Jennifer S; Bryce, Jessica; Brunton, Karen; Inness, Elizabeth L; Knorr, Svetlana; Jones, Simon; Taati, Babak; McIlroy, William E

    2015-10-01

    Regaining independent ambulation is important to those with stroke. Increased walking practice during "down time" in rehabilitation could improve walking function for individuals with stroke. To determine the effect of providing physiotherapists with accelerometer-based feedback on patient activity and walking-related goals during inpatient stroke rehabilitation. Participants with stroke wore accelerometers around both ankles every weekday during inpatient rehabilitation. Participants were randomly assigned to receive daily feedback about walking activity via their physiotherapists (n = 29) or to receive no feedback (n = 28). Changes in measures of daily walking (walking time, number of steps, average cadence, longest bout duration, and number of "long" walking bouts) and changes in gait control and function assessed in-laboratory were compared between groups. There was no significant increase in walking time, number of steps, longest bout duration, or number of long walking bouts for the feedback group compared with the control group (P values > .20). However, individuals who received feedback significantly increased cadence of daily walking more than the control group (P = .013). From the in-laboratory gait assessment, individuals who received feedback had a greater increase in walking speed and decrease in step time variability than the control group (P values < .030). Feedback did not increase the amount of walking completed by individuals with stroke. However, there was a significant increase in cadence, indicating that intensity of daily walking was greater for those who received feedback than the control group. Additionally, more intense daily walking activity appeared to translate to greater improvements in walking speed. © The Author(s) 2015.

  17. An Online Social Network to Increase Walking in Dog Owners: A Randomized Trial

    PubMed Central

    Schneider, Kristin L.; Murphy, Deirdra; Ferrara, Cynthia; Oleski, Jessica; Panza, Emily; Savage, Clara; Gada, Kimberly; Bozzella, Brianne; Olendzki, Effie; Kern, Daniel; Lemon, Stephenie C.

    2014-01-01

    PURPOSE Encouraging dog walking may increase physical activity in dog owners. This cluster randomized controlled trial investigated whether a social networking website (Meetup™) could be used to deliver a multi-component dog walking intervention to increase physical activity. METHODS Sedentary dog owners (n=102) participated. Eight neighborhoods were randomly assigned to the Meetup condition (Meetup) or a condition where participants received monthly emails with content from the American Heart Association on increasing physical activity (AHA). The Meetup intervention was delivered over 6 months and consisted of newsletters, dog walks, community events and an activity monitor. The primary outcome was steps; secondary outcomes included social support for walking, sense of community, perceived dog walking outcomes, barriers to dog walking and feasibility of the intervention. RESULTS Mixed model analyses examined change from baseline to post-intervention (6 months) and whether change in outcomes differed by condition. Daily steps increased over time (p=0.04, d=0.28), with no differences by condition. The time x condition interaction was significant for the perceived outcomes of dog walking (p=0.04, d=0.40), such that the Meetup condition reported an increase in the perceived positive outcomes of dog walking, whereas the AHA condition did not. Social support, sense of community and dog walking barriers did not significantly change. Meetup logins averaged 58.38 per week (SD=11.62). Within two months of the intervention ending, organization of the Meetup groups transitioned from study staff to Meetup members. CONCLUSION Results suggest that a Meetup group is feasible for increasing physical activity in dog owners. Further research is needed to understand how to increase participation in the Meetup group and facilitate greater connection among dog owners. PMID:25003777

  18. A random walk on water (Henry Darcy Medal Lecture)

    NASA Astrophysics Data System (ADS)

    Koutsoyiannis, D.

    2009-04-01

    . Experimentation with this toy model demonstrates, inter alia, that: (1) for short time horizons the deterministic dynamics is able to give good predictions; but (2) these predictions become extremely inaccurate and useless for long time horizons; (3) for such horizons a naïve statistical prediction (average of past data) which fully neglects the deterministic dynamics is more skilful; and (4) if this statistical prediction, in addition to past data, is combined with the probability theory (the principle of maximum entropy, in particular), it can provide a more informative prediction. Also, the toy model shows that the trajectories of the system state (and derivative properties thereof) do not resemble a regular (e.g., periodic) deterministic process nor a purely random process, but exhibit patterns indicating anti-persistence and persistence (where the latter statistically complies with a Hurst-Kolmogorov behaviour). If the process is averaged over long time scales, the anti-persistent behaviour improves predictability, whereas the persistent behaviour substantially deteriorates it. A stochastic representation of this deterministic system, which incorporates dynamics, is not only possible, but also powerful as it provides good predictions for both short and long horizons and helps to decide on when the deterministic dynamics should be considered or neglected. Obviously, a natural system is extremely more complex than this simple toy model and hence unpredictability is naturally even more prominent in the former. In addition, in a complex natural system, we can never know the exact dynamics and we must infer it from past data, which implies additional uncertainty and an additional role of stochastics in the process of formulating the system equations and estimating the involved parameters. Data also offer the only solid grounds to test any hypothesis about the dynamics, and failure of performing such testing against evidence from data renders the hypothesised dynamics worthless

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

    PubMed Central

    Yang, Yu-Guang; Zhao, Qian-Qian

    2016-01-01

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

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

    PubMed

    Yang, Yu-Guang; Zhao, Qian-Qian

    2016-02-04

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

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

    NASA Astrophysics Data System (ADS)

    Yang, Yu-Guang; Zhao, Qian-Qian

    2016-02-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2011-03-01

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

  3. Scaling behavior for random walks with memory of the largest distance from the origin

    NASA Astrophysics Data System (ADS)

    Serva, Maurizio

    2013-11-01

    We study a one-dimensional random walk with memory. The behavior of the walker is modified with respect to the simple symmetric random walk only when he or she is at the maximum distance ever reached from his or her starting point (home). In this case, having the choice to move farther or to move closer, the walker decides with different probabilities. If the probability of a forward step is higher then the probability of a backward step, the walker is bold, otherwise he or she is timorous. We investigate the asymptotic properties of this bold-timorous random walk, showing that the scaling behavior varies continuously from subdiffusive (timorous) to superdiffusive (bold). The scaling exponents are fully determined with a new mathematical approach based on a decomposition of the dynamics in active journeys (the walker is at the maximum distance) and lazy journeys (the walker is not at the maximum distance).

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

    PubMed

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

    2011-03-01

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

  5. Estimated V(O2)max from the rockport walk test on a nonmotorized curved treadmill.

    PubMed

    Seneli, Rhiannon M; Ebersole, Kyle T; OʼConnor, Kristian M; Snyder, Ann C

    2013-12-01

    The Rockport Walk Test (RWT) is a 1-mile walk used to estimate the maximal volume of oxygen uptake (V(O2)max). The purpose of this study was to validate the RWT on a nonmotorized curved treadmill (CT). Twenty-three healthy adults (10 females; 19-44 years old) participated. One trial of the RWT was performed on a measured indoor track (RWTO) and another on the CT (RWTC) on different days in randomized order. Heart rate (HR) and completion time were used to calculate V(O2)max using 6 different general and gender specific equations from previous research. Subjects also performed a treadmill graded exercise test (GXT), which was used as the criterion measure for V(O2)max. Completion times and HR between the 2 RWT were compared using dependent t-tests. Estimated V(O2)max values were compared between the RWTC, RWTO, and GXT through repeated measures analysis of variance, Pearson's correlations (r), and Bland-Altman's plots. There was no difference between completion times for the RWTO and RWTC but HRs were significantly higher with RWTC. When the same equation was applied to the RWTO and RWTC, there were no similar results. All V(O2)max estimations were different from observed V(O2)max except for the estimation from the relative general Kline et al. equation on the RWTO. Despite high correlations (r = 0.75-0.91), the RWTC underestimated V(O2)max. The RWTC underestimates V(O2)max but may be beneficial if a new equation were created specifically for the CT. With appropriate equations for the CT, the RWTC would provide an alternate form of V(O2)max testing.

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

    PubMed

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

    2017-02-01

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

  7. Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

    NASA Astrophysics Data System (ADS)

    Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.

    2012-09-01

    Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

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

    NASA Astrophysics Data System (ADS)

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

    1985-11-01

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

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

    NASA Astrophysics Data System (ADS)

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

    1982-06-01

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

  10. Random-Walk Type Model with Fat Tails for Financial Markets

    NASA Astrophysics Data System (ADS)

    Matuttis, Hans-Geors

    Starting from the random-walk model, practices of financial markets are included into the random-walk so that fat tail distributions like those in the high frequency data of the SP500 index are reproduced, though the individual mechanisms are modeled by normally distributed data. The incorporation of local correlation narrows the distribution for "frequent" events, whereas global correlations due to technical analysis leads to fat tails. Delay of market transactions in the trading process shifts the fat tail probabilities downwards. Such an inclusion of reactions to market fluctuations leads to mini-trends which are distributed with unit variance.

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

    NASA Astrophysics Data System (ADS)

    Zatloukal, Václav

    2017-05-01

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

  12. Estimation of Human Foot Motion During Normal Walking Using Inertial and Magnetic Sensor Measurements

    DTIC Science & Technology

    2012-07-01

    OF: A foot motion filtering algorithm is presented for estimating foot kinematics relative to an earth -fixed reference frame during normal walking...Title ABSTRACT A foot motion filtering algorithm is presented for estimating foot kinematics relative to an earth -fixed reference frame during...filtering algorithm is presented for es- timating foot kinematics relative to an earth -fixed reference frame during normal walking motion. Algorithm

  13. Random time averaged diffusivities for Lévy walks

    NASA Astrophysics Data System (ADS)

    Froemberg, D.; Barkai, E.

    2013-07-01

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

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

    PubMed

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

    1995-01-01

    Complex fluctuations of unknown origin appear in the normal gait pattern. These fluctuations might be described as being 1) uncorrelated white noise, 2) short-range correlations, or 3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series, we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that successfully accounts for the experimentally observed long-range correlations.

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

    NASA Technical Reports Server (NTRS)

    Hausdorff, Jeffrey M.; Peng, C.-K.; Ladin, Zvi; Wei, Jeanne Y.; Goldberger, Ary L.

    1995-01-01

    Complex fluctuation of unknown origin appear in the normal gait pattern. These fluctuations might be described as being (1) uncorrelated white noise, (2) short-range correlations, or (3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that sucessfully accounts for the experimentally observed long-range correlations.

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

    NASA Technical Reports Server (NTRS)

    Hausdorff, Jeffrey M.; Peng, C.-K.; Ladin, Zvi; Wei, Jeanne Y.; Goldberger, Ary L.

    1995-01-01

    Complex fluctuation of unknown origin appear in the normal gait pattern. These fluctuations might be described as being (1) uncorrelated white noise, (2) short-range correlations, or (3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that sucessfully accounts for the experimentally observed long-range correlations.

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

    PubMed

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

    2014-05-01

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

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

    PubMed

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

    2011-05-01

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

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

    PubMed

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

    2014-04-17

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

  20. Inertial sensor-based methods in walking speed estimation: a systematic review.

    PubMed

    Yang, Shuozhi; Li, Qingguo

    2012-01-01

    Self-selected walking speed is an important measure of ambulation ability used in various clinical gait experiments. Inertial sensors, i.e., accelerometers and gyroscopes, have been gradually introduced to estimate walking speed. This research area has attracted a lot of attention for the past two decades, and the trend is continuing due to the improvement of performance and decrease in cost of the miniature inertial sensors. With the intention of understanding the state of the art of current development in this area, a systematic review on the exiting methods was done in the following electronic engines/databases: PubMed, ISI Web of Knowledge, SportDiscus and IEEE Xplore. Sixteen journal articles and papers in proceedings focusing on inertial sensor based walking speed estimation were fully reviewed. The existing methods were categorized by sensor specification, sensor attachment location, experimental design, and walking speed estimation algorithm.

  1. Inertial Sensor-Based Methods in Walking Speed Estimation: A Systematic Review

    PubMed Central

    Yang, Shuozhi; Li, Qingguo

    2012-01-01

    Self-selected walking speed is an important measure of ambulation ability used in various clinical gait experiments. Inertial sensors, i.e., accelerometers and gyroscopes, have been gradually introduced to estimate walking speed. This research area has attracted a lot of attention for the past two decades, and the trend is continuing due to the improvement of performance and decrease in cost of the miniature inertial sensors. With the intention of understanding the state of the art of current development in this area, a systematic review on the exiting methods was done in the following electronic engines/databases: PubMed, ISI Web of Knowledge, SportDiscus and IEEE Xplore. Sixteen journal articles and papers in proceedings focusing on inertial sensor based walking speed estimation were fully reviewed. The existing methods were categorized by sensor specification, sensor attachment location, experimental design, and walking speed estimation algorithm. PMID:22778632

  2. Regression Model-Based Walking Speed Estimation Using Wrist-Worn Inertial Sensor

    PubMed Central

    Park, Edward J.

    2016-01-01

    Walking speed is widely used to study human health status. Wearable inertial measurement units (IMU) are promising tools for the ambulatory measurement of walking speed. Among wearable inertial sensors, the ones worn on the wrist, such as a watch or band, have relatively higher potential to be easily incorporated into daily lifestyle. Using the arm swing motion in walking, this paper proposes a regression model-based method for longitudinal walking speed estimation using a wrist-worn IMU. A novel kinematic variable is proposed, which finds the wrist acceleration in the principal axis (i.e. the direction of the arm swing). This variable (called pca-acc) is obtained by applying sensor fusion on IMU data to find the orientation followed by the use of principal component analysis. An experimental evaluation was performed on 15 healthy young subjects during free walking trials. The experimental results show that the use of the proposed pca-acc variable can significantly improve the walking speed estimation accuracy when compared to the use of raw acceleration information (p<0.01). When Gaussian process regression is used, the resulting walking speed estimation accuracy and precision is about 5.9% and 4.7%, respectively. PMID:27764231

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

    PubMed Central

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

    2010-01-01

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

  4. Estimation of METs by Accelerometers while Walking and Running

    NASA Astrophysics Data System (ADS)

    Kurihara, Yosuke; Watanabe, Kajiro; Yoneyama, Mitsuru

    It is quite important for Japan to maintain or promote the health condition of elderly citizens. Given the circumstances, the Ministry of Health, Labour and Welfare has established the standards for the activities and exercises for promoting the health, and quantitatively determined the exercise intensity on 107 items of activities. This exercise intensity, however, requires recording the type and the duration of the activity to be calculated. In this paper, the exercise intensities are surmised using 3D accelerometer while the subjects are walking and running. As the result, the exercise intensities were surmised to be within the root mean square error of 1.2[METs] for walking and 3.2[METs] for running respectively.

  5. Nordic Walking and chronic low back pain: design of a randomized clinical trial

    PubMed Central

    Morsø, Lars; Hartvigsen, Jan; Puggaard, Lis; Manniche, Claus

    2006-01-01

    Background Low Back Pain is a major public health problem all over the western world. Active approaches including exercise in the treatment of low back pain results in better outcomes for patients, but it is not known exactly which types of back exercises are most beneficial or whether general physical activity provide similar benefits. Nordic Walking is a popular and fast growing type of exercise in Northern Europe. Initial studies have demonstrated that persons performing Nordic Walking are able to exercise longer and harder compared to normal walking thereby increasing their cardiovascular metabolism. Until now no studies have been performed to investigate whether Nordic Walking has beneficial effects in relation to low back pain. The primary aim of this study is to investigate whether supervised Nordic Walking can reduce pain and improve function in a population of chronic low back pain patients when compared to unsupervised Nordic Walking and advice to stay active. In addition we investigate whether there is an increase in the cardiovascular metabolism in persons performing supervised Nordic Walking compared to persons who are advised to stay active. Finally, we investigate whether there is a difference in compliance between persons receiving supervised Nordic Walking and persons doing unsupervised Nordic Walking. Methods One hundred and fifty patients with low back pain for at least eight weeks and referred to a specialized secondary sector outpatient back pain clinic are included in the study. After completion of the standard back centre treatment patients are randomized into one of three groups: A) Nordic Walking twice a week for eight weeks under supervision of a specially trained instructor; B) Unsupervised Nordic Walking for eight weeks after one training session with an instructor; C) A one hour motivational talk including advice to stay active. Outcome measures are pain, function, overall health, cardiovascular ability and activity level. Results No

  6. The random walk of a drilling laser beam

    NASA Technical Reports Server (NTRS)

    Anthony, T. R.

    1980-01-01

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

  7. Erosion by a one-dimensional random walk

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

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

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

    NASA Astrophysics Data System (ADS)

    Larralde, Hernan; Weiss, George H.

    1995-08-01

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

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

    DTIC Science & Technology

    1984-05-01

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

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

    PubMed

    Min, Donghong; Yang, Wei

    2008-05-21

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-12-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

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

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

    PubMed

    Elavsky, Steriani; McAuley, Edward

    2007-01-01

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

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

    PubMed

    Lin, Yuan; Zhang, Zhongzhi

    2013-06-01

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

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

    DTIC Science & Technology

    2011-07-21

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

  16. On the genealogy of branching random walks and of directed polymers

    NASA Astrophysics Data System (ADS)

    Derrida, Bernard; Mottishaw, Peter

    2016-08-01

    It is well known that the mean-field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite-size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks.

  17. Do low step count goals inhibit walking behavior: a randomized controlled study.

    PubMed

    Anson, Denis; Madras, Diane

    2016-07-01

    Confirmation and quantification of observed differences in goal-directed walking behavior. Single-blind, split-half randomized trial. Small rural university, Pennsylvania, United States. A total of 94 able-bodied subjects (self-selected volunteer students, faculty and staff of a small university) were randomly assigned walking goals, and 53 completed the study. Incentivized pedometer-monitored program requiring recording the step-count for 56-days into a custom-made website providing daily feedback. Steps logged per day. During the first half of the study, the 5000 and 10,000 step group logged significantly different steps 7500 and 9000, respectively (P > 0.05). During the second half of the study, the 5000 and 10,000 step groups logged 7000 and 8600 steps, respectively (significance P > 0.05). The group switched from 5000 to →10,000 steps logged, 7900 steps for the first half and 9500 steps for the second half (significance P > 0.05). The group switched from 10,000 to 5000 steps logged 9700 steps for the first half and 9000 steps for the second half, which was significant (p > 0.05). Levels of walking behavior are influenced by the goals assigned. Subjects with high goals walk more than those with low goals, even if they do not meet the assigned goal. Reducing goals from a high to low level can reduce walking behavior. © The Author(s) 2015.

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

    PubMed

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

    2015-01-01

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

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

    PubMed Central

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

    2015-01-01

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

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

    PubMed

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

    2013-02-01

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

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

    NASA Astrophysics Data System (ADS)

    Larralde, H.

    1997-11-01

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

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

    PubMed

    Altendorf, Hellen; Jeulin, Dominique

    2011-04-01

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

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

    PubMed

    Kitazawa, Shigeru

    2002-08-01

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

  4. δ-exceedance records and random adaptive walks

    NASA Astrophysics Data System (ADS)

    Park, Su-Chan; Krug, Joachim

    2016-08-01

    We study a modified record process where the kth record in a series of independent and identically distributed random variables is defined recursively through the condition {Y}k\\gt {Y}k-1-{δ }k-1 with a deterministic sequence {δ }k\\gt 0 called the handicap. For constant {δ }k\\equiv δ and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of δ between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records (Park et al 2015 Phys. Rev. E 91 042707). Here we explore the behavior for general probability distributions and decreasing and increasing sequences {δ }k, focusing in particular on the case when {δ }k matches the typical spacing between subsequent records in the underlying simple record process without handicap. We find that a continuous phase transition occurs only in the exponential case, but a novel kind of first order transition emerges when {δ }k is increasing. The problem is partly motivated by the dynamics of evolutionary adaptation in biological fitness landscapes, where {δ }k corresponds to the change of the deterministic fitness component after k mutational steps. The results for the record process are used to compute the mean number of steps that a population performs in such a landscape before being trapped at a local fitness maximum.

