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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. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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

  19. 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.

  20. 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.

  1. 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

  2. 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

  3. 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.

  4. 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.

  5. 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

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  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. 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

  19. 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.

  20. 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.

  1. 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.

  2. 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

  3. 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

  4. 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…

  5. 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.

  6. 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.

  7. 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.

  8. 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

  9. 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

  10. 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.

  11. 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

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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}.

  6. 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

  7. 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.

  8. 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.

  9. 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

  10. 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.

  11. 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

  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. 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.

  14. 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

  15. 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

  16. 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.

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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

  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. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. [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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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

  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. 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…

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  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. 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.

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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 $\\mu \\gt 2$.

  12. 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.

  13. 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.

  14. 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).

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  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. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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.

  6. 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.

  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. 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.

  9. 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.

  10. 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.

  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. 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

  13. 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.

  14. 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

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. 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.

  3. 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

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. 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

  13. 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.

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

    Technology Transfer Automated Retrieval System (TEKTRAN)

    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...

  15. 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

  16. 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.

  17. 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.

  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. 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

  20. 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.

  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. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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

  10. 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.

  11. 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.

  12. 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

  13. 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.

  14. 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.

  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. 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

  17. 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.

  18. 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.

  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. 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.

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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%.

  6. 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.

  7. 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

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  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. 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.

  14. 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

  15. 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).

  16. 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.

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. 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

  8. 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.

  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. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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 .

  20. 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.

  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. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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

  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. 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.

  9. 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

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  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. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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

  9. 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

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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}.

  17. 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.

  18. 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.

  19. The Mixing Time of a Random Walk on a Long-Range Percolation Cluster in Pre-Sierpinski Gasket

    NASA Astrophysics Data System (ADS)

    Misumi, Jun

    2016-10-01

    We consider a random graph created by the long-range percolation on the nth stage finite subset of a fractal lattice called the pre-Sierpinski gasket. The long-range percolation is a stochastic model in which any pair of two points is connected by a random bond independently. On the random graph obtained as above, we consider a discrete-time random walk. We show that the mixing time of the random walk is of order 2^{(s-d)n} if drandom bonds exist, and d=log 3/log 2 is the Hausdorff dimension of the pre-Sierpinski gasket.

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.)

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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/.

  8. 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.

  9. 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

  10. 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.

  11. 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

  12. Effectiveness of Functional Progressive Resistance Exercise Training on Walking Ability in Children with Cerebral Palsy: A Randomized Controlled Trial

    ERIC Educational Resources Information Center

    Scholtes, Vanessa A.; Becher, Jules G.; Janssen-Potten, Yvonne J.; Dekkers, Hurnet; Smallenbroek, Linda; Dallmeijer, Annet J.

    2012-01-01

    The objective of the study was to evaluate the effectiveness of functional progressive resistance exercise (PRE) training on walking ability in children with cerebral palsy (CP). Fifty-one ambulant children with spastic CP (mean age 10 years 5 months, 29 boys) were randomized to an intervention (n=26) or control group (n=25, receiving usual care).…

  13. Effects of Practice on Task Architecture: Combined Evidence from Interference Experiments and Random-Walk Models of Decision Making

    ERIC Educational Resources Information Center

    Kamienkowski, Juan E.; Pashler, Harold; Dehaene, Stanislas; Sigman, Mariano

    2011-01-01

    Does extensive practice reduce or eliminate central interference in dual-task processing? We explored the reorganization of task architecture with practice by combining interference analysis (delays in dual-task experiment) and random-walk models of decision making (measuring the decision and non-decision contributions to RT). The main delay…

  14. 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…

  15. A Web-Based Intervention to Encourage Walking (StepWise): Pilot Randomized Controlled Trial

    PubMed Central

    Mutrie, Nanette; Fleming, Jade Dallas

    2016-01-01

    Background Despite Internet-based interventions that incorporate pedometers with appropriate goal-setting processes and other theoretically-based behavior change strategies being proposed as