  5. Correlated random walks caused by dynamical wavefunction collapse

    NASA Astrophysics Data System (ADS)

    Bedingham, D. J.; Ulbricht, H.

    2015-08-01

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

  6. Correlated random walks caused by dynamical wavefunction collapse

    PubMed Central

    Bedingham, D. J.; Ulbricht, H.

    2015-01-01

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

  7. Random walks on cubic lattices with bond disorder

    SciTech Connect

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

    1986-12-01

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

  8. Calibrating random forests for probability estimation.

    PubMed

    Dankowski, Theresa; Ziegler, Andreas

    2016-09-30

    Probabilities can be consistently estimated using random forests. It is, however, unclear how random forests should be updated to make predictions for other centers or at different time points. In this work, we present two approaches for updating random forests for probability estimation. The first method has been proposed by Elkan and may be used for updating any machine learning approach yielding consistent probabilities, so-called probability machines. The second approach is a new strategy specifically developed for random forests. Using the terminal nodes, which represent conditional probabilities, the random forest is first translated to logistic regression models. These are, in turn, used for re-calibration. The two updating strategies were compared in a simulation study and are illustrated with data from the German Stroke Study Collaboration. In most simulation scenarios, both methods led to similar improvements. In the simulation scenario in which the stricter assumptions of Elkan's method were not met, the logistic regression-based re-calibration approach for random forests outperformed Elkan's method. It also performed better on the stroke data than Elkan's method. The strength of Elkan's method is its general applicability to any probability machine. However, if the strict assumptions underlying this approach are not met, the logistic regression-based approach is preferable for updating random forests for probability estimation. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

  9. Comparison of the Effect of Lateral and Backward Walking Training on Walking Function in Patients with Poststroke Hemiplegia: A Pilot Randomized Controlled Trial.

    PubMed

    Kim, Chang-Yong; Lee, Jung-Sun; Kim, Hyeong-Dong

    2017-02-01

    The purposes of the present study were to compare the effects of backward and lateral walking training and to identify whether additional backward or lateral walking training would be more effective in increasing the walking function of poststroke patients. Fifty-one subjects with hemiplegic stroke were randomly allocated to 3 groups, each containing 17 subjects: the control group, the backward walking training group, and the lateral walking training group. The walking abilities of each group were assessed using a 10-m walk test and the GAITRite system for spatiotemporal gait. The results show that there were significantly greater posttest increases in gait velocity (F = -12.09, P = 0.02) and stride length (F = -11.50, P = 0.02), decreases in the values of the 10-m walk test (F = -7.10, P = 0.03) (P < 0.05) and double-limb support period (F = 40.15, P = 0.000), and improvements in gait asymmetry (F = 13.88, P = 0.002) (P < 0.01) in subjects in the lateral walking training group compared with those in the other 2 groups. These findings demonstrate that asymmetric gait patterns in poststroke patients could be improved by receiving additional lateral walking training therapy rather than backward walking training. Complete the self-assessment activity and evaluation online at http://www.physiatry.org/JournalCME CME OBJECTIVES: Upon completion of this article, the reader should be able to: (1) understand the potential benefits of backward walking (BW) and lateral walking (LW) training on improving muscle strength and gait; (2) appreciate the potential value of backward and lateral walking gait training in the treatment of hemiplegic stroke patients; and (3) appropriately incorporate backward and lateral walking gait training into the treatment plan of hemiplegic stroke patients. Advanced ACCREDITATION: The Association of Academic Physiatrists is accredited by the Accreditation Council for Continuing Medical Education to provide continuing medical education for

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

    PubMed

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

    2014-01-01

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

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

    SciTech Connect

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

    2013-01-01

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

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

    PubMed

    Fu, Jun-Song; Liu, Yun

    2015-05-26

    In wireless sensor networks, filter-based top-  query approaches are the state-of-the-art solutions and have been extensively researched in the literature, however, they are very sensitive to the network parameters, including the size of the network, dynamics of the sensors' readings and declines in the overall range of all the readings. In this work, a random walk-based top-  query approach called RWTQ and a directed walk-based top-  query approach called DWTQ are proposed. At the beginning of a top-  query, one or several tokens are sent to the specific node(s) in the network by the base station. Then, each token walks in the network independently to record and process the readings in a random or directed way. A strategy of choosing the "right" way in DWTQ is carefully designed for the token(s) to arrive at the high-value regions as soon as possible. When designing the walking strategy for DWTQ, the spatial correlations of the readings are also considered. Theoretical analysis and simulation results indicate that RWTQ and DWTQ both are very robust against these parameters discussed previously. In addition, DWTQ outperforms TAG, FILA and EXTOK in transmission cost, energy consumption and network lifetime.

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

    PubMed

    Tadayon, M; Abedi, P; Farshadbakht, F

    2016-08-01

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

  14. Musical motor feedback (MMF) in walking hemiparetic stroke patients: randomized trials of gait improvement.

    PubMed

    Schauer, Michael; Mauritz, Karl-Heinz

    2003-11-01

    To demonstrate the effect of rhythmical auditory stimulation in a musical context for gait therapy in hemiparetic stroke patients, when the stimulation is played back measure by measure initiated by the patient's heel-strikes (musical motor feedback). Does this type of musical feedback improve walking more than a less specific gait therapy? The randomized controlled trial considered 23 registered stroke patients. Two groups were created by randomization: the control group received 15 sessions of conventional gait therapy and the test group received 15 therapy sessions with musical motor feedback. Inpatient rehabilitation hospital. Median post-stroke interval was 44 days and the patients were able to walk without technical aids with a speed of approximately 0.71 m/s. Gait velocity, step duration, gait symmetry, stride length and foot rollover path length (heel-on-toe-off distance). The test group showed more mean improvement than the control group: stride length increased by 18% versus 0%, symmetry deviation decreased by 58% versus 20%, walking speed increased by 27% versus 4% and rollover path length increased by 28% versus 11%. Musical motor feedback improves the stroke patient's walk in selected parameters more than conventional gait therapy. A fixed memory in the patient's mind about the song and its timing may stimulate the improvement of gait even without the presence of an external pacemaker.

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

    NASA Astrophysics Data System (ADS)

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

    1993-11-01

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

  16. Biased and greedy random walks on two-dimensional lattices with quenched randomness: The greedy ant within a disordered environment

    NASA Astrophysics Data System (ADS)

    Mitran, T. L.; Melchert, O.; Hartmann, A. K.

    2013-12-01

    The main characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here the disorder allows for negative edge weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter ρ that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. The random walks are “greedy” in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight (associated with a net gain of “energy” for the walker). Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of ρ for different bias strengths B is put under scrutiny. Upon tuning ρ, the probability to find such a feasible lattice walk increases from zero to 1. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point ρc, resulting from numerically exact and “static” simulations in terms of the NWP model, can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems.

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

    PubMed

    Langhammer, Birgitta; Stanghelle, Johan K

    2010-01-01

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

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

    PubMed

    Jeong, Yeon-Gyu; Koo, Jung-Wan

    2016-12-01

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

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

    NASA Astrophysics Data System (ADS)

    Teimouri, Hamid; Kolomeisky, Anatoly B.

    2013-02-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-03-01

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

  1. Elephant random walks and their connection to Pólya-type urns

    NASA Astrophysics Data System (ADS)

    Baur, Erich; Bertoin, Jean

    2016-11-01

    In this paper, we explain the connection between the elephant random walk (ERW) and an urn model à la Pólya and derive functional limit theorems for the former. The ERW model was introduced in [Phys. Rev. E 70, 045101 (2004), 10.1103/PhysRevE.70.045101] to study memory effects in a highly non-Markovian setting. More specifically, the ERW is a one-dimensional discrete-time random walk with a complete memory of its past. The influence of the memory is measured in terms of a memory parameter p between zero and one. In the past years, a considerable effort has been undertaken to understand the large-scale behavior of the ERW, depending on the choice of p . Here, we use known results on urns to explicitly solve the ERW in all memory regimes. The method works as well for ERWs in higher dimensions and is widely applicable to related models.

  2. Parameter adaptive estimation of random processes

    NASA Technical Reports Server (NTRS)

    Caglayan, A. K.; Vanlandingham, H. F.

    1975-01-01

    This paper is concerned with the parameter adaptive least squares estimation of random processes. The main result is a general representation theorem for the conditional expectation of a random variable on a product probability space. Using this theorem along with the general likelihood ratio expression, the least squares estimate of the process is found in terms of the parameter conditioned estimates. The stochastic differential for the a posteriori probability and the stochastic differential equation for the a posteriori density are found by using simple stochastic calculus on the representations obtained. The results are specialized to the case when the parameter has a discrete distribution. The results can be used to construct an implementable recursive estimator for certain types of nonlinear filtering problems. This is illustrated by some simple examples.

  3. Fast Inbound Top-K Query for Random Walk with Restart

    PubMed Central

    Zhang, Chao; Jiang, Shan; Chen, Yucheng; Sun, Yidan; Han, Jiawei

    2015-01-01

    Random walk with restart (RWR) is widely recognized as one of the most important node proximity measures for graphs, as it captures the holistic graph structure and is robust to noise in the graph. In this paper, we study a novel query based on the RWR measure, called the inbound top-k (Ink) query. Given a query node q and a number k, the Ink query aims at retrieving k nodes in the graph that have the largest weighted RWR scores to q. Ink queries can be highly useful for various applications such as traffic scheduling, disease treatment, and targeted advertising. Nevertheless, none of the existing RWR computation techniques can accurately and efficiently process the Ink query in large graphs. We propose two algorithms, namely Squeeze and Ripple, both of which can accurately answer the Ink query in a fast and incremental manner. To identify the top-k nodes, Squeeze iteratively performs matrix-vector multiplication and estimates the lower and upper bounds for all the nodes in the graph. Ripple employs a more aggressive strategy by only estimating the RWR scores for the nodes falling in the vicinity of q, the nodes outside the vicinity do not need to be evaluated because their RWR scores are propagated from the boundary of the vicinity and thus upper bounded. Ripple incrementally expands the vicinity until the top-k result set can be obtained. Our extensive experiments on real-life graph data sets show that Ink queries can retrieve interesting results, and the proposed algorithms are orders of magnitude faster than state-of-the-art method. PMID:26709392

  4. First passage time: Connecting random walks to functional responses in heterogeneous environments (Invited)

    NASA Astrophysics Data System (ADS)

    Lewis, M. A.; McKenzie, H.; Merrill, E.

    2010-12-01

    In this talk I will outline first passage time analysis for animals undertaking complex movement patterns, and will demonstrate how first passage time can be used to derive functional responses in predator prey systems. The result is a new approach to understanding type III functional responses based on a random walk model. I will extend the analysis to heterogeneous environments to assess the effects of linear features on functional responses in wolves and elk using GPS tracking data.

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

    PubMed

    Montroll, E W; Shuler, K E

    1979-12-01

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

  6. Record statistics for biased random walks, with an application to financial data

    NASA Astrophysics Data System (ADS)

    Wergen, Gregor; Bogner, Miro; Krug, Joachim

    2011-05-01

    We consider the occurrence of record-breaking events in random walks with asymmetric jump distributions. The statistics of records in symmetric random walks was previously analyzed by Majumdar and Ziff [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.101.050601 101, 050601 (2008)] and is well understood. Unlike the case of symmetric jump distributions, in the asymmetric case the statistics of records depends on the choice of the jump distribution. We compute the record rate Pn(c), defined as the probability for the nth value to be larger than all previous values, for a Gaussian jump distribution with standard deviation σ that is shifted by a constant drift c. For small drift, in the sense of c/σ≪n-1/2, the correction to Pn(c) grows proportional to arctan(n) and saturates at the value (c)/(2σ). For large n the record rate approaches a constant, which is approximately given by 1-(σ/2πc)exp(-c2/2σ2) for c/σ≫1. These asymptotic results carry over to other continuous jump distributions with finite variance. As an application, we compare our analytical results to the record statistics of 366 daily stock prices from the Standard & Poor's 500 index. The biased random walk accounts quantitatively for the increase in the number of upper records due to the overall trend in the stock prices, and after detrending the number of upper records is in good agreement with the symmetric random walk. However the number of lower records in the detrended data is significantly reduced by a mechanism that remains to be identified.

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

    PubMed Central

    Gerstein, George L.; Mandelbrot, Benoit

    1964-01-01

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

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

    SciTech Connect

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

    1988-01-01

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

  9. A Mixed-Methods Randomized Controlled Trial of Financial Incentives and Peer Networks to Promote Walking among Older Adults

    ERIC Educational Resources Information Center

    Kullgren, Jeffrey T.; Harkins, Kristin A.; Bellamy, Scarlett L.; Gonzales, Amy; Tao, Yuanyuan; Zhu, Jingsan; Volpp, Kevin G.; Asch, David A.; Heisler, Michele; Karlawish, Jason

    2014-01-01

    Background: Financial incentives and peer networks could be delivered through eHealth technologies to encourage older adults to walk more. Methods: We conducted a 24-week randomized trial in which 92 older adults with a computer and Internet access received a pedometer, daily walking goals, and weekly feedback on goal achievement. Participants…

  10. A Mixed-Methods Randomized Controlled Trial of Financial Incentives and Peer Networks to Promote Walking among Older Adults

    ERIC Educational Resources Information Center

    Kullgren, Jeffrey T.; Harkins, Kristin A.; Bellamy, Scarlett L.; Gonzales, Amy; Tao, Yuanyuan; Zhu, Jingsan; Volpp, Kevin G.; Asch, David A.; Heisler, Michele; Karlawish, Jason

    2014-01-01

    Background: Financial incentives and peer networks could be delivered through eHealth technologies to encourage older adults to walk more. Methods: We conducted a 24-week randomized trial in which 92 older adults with a computer and Internet access received a pedometer, daily walking goals, and weekly feedback on goal achievement. Participants…

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

    PubMed

    Lin, Yuan; Zhang, Zhongzhi

    2014-06-20

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

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

    PubMed

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

    2014-07-29

    Efficient searching is crucial for timely location of food and other resources. Recent studies show that diverse living animals use a theoretically optimal scale-free random search for sparse resources known as a Lévy walk, but little is known of the origins and evolution of foraging behavior and the search strategies of extinct organisms. Here, using simulations of self-avoiding trace fossil trails, we show that randomly introduced strophotaxis (U-turns)--initiated by obstructions such as self-trail avoidance or innate cueing--leads to random looping patterns with clustering across increasing scales that is consistent with the presence of Lévy walks. This predicts that optimal Lévy searches may emerge from simple behaviors observed in fossil trails. We then analyzed fossilized trails of benthic marine organisms by using a novel path analysis technique and find the first evidence, to our knowledge, of Lévy-like search strategies in extinct animals. Our results show that simple search behaviors of extinct animals in heterogeneous environments give rise to hierarchically nested Brownian walk clusters that converge to optimal Lévy patterns. Primary productivity collapse and large-scale food scarcity characterizing mass extinctions evident in the fossil record may have triggered adaptation of optimal Lévy-like searches. The findings suggest that Lévy-like behavior has been used by foragers since at least the Eocene but may have a more ancient origin, which might explain recent widespread observations of such patterns among modern taxa.

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

    NASA Astrophysics Data System (ADS)

    Fedotov, Sergei; Korabel, Nickolay

    2015-12-01

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

  14. Distributed clone detection in static wireless sensor networks: random walk with network division.

    PubMed

    Khan, Wazir Zada; Aalsalem, Mohammed Y; Saad, N M

    2015-01-01

    Wireless Sensor Networks (WSNs) are vulnerable to clone attacks or node replication attacks as they are deployed in hostile and unattended environments where they are deprived of physical protection, lacking physical tamper-resistance of sensor nodes. As a result, an adversary can easily capture and compromise sensor nodes and after replicating them, he inserts arbitrary number of clones/replicas into the network. If these clones are not efficiently detected, an adversary can be further capable to mount a wide variety of internal attacks which can emasculate the various protocols and sensor applications. Several solutions have been proposed in the literature to address the crucial problem of clone detection, which are not satisfactory as they suffer from some serious drawbacks. In this paper we propose a novel distributed solution called Random Walk with Network Division (RWND) for the detection of node replication attack in static WSNs which is based on claimer-reporter-witness framework and combines a simple random walk with network division. RWND detects clone(s) by following a claimer-reporter-witness framework and a random walk is employed within each area for the selection of witness nodes. Splitting the network into levels and areas makes clone detection more efficient and the high security of witness nodes is ensured with moderate communication and memory overheads. Our simulation results show that RWND outperforms the existing witness node based strategies with moderate communication and memory overheads.

  15. Distributed Clone Detection in Static Wireless Sensor Networks: Random Walk with Network Division

    PubMed Central

    Khan, Wazir Zada; Aalsalem, Mohammed Y.; Saad, N. M.

    2015-01-01

    Wireless Sensor Networks (WSNs) are vulnerable to clone attacks or node replication attacks as they are deployed in hostile and unattended environments where they are deprived of physical protection, lacking physical tamper-resistance of sensor nodes. As a result, an adversary can easily capture and compromise sensor nodes and after replicating them, he inserts arbitrary number of clones/replicas into the network. If these clones are not efficiently detected, an adversary can be further capable to mount a wide variety of internal attacks which can emasculate the various protocols and sensor applications. Several solutions have been proposed in the literature to address the crucial problem of clone detection, which are not satisfactory as they suffer from some serious drawbacks. In this paper we propose a novel distributed solution called Random Walk with Network Division (RWND) for the detection of node replication attack in static WSNs which is based on claimer-reporter-witness framework and combines a simple random walk with network division. RWND detects clone(s) by following a claimer-reporter-witness framework and a random walk is employed within each area for the selection of witness nodes. Splitting the network into levels and areas makes clone detection more efficient and the high security of witness nodes is ensured with moderate communication and memory overheads. Our simulation results show that RWND outperforms the existing witness node based strategies with moderate communication and memory overheads. PMID:25992913

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

    PubMed

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

    2016-02-27

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

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

    PubMed Central

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

    2016-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Huillet, Thierry

    2010-03-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

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

    PubMed

    Fedotov, Sergei; Korabel, Nickolay

    2015-12-01

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

  2. An Extended Kalman Filter to Estimate Human Gait Parameters and Walking Distance

    PubMed Central

    Bennett, Terrell; Jafari, Roozbeh; Gans, Nicholas

    2017-01-01

    In this work, we present a novel method to estimate joint angles and distance traveled by a human while walking. We model the human leg as a two-link revolute robot. Inertial measurement sensors placed on the thigh and shin provide the required measurement inputs. The model and inputs are then used to estimate the desired state parameters associated with forward motion using an extended Kalman filter (EKF). Experimental results with subjects walking in a straight line show that distance walked can be measured with accuracy comparable to a state of the art motion tracking systems. The EKF had an average RMSE of 7 cm over the trials with an average accuracy of greater than 97% for linear displacement.

  3. A novel walking speed estimation scheme and its application to treadmill control for gait rehabilitation.

    PubMed

    Yoon, Jungwon; Park, Hyung-Soon; Damiano, Diane Louise

    2012-08-28

    Virtual reality (VR) technology along with treadmill training (TT) can effectively provide goal-oriented practice and promote improved motor learning in patients with neurological disorders. Moreover, the VR + TT scheme may enhance cognitive engagement for more effective gait rehabilitation and greater transfer to over ground walking. For this purpose, we developed an individualized treadmill controller with a novel speed estimation scheme using swing foot velocity, which can enable user-driven treadmill walking (UDW) to more closely simulate over ground walking (OGW) during treadmill training. OGW involves a cyclic acceleration-deceleration profile of pelvic velocity that contrasts with typical treadmill-driven walking (TDW), which constrains a person to walk at a preset constant speed. In this study, we investigated the effects of the proposed speed adaptation controller by analyzing the gait kinematics of UDW and TDW, which were compared to those of OGW at three pre-determined velocities. Ten healthy subjects were asked to walk in each mode (TDW, UDW, and OGW) at three pre-determined speeds (0.5 m/s, 1.0 m/s, and 1.5 m/s) with real time feedback provided through visual displays. Temporal-spatial gait data and 3D pelvic kinematics were analyzed and comparisons were made between UDW on a treadmill, TDW, and OGW. The observed step length, cadence, and walk ratio defined as the ratio of stride length to cadence were not significantly different between UDW and TDW. Additionally, the average magnitude of pelvic acceleration peak values along the anterior-posterior direction for each step and the associated standard deviations (variability) were not significantly different between the two modalities. The differences between OGW and UDW and TDW were mainly in swing time and cadence, as have been reported previously. Also, step lengths between OGW and TDW were different for 0.5 m/s and 1.5 m/s gait velocities, and walk ratio between OGS and UDW was

  4. A novel walking speed estimation scheme and its application to treadmill control for gait rehabilitation

    PubMed Central

    2012-01-01

    Background Virtual reality (VR) technology along with treadmill training (TT) can effectively provide goal-oriented practice and promote improved motor learning in patients with neurological disorders. Moreover, the VR + TT scheme may enhance cognitive engagement for more effective gait rehabilitation and greater transfer to over ground walking. For this purpose, we developed an individualized treadmill controller with a novel speed estimation scheme using swing foot velocity, which can enable user-driven treadmill walking (UDW) to more closely simulate over ground walking (OGW) during treadmill training. OGW involves a cyclic acceleration-deceleration profile of pelvic velocity that contrasts with typical treadmill-driven walking (TDW), which constrains a person to walk at a preset constant speed. In this study, we investigated the effects of the proposed speed adaptation controller by analyzing the gait kinematics of UDW and TDW, which were compared to those of OGW at three pre-determined velocities. Methods Ten healthy subjects were asked to walk in each mode (TDW, UDW, and OGW) at three pre-determined speeds (0.5 m/s, 1.0 m/s, and 1.5 m/s) with real time feedback provided through visual displays. Temporal-spatial gait data and 3D pelvic kinematics were analyzed and comparisons were made between UDW on a treadmill, TDW, and OGW. Results The observed step length, cadence, and walk ratio defined as the ratio of stride length to cadence were not significantly different between UDW and TDW. Additionally, the average magnitude of pelvic acceleration peak values along the anterior-posterior direction for each step and the associated standard deviations (variability) were not significantly different between the two modalities. The differences between OGW and UDW and TDW were mainly in swing time and cadence, as have been reported previously. Also, step lengths between OGW and TDW were different for 0.5 m/s and 1.5 m/s gait velocities, and walk ratio

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

    NASA Astrophysics Data System (ADS)

    Brunet, É.; Derrida, B.

    2009-09-01

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

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

    PubMed

    Adib, Artur B

    2008-02-01

    A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3 . Extensive numerical simulations were also performed to elucidate the role of the approximations involved.

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

    NASA Astrophysics Data System (ADS)

    Montero, Miquel

    2011-11-01

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

  8. Evaluation of the Effectiveness of Tai Chi versus Brisk Walking in Reducing Cardiovascular Risk Factors: Protocol for a Randomized Controlled Trial

    PubMed Central

    Chan, Aileen W. K.; Sit, Janet W. H.; Chair, Sek Ying; Leung, Doris Y. P.; Lee, Diana T. F.; Wong, Eliza M. L.; Fung, Lawrence C. W.

    2016-01-01

    Physical inactivity is one of the major modifiable lifestyle risk factors for cardiovascular disease (CVD). This protocol aims to evaluate the effectiveness of Tai Chi versus brisk walking in reducing CVD risk factors. This is a randomized controlled trial with three arms, namely, Tai Chi group, walking group, and control group. The Tai Chi group will receive Tai Chi training, which consists of two 60-min sessions each week for three months, and self-practice for 30 min every day. The walking group will perform brisk walking for 30 min every day. The control group will receive their usual care. 246 subjects with CVD risk factors will be recruited from two outpatient clinics. The primary outcome is blood pressure. Secondary outcomes include fasting blood for lipid profile, sugar and glycated haemoglobin (HbA1c); body mass index, waist circumference, body fat percentage; perceived stress level and quality of life. Data collections will be conducted at baseline, 3-month, 6-month and 9-month. Generalized estimating equations model will be used to compare the changes in outcomes across time between groups. It is expected that both the Tai Chi and walking groups could maintain better health and have improved quality of life, and that Tai Chi will be more effective than brisk walking in reducing CVD risk factors. PMID:27399735

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

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

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

  10. Modified cumulative distribution function in application to waiting time analysis in the continuous time random walk scenario

    NASA Astrophysics Data System (ADS)

    Połoczański, Rafał; Wyłomańska, Agnieszka; Maciejewska, Monika; Szczurek, Andrzej; Gajda, Janusz

    2017-01-01

    The continuous time random walk model plays an important role in modelling of the so-called anomalous diffusion behaviour. One of the specific properties of such model is the appearance of constant time periods in the trajectory. In the continuous time random walk approach they are realizations of the sequence called waiting times. In this work we focus on the analysis of waiting time distribution by introducing novel methods of parameter estimation and statistical investigation of such a distribution. These methods are based on the modified cumulative distribution function. In this paper we consider three special cases of waiting time distributions, namely α-stable, tempered stable and gamma. However, the proposed methodology can be applied to broad set of distributions—in general it may serve as a method of fitting any distribution function if the observations are rounded. The new statistical techniques are applied to the simulated data as well as to the real data of \\text{C}{{\\text{O}}2} concentration in indoor air.

  11. An improved label propagation algorithm based on the similarity matrix using random walk

    NASA Astrophysics Data System (ADS)

    Zhang, Xian-Kun; Song, Chen; Jia, Jia; Lu, Zeng-Lei; Zhang, Qian

    2016-05-01

    Community detection based on label propagation algorithm (LPA) has attracted widespread concern because of its high efficiency. But it is difficult to guarantee the accuracy of community detection as the label spreading is random in the algorithm. In response to the problem, an improved LPA based on random walk (RWLPA) is proposed in this paper. Firstly, a matrix measuring similarity among various nodes in the network is obtained through calculation. Secondly, during the process of label propagation, when a node has more than a neighbor label with the highest frequency, not the label of a random neighbor but the label of the neighbor with the highest similarity will be chosen to update. It can avoid label propagating randomly among communities. Finally, we test LPA and the improved LPA in benchmark networks and real-world networks. The results show that the quality of communities discovered by the improved algorithm is improved compared with the traditional algorithm.

  12. Walking and Non–HDL-C in Adults: A Meta-Analysis of Randomized Controlled Trials

    PubMed Central

    Kelley, George A.; Kelley, Kristi S.; Tran, Zung Vu

    2007-01-01

    An elevated level of non–high-density lipoprotein cholesterol (non–HDL-C) is a major risk factor for cardiovascular disease. The purpose of this study was to use the meta-analytic approach to examine the effects of walking on non–HDL-C in adults. Twenty-two randomized controlled trials representing 30 outcomes from 948 subjects (573 exercise, 375 control) met our inclusion criteria. Across all designs and categories, random effects modeling resulted in a significantly greater decrease in the walking group when compared with the control group of approximately 4% for non–HDL-C (X̄ ± standard error of the mean, −5.6±1.8 mg/dL, 95% confidence interval, −8.8 to −2.4 mg/dL). Meta-regression showed a statistically significant association between changes in non–HDL-C and the year of publication, with greater reductions associated with more recent publication year (R2=0.23, p=0.005). The results of this meta-analytic review suggest that walking reduces non–HDL-C in adult humans. PMID:15860986

  13. Solvable continuous-time random walk model of the motion of tracer particles through porous media.

    PubMed

    Fouxon, Itzhak; Holzner, Markus

    2016-08-01

    We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)PLEEE81539-375510.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ, length l, and velocity v. We solve our model with independent l and v. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ. Universality of tracer diffusion in the porous medium is considered.

  14. Solvable continuous-time random walk model of the motion of tracer particles through porous media

    NASA Astrophysics Data System (ADS)

    Fouxon, Itzhak; Holzner, Markus

    2016-08-01

    We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015), 10.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ , length l , and velocity v . We solve our model with independent l and v . The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α . Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α , ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ . Universality of tracer diffusion in the porous medium is considered.

  15. Lattice statistical theory of random walks on a fractal-like geometry.

    PubMed

    Kozak, John J; Garza-López, Roberto A; Abad, Enrique

    2014-03-01

    We have designed a two-dimensional, fractal-like lattice and explored, both numerically and analytically, the differences between random walks on this lattice and a regular, square-planar Euclidean lattice. We study the efficiency of diffusion-controlled processes for flows from external sites to a centrosymmetric reaction center and, conversely, for flows from a centrosymmetric source to boundary sites. In both cases, we find that analytic expressions derived for the mean walk length on the fractal-like lattice have an algebraic dependence on system size, whereas for regular Euclidean lattices the dependence can be transcendental. These expressions are compared with those derived in the continuum limit using classical diffusion theory. Our analysis and the numerical results quantify the extent to which one paradigmatic class of spatial inhomogeneities can compromise the efficiency of adatom diffusion on solid supports and of surface-assisted self-assembly in metal-organic materials.

  16. Interpolating between random walks and optimal transportation routes: Flow with multiple sources and targets

    NASA Astrophysics Data System (ADS)

    Guex, Guillaume

    2016-05-01

    In recent articles about graphs, different models proposed a formalism to find a type of path between two nodes, the source and the target, at crossroads between the shortest-path and the random-walk path. These models include a freely adjustable parameter, allowing to tune the behavior of the path toward randomized movements or direct routes. This article presents a natural generalization of these models, namely a model with multiple sources and targets. In this context, source nodes can be viewed as locations with a supply of a certain good (e.g. people, money, information) and target nodes as locations with a demand of the same good. An algorithm is constructed to display the flow of goods in the network between sources and targets. With again a freely adjustable parameter, this flow can be tuned to follow routes of minimum cost, thus displaying the flow in the context of the optimal transportation problem or, by contrast, a random flow, known to be similar to the electrical current flow if the random-walk is reversible. Moreover, a source-targetcoupling can be retrieved from this flow, offering an optimal assignment to the transportation problem. This algorithm is described in the first part of this article and then illustrated with case studies.

  17. An improved label propagation algorithm based on node importance and random walk for community detection

    NASA Astrophysics Data System (ADS)

    Ma, Tianren; Xia, Zhengyou

    2017-05-01

    Currently, with the rapid development of information technology, the electronic media for social communication is becoming more and more popular. Discovery of communities is a very effective way to understand the properties of complex networks. However, traditional community detection algorithms consider the structural characteristics of a social organization only, with more information about nodes and edges wasted. In the meanwhile, these algorithms do not consider each node on its merits. Label propagation algorithm (LPA) is a near linear time algorithm which aims to find the community in the network. It attracts many scholars owing to its high efficiency. In recent years, there are more improved algorithms that were put forward based on LPA. In this paper, an improved LPA based on random walk and node importance (NILPA) is proposed. Firstly, a list of node importance is obtained through calculation. The nodes in the network are sorted in descending order of importance. On the basis of random walk, a matrix is constructed to measure the similarity of nodes and it avoids the random choice in the LPA. Secondly, a new metric IAS (importance and similarity) is calculated by node importance and similarity matrix, which we can use to avoid the random selection in the original LPA and improve the algorithm stability. Finally, a test in real-world and synthetic networks is given. The result shows that this algorithm has better performance than existing methods in finding community structure.

  18. Solvable random-walk model with memory and its relations with Markovian models of anomalous diffusion

    NASA Astrophysics Data System (ADS)

    Boyer, D.; Romo-Cruz, J. C. R.

    2014-10-01

    Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random-walk model with long-range memory for which not only the mean-square displacement (MSD) but also the propagator can be obtained exactly in the asymptotic limit. The model consists of a random walker on a lattice, which, at a constant rate, stochastically relocates at a site occupied at some earlier time. This time in the past is chosen randomly according to a memory kernel, whose temporal decay can be varied via an exponent parameter. In the weakly non-Markovian regime, memory reduces the diffusion coefficient from the bare value. When the mean backward jump in time diverges, the diffusion coefficient vanishes and a transition to an anomalous subdiffusive regime occurs. Paradoxically, at the transition, the process is an anticorrelated Lévy flight. Although in the subdiffusive regime the model exhibits some features of the continuous time random walk with infinite mean waiting time, it belongs to another universality class. If memory is very long-ranged, a second transition takes place to a regime characterized by a logarithmic growth of the MSD with time. In this case the process is asymptotically Gaussian and effectively described as a scaled Brownian motion with a diffusion coefficient decaying as 1 /t .

  19. Propagators and related descriptors for non-Markovian asymmetric random walks with and without boundaries.

    PubMed

    Berezhkovskii, Alexander M; Weiss, George H

    2008-01-28

    There are many current applications of the continuous-time random walk (CTRW), particularly in describing kinetic and transport processes in different chemical and biophysical phenomena. We derive exact solutions for the Laplace transforms of the propagators for non-Markovian asymmetric one-dimensional CTRW's in an infinite space and in the presence of an absorbing boundary. The former is used to produce exact results for the Laplace transforms of the first two moments of the displacement of the random walker, the asymptotic behavior of the moments as t-->infinity, and the effective diffusion constant. We show that in the infinite space, the propagator satisfies a relation that can be interpreted as a generalized fluctuation theorem since it reduces to the conventional fluctuation theorem at large times. Based on the Laplace transform of the propagator in the presence of an absorbing boundary, we derive the Laplace transform of the survival probability of the random walker, which is then used to find the mean lifetime for terminated trajectories of the random walk.

  20. Automatic Oxygen Titration During Walking in Subjects With COPD: A Randomized Crossover Controlled Study.

    PubMed

    Lellouche, François; L'Her, Erwan; Bouchard, Pierre-Alexandre; Brouillard, Cynthia; Maltais, François

    2016-11-01

    Arterial oxygen desaturation frequently occurs in patients with COPD during daily activities at home. Oxygen flow is usually set at fixed and low rates for ambulatory patients. We evaluated an innovative closed-loop system (FreeO2) that automatically adjusts the oxygen flow to the patient's needs in subjects with COPD during walking followed by recovery time, such as during ambulatory conditions. Patients with COPD who exhibited oxygen desaturation on exertion were included in the study. Subjects performed endurance shuttle walk tests followed by 10 min of recovery. The tests were conducted in a random order and in crossover with the 3 following conditions: subjects breathing (1) air at 2 L/min, (2) oxygen at 2 L/min, or (3) FreeO2 (variable oxygen flow). SpO2, pulse rate, PETCO2 , breathing frequency, and oxygen flow were continuously recorded during the 3 conditions. The primary outcome was the percentage of time within the SpO2 target of 92-96%. Secondary outcomes included the endurance shuttle walk test time and distance. Sixteen subjects with COPD were recruited. The percentage of time with SpO2 in the target range (92-96%) was higher while using the FreeO2, and time with severe oxygen desaturation (SpO2 <88%) was lower with FreeO2 in comparison with constant-flow oxygen and air testing conditions (0.6% vs 23.9% vs 52.2%, P < .001). In comparison with air, walking distance was increased by 35% with oxygen (P = .045) and by 63% with FreeO2 (P < .001). The walking distance was increased by 17% with FreeO2 in comparison with constant oxygen, but the difference was not statistically significant (P = .22). Automatic titration of oxygen flow during walking to maintain oxygen saturation in a specified range improves oxygenation and may improve exercise tolerance during daily activity, such as walking, in patients with COPD in comparison with room air and fixed oxygen administration. (ClinicalTrials.gov registration: NCT02150434.). Copyright © 2016 by Daedalus

  1. Randomized controlled trial of physical activity, cognition, and walking in multiple sclerosis.

    PubMed

    Sandroff, Brian M; Klaren, Rachel E; Pilutti, Lara A; Dlugonski, Deirdre; Benedict, Ralph H B; Motl, Robert W

    2014-02-01

    The present study adopted a randomized controlled trial design and examined the effect of a physical activity behavioral intervention on cognitive and walking performance among persons with MS who have mild or moderate disability status. A total of 82 MS patients were randomly allocated into intervention or wait-list control conditions. The intervention condition received a theory-based program for increasing physical activity behavior that was delivered via the Internet, and one-on-one video chat sessions with a behavior-change coach. Participants completed self-report measures of physical activity and disability status, and underwent the oral Symbol Digit Modalities Test (SDMT) and 6-minute walk (6MW) test before and after the 6-month period. Analysis using mixed-model ANOVA indicated a significant time × condition × disability group interaction on SDMT scores (p = 0.02, partial-η (2) = 0.08), such that persons with mild disability in the intervention condition demonstrated a clinically meaningful improvement in SDMT scores (~6 point change). There was a further significant time × condition interaction on 6MW distance (p = 0.02, partial-η (2) = 0.07), such that those in the intervention condition demonstrated an increase in 6MW distance relative to those in the control group. The current study supports physical activity as a promising tool for managing cognitive impairment and impaired walking performance in persons with MS, and suggests that physical activity might have specific effects on cognition and non-specific effects on walking performance in this population.

  2. Effectiveness of an innovative hip energy storage walking orthosis for improving paraplegic walking: A pilot randomized controlled study.

    PubMed

    Yang, Mingliang; Li, Jianjun; Guan, Xinyu; Gao, Lianjun; Gao, Feng; Du, Liangjie; Zhao, Hongmei; Yang, Degang; Yu, Yan; Wang, Qimin; Wang, Rencheng; Ji, Linhong

    2017-09-01

    The high energy cost of paraplegic walking using a reciprocating gait orthosis (RGO) is attributed to limited hip motion and excessive upper limb loading for support. To address the limitation, we designed the hip energy storage walking orthosis (HESWO) which uses a spring assembly on the pelvic shell to store energy from the movements of the healthy upper limbs and flexion-extension of the lumbar spine and hip and returns this energy to lift the pelvis and lower limb to assist with the swing and stance components of a stride. Our aim was to evaluate gait and energy cost indices for the HESWO compared to the RGO in patients with paraplegia. The cross-over design was used in the pilot study. Twelve patients with a complete T4-L5 chronic spinal cord injury underwent gait training using the HESWO and RGO. Gait performance (continuous walking distance, as well as the maximum and comfortable walking speeds) and energy expenditure (at a walking speed of 3.3m/min on a treadmill) were measured at the end of the 4-week training session. Compared to the RGO, the HESWO increased continuous walking distance by 24.7% (P<0.05), maximum walking speed by 20.4% (P<0.05) and the comfortable walking speed by 15.3% (P<0.05), as well as decreasing energy expenditure by 13.9% (P<0.05). Our preliminary results provide support for the use of the HESWO as an alternative support for paraplegic walking. Copyright © 2017. Published by Elsevier B.V.

  3. Intra-fraction motion of the prostate is a random walk

    NASA Astrophysics Data System (ADS)

    Ballhausen, H.; Li, M.; Hegemann, N.-S.; Ganswindt, U.; Belka, C.

    2015-01-01

    A random walk model for intra-fraction motion has been proposed, where at each step the prostate moves a small amount from its current position in a random direction. Online tracking data from perineal ultrasound is used to validate or reject this model against alternatives. Intra-fraction motion of a prostate was recorded by 4D ultrasound (Elekta Clarity system) during 84 fractions of external beam radiotherapy of six patients. In total, the center of the prostate was tracked for 8 h in intervals of 4 s. Maximum likelihood model parameters were fitted to the data. The null hypothesis of a random walk was tested with the Dickey-Fuller test. The null hypothesis of stationarity was tested by the Kwiatkowski-Phillips-Schmidt-Shin test. The increase of variance in prostate position over time and the variability in motility between fractions were analyzed. Intra-fraction motion of the prostate was best described as a stochastic process with an auto-correlation coefficient of ρ = 0.92  ±  0.13. The random walk hypothesis (ρ = 1) could not be rejected (p = 0.27). The static noise hypothesis (ρ = 0) was rejected (p < 0.001). The Dickey-Fuller test rejected the null hypothesis ρ = 1 in 25% to 32% of cases. On average, the Kwiatkowski-Phillips-Schmidt-Shin test rejected the null hypothesis ρ = 0 with a probability of 93% to 96%. The variance in prostate position increased linearly over time (r2 = 0.9  ±  0.1). Variance kept increasing and did not settle at a maximum as would be expected from a stationary process. There was substantial variability in motility between fractions and patients with maximum aberrations from isocenter ranging from 0.5 mm to over 10 mm in one patient alone. In conclusion, evidence strongly suggests that intra-fraction motion of the prostate is a random walk and neither static (like inter-fraction setup errors) nor stationary (like a cyclic motion such as breathing, for example). The prostate tends to drift away from the

  4. Home-based walking during pregnancy affects mood and birth outcomes among sedentary women: A randomized controlled trial.

    PubMed

    Taniguchi, Chie; Sato, Chifumi

    2016-10-01

    We examined the effects of home-based walking on sedentary Japanese women's pregnancy outcomes and mood. A randomized controlled trial was conducted, involving 118 women aged 22-36 years. Participants were randomly assigned to walking intervention (n = 60) or control (n = 58) groups. The walking group was instructed to walk briskly for 30 min, three times weekly from 30 weeks' gestation until delivery. Both groups counted their daily steps using pedometers. Pregnancy and delivery outcomes were assessed, participants completed the Profile of Mood States, and we used the intention-to-treat principle. Groups showed no differences regarding pregnancy or delivery outcomes. The walking group exhibited decreased scores on the depression-dejection and confusion subscales of the Profile of Mood States. Five of the 54 women in the intervention group who remained in the study (9.2%) completed 100% of the prescribed walking program; 32 (59.3%) women completed 80% or more. Unsupervised walking improves sedentary pregnant women's mood, indicating that regular walking during pregnancy should be promoted in this group. © 2016 John Wiley & Sons Australia, Ltd.

  5. Random Walks with Preferential Relocations to Places Visited in the Past and their Application to Biology

    NASA Astrophysics Data System (ADS)

    Boyer, Denis; Solis-Salas, Citlali

    2014-06-01

    Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where a random walker intermittently revisits previously visited sites according to a reinforced rule. The emergence of frequently visited locations generates very slow diffusion, logarithmic in time, whereas the walker probability density tends to a Gaussian. This scaling form does not emerge from the central limit theorem but from an unusual balance between random and long-range memory steps. In single trajectories, occupation patterns are heterogeneous and have a scale-free structure. The model exhibits good agreement with data of free-ranging capuchin monkeys.

  6. Self-avoiding walks on random networks of resistors and diodes

    NASA Astrophysics Data System (ADS)

    Marković, D.; Milošević, S.; Stanley, H. E.

    1987-07-01

    We study the self-avoiding walks (SAW) on a square lattice whose various degrees of randomness encompasses many different random networks, including the incipient clusters of the directed, mixed and isotropic bond percolation. We apply the position-space renormalization group (PSRG) method and demonstrate that within the framework of this method one is bound to find that the critical exponent v of the mean end-to-end distance of SAW on various two-dimensional random networks should be equal to the critical exponent of SAW on the ordinary square lattice. A detailed analysis of this finding, and similar findings of other authors, lead us to conclude that a debatable opposite finding, which has been predicted on the basis of different approaches, could be attained after a substantial refinement of the method applied.

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

    NASA Astrophysics Data System (ADS)

    Calvo-Muñoz, Elisa M.; Selvan, Myvizhi Esai; Xiong, Ruichang; Ojha, Madhusudan; Keffer, David J.; Nicholson, Donald M.; Egami, Takeshi

    2011-01-01

    A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.

  8. Continuous time random walks for non-local radial solute transport

    NASA Astrophysics Data System (ADS)

    Dentz, Marco; Kang, Peter K.; Le Borgne, Tanguy

    2015-08-01

    This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile-immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection-dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer

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

    PubMed Central

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

    2014-01-01

    Efficient searching is crucial for timely location of food and other resources. Recent studies show that diverse living animals use a theoretically optimal scale-free random search for sparse resources known as a Lévy walk, but little is known of the origins and evolution of foraging behavior and the search strategies of extinct organisms. Here, using simulations of self-avoiding trace fossil trails, we show that randomly introduced strophotaxis (U-turns)—initiated by obstructions such as self-trail avoidance or innate cueing—leads to random looping patterns with clustering across increasing scales that is consistent with the presence of Lévy walks. This predicts that optimal Lévy searches may emerge from simple behaviors observed in fossil trails. We then analyzed fossilized trails of benthic marine organisms by using a novel path analysis technique and find the first evidence, to our knowledge, of Lévy-like search strategies in extinct animals. Our results show that simple search behaviors of extinct animals in heterogeneous environments give rise to hierarchically nested Brownian walk clusters that converge to optimal Lévy patterns. Primary productivity collapse and large-scale food scarcity characterizing mass extinctions evident in the fossil record may have triggered adaptation of optimal Lévy-like searches. The findings suggest that Lévy-like behavior has been used by foragers since at least the Eocene but may have a more ancient origin, which might explain recent widespread observations of such patterns among modern taxa. PMID:25024221

  10. Generalized Hammersley Process and Phase Transition for Activated Random Walk Models

    NASA Astrophysics Data System (ADS)

    Rolla, Leonardo T.

    2008-12-01

    * ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to passive, then stopping to jump. When particles of both types occupy the same site, they all become active. This model exhibits phase transition in the sense that for low initial densities the system locally fixates and for high densities it keeps active. Though extensively studied in the physics literature, the matter of giving a mathematical proof of such phase transition remained as an open problem for several years. In this work we identify some variables that are sufficient to characterize fixation and at the same time are stochastically monotone in the model's parameters. We employ an explicit graphical representation in order to obtain the monotonicity. With this method we prove that there is a unique phase transition for the one-dimensional finite-range random walk. Joint with V. Sidoravicius. * BROKEN LINE PROCESS * We introduce the broken line process and derive some of its properties. Its discrete version is presented first and a natural generalization to the continuum is then proposed and studied. The broken lines are related to the Young diagram and the Hammersley process and are useful for computing last passage percolation values and finding maximal oriented paths. For a class of passage time distributions there is a family of boundary conditions that make the process stationary and reversible. One application is a simple proof of the explicit law of large numbers for last passage percolation with exponential and geometric distributions. Joint with V. Sidoravicius, D. Surgailis, and M. E. Vares.

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

    PubMed

    Calvo-Muñoz, Elisa M; Selvan, Myvizhi Esai; Xiong, Ruichang; Ojha, Madhusudan; Keffer, David J; Nicholson, Donald M; Egami, Takeshi

    2011-01-01

    A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.

  12. Attributes of environments supporting walking.

    PubMed

    Moudon, Anne Vernez; Lee, Chanam; Cheadle, Allen D; Garvin, Cheza; Rd, Donna B Johnson; Schmid, Thomas L; Weathers, Robert D

    2007-01-01

    This study established a framework to audit environments supporting walking in neighborhoods. Cross-sectional analysis using a telephone survey and 200 objective environmental variables. SETTING. Urbanized King County, WA. SUBJECTS. 608 randomly sampled adults. Measures. Walking measures constructed from survey questions; objective environmental measures taken from parcel-level databases in Geographic Information Systems. Multinomial models estimated the odds of people engaging in moderate walking (<149 min/wk) and in walking sufficiently to meet recommendations for health (150+ min/ wk), relative to not walking" and in walking sufficiently, relative to walking moderately. A base model consisted of survey variables, and final models incorporated both survey and environmental variables. RESULTS. Survey variables strongly associated with walking sufficiently to enhance health included household income, not having difficulty walking, using transit, perceiving social support for walking walking outside of the neighborhood, and having a dog (p < .01). The models isolated 14 environmental variables associated with walking sufficiently (pseudo R2 up to 0. 46). Measures of distance to neighborhood destinations dominated the results: shorter distances to grocery stores/markets, restaurants, and retail stores, but longer distances to offices or mixed-use buildings (p < .01 or .05). The density of the respondent's parcel was also strongly associated with walking sufficiently (p < .01). Conclusions. The study offered valid environmental measures of neighborhood walkability.

  13. Magnetic field line random walk in models and simulations of reduced magnetohydrodynamic turbulence

    SciTech Connect

    Snodin, A. P.; Ruffolo, D.; Oughton, S.; Servidio, S.; Matthaeus, W. H.

    2013-12-10

    The random walk of magnetic field lines is examined numerically and analytically in the context of reduced magnetohydrodynamic (RMHD) turbulence, which provides a useful description of plasmas dominated by a strong mean field, such as in the solar corona. A recently developed non-perturbative theory of magnetic field line diffusion is compared with the diffusion coefficients obtained by accurate numerical tracing of magnetic field lines for both synthetic models and direct numerical simulations of RMHD. Statistical analysis of an ensemble of trajectories confirms the applicability of the theory, which very closely matches the numerical field line diffusion coefficient as a function of distance z along the mean magnetic field for a wide range of the Kubo number R. This theory employs Corrsin's independence hypothesis, sometimes thought to be valid only at low R. However, the results demonstrate that it works well up to R = 10, both for a synthetic RMHD model and an RMHD simulation. The numerical results from the RMHD simulation are compared with and without phase randomization, demonstrating a clear effect of coherent structures on the field line random walk for a very low Kubo number.

  14. Self organization of social hierarchy and clusters in a challenging society with free random walks

    NASA Astrophysics Data System (ADS)

    Fujie, Ryo; Odagaki, Takashi

    2010-04-01

    Emergence of social hierarchy and clusters in a challenging equal-right society is studied on the basis of the agent-based model, where warlike individuals who have own power or wealth perform random walks in a random order on a lattice and when meeting others the individuals challenge the strongest among the neighbors. We assume that the winning probability depends on the difference in their wealth and after the fight the winner gets and the loser loses a unit of the wealth. We show that hierarchy is self organized when the population exceeds a critical value and the transition from egalitarian state to hierarchical state occurs in two steps. The first transition is continuous to the society with widespread winning-probability. At the second transition the variance of the winning fraction decrease discontinuously, which was not observed in previous studies. The second hierarchical society consists of a small number of extreme winners and many individuals in the middle class and losers. We also show that when the relaxation parameter for the wealth is large, the first transition disappears. In the second hierarchical society, a giant cluster of individuals is formed with a layered structure in the power order and some people stray around it. The structure of the cluster and the distribution of wealth are quite different from the results of the previous challenging model [M. Tsujiguchi and T. Odagaki, Physica A 375 (2007) 317] which adopts the preassigned order for random walk.

  15. Multiple random walks on complex networks: A harmonic law predicts search time.

    PubMed

    Weng, Tongfeng; Zhang, Jie; Small, Michael; Hui, Pan

    2017-05-01

    We investigate multiple random walks traversing independently and concurrently on complex networks and introduce the concept of mean first parallel passage time (MFPPT) to quantify their search efficiency. The mean first parallel passage time represents the expected time required to find a given target by one or some of the multiple walkers. We develop a general theory that allows us to calculate the MFPPT analytically. Interestingly, we find that the global MFPPT follows a harmonic law with respect to the global mean first passage times of the associated walkers. Remarkably, when the properties of multiple walkers are identical, the global MFPPT decays in a power law manner with an exponent of unity, irrespective of network structure. These findings are confirmed by numerical and theoretical results on various synthetic and real networks. The harmonic law reveals a universal principle governing multiple random walks on networks that uncovers the contribution and role of the combined walkers in a target search. Our paradigm is also applicable to a broad range of random search processes.

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

    NASA Astrophysics Data System (ADS)

    Lechman, Jeremy; Pierce, Flint

    2012-02-01

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

  17. Random walk model of subdiffusion in a system with a thin membrane.

    PubMed

    Kosztołowicz, Tadeusz

    2015-02-01

    We consider in this paper subdiffusion in a system with a thin membrane. The subdiffusion parameters are the same in both parts of the system separated by the membrane. Using the random walk model with discrete time and space variables the probabilities (Green's functions) P(x,t) describing a particle's random walk are found. The membrane, which can be asymmetrical, is characterized by the two probabilities of stopping a random walker by the membrane when it tries to pass through the membrane in both opposite directions. Green's functions are transformed to the system in which the variables are continuous, and then the membrane permeability coefficients are given by special formulas which involve the probabilities mentioned above. From the obtained Green's functions, we derive boundary conditions at the membrane. One of the conditions demands the continuity of a flux at the membrane, but the other one is rather unexpected and contains the Riemann-Liouville fractional time derivative P(x(N)(-),t)=λ(1)P(x(N)(+),t)+λ(2)∂(α/2)P(x(N)(+),t)/∂t(α/2), where λ(1),λ(2) depending on membrane permeability coefficients (λ(1)=1 for a symmetrical membrane), α is a subdiffusion parameter, and x(N) is the position of the membrane. This boundary condition shows that the additional "memory effect," represented by the fractional derivative, is created by the membrane. This effect is also created by the membrane for a normal diffusion case in which α=1.

  18. Multiple random walks on complex networks: A harmonic law predicts search time

    NASA Astrophysics Data System (ADS)

    Weng, Tongfeng; Zhang, Jie; Small, Michael; Hui, Pan

    2017-05-01

    We investigate multiple random walks traversing independently and concurrently on complex networks and introduce the concept of mean first parallel passage time (MFPPT) to quantify their search efficiency. The mean first parallel passage time represents the expected time required to find a given target by one or some of the multiple walkers. We develop a general theory that allows us to calculate the MFPPT analytically. Interestingly, we find that the global MFPPT follows a harmonic law with respect to the global mean first passage times of the associated walkers. Remarkably, when the properties of multiple walkers are identical, the global MFPPT decays in a power law manner with an exponent of unity, irrespective of network structure. These findings are confirmed by numerical and theoretical results on various synthetic and real networks. The harmonic law reveals a universal principle governing multiple random walks on networks that uncovers the contribution and role of the combined walkers in a target search. Our paradigm is also applicable to a broad range of random search processes.

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

    NASA Astrophysics Data System (ADS)

    Iomin, A.

    A theory of fractional kinetics of glial cancer cells is presented. A role of the migration-proliferation dichotomy in the fractional cancer cell dynamics in the outer-invasive zone is discussed and explained in the framework of a continuous time random walk. The main suggested model is based on a construction of a 3D comb model, where the migration-proliferation dichotomy becomes naturally apparent and the outer-invasive zone of glioma cancer is considered as a fractal composite with a fractal dimension Dfr < 3.

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

    NASA Astrophysics Data System (ADS)

    Iomin, A.

    2015-10-01

    A theory of fractional kinetics of glial cancer cells is presented. A role of the migration-proliferation dichotomy in the fractional cancer cell dynamics in the outer-invasive zone is discussed and explained in the framework of a continuous time random walk. The main suggested model is based on a construction of a 3D comb model, where the migration-proliferation dichotomy becomes naturally apparent and the outer-invasive zone of glioma cancer is considered as a fractal composite with a fractal dimension Dfr < 3.

  1. Comparing quantum versus Markov random walk models of judgements measured by rating scales

    PubMed Central

    Wang, Z.; Busemeyer, J. R.

    2016-01-01

    Quantum and Markov random walk models are proposed for describing how people evaluate stimuli using rating scales. To empirically test these competing models, we conducted an experiment in which participants judged the effectiveness of public health service announcements from either their own personal perspective or from the perspective of another person. The order of the self versus other judgements was manipulated, which produced significant sequential effects. The quantum and Markov models were fitted to the data using the same number of parameters, and the model comparison strongly supported the quantum over the Markov model. PMID:26621984

  2. Tracking Random Walk of Individual Domain Walls in Cylindrical Nanomagnets with Resistance Noise

    NASA Astrophysics Data System (ADS)

    Singh, Amrita; Mukhopadhyay, Soumik; Ghosh, Arindam

    2010-08-01

    The stochasticity of domain-wall (DW) motion in magnetic nanowires has been probed by measuring slow fluctuations, or noise, in electrical resistance at small magnetic fields. By controlled injection of DWs into isolated cylindrical nanowires of nickel, we have been able to track the motion of the DWs between the electrical leads by discrete steps in the resistance. Closer inspection of the time dependence of noise reveals a diffusive random walk of the DWs with a universal kinetic exponent. Our experiments outline a method with which electrical resistance is able to detect the kinetic state of the DWs inside the nanowires, which can be useful in DW-based memory designs.

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

    NASA Astrophysics Data System (ADS)

    Fa, Kwok Sau

    2013-08-01

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

  4. Experimental implementation of a quantum random-walk search algorithm using strongly dipolar coupled spins

    NASA Astrophysics Data System (ADS)

    Lu, Dawei; Zhu, Jing; Zou, Ping; Peng, Xinhua; Yu, Yihua; Zhang, Shanmin; Chen, Qun; Du, Jiangfeng

    2010-02-01

    An important quantum search algorithm based on the quantum random walk performs an oracle search on a database of N items with O(phN) calls, yielding a speedup similar to the Grover quantum search algorithm. The algorithm was implemented on a quantum information processor of three-qubit liquid-crystal nuclear magnetic resonance (NMR) in the case of finding 1 out of 4, and the diagonal elements’ tomography of all the final density matrices was completed with comprehensible one-dimensional NMR spectra. The experimental results agree well with the theoretical predictions.

  5. Fluid limit of nonintegrable continuous-time random walks in terms of fractional differential equations.

    PubMed

    Sánchez, R; Carreras, B A; van Milligen, B Ph

    2005-01-01

    The fluid limit of a recently introduced family of nonintegrable (nonlinear) continuous-time random walks is derived in terms of fractional differential equations. In this limit, it is shown that the formalism allows for the modeling of the interaction between multiple transport mechanisms with not only disparate spatial scales but also different temporal scales. For this reason, the resulting fluid equations may find application in the study of a large number of nonlinear multiscale transport problems, ranging from the study of self-organized criticality to the modeling of turbulent transport in fluids and plasmas.

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

    PubMed Central

    Montroll, Elliott W.; Shuler, Kurt E.

    1979-01-01

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

  7. The exact probability distribution of a two-dimensional random walk

    NASA Astrophysics Data System (ADS)

    Stadje, W.

    1987-01-01

    A calculation is made of the exact probability distribution of the two-dimensional displacement of a particle at time t that starts at the origin, moves in straight-line paths at constant speed, and changes its direction after exponentially distributed time intervals, where the lengths of the straight-line paths and the turn angles are independent, the angles being uniformly distributed. This random walk is the simplest model for the locomotion of microorganisms on surfaces. Its weak convergence to a Wiener process is also shown.

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

    PubMed

    Fa, Kwok Sau

    2013-08-14

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

  9. A boundary element-Random walk model of mass transport in groundwater

    USGS Publications Warehouse

    Kemblowski, M.

    1986-01-01

    A boundary element solution to the convective mass transport in groundwater is presented. This solution produces a continuous velocity field and reduces the amount of data preparation time and bookkeeping. By combining this solution and the random walk procedure, a convective-dispersive mass transport model is obtained. This model may be easily used to simulate groundwater contamination problems. The accuracy of the boundary element model has been verified by reproducing the analytical solution to a two-dimensional convective mass transport problem. The method was also used to simulate a convective-dispersive problem. ?? 1986.

  10. Slower deviations of the branching Brownian motion and of branching random walks

    NASA Astrophysics Data System (ADS)

    Derrida, Bernard; Shi, Zhan

    2017-08-01

    We have shown recently how to calculate the large deviation function of the position X\\max(t) of the rightmost particle of a branching Brownian motion at time t. This large deviation function exhibits a phase transition at a certain negative velocity. Here we extend this result to more general branching random walks and show that the probability distribution of X\\max(t) has, asymptotically in time, a prefactor characterized by a non trivial power law. Dedicated to John Cardy on the occasion of his 70th birthday.

  11. Experimental implementation of a quantum random-walk search algorithm using strongly dipolar coupled spins

    SciTech Connect

    Lu Dawei; Peng Xinhua; Du Jiangfeng; Zhu Jing; Zou Ping; Yu Yihua; Zhang Shanmin; Chen Qun

    2010-02-15

    An important quantum search algorithm based on the quantum random walk performs an oracle search on a database of N items with O({radical}(phN)) calls, yielding a speedup similar to the Grover quantum search algorithm. The algorithm was implemented on a quantum information processor of three-qubit liquid-crystal nuclear magnetic resonance (NMR) in the case of finding 1 out of 4, and the diagonal elements' tomography of all the final density matrices was completed with comprehensible one-dimensional NMR spectra. The experimental results agree well with the theoretical predictions.

  12. Position Estimation by Wearable Walking Navigation System for Visually Impaired with Sensor Fusion

    NASA Astrophysics Data System (ADS)

    Watanabe, Hiromi; Yamamoto, Yoshihiko; Tanzawa, Tsutomu; Kotani, Shinji

    A wearable walking navigation system without any special infrastructures has been developed to guide visually impaired. It is important to estimate a position correctly so that safe navigation can be realized. In our system, different sensor data are fused to estimate a pedestrian's position. An image processing system and a laser range finder were used to estimate the positions indoors. In this paper, we introduce the concept of “similarity” between map information and sensor data. This similarity is used to estimate the positions. Experimental results show that highly accurate position estimation can be achieved by sensor fusion. The positions in a linear passage were estimated using image processing data, and when the passage turns, the positions were estimated using LRF data.

  13. Experimental evaluation of regression model-based walking speed estimation using lower body-mounted IMU.

    PubMed

    Zihajehzadeh, Shaghayegh; Park, Edward J

    2016-08-01

    This study provides a concurrent comparison of regression model-based walking speed estimation accuracy using lower body mounted inertial sensors. The comparison is based on different sets of variables, features, mounting locations and regression methods. An experimental evaluation was performed on 15 healthy subjects during free walking trials. Our results show better accuracy of Gaussian process regression compared to least square regression using Lasso. Among the variables, external acceleration tends to provide improved accuracy. By using both time-domain and frequency-domain features, waist and ankle-mounted sensors result in similar accuracies: 4.5% for the waist and 4.9% for the ankle. When using only frequency-domain features, estimation accuracy based on a waist-mounted sensor suffers more compared to the one from ankle.

  14. Random walk to describe diffusion phenomena in three-dimensional discontinuous media: Step-balance and fictitious-velocity corrections

    NASA Astrophysics Data System (ADS)

    Maruyama, Yutaka

    2017-09-01

    In this paper, we show that diffusion phenomena in three-dimensional discontinuous media can be described as a random walk by two simple interface-correction methods, namely step-balance and fictitious-velocity corrections, which are completely different in a physical picture but equivalent in that the continuity of the random walk at interfaces is considered. In both corrections, asymmetric interface permeability of a random walker, which comes from ensuring the continuity, causes apparent confinement of the walker in higher-diffusivity layers for benchmark tests on heat diffusion in two-phase multilayered systems. Effective thermal conductivities (walker diffusivities) computed from the trajectories are in excellent agreement with the series and parallel conduction formulas, indicating the equivalence of the two corrections and the importance of ensuring the continuity of a random walk at interfaces.

  15. Validation of a Brazilian Portuguese Version of the Walking Estimated-Limitation Calculated by History (WELCH)

    PubMed Central

    Cucato, Gabriel Grizzo; Correia, Marilia de Almeida; Farah, Breno Quintella; Saes, Glauco Fernandes; Lima, Aluísio Henrique de Andrade; Ritti-Dias, Raphael Mendes; Wolosker, Nelson

    2016-01-01

    Background The Walking Estimated-Limitation Calculated by History (WELCH) questionnaire has been proposed to evaluate walking impairment in patients with intermittent claudication (IC), presenting satisfactory psychometric properties. However, a Brazilian Portuguese version of the questionnaire is unavailable, limiting its application in Brazilian patients. Objective To analyze the psychometric properties of a translated Brazilian Portuguese version of the WELCH in Brazilian patients with IC. Methods Eighty-four patients with IC participated in the study. After translation and back-translation, carried out by two independent translators, the concurrent validity of the WELCH was analyzed by correlating the questionnaire scores with the walking capacity assessed with the Gardner treadmill test. To determine the reliability of the WELCH, internal consistency and test-retest reliability with a seven-day interval between the two questionnaire applications were calculated. Results There were significant correlations between the WELCH score and the claudication onset distance (r = 0.64, p = 0.01) and total walking distance (r = 0.61, p = 0.01). The internal consistency was 0.84 and the intraclass correlation coefficient between questionnaire evaluations was 0.84. There were no differences in WELCH scores between the two questionnaire applications. Conclusion The Brazilian Portuguese version of the WELCH presents adequate validity and reliability indicators, which support its application to Brazilian patients with IC. PMID:26647720

  16. Validity of four gait models to estimate walked distance from vertical COG acceleration.

    PubMed

    Lopez, Antonio M; Alvarez, Diego; Gonzalez, Rafael C; Alvarez, Juan C

    2008-11-01

    Pedometers are basically step counters usually used to estimate the distance walked by a pedestrian. Although their precision to compute the number of steps is quite accurate (about 1%), their feasibility to estimate the walked distance is very poor, as they do not consider the intrinsic variability of human gait. Reported results show values of 10% of precision in optimal conditions, increasing to 50% when conditions differ. Electronic accelerometer-based pedometers base their functioning on a basic processing of the vertical acceleration of the waist. Recently, different approaches have been proposed to relate such signals to the step length. This can lead to an improvement of the performance of this kind of device for estimating the walked distance. In this article, we analyze four gait models applied to the vertical accelerations of the body's center of gravity, three biomechanical and one empirical. We compare their precision and accuracy. Results support the superior performance of three of them over an ideal pedometer. We also analyze their feasibility to be implemented in pedometer-like devices.

  17. The survival probability of a branching random walk in presence of an absorbing wall

    NASA Astrophysics Data System (ADS)

    Derrida, B.; Simon, D.

    2007-06-01

    A branching random walk in presence of an absorbing wall moving at a constant velocity v undergoes a phase transition as v varies. The problem can be analyzed using the properties of the Fisher-Kolmogorov-Petrovsky-Piscounov (F-KPP) equation. We find that the survival probability of the branching random walk vanishes at a critical velocity vc of the wall with an essential singularity and we characterize the divergences of the relaxation times for vvc. At v=vc the survival probability decays like a stretched exponential. Using the F-KPP equation, one can also calculate the distribution of the population size at time t conditioned by the survival of one individual at a later time T>t. Our numerical results indicate that the size of the population diverges like the exponential of (vc-v)-1/2 in the quasi-stationary regime below vc. Moreover for v>vc, our data indicate that there is no quasi-stationary regime.

  18. BRWLDA: bi-random walks for predicting lncRNA-disease associations

    PubMed Central

    Yu, Guoxian; Fu, Guangyuan; Lu, Chang; Ren, Yazhou; Wang, Jun

    2017-01-01

    Increasing efforts have been done to figure out the association between lncRNAs and complex diseases. Many computational models construct various lncRNA similarity networks, disease similarity networks, along with known lncRNA-disease associations to infer novel associations. However, most of them neglect the structural difference between lncRNAs network and diseases network, hierarchical relationships between diseases and pattern of newly discovered associations. In this study, we developed a model that performs Bi-Random Walks to predict novel LncRNA-Disease Associations (BRWLDA in short). This model utilizes multiple heterogeneous data to construct the lncRNA functional similarity network, and Disease Ontology to construct a disease network. It then constructs a directed bi-relational network based on these two networks and available lncRNAs-disease associations. Next, it applies bi-random walks on the network to predict potential associations. BRWLDA achieves reliable and better performance than other comparing methods not only on experiment verified associations, but also on the simulated experiments with masked associations. Case studies further demonstrate the feasibility of BRWLDA in identifying new lncRNA-disease associations.

  19. BRWLDA: bi-random walks for predicting lncRNA-disease associations.

    PubMed

    Yu, Guoxian; Fu, Guangyuan; Lu, Chang; Ren, Yazhou; Wang, Jun

    2017-09-01

    Increasing efforts have been done to figure out the association between lncRNAs and complex diseases. Many computational models construct various lncRNA similarity networks, disease similarity networks, along with known lncRNA-disease associations to infer novel associations. However, most of them neglect the structural difference between lncRNAs network and diseases network, hierarchical relationships between diseases and pattern of newly discovered associations. In this study, we developed a model that performs Bi-Random Walks to predict novel LncRNA-Disease Associations (BRWLDA in short). This model utilizes multiple heterogeneous data to construct the lncRNA functional similarity network, and Disease Ontology to construct a disease network. It then constructs a directed bi-relational network based on these two networks and available lncRNAs-disease associations. Next, it applies bi-random walks on the network to predict potential associations. BRWLDA achieves reliable and better performance than other comparing methods not only on experiment verified associations, but also on the simulated experiments with masked associations. Case studies further demonstrate the feasibility of BRWLDA in identifying new lncRNA-disease associations.

  20. Random walk theory of a trap-controlled hopping transport process

    PubMed Central

    Scher, H.; Wu, C. H.

    1981-01-01

    A random walk theory of hopping motion in the presence of a periodic distribution of traps is presented. The solution of the continuous-time random walk equations is exact and valid for arbitrary intersite interactions and trap concentration. The treatment is shown to be equivalent to an exact solution of the master equation for this trapping problem. These interactions can be a general function of electric field and are not restricted to nearest neighbors. In particular, with the inclusion of trap-to-trap interactions, as well as trap-to-host interactions, an exact treatment of the change from one hopping channel to another has been obtained. The trap-modulated propagator has been derived in terms of a type of Green's function that is introduced. The results are specialized to spatial moments of the propagator, from which expressions for the drift velocity and diffusion coefficient are obtained. Numerical results for the drift velocity are presented and shown to account for the change in hopping channels in recent transport measurements in mixed molecularly doped polymers. PMID:16592944

  1. IRWRLDA: improved random walk with restart for lncRNA-disease association prediction

    PubMed Central

    Chen, Xing; You, Zhu-Hong; Yan, Gui-Ying; Gong, Dun-Wei

    2016-01-01

    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. PMID:27517318

  2. Seed-weighted random walk ranking for cancer biomarker prioritisation: a case study in leukaemia.

    PubMed

    Huan, Tianxiao; Wu, Xiaogang; Bai, Zengliang; Chen, Jake Y

    2014-01-01

    A central focus of clinical proteomics for cancer is to identify protein biomarkers with diagnostic and therapeutic application potential. Network-based analyses have been used in computational disease-related gene prioritisation for several years. The Random Walk Ranking (RWR) algorithm has been successfully applied to prioritising disease-related gene candidates by exploiting global network topology in a Protein-Protein Interaction (PPI) network. Increasing the specificity and sensitivity ofbiomarkers may require consideration of similar or closely-related disease phenotypes and molecular pathological mechanisms shared across different disease phenotypes. In this paper, we propose a method called Seed-Weighted Random Walk Ranking (SW-RWR) for prioritizing cancer biomarker candidates. This method uses the information of cancer phenotype association to assign to each gene a disease-specific, weighted value to guide the RWR algorithm in a global human PPI network. In a case study of prioritizing leukaemia biomarkers, SW-RWR outperformed a typical local network-based analysis in coverage and also showed better accuracy and sensitivity than the original RWR method (global network-based analysis). Our results suggest that the tight correlation among different cancer phenotypes could play an important role in cancer biomarker discovery.

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

    PubMed

    Lv, Chao; Zheng, Lianqing; Yang, Wei

    2012-01-28

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

  4. Random Walks on Digraphs, the Generalized Digraph Laplacian and the Degree of Asymmetry

    NASA Astrophysics Data System (ADS)

    Li, Yanhua; Zhang, Zhi-Li

    In this paper we extend and generalize the standard random walk theory (or spectral graph theory) on undirected graphs to digraphs. In particular, we introduce and define a (normalized) digraph Laplacian matrix, and prove that 1) its Moore-Penrose pseudo-inverse is the (discrete) Green's function of the digraph Laplacian matrix (as an operator on digraphs), and 2) it is the normalized fundamental matrix of the Markov chain governing random walks on digraphs. Using these results, we derive new formula for computing hitting and commute times in terms of the Moore-Penrose pseudo-inverse of the digraph Laplacian, or equivalently, the singular values and vectors of the digraph Laplacian. Furthermore, we show that the Cheeger constant defined in [6] is intrinsically a quantity associated with undirected graphs. This motivates us to introduce a metric - the largest singular value of Δ:=(tilde{\\cal L}-tilde{\\cal L}^T)/2 - to quantify and measure the degree of asymmetry in a digraph. Using this measure, we establish several new results, such as a tighter bound (than that of Fill's in [9] and Chung's in [6]) on the Markov chain mixing rate, and a bound on the second smallest singular value of tilde{\\cal L}.

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

    NASA Astrophysics Data System (ADS)

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

    2013-10-01

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

  6. The continuous time random walk, still trendy: fifty-year history, state of art and outlook

    NASA Astrophysics Data System (ADS)

    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 [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.

  7. Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?

    NASA Astrophysics Data System (ADS)

    Czégel, Dániel; Palla, Gergely

    2015-12-01

    Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or connections between the fundamental units of the studied system. Although a number of notable methods are already available, their vast majority is treating all directed acyclic graphs as already maximally hierarchical. Here we propose a hierarchy measure based on random walks on the network. The novelty of our approach is that directed trees corresponding to multi level pyramidal structures obtain higher hierarchy scores compared to directed chains and directed stars. Furthermore, in the thermodynamic limit the hierarchy measure of regular trees is converging to a well defined limit depending only on the branching number. When applied to real networks, our method is computationally very effective, as the result can be evaluated with arbitrary precision by subsequent multiplications of the transition matrix describing the random walk process. In addition, the tests on real world networks provided very intuitive results, e.g., the trophic levels obtained from our approach on a food web were highly consistent with former results from ecology.

  8. Phylogeography Takes a Relaxed Random Walk in Continuous Space and Time

    PubMed Central

    Lemey, Philippe; Rambaut, Andrew; Welch, John J.; Suchard, Marc A.

    2010-01-01

    Research aimed at understanding the geographic context of evolutionary histories is burgeoning across biological disciplines. Recent endeavors attempt to interpret contemporaneous genetic variation in the light of increasingly detailed geographical and environmental observations. Such interest has promoted the development of phylogeographic inference techniques that explicitly aim to integrate such heterogeneous data. One promising development involves reconstructing phylogeographic history on a continuous landscape. Here, we present a Bayesian statistical approach to infer continuous phylogeographic diffusion using random walk models while simultaneously reconstructing the evolutionary history in time from molecular sequence data. Moreover, by accommodating branch-specific variation in dispersal rates, we relax the most restrictive assumption of the standard Brownian diffusion process and demonstrate increased statistical efficiency in spatial reconstructions of overdispersed random walks by analyzing both simulated and real viral genetic data. We further illustrate how drawing inference about summary statistics from a fully specified stochastic process over both sequence evolution and spatial movement reveals important characteristics of a rabies epidemic. Together with recent advances in discrete phylogeographic inference, the continuous model developments furnish a flexible statistical framework for biogeographical reconstructions that is easily expanded upon to accommodate various landscape genetic features. PMID:20203288

  9. Three-dimensional cell migration does not follow a random walk.

    PubMed

    Wu, Pei-Hsun; Giri, Anjil; Sun, Sean X; Wirtz, Denis

    2014-03-18

    Cell migration through 3D extracellular matrices is critical to the normal development of tissues and organs and in disease processes, yet adequate analytical tools to characterize 3D migration are lacking. Here, we quantified the migration patterns of individual fibrosarcoma cells on 2D substrates and in 3D collagen matrices and found that 3D migration does not follow a random walk. Both 2D and 3D migration features a non-Gaussian, exponential mean cell velocity distribution, which we show is primarily a result of cell-to-cell variations. Unlike in the 2D case, 3D cell migration is anisotropic: velocity profiles display different speed and self-correlation processes in different directions, rendering the classical persistent random walk (PRW) model of cell migration inadequate. By incorporating cell heterogeneity and local anisotropy to the PRW model, we predict 3D cell motility over a wide range of matrix densities, which identifies density-independent emerging migratory properties. This analysis also reveals the unexpected robust relation between cell speed and persistence of migration over a wide range of matrix densities.

  10. The relative importance of directional change, random walks, and stasis in the evolution of fossil lineages.

    PubMed

    Hunt, Gene

    2007-11-20

    The nature of evolutionary changes recorded by the fossil record has long been controversial, with particular disagreement concerning the relative frequency of gradual change versus stasis within lineages. Here, I present a large-scale, statistical survey of evolutionary mode in fossil lineages. Over 250 sequences of evolving traits were fit by using maximum likelihood to three evolutionary models: directional change, random walk, and stasis. Evolution in these traits was rarely directional; in only 5% of fossil sequences was directional evolution the most strongly supported of the three modes of change. The remaining 95% of sequences were divided nearly equally between random walks and stasis. Variables related to body size were significantly less likely than shape traits to experience stasis. This finding is in accord with previous suggestions that size may be more evolutionarily labile than shape and is consistent with some but not all of the mechanisms proposed to explain evolutionary stasis. In general, similar evolutionary patterns are observed across other variables, such as clade membership and temporal resolution, but there is some evidence that directional change in planktonic organisms is more frequent than in benthic organisms. The rarity with which directional evolution was observed in this study corroborates a key claim of punctuated equilibria and suggests that truly directional evolution is infrequent or, perhaps more importantly, of short enough duration so as to rarely register in paleontological sampling.

  11. Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?

    PubMed Central

    Czégel, Dániel; Palla, Gergely

    2015-01-01

    Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or connections between the fundamental units of the studied system. Although a number of notable methods are already available, their vast majority is treating all directed acyclic graphs as already maximally hierarchical. Here we propose a hierarchy measure based on random walks on the network. The novelty of our approach is that directed trees corresponding to multi level pyramidal structures obtain higher hierarchy scores compared to directed chains and directed stars. Furthermore, in the thermodynamic limit the hierarchy measure of regular trees is converging to a well defined limit depending only on the branching number. When applied to real networks, our method is computationally very effective, as the result can be evaluated with arbitrary precision by subsequent multiplications of the transition matrix describing the random walk process. In addition, the tests on real world networks provided very intuitive results, e.g., the trophic levels obtained from our approach on a food web were highly consistent with former results from ecology. PMID:26657012

  12. Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?

    PubMed

    Czégel, Dániel; Palla, Gergely

    2015-12-10

    Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or connections between the fundamental units of the studied system. Although a number of notable methods are already available, their vast majority is treating all directed acyclic graphs as already maximally hierarchical. Here we propose a hierarchy measure based on random walks on the network. The novelty of our approach is that directed trees corresponding to multi level pyramidal structures obtain higher hierarchy scores compared to directed chains and directed stars. Furthermore, in the thermodynamic limit the hierarchy measure of regular trees is converging to a well defined limit depending only on the branching number. When applied to real networks, our method is computationally very effective, as the result can be evaluated with arbitrary precision by subsequent multiplications of the transition matrix describing the random walk process. In addition, the tests on real world networks provided very intuitive results, e.g., the trophic levels obtained from our approach on a food web were highly consistent with former results from ecology.

  13. Mean first passage time for random walk on dual structure of dendrimer

    NASA Astrophysics Data System (ADS)

    Li, Ling; Guan, Jihong; Zhou, Shuigeng

    2014-12-01

    The random walk approach has recently been widely employed to study the relations between the underlying structure and dynamic of complex systems. The mean first-passage time (MFPT) for random walks is a key index to evaluate the transport efficiency in a given system. In this paper we study analytically the MFPT in a dual structure of dendrimer network, Husimi cactus, which has different application background and different structure (contains loops) from dendrimer. By making use of the iterative construction, we explicitly determine both the partial mean first-passage time (PMFT, the average of MFPTs to a given target) and the global mean first-passage time (GMFT, the average of MFPTs over all couples of nodes) on Husimi cactus. The obtained closed-form results show that PMFPT and EMFPT follow different scaling with the network order, suggesting that the target location has essential influence on the transport efficiency. Finally, the impact that loop structure could bring is analyzed and discussed.

  14. Random-walk mobility analysis of Lisbon's plans for the post-1755 reconstruction

    NASA Astrophysics Data System (ADS)

    de Sampayo, Mafalda Teixeira; Sousa-Rodrigues, David

    2016-11-01

    The different options for the reconstruction of the city of Lisbon in the aftermath of the 1755 earthquake are studied with an agent-based model based on randomwalks. This method gives a comparative quantitative measure of mobility of the circulation spaces within the city. The plans proposed for the city of Lisbon signified a departure from the medieval mobility city model. The intricacy of the old city circulation spaces is greatly reduced in the new plans and the mobility between different areas is substantially improved. The simulation results of the random-walk model show that those plans keeping the main force lines of the old city presented less improvement in terms ofmobility. The plans that had greater design freedom were, by contrast, easier to navigate. Lisbon's reconstruction followed a plan that included a shift in the traditional notions of mobility. This affected the daily lives of its citizens by potentiating an easy access to the waterfront, simplifying orientation and navigability. Using the random-walk model it is shown how to quantitatively measure the potential that synthetic plans have in terms of the permeability and navigability of different city public spaces.

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

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

  16. Random walk particle tracking simulations of non-Fickian transport in heterogeneous media

    SciTech Connect

    Srinivasan, G. Tartakovsky, D.M. Dentz, M. Viswanathan, H.; Berkowitz, B.; Robinson, B.A.

    2010-06-01

    Derivations of continuum nonlocal models of non-Fickian (anomalous) transport require assumptions that might limit their applicability. We present a particle-based algorithm, which obviates the need for many of these assumptions by allowing stochastic processes that represent spatial and temporal random increments to be correlated in space and time, be stationary or non-stationary, and to have arbitrary distributions. The approach treats a particle trajectory as a subordinated stochastic process that is described by a set of Langevin equations, which represent a continuous time random walk (CTRW). Convolution-based particle tracking (CBPT) is used to increase the computational efficiency and accuracy of these particle-based simulations. The combined CTRW-CBPT approach enables one to convert any particle tracking legacy code into a simulator capable of handling non-Fickian transport.

  17. Random-Walk Monte Carlo Simulation of Intergranular Gas Bubble Nucleation in UO2 Fuel

    SciTech Connect

    Yongfeng Zhang; Michael R. Tonks; S. B. Biner; D.A. Andersson

    2012-11-01

    Using a random-walk particle algorithm, we investigate the clustering of fission gas atoms on grain bound- aries in oxide fuels. The computational algorithm implemented in this work considers a planar surface representing a grain boundary on which particles appear at a rate dictated by the Booth flux, migrate two dimensionally according to their grain boundary diffusivity, and coalesce by random encounters. Specifically, the intergranular bubble nucleation density is the key variable we investigate using a parametric study in which the temperature, grain boundary gas diffusivity, and grain boundary segregation energy are varied. The results reveal that the grain boundary bubble nucleation density can vary widely due to these three parameters, which may be an important factor in the observed variability in intergranular bubble percolation among grain boundaries in oxide fuel during fission gas release.

  18. SLE on Doubly-Connected Domains and the Winding of Loop-Erased Random Walks

    NASA Astrophysics Data System (ADS)

    Hagendorf, Christian; Le Doussal, Pierre

    2008-10-01

    Two-dimensional loop-erased random walks (LERWs) are random planar curves whose scaling limit is known to be a Schramm-Loewner evolution SLE κ with parameter κ=2. In this note, some properties of an SLE κ trace on doubly-connected domains are studied and a connection to passive scalar diffusion in a Burgers flow is emphasised. In particular, the endpoint probability distribution and winding probabilities for SLE2 on a cylinder, starting from one boundary component and stopped when hitting the other, are found. A relation of the result to conditioned one-dimensional Brownian motion is pointed out. Moreover, this result permits to study the statistics of the winding number for SLE2 with fixed endpoints. A solution for the endpoint distribution of SLE4 on the cylinder is obtained and a relation to reflected Brownian motion pointed out.

  19. From randomly accelerated particles to Lévy walks: non-ergodic behavior and aging

    NASA Astrophysics Data System (ADS)

    Radons, Guenter; Albers, Tony; Institute of Physics, Complex Systems; Nonlinear Dynamics Team

    For randomly accelerated particles we detected, and were able to analyze in detail (PRL 113, 184101 (2014)), the phenomenon of weak-ergodicity breaking (WEB), i.e. the inequivalence of ensemble- and time-averaged mean-squared displacements (MSD). These results, including their aging time dependence, are relevant for anomalous chaotic diffusion in Hamiltonian systems, for passive tracer transport in turbulent flows, and many other systems showing momentum diffusion. There are, however, several related models, such as the integrated random excursion model, or, space-time correlated Lévy walks and flights, with similar statistical behavior. We compare the WEB related properties of these models and find surprising differences although, for equivalent parameters, all of them are supposed to lead to the same ensemble-averaged MSD. Our findings are relevant for distinguishing possible models for the anomalous diffusion occurring in experimental situations.

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

    NASA Astrophysics Data System (ADS)

    Thiel, Felix; Sokolov, Igor M.

    2016-07-01

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

  1. Scaling Behavior of the First Arrival Time of a Random-Walking Magnetic Domain

    SciTech Connect

    Im, M.-Y.; Lee, S.-H.; Kim, D.-H.; Fischer, P.; Shin, S.-C.

    2008-02-04

    We report a universal scaling behavior of the first arrival time of a traveling magnetic domain wall into a finite space-time observation window of a magneto-optical microscope enabling direct visualization of a Barkhausen avalanche in real time. The first arrival time of the traveling magnetic domain wall exhibits a nontrivial fluctuation and its statistical distribution is described by universal power-law scaling with scaling exponents of 1.34 {+-} 0.07 for CoCr and CoCrPt films, despite their quite different domain evolution patterns. Numerical simulation of the first arrival time with an assumption that the magnetic domain wall traveled as a random walker well matches our experimentally observed scaling behavior, providing an experimental support for the random-walking model of traveling magnetic domain walls.

  2. Equations for the distributions of functionals of a random-walk trajectory in an inhomogeneous medium

    SciTech Connect

    Shkilev, V. P.

    2012-01-15

    Based on the random-trap model and using the mean-field approximation, we derive an equation that allows the distribution of a functional of the trajectory of a particle making random walks over inhomogeneous-lattice site to be calculated. The derived equation is a generalization of the Feynman-Kac equation to an inhomogeneous medium. We also derive a backward equation in which not the final position of the particle but its position at the initial time is used as an independent variable. As an example of applying the derived equations, we consider the one-dimensional problem of calculating the first-passage time distribution. We show that the average first-passage times for homogeneous and inhomogeneous media with identical diffusion coefficients coincide, but the variance of the distribution for an inhomogeneous medium can be many times larger than that for a homogeneous one.

  3. Pearson's random walk in the space of the CMB phases: Evidence for parity asymmetry

    SciTech Connect

    Hansen, M.; Frejsel, A. M.; Kim, J.; Naselsky, P.; Nesti, F.

    2011-05-15

    The temperature fluctuations of the cosmic microwave background (CMB) are supposed to be distributed randomly in both magnitude and phase, following to the simplest model of inflation. In this paper, we look at the odd and even multipoles of the spherical harmonic decomposition of the CMB, and the different characteristics of these, giving rise to a parity asymmetry. We compare the even and odd multipoles in the CMB power spectrum, and also the even and odd mean angles. We find for the multipoles of the power spectrum that there is power excess in odd multipoles, compared to even ones, meaning that we have a parity asymmetry. Further, for the phases, we present a random walk for the mean angles, and find a significant separation for even/odd mean angles, especially so for galactic coordinates. This is further tested and confirmed with a directional parity test, comparing the parity asymmetry in galactic and ecliptic coordinates.

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

    NASA Astrophysics Data System (ADS)

    Juhász, Róbert

    2014-03-01

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

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

    NASA Astrophysics Data System (ADS)

    Zhou, Haijun

    2010-02-01

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

  6. The effect of an arm sling on energy consumption while walking in hemiplegic patients: a randomized comparison

    PubMed Central

    Han, Seung Hoon; Kim, Taikon; Jang, Seong Ho; Kim, Mi Jung; Park, Si-bog; Yoon, Seoung Ic; Choi, Bong-Kun; Lee, Michael Y

    2011-01-01

    Objective: To evaluate the effect of an arm sling on gait speed and energy efficiency of patients with hemiplegia. Design: A randomized crossover design. Setting: A rehabilitation department of a university hospital. Subjects: Thirty-seven outpatients with hemiplegia were included in this study. Interventions: All patients walked on a 20-m walkway twice on the same day, randomly with and without an arm sling, at a self selected speed. Main measures: The heart rate, gait speed, oxygen cost and oxygen rate were measured on all patients. We analysed all values with and without an arm sling and also compared them after all patients being stratified according to demographic and clinical characteristics. Results: When we compared the heart rate between walking with (90.7 ± 17.2 beats/min) and without (91.2 ± 18.6 beats/min) the arm sling, it was significantly decreased while walking with the arm sling. When we compared the gait speed between walking with (32.8 m/min) and without (30.1 m/min), it was significantly increased with the arm sling walking. The O2 rate in hemiplegic patients walking with the arm sling was significantly decreased by 7%, compared to walking without arm sling (5.8 mL/kg min and 6.2 mL/kg min, respectively). The O2 cost in hemiplegic patients walking without arm sling was significantly 1.4 times greater than walking with it (0.2 mL/kg m and 0.3 mL/kg m, respectively). Conclusion: An arm sling can be used to improve the gait efficiency. PMID:21059662

  7. Effect of Body Weight-supported Walking on Exercise Capacity and Walking Speed in Patients with Knee Osteoarthritis: A Randomized Controlled Trial.

    PubMed

    Watanabe, Shinichi; Someya, Fujiko

    2013-01-01

    To compare the effect of body-weight-supported treadmill training (BWSTT) and full-body-weight treadmill training (FBWTT) on patients with knee osteoarthritis (OA). Design was Randomized controlled trial. Patients with knee osteoarthritis (n = 30; mean age, 76.0±7.5 y) were randomly assigned to BWSTT or FBWTT group. All patients performed 20 min walking exercise twice a week for 6 weeks under the supervision of the therapist. Main measures were 10-meter walking test (10MWT), functional reach test (FRT), timed get up and go test (TUG), one-leg standing test, 6-minute walking test (6MWT), the parameters set on the treadmill, MOS Short-Form 36-Item Health Survey (SF36), Japanese Knee Osteoarthritis Measure (JKOM). Twenty-five patients (10 men, 15 women; mean age, 76.5 ± 8.0 y) completed the experiment. Exercise capacity, indicated by the heart rate, was similar in both groups. After 3 weeks of BWSTT, the patients performed significantly better in the 10-m and 6-min walking tests. This was not the case with FBWTT even after 6 weeks training. Pain levels assessed were significantly improved after 3 weeks of BWSTT and 6 weeks of FBWTT. There were no significant improvements in either group assessed by the FRT, one-leg standing time test, TUG, or SF -36 questionnaire. BWSTT enhanced exercise capacity in terms of walking speed and pain reduction after 3 weeks; however, there was no significant improvement in patients' functional abilities or quality of life.

  8. Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach

    NASA Astrophysics Data System (ADS)

    Bauer, Frank; Lizier, Joseph T.

    2012-09-01

    We introduce a new method to efficiently approximate the number of infections resulting from a given initially infected node in a network of susceptible individuals. Our approach is based on counting the number of possible infection walks of various lengths to each other node in the network. We analytically study the properties of our method, in particular demonstrating different forms for SIS and SIR disease spreading (e.g., under the SIR model our method counts self-avoiding walks). In comparison to existing methods to infer the spreading efficiency of different nodes in the network (based on degree, k-shell decomposition analysis and different centrality measures), our method directly considers the spreading process and, as such, is unique in providing estimation of actual numbers of infections. Crucially, in simulating infections on various real-world networks with the SIR model, we show that our walks-based method improves the inference of the effectiveness of nodes over a wide range of infection rates compared to existing methods. We also analyse the trade-off between estimate accuracy and computational cost, showing that the better accuracy here can still be obtained at a comparable computational cost to other methods.

  9. The brain weights body-based cues higher than vision when estimating walked distances.

    PubMed

    Campos, Jennifer L; Byrne, Patrick; Sun, Hong-Jin

    2010-05-01

    Optic flow is the stream of retinal information generated when an observer's body, head or eyes move relative to their environment, and it plays a defining role in many influential theories of active perception. Traditionally, studies of optic flow have used artificially generated flow in the absence of the body-based cues typically coincident with self-motion (e.g. proprioceptive, efference copy, and vestibular). While optic flow alone can be used to judge the direction, speed and magnitude of self-motion, little is known about the precise extent to which it is used during natural locomotor behaviours such as walking. In this study, walked distances were estimated in an open outdoor environment. This study employed two novel complementary techniques to dissociate the contributions of optic flow from body-based cues when estimating distance travelled in a flat, open, outdoor environment void of distinct proximal visual landmarks. First, lenses were used to magnify or minify the visual environment. Second, two walked distances were presented in succession and were either the same or different in magnitude; vision was either present or absent in each. A computational model was developed based on the results of both experiments. Highly convergent cue-weighting values were observed, indicating that the brain consistently weighted body-based cues about twice as high as optic flow, the combination of the two cues being additive. The current experiments represent some of the first to isolate and quantify the contributions of optic flow during natural human locomotor behaviour.

  10. Dynamically adjustable foot-ground contact model to estimate ground reaction force during walking and running.

    PubMed

    Jung, Yihwan; Jung, Moonki; Ryu, Jiseon; Yoon, Sukhoon; Park, Sang-Kyoon; Koo, Seungbum

    2016-03-01

    Human dynamic models have been used to estimate joint kinetics during various activities. Kinetics estimation is in demand in sports and clinical applications where data on external forces, such as the ground reaction force (GRF), are not available. The purpose of this study was to estimate the GRF during gait by utilizing distance- and velocity-dependent force models between the foot and ground in an inverse-dynamics-based optimization. Ten males were tested as they walked at four different speeds on a force plate-embedded treadmill system. The full-GRF model whose foot-ground reaction elements were dynamically adjusted according to vertical displacement and anterior-posterior speed between the foot and ground was implemented in a full-body skeletal model. The model estimated the vertical and shear forces of the GRF from body kinematics. The shear-GRF model with dynamically adjustable shear reaction elements according to the input vertical force was also implemented in the foot of a full-body skeletal model. Shear forces of the GRF were estimated from body kinematics, vertical GRF, and center of pressure. The estimated full GRF had the lowest root mean square (RMS) errors at the slow walking speed (1.0m/s) with 4.2, 1.3, and 5.7% BW for anterior-posterior, medial-lateral, and vertical forces, respectively. The estimated shear forces were not significantly different between the full-GRF and shear-GRF models, but the RMS errors of the estimated knee joint kinetics were significantly lower for the shear-GRF model. Providing COP and vertical GRF with sensors, such as an insole-type pressure mat, can help estimate shear forces of the GRF and increase accuracy for estimation of joint kinetics. Copyright © 2016 Elsevier B.V. All rights reserved.

  11. Approximation of the Lévy Feller advection dispersion process by random walk and finite difference method

    NASA Astrophysics Data System (ADS)

    Liu, Q.; Liu, F.; Turner, I.; Anh, V.

    2007-03-01

    In this paper we present a random walk model for approximating a Lévy-Feller advection-dispersion process, governed by the Lévy-Feller advection-dispersion differential equation (LFADE). We show that the random walk model converges to LFADE by use of a properly scaled transition to vanishing space and time steps. We propose an explicit finite difference approximation (EFDA) for LFADE, resulting from the Grünwald-Letnikov discretization of fractional derivatives. As a result of the interpretation of the random walk model, the stability and convergence of EFDA for LFADE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

  12. Image Based Location Estimation for Walking Out of Visual Impaired Person.

    PubMed

    Kamasaka, Kazuho; Kitahara, Itaru; Kameda, Yoshinari

    2017-01-01

    A new and intelligent walking navigation system could be helpful for visually impaired people so that they do not need helpers or guide dogs on going out. Conventional navigation systems using GPS are not available indoors or undergrounds. A new location estimation method that is available in such situations is necessary. We propose to estimate pedestrian's location with only a single camera attached to the pedestrian. Our proposed method uses only computer vision and no other sensors are needed. The location estimation is achieved by image retrieval. The retrieval database is built from a pre-recorded video taken along a planned walking path. Simple image retrieval using local image features does not work well when the images were taken in different conditions of time and weather. In this paper, we especially explore robustness for the change of sunlight condition due to its recording time. We propose a new method of robust location estimation based on our database built by combining more than one video that is taken under different conditions. Experiment results showed that the accuracy of the location estimation using the proposed database is better than the one from a conventional database built by using a single video.

  13. Canonical ensemble of particles in a self-avoiding random walk

    NASA Astrophysics Data System (ADS)

    Alkhimov, V. I.

    2017-04-01

    We consider an ensemble of particles not interacting with each other and randomly walking in the d-dimensional Euclidean space ℝ d . The individual moves of each particle are governed by the same distribution, but after the completion of each such move of a particle, its position in the medium is "marked" as a region in the form of a ball of diameter r 0, which is not available for subsequent visits by this particle. As a result, we obtain the corresponding ensemble in ℝ d of marked trajectories in each of which the distance between the centers of any pair of these balls is greater than r 0. We describe a method for computing the asymptotic form of the probability density W n ( r) of the distance r between the centers of the initial and final balls of a trajectory consisting of n individual moves of a particle of the ensemble. The number n, the trajectory modulus, is a random variable in this model in addition to the distance r. This makes it necessary to determine the distribution of n, for which we use the canonical distribution obtained from the most probable distribution of particles in the ensemble over the moduli of their trajectories. Averaging the density W n ( r) over the canonical distribution of the modulus n allows finding the asymptotic behavior of the probability density of the distance r between the ends of the paths of the canonical ensemble of particles in a self-avoiding random walk in ℝ d for 2 ≤ d < 4.

  14. Effects of exercise on brain activity during walking in older adults: a randomized controlled trial.

    PubMed

    Shimada, Hiroyuki; Ishii, Kenji; Makizako, Hyuma; Ishiwata, Kiichi; Oda, Keiichi; Suzukawa, Megumi

    2017-05-30

    Physical activity may preserve neuronal plasticity, increase synapse formation, and cause the release of hormonal factors that promote neurogenesis and neuronal function. Previous studies have reported enhanced neurocognitive function following exercise training. However, the specific cortical regions activated during exercise training remain largely undefined. In this study, we quantitatively and objectively evaluated the effects of exercise on brain activity during walking in healthy older adults. A total of 24 elderly women (75-83 years old) were randomly allocated to either an intervention group or a control group. Those in the intervention group attended 3 months of biweekly 90-min sessions focused on aerobic exercise, strength training, and physical therapy. We monitored changes in regional cerebral glucose metabolism during walking in both groups using positron emission tomography (PET) and [(18)F]fluorodeoxyglucose (FDG). All subjects completed the 3-month experiment and the adherence to the exercise program was 100%. Compared with the control group, the intervention group showed a significantly greater step length in the right foot after 3 months of physical activity. The FDG-PET assessment revealed a significant post-intervention increase in regional glucose metabolism in the left posterior entorhinal cortex, left superior temporal gyrus, and right superior temporopolar area in the intervention group. Interestingly, the control group showed a relative increase in regional glucose metabolism in the left premotor and supplemental motor areas, left and right somatosensory association cortex, and right primary visual cortex after the 3-month period. We found no significant differences in FDG uptake between the intervention and control groups before vs. after the intervention. Exercise training increased activity in specific brain regions, such as the precuneus and entorhinal cortices, which play an important role in episodic and spatial memory. Further

  15. Exact solution for a random walk in a time-dependent 1D random environment: the point-to-point Beta polymer

    NASA Astrophysics Data System (ADS)

    Thiery, Thimothée; Le Doussal, Pierre

    2017-01-01

    We consider the Beta polymer, an exactly solvable model of directed polymer on the square lattice, introduced by Barraquand and Corwin (BC) (2016 Probab. Theory Relat. Fields 1-16). We study the statistical properties of its point to point partition sum. The problem is equivalent to a model of a random walk in a time-dependent (and in general biased) 1D random environment. In this formulation, we study the sample to sample fluctuations of the transition probability distribution function (PDF) of the random walk. Using the Bethe ansatz we obtain exact formulas for the integer moments, and Fredholm determinant formulas for the Laplace transform of the directed polymer partition sum/random walk transition probability. The asymptotic analysis of these formulas at large time t is performed both (i) in a diffusive vicinity, x˜ {{t}1/2} , of the optimal direction (in space-time) chosen by the random walk, where the fluctuations of the PDF are found to be Gamma distributed; (ii) in the large deviations regime, x˜ t , of the random walk, where the fluctuations of the logarithm of the PDF are found to grow with time as t 1/3 and to be distributed according to the Tracy-Widom GUE distribution. Our exact results complement those of BC for the cumulative distribution function of the random walk in regime (ii), and in regime (i) they unveil a novel fluctuation behavior. We also discuss the crossover regime between (i) and (ii), identified as x˜ {{t}3/4} . Our results are confronted to extensive numerical simulations of the model.

  16. Centric rings, acentric rings and excess acentric fragments based on a random-walk interphase chromosome model

    NASA Technical Reports Server (NTRS)

    Wu, H.; Durante, M.; Sachs, R. K.; Yang, T. C.

    1997-01-01

    Excess acentric fragments, consisting of acentric rings and acentric linear fragments, are among the most frequent kinds of chromosome-type aberrations produced by radiation. The frequency of acentric rings cannot be obtained directly by experiment but is estimated here from the ratio of acentric to centric rings, evaluated using a random-walk model for the organization of chromatin during interphase and an assumption that the probability of an exchange formation is proportional to the rate of collision between two DSB. This ratio is calculated to be 2.5 in low-LET irradiated human fibroblasts, significantly greater than the ratio if proximity effects are not considered. The calculated frequency of acentric rings is insufficient to account for all the observed excess acentric fragments. Assuming that the rest of the excess acentric fragments are due to incomplete exchanges, all possible recombinations between two DSB that result in acentric rings and acentric linear fragments have been identified. From the chromosome aberration data, the incompleteness parameter has been estimated. Intra-arm chromosome exchanges, either complete or incomplete, were estimated to account for more than 50% of the excess acentric fragments in human fibroblasts.

  17. Centric rings, acentric rings and excess acentric fragments based on a random-walk interphase chromosome model

    NASA Technical Reports Server (NTRS)

    Wu, H.; Durante, M.; Sachs, R. K.; Yang, T. C.

    1997-01-01

    Excess acentric fragments, consisting of acentric rings and acentric linear fragments, are among the most frequent kinds of chromosome-type aberrations produced by radiation. The frequency of acentric rings cannot be obtained directly by experiment but is estimated here from the ratio of acentric to centric rings, evaluated using a random-walk model for the organization of chromatin during interphase and an assumption that the probability of an exchange formation is proportional to the rate of collision between two DSB. This ratio is calculated to be 2.5 in low-LET irradiated human fibroblasts, significantly greater than the ratio if proximity effects are not considered. The calculated frequency of acentric rings is insufficient to account for all the observed excess acentric fragments. Assuming that the rest of the excess acentric fragments are due to incomplete exchanges, all possible recombinations between two DSB that result in acentric rings and acentric linear fragments have been identified. From the chromosome aberration data, the incompleteness parameter has been estimated. Intra-arm chromosome exchanges, either complete or incomplete, were estimated to account for more than 50% of the excess acentric fragments in human fibroblasts.

  18. Estimation of traversed distance in level walking using a single inertial measurement unit attached to the waist.

    PubMed

    Kose, Alper; Cereatti, Andrea; Della Croce, Ugo

    2011-01-01

    A method for estimating step length during level walking using a single inertial measurement unit is proposed. A combination of an optimally filtered direct and reverse integration technique and a velocity update technique for the initial velocity values identification was implemented to reduce the effects of the acceleration signals drift. The method takes advantage of the cyclic nature of gait. The inertial measurement unit was placed at waist level on the right side and the method was validated on eight subjects walking for 75 m while varying their speed. The traversed distance was estimated with an average error equal to 0.8% of the total walking distance.

  19. SPARSE: Seed Point Auto-Generation for Random Walks Segmentation Enhancement in medical inhomogeneous targets delineation of morphological MR and CT images.

    PubMed

    Chen, Haibin; Zhen, Xin; Gu, Xuejun; Yan, Hao; Cervino, Laura; Xiao, Yang; Zhou, Linghong

    2015-03-08

    In medical image processing, robust segmentation of inhomogeneous targets is a challenging problem. Because of the complexity and diversity in medical images, the commonly used semiautomatic segmentation algorithms usually fail in the segmentation of inhomogeneous objects. In this study, we propose a novel algorithm imbedded with a seed point autogeneration for random walks segmentation enhancement, namely SPARSE, for better segmentation of inhomogeneous objects. With a few user-labeled points, SPARSE is able to generate extended seed points by estimating the probability of each voxel with respect to the labels. The random walks algorithm is then applied upon the extended seed points to achieve improved segmentation result. SPARSE is implemented under the compute unified device architecture (CUDA) programming environment on graphic processing unit (GPU) hardware platform. Quantitative evaluations are performed using clinical homogeneous and inhomogeneous cases. It is found that the SPARSE can greatly decrease the sensitiveness to initial seed points in terms of location and quantity, as well as the freedom of selecting parameters in edge weighting function. The evaluation results of SPARSE also demonstrate substantial improvements in accuracy and robustness to inhomogeneous target segmentation over the original random walks algorithm.

  20. A comparison of robotic walking therapy and conventional walking therapy in individuals with upper versus lower motor neuron lesions: a randomized controlled trial.

    PubMed

    Esclarín-Ruz, Ana; Alcobendas-Maestro, Monica; Casado-Lopez, Rosa; Perez-Mateos, Guillermo; Florido-Sanchez, Miguel Angel; Gonzalez-Valdizan, Esteban; Martin, Jose Luis R

    2014-06-01

    To compare a walking reeducation program with robotic locomotor training plus overground therapy (LKOGT) to conventional overground training (OGT) in individuals with incomplete upper motor neuron (UMN) or lower motor neuron (LMN) injuries having either traumatic or nontraumatic nonprogressive etiology. Randomized open controlled trial with blind evaluation by an independent observer. An inpatient spinal cord injury rehabilitation center. A total of 88 adults within 6 months of spinal cord injury onset (group A, 44 with UMN injury, and group B, 44 with LMN injury) were graded on the American Spinal Injury Association Impairment Scale as C or D. Each of these groups was then randomly allocated to conditions 1 or 2. Condition 1: Subgroups A1 and B1 were treated with LKOGT for 60 minutes. Condition 2: Subgroups A2 and B2 received 60 minutes of conventional OGT 5 days per week for 8 weeks. Subjects with UMN and LMN were randomized into 2 training groups. Ten-meter walk test and 6-minute walk test (6MWT). Walking Index for Spinal Cord Injury II, lower extremity motor score (LEMS), and the FIM-Locomotor were secondary outcome measures. By using the LKOGT program compared with OGT, we found significant differences in the 6MWT for groups A1 and B1. LKOGT also provided higher scores than did OGT in secondary outcomes such as the LEMS and the FIM-Locomotor. Robotic-assisted step training yielded better results in the 6MWT and the LEMS in patients with UMN and LMN. Copyright © 2014 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

  1. Body weight supported treadmill training versus traditional training in patients dependent on walking assistance after stroke: a randomized controlled trial.

    PubMed

    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.

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

    PubMed

    Reuveni, Shlomi; Granek, Rony; Klafter, Joseph

    2010-10-01

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

  3. Collapse transition of a hydrophobic self-avoiding random walk in a coarse-grained model solvent.

    PubMed

    Gaudreault, Mathieu; Viñals, Jorge

    2009-08-01

    In order to study solvation effects on protein folding, we analyze the collapse transition of a self-avoiding random walk composed of hydrophobic segments that is embedded in a lattice model of a solvent. As expected, hydrophobic interactions lead to an attractive potential of mean force among chain segments. As a consequence, the random walk in solvent undergoes a collapse transition at a higher temperature than in its absence. Chain collapse is accompanied by the formation of a region depleted of solvent around the chain. In our simulation, the depleted region at collapse is as large as our computational domain.

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

    PubMed Central

    Bertrand, Sophie; Joo, Rocío; Fablet, Ronan

    2015-01-01

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

  5. Convex hulls of multiple random walks: A large-deviation study

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

    We study the polygons governing the convex hull of a point set created by the steps of n independent two-dimensional random walkers. Each such walk consists of T discrete time steps, where x and y increments are independent and identically distributed Gaussian. We analyze area A and perimeter L of the convex hulls. We obtain probability densities for these two quantities over a large range of the support by using a large-deviation approach allowing us to study densities below 10-900. We find that the densities exhibit in the limit T →∞ a time-independent scaling behavior as a function of A /T and L /√{T } , respectively. As in the case of one walker (n =1 ), the densities follow Gaussian distributions for L and √{A }, respectively. We also obtained the rate functions for the area and perimeter, rescaled with the scaling behavior of their maximum possible values, and found limiting functions for T →∞ , revealing that the densities follow the large-deviation principle. These rate functions can be described by a power law for n →∞ as found in the n =1 case. We also investigated the behavior of the averages as a function of the number of walks n and found good agreement with the predicted behavior.

  6. Convex hulls of multiple random walks: A large-deviation study.

    PubMed

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

    2016-11-01

    We study the polygons governing the convex hull of a point set created by the steps of n independent two-dimensional random walkers. Each such walk consists of T discrete time steps, where x and y increments are independent and identically distributed Gaussian. We analyze area A and perimeter L of the convex hulls. We obtain probability densities for these two quantities over a large range of the support by using a large-deviation approach allowing us to study densities below 10^{-900}. We find that the densities exhibit in the limit T→∞ a time-independent scaling behavior as a function of A/T and L/sqrt[T], respectively. As in the case of one walker (n=1), the densities follow Gaussian distributions for L and sqrt[A], respectively. We also obtained the rate functions for the area and perimeter, rescaled with the scaling behavior of their maximum possible values, and found limiting functions for T→∞, revealing that the densities follow the large-deviation principle. These rate functions can be described by a power law for n→∞ as found in the n=1 case. We also investigated the behavior of the averages as a function of the number of walks n and found good agreement with the predicted behavior.

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

    PubMed

    Bertrand, Sophie; Joo, Rocío; Fablet, Ronan

    2015-01-01

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

  8. Study protocol of "Worth the Walk": a randomized controlled trial of a stroke risk reduction walking intervention among racial/ethnic minority older adults with hypertension in community senior centers.

    PubMed

    Kwon, Ivy; Choi, Sarah; Mittman, Brian; Bharmal, Nazleen; Liu, Honghu; Vickrey, Barbara; Song, Sarah; Araiza, Daniel; McCreath, Heather; Seeman, Teresa; Oh, Sang-Mi; Trejo, Laura; Sarkisian, Catherine

    2015-06-15

    Stroke disproportionately kills and disables ethnic minority seniors. Up to 30 % of ischemic strokes in the U.S. can be attributed to physical inactivity, yet most Americans, especially older racial/ethnic minorities, fail to participate in regular physical activity. We are conducting a randomized controlled trial (RCT) to test a culturally-tailored community-based walking intervention designed to reduce stroke risk by increasing physical activity among African American, Latino, Chinese, and Korean seniors with hypertension. We hypothesize that the intervention will yield meaningful changes in seniors' walking levels and stroke risk with feasibility to sustain and scale up across the aging services network. In this randomized single-blind wait-list control study, high-risk ethnic minority seniors are enrolled at senior centers, complete baseline data collection, and are randomly assigned to receive the intervention "Worth the Walk" immediately (N = 120, intervention group) or in 90 days upon completion of follow-up data collection (N = 120, control group). Trained case managers employed by the senior centers implement hour-long intervention sessions twice weekly for four consecutive weeks to the intervention group. Research staff blinded to participants' group assignment collect outcome data from both intervention and wait-list control participants 1 and 3-months after baseline data collection. Primary outcome measures are mean steps/day over 7 days, stroke knowledge, and self-efficacy for reducing stroke risk. Secondary and exploratory outcome measures include selected biological markers of health, healthcare seeking, and health-related quality of life. Outcomes will be compared between the two groups using standard analytic methods for randomized trials. We will conduct a formal process evaluation to assess barriers and facilitators to successful integration of Worth the Walk into the aging services network and to calculate estimated costs to sustain

  9. Determining inertial measurement unit placement for estimating human trunk sway while standing, walking and running.

    PubMed

    Bo Yu; Tian Bao; Dingguo Zhang; Carender, Wendy; Sienko, Kathleen H; Shull, Peter B

    2015-08-01

    Inertial measurement units (IMU) are often used to estimate medial-lateral (M/L) trunk sway for assessing and treating gait disorders, and IMU sensor placement is an important factor effecting estimation accuracy. This study tracked multi-segment spine movements during standing and ambulation tasks to determine optimal IMU placement. Ten young healthy subjects, wearing markers placed along the spine, left/right acromion, and left/right posterior superior iliac spine performed standing and walking trials in a motion capture laboratory. Results showed that movement at the spine location T7-T8 most closely matched the clinical definition of M/L trunk sway for standing trials (0.5 deg error) and at the spine location T9-T10 for walking trials (1.0 deg error), while movement at the lower spine L2-L4 tended to be the least accurate for standing and ambulation tasks (1.5 deg error and 4.0 deg error, respectively). Based on these results, a second study was performed to develop and validate a trunk sway estimation algorithm during walking trials with a single optimally-placed IMU. IMU trunk sway estimation was compared to the clinical definition of trunk sway from motion capture markers and showed root-mean-square errors of 2.5 deg and peak trunk sway errors of 2.0 deg. The results of this study suggest that IMUs should be placed on the mid-back to reduce errors associated with spine movements not matching clinically-defined M/L trunk motion.

  10. Hull early walking aid for rehabilitation of transtibial amputees--randomized controlled trial (HEART).

    PubMed

    Mazari, Fayyaz Ali Khan; Mockford, Katherine; Barnett, Cleveland; Khan, Junaid A; Brown, Barbara; Smith, Lynne; Polman, Remco C; Hancock, Amanda; Vanicek, Natalie K; Chetter, Ian C

    2010-12-01

    To compare articulated and nonarticulated early walking aids (EWAs) for clinical and quality-of-life outcomes in transtibial amputees. Patients undergoing lower limb amputation in a tertiary-care vascular surgical unit were screened over a 4-year period. Recruited patients were randomized to receive articulated amputee mobility aid (AMA) or nonarticulated pneumatic postamputation mobility aid (PPAMA) during early rehabilitation. Primary (10-meter walking velocity) and secondary clinical (number and duration of physiotherapy treatments during EWA/prosthesis use) and quality-of-life (SF-36) outcome measures were recorded at five standardized assessment visits. Inter-group and intra-group analyses were performed. Two hundred seventy-two patients were screened and 29 transtibial amputees (median age, 56 years) were recruited (14/treatment arm). No significant difference was seen in demographics and comorbidities at baseline. Inter-group analysis: Median 10-meter walking velocity was significantly (Mann-Whitney, P = .020) faster in the PPAMA group (0.245 m/s, interquartile range [IQR] 0.218-0.402 m/s) compared with the AMA group (0.165 m/s; IQR, 0.118-0.265 m/s) at visit 1. However, there was no difference between the groups at any other visit. Similarly, the number of treatments using EWA was significantly (P = .045) lower in the PPAMA group (5.0; IQR, 3.5-8.0) compared with the AMA group (6.0; IQR, 6.0-10.5). No difference was observed between the groups in duration of physiotherapy or SF-36 domain and summary scores. Intra-group analysis: Both treatment groups showed significant improvement in 10-meter walking velocity (Friedman test; AMA P = .001; PPAMA P = .007); however, other clinical outcomes did not show any statistically significant improvement. Only physical function domain of SF-36 demonstrated significant improvement (Friedman test; AMA P = .037; PPAMA P = .029). There is no difference in clinical and QOL outcomes between articulated and nonarticulated EWAs

  11. A Mixed Methods Randomized Controlled Trial of Financial Incentives and Peer Networks to Promote Walking among Older Adults

    PubMed Central

    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

    2015-01-01

    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 were randomized to weekly feedback only (Comparison), entry into a lottery with potential to earn up to $200 each week walking goals were met (Financial Incentive), linkage to 4 other participants through an online message board (Peer Network), or both interventions (Combined). Main outcomes were the proportion of days walking goals were met during the 16-week intervention and 8-week follow-up. We conducted a content analysis of messages posted by Peer Network and Combined arm participants. Results During the 16-week intervention, there were no differences in the proportion of days walking goals were met in the Financial Incentive (39.7%; P = 0.78), Peer Network (24.9%; P = 0.08), and Combined (36.0%; P = 0.77) arms compared to the Comparison arm (36.0%). During 8 weeks of follow-up, the proportion of days walking goals were met was lower in the Peer Network arm (18.7%; P = 0.025), but not in the Financial Incentive (29.3%; P = 0.50) or Combined (24.8%; P = 0.37) arms, relative to the Comparison arm (34.5%). Messages posted by participants focused on barriers to walking and provision of social support. Conclusions Financial incentives and peer networks delivered through eHealth technologies did not result in older adults walking more. PMID:25274710

  12. On the temporal order of first-passage times in one-dimensional lattice random walks

    NASA Astrophysics Data System (ADS)

    Sanders, J. B.; Temme, N. M.

    2005-10-01

    A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing modified Bessel functions of the first kind. By using several transformations, simpler integrals are obtained from which for two and three particles asymptotic approximations are derived for large values of the parameters. Expressions of the probability for n particles are also derived.I returned and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all. George Orwell, Politics and the English Language, Selected Essays, Penguin Books, 1957. (The citation is from Ecclesiastes 9:11.)

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

    NASA Astrophysics Data System (ADS)

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

    2013-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2009-10-01

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

  15. RecRWR: a recursive random walk method for improved identification of diseases.

    PubMed

    Arrais, Joel Perdiz; Oliveira, José Luís

    2015-01-01

    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.

  16. Random walk in nonhomogeneous environments: A possible approach to human and animal mobility

    NASA Astrophysics Data System (ADS)

    Srokowski, Tomasz

    2017-03-01

    The random walk process in a nonhomogeneous medium, characterized by a Lévy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is affected by the variable width and the variance may be finite; then all kinds of the anomalous diffusion are predicted. In the former case, only the time characteristics are sensitive to the variable width. The corresponding Langevin equation with different interpretations of the multiplicative noise is discussed. The dependence of the distribution width on position after jump is interpreted in terms of cognitive abilities and related to such problems as migration in a human population and foraging habits of animals.

  17. Random walks with efficient search and contextually adapted image similarity for deformable registration.

    PubMed

    Tang, Lisa Y W; Hamarneh, Ghassan

    2013-01-01

    We develop a random walk-based image registration method that incorporates two novelties: 1) a progressive optimization scheme that conducts the solution search efficiently via a novel use of information derived from the obtained probabilistic solution, and 2) a data-likelihood re-weighting step that contextually performs feature selection in a spatially adaptive manner so that the data costs are based primarily on trusted information sources. Synthetic experiments on three public datasets of different anatomical regions and modalities showed that our method performed efficient search without sacrificing registration accuracy. Experiments performed on 60 real brain image pairs from a public dataset also demonstrated our method's better performance over existing non-probabilistic image registration methods.

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

    NASA Astrophysics Data System (ADS)

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

    2011-06-01

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

  19. Modeling spreading of oil slicks based on random walk methods and Voronoi diagrams.

    PubMed

    Durgut, İsmail; Reed, Mark

    2017-02-19

    We introduce a methodology for representation of a surface oil slick using a Voronoi diagram updated at each time step. The Voronoi cells scale the Gaussian random walk procedure representing the spreading process by individual particle stepping. The step length of stochastically moving particles is based on a theoretical model of the spreading process, establishing a relationship between the step length of diffusive spreading and the thickness of the slick at the particle locations. The Voronoi tessellation provides the areal extent of the slick particles and in turn the thicknesses of the slick and the diffusive-type spreading length for all particles. The algorithm successfully simulates the spreading process and results show very good agreement with the analytical solution. Moreover, the results are robust for a wide range of values for computational time step and total number of particles.

  20. Exact Statistics of Record Increments of Random Walks and Lévy Flights.

    PubMed

    Godrèche, Claude; Majumdar, Satya N; Schehr, Grégory

    2016-07-01

    We study the statistics of increments in record values in a time series {x_{0}=0,x_{1},x_{2},…,x_{n}} generated by the positions of a random walk (discrete time, continuous space) of duration n steps. For arbitrary jump length distribution, including Lévy flights, we show that the distribution of the record increment becomes stationary, i.e., independent of n for large n, and compute it explicitly for a wide class of jump distributions. In addition, we compute exactly the probability Q(n) that the record increments decrease monotonically up to step n. Remarkably, Q(n) is universal (i.e., independent of the jump distribution) for each n, decaying as Q(n)∼A/sqrt[n] for large n, with a universal amplitude A=e/sqrt[π]=1.53362….

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

    PubMed

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

    1987-04-01

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

  2. Observations of Random Walk of the Ground In Space and Time

    SciTech Connect

    Shiltsev, Vladimir; /Fermilab

    2010-01-01

    We present results of micron-resolution measurements of the ground motions in large particle accelerators over the range of spatial scales L from several meters to tens of km and time intervals T from minutes to several years and show that in addition to systematic changes due to tides or slow drifts, there is a stochastic component which has a 'random-walk' character both in time and in space. The measured mean square of the relative displacement of ground elements scales as dY{sup 2} {approx} ATL over broad range of the intervals, and the site dependent constant A is of the order of 10{sup -5{+-}1} {micro}m{sup 2}/(s{center_dot}m).

  3. Random-walk model to study cycles emerging from the exploration-exploitation trade-off

    NASA Astrophysics Data System (ADS)

    Kazimierski, Laila D.; Abramson, Guillermo; Kuperman, Marcelo N.

    2015-01-01

    We present a model for a random walk with memory, phenomenologically inspired in a biological system. The walker has the capacity to remember the time of the last visit to each site and the step taken from there. This memory affects the behavior of the walker each time it reaches an already visited site modulating the probability of repeating previous moves. This probability increases with the time elapsed from the last visit. A biological analog of the walker is a frugivore, with the lattice sites representing plants. The memory effect can be associated with the time needed by plants to recover its fruit load. We propose two different strategies, conservative and explorative, as well as intermediate cases, leading to nonintuitive interesting results, such as the emergence of cycles.

  4. Random walk-based similarity measure method for patterns in complex object

    NASA Astrophysics Data System (ADS)

    Liu, Shihu; Chen, Xiaozhou

    2017-04-01

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2017-08-01

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

  6. Branching and annihilating random walks: exact results at low branching rate.

    PubMed

    Benitez, Federico; Wschebor, Nicolás

    2013-05-01

    We present some exact results on the behavior of branching and annihilating random walks, both in the directed percolation and parity conserving universality classes. Contrary to usual perturbation theory, we perform an expansion in the branching rate around the nontrivial pure annihilation (PA) model, whose correlation and response function we compute exactly. With this, the nonuniversal threshold value for having a phase transition in the simplest system belonging to the directed percolation universality class is found to coincide with previous nonperturbative renormalization group (RG) approximate results. We also show that the parity conserving universality class has an unexpected RG fixed point structure, with a PA fixed point which is unstable in all dimensions of physical interest.

  7. Renormalized Random Walk Study of Oxygen Absorption in the Human Lung

    NASA Astrophysics Data System (ADS)

    Felici, M.; Filoche, M.; Sapoval, B.

    2004-02-01

    The possibility to renormalize random walks is used to study numerically the oxygen diffusion and permeation in the acinus, the diffusion cell terminating the mammalian airway tree. This is done in a 3D tree structure which can be studied from its topology only. The method is applied to the human acinus real morphology as studied by Haefeli-Bleuer and Weibel in order to compute the respiratory efficiency of the human lung. It provides the first quantitative evidence of the role of diffusion screening in real 3D mammalian respiration. The net result of this study is that, at rest, the efficiency of the human acinus is only of order 33%. Application of these results to CO2 clearance provides for the first time a theoretical support to the empirical relation between the O2 and CO2 partial pressures in blood.

  8. Delayed uncoupled continuous-time random walks do not provide a model for the telegraph equation.

    PubMed

    Rukolaine, S A; Samsonov, A M

    2012-02-01

    It has been alleged in several papers that the so-called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since the telegraph equation describes phenomena with finite propagation speed, while the velocity of the motion of particles in the DCTRWs is infinite. In this paper we investigate the accuracy of the approximations to the DCTRWs provided by the telegraph equation. We show that the diffusion equation, being the correct limit of the DCTRWs, gives better approximations in L(2) norm to the DCTRWs than the telegraph equation. We conclude, therefore, that first, the DCTRWs do not provide any correct microscopic interpretation of the one-dimensional telegraph equation, and second, the kinetic (exact) model of the telegraph equation is different from the model based on the DCTRWs.

  9. Random walk of magnetic field-lines for different values of the energy range spectral index

    SciTech Connect

    Shalchi, A.; Kourakis, I.

    2007-11-15

    An analytical nonlinear description of field-line wandering in partially statistically magnetic systems was proposed recently. In this article the influence of the wave spectrum in the energy range onto field-line random walk is investigated by applying this formulation. It is demonstrated that in all considered cases we clearly obtain a superdiffusive behavior of the field-lines. If the energy range spectral index exceeds unity a free-streaming behavior of the field-lines can be found for all relevant length-scales of turbulence. Since the superdiffusive results obtained for the slab model are exact, it seems that superdiffusion is the normal behavior of field-line wandering.

  10. Simply and multiply scaled diffusion limits for continuous time random walks

    NASA Astrophysics Data System (ADS)

    Gorenflo, Rudolf; Mainardi, Francesco

    2005-01-01

    First a survey is presented on how space-time fractional diffusion processes can be obtained by well-scaled limiting from continuous time random walks under the sole assumption of asymptotic power laws (with appropriate exponents for the tail behaviour of waiting times and jumps). The spatial operator in the limiting pseudo-differential equation is the inverse of a general Riesz-Feller potential operator. The analysis is carried out via the transforms of Fourier and Laplace. Then mixtures of waiting time distributions, likewise of jump distributions, are considered, and it is shown that correct multiple scaling in the limit yields diffusion equations with distributed order fractional derivatives (fractional operators being replaced by integrals over such ones, with the order of differentiation as variable of integration). It is outlined how in this way super-fast and super-slow diffusion can be modelled.

  11. Efficiency analysis of diffusion on T-fractals in the sense of random walks.

    PubMed

    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.

  12. Flexible sampling large-scale social networks by self-adjustable random walk

    NASA Astrophysics Data System (ADS)

    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.

  13. An improved random walk algorithm for the implicit Monte Carlo method

    SciTech Connect

    Keady, Kendra P. Cleveland, Mathew A.

    2017-01-01

    In this work, we introduce a modified Implicit Monte Carlo (IMC) Random Walk (RW) algorithm, which increases simulation efficiency for multigroup radiative transfer problems with strongly frequency-dependent opacities. To date, the RW method has only been implemented in “fully-gray” form; that is, the multigroup IMC opacities are group-collapsed over the full frequency domain of the problem to obtain a gray diffusion problem for RW. This formulation works well for problems with large spatial cells and/or opacities that are weakly dependent on frequency; however, the efficiency of the RW method degrades when the spatial cells are thin or the opacities are a strong function of frequency. To address this inefficiency, we introduce a RW frequency group cutoff in each spatial cell, which divides the frequency domain into optically thick and optically thin components. In the modified algorithm, opacities for the RW diffusion problem are obtained by group-collapsing IMC opacities below the frequency group cutoff. Particles with frequencies above the cutoff are transported via standard IMC, while particles below the cutoff are eligible for RW. This greatly increases the total number of RW steps taken per IMC time-step, which in turn improves the efficiency of the simulation. We refer to this new method as Partially-Gray Random Walk (PGRW). We present numerical results for several multigroup radiative transfer problems, which show that the PGRW method is significantly more efficient than standard RW for several problems of interest. In general, PGRW decreases runtimes by a factor of ∼2–4 compared to standard RW, and a factor of ∼3–6 compared to standard IMC. While PGRW is slower than frequency-dependent Discrete Diffusion Monte Carlo (DDMC), it is also easier to adapt to unstructured meshes and can be used in spatial cells where DDMC is not applicable. This suggests that it may be optimal to employ both DDMC and PGRW in a single simulation.

  14. SU-F-BRD-09: A Random Walk Model Algorithm for Proton Dose Calculation

    SciTech Connect

    Yao, W; Farr, J

    2015-06-15

    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.

  15. An improved random walk algorithm for the implicit Monte Carlo method

    NASA Astrophysics Data System (ADS)

    Keady, Kendra P.; Cleveland, Mathew A.

    2017-01-01

    In this work, we introduce a modified Implicit Monte Carlo (IMC) Random Walk (RW) algorithm, which increases simulation efficiency for multigroup radiative transfer problems with strongly frequency-dependent opacities. To date, the RW method has only been implemented in "fully-gray" form; that is, the multigroup IMC opacities are group-collapsed over the full frequency domain of the problem to obtain a gray diffusion problem for RW. This formulation works well for problems with large spatial cells and/or opacities that are weakly dependent on frequency; however, the efficiency of the RW method degrades when the spatial cells are thin or the opacities are a strong function of frequency. To address this inefficiency, we introduce a RW frequency group cutoff in each spatial cell, which divides the frequency domain into optically thick and optically thin components. In the modified algorithm, opacities for the RW diffusion problem are obtained by group-collapsing IMC opacities below the frequency group cutoff. Particles with frequencies above the cutoff are transported via standard IMC, while particles below the cutoff are eligible for RW. This greatly increases the total number of RW steps taken per IMC time-step, which in turn improves the efficiency of the simulation. We refer to this new method as Partially-Gray Random Walk (PGRW). We present numerical results for several multigroup radiative transfer problems, which show that the PGRW method is significantly more efficient than standard RW for several problems of interest. In general, PGRW decreases runtimes by a factor of ∼2-4 compared to standard RW, and a factor of ∼3-6 compared to standard IMC. While PGRW is slower than frequency-dependent Discrete Diffusion Monte Carlo (DDMC), it is also easier to adapt to unstructured meshes and can be used in spatial cells where DDMC is not applicable. This suggests that it may be optimal to employ both DDMC and PGRW in a single simulation.

  16. The Walking School Bus and Children's Physical Activity: A Pilot Cluster Randomized Controlled Trial

    PubMed Central

    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

  17. The Walking Interventions Through Texting (WalkIT) Trial: Rationale, Design, and Protocol for a Factorial Randomized Controlled Trial of Adaptive Interventions for Overweight and Obese, Inactive Adults

    PubMed Central

    Hurley, Jane C; Hollingshead, Kevin E; Todd, Michael; Jarrett, Catherine L; Tucker, Wesley J; Angadi, Siddhartha S

    2015-01-01

    Background Walking is a widely accepted and frequently targeted health promotion approach to increase physical activity (PA). Interventions to increase PA have produced only small improvements. Stronger and more potent behavioral intervention components are needed to increase time spent in PA, improve cardiometabolic risk markers, and optimize health. Objective Our aim is to present the rationale and methods from the WalkIT Trial, a 4-month factorial randomized controlled trial (RCT) in inactive, overweight/obese adults. The main purpose of the study was to evaluate whether intensive adaptive components result in greater improvements to adults’ PA compared to the static intervention components. Methods Participants enrolled in a 2x2 factorial RCT and were assigned to one of four semi-automated, text message–based walking interventions. Experimental components included adaptive versus static steps/day goals, and immediate versus delayed reinforcement. Principles of percentile shaping and behavioral economics were used to operationalize experimental components. A Fitbit Zip measured the main outcome: participants’ daily physical activity (steps and cadence) over the 4-month duration of the study. Secondary outcomes included self-reported PA, psychosocial outcomes, aerobic fitness, and cardiorespiratory risk factors assessed pre/post in a laboratory setting. Participants were recruited through email listservs and websites affiliated with the university campus, community businesses and local government, social groups, and social media advertising. Results This study has completed data collection as of December 2014, but data cleaning and preliminary analyses are still in progress. We expect to complete analysis of the main outcomes in late 2015 to early 2016. Conclusions The Walking Interventions through Texting (WalkIT) Trial will further the understanding of theory-based intervention components to increase the PA of men and women who are healthy, insufficiently

  18. The Walking Interventions Through Texting (WalkIT) Trial: Rationale, Design, and Protocol for a Factorial Randomized Controlled Trial of Adaptive Interventions for Overweight and Obese, Inactive Adults.

    PubMed

    Hurley, Jane C; Hollingshead, Kevin E; Todd, Michael; Jarrett, Catherine L; Tucker, Wesley J; Angadi, Siddhartha S; Adams, Marc A

    2015-09-11

    Walking is a widely accepted and frequently targeted health promotion approach to increase physical activity (PA). Interventions to increase PA have produced only small improvements. Stronger and more potent behavioral intervention components are needed to increase time spent in PA, improve cardiometabolic risk markers, and optimize health. Our aim is to present the rationale and methods from the WalkIT Trial, a 4-month factorial randomized controlled trial (RCT) in inactive, overweight/obese adults. The main purpose of the study was to evaluate whether intensive adaptive components result in greater improvements to adults' PA compared to the static intervention components. Participants enrolled in a 2x2 factorial RCT and were assigned to one of four semi-automated, text message-based walking interventions. Experimental components included adaptive versus static steps/day goals, and immediate versus delayed reinforcement. Principles of percentile shaping and behavioral economics were used to operationalize experimental components. A Fitbit Zip measured the main outcome: participants' daily physical activity (steps and cadence) over the 4-month duration of the study. Secondary outcomes included self-reported PA, psychosocial outcomes, aerobic fitness, and cardiorespiratory risk factors assessed pre/post in a laboratory setting. Participants were recruited through email listservs and websites affiliated with the university campus, community businesses and local government, social groups, and social media advertising. This study has completed data collection as of December 2014, but data cleaning and preliminary analyses are still in progress. We expect to complete analysis of the main outcomes in late 2015 to early 2016. The Walking Interventions through Texting (WalkIT) Trial will further the understanding of theory-based intervention components to increase the PA of men and women who are healthy, insufficiently active and are overweight or obese. WalkIT is one of

  19. Graph-Driven Diffusion and Random Walk Schemes for Image Segmentation.

    PubMed

    Bampis, Christos G; Maragos, Petros; Bovik, Alan C

    2016-10-26

    We propose graph-driven approaches to image segmentation by developing diffusion processes defined on arbitrary graphs. We formulate a solution to the image segmentation problem modeled as the result of infectious wavefronts propagating on an image-driven graph where pixels correspond to nodes of an arbitrary graph. By relating the popular Susceptible - Infected - Recovered epidemic propagation model to the Random Walker algorithm, we develop the Normalized Random Walker and a lazy random walker variant. The underlying iterative solutions of these methods are derived as the result of infections transmitted on this arbitrary graph. The main idea is to incorporate a degree-aware term into the original Random Walker algorithm in order to account for the node centrality of every neighboring node and to weigh the contribution of every neighbor to the underlying diffusion process. Our lazy random walk variant models the tendency of patients or nodes to resist changes in their infection status. We also show how previous work can be naturally extended to take advantage of this degreeaware term which enables the design of other novel methods. Through an extensive experimental analysis, we demonstrate the reliability of our approach, its small computational burden and the dimensionality reduction capabilities of graph-driven approaches. Without applying any regular grid constraint, the proposed graph clustering scheme allows us to consider pixellevel, node-level approaches and multidimensional input data by naturally integrating the importance of each node to the final clustering or segmentation solution. A software release containing implementations of this work and supplementary material can be found at: http://cvsp.cs.ntua.gr/research/GraphClustering/.

  20. One Model Fits All: Explaining Many Aspects of Number Comparison within a Single Coherent Model-A Random Walk Account

    ERIC Educational Resources Information Center

    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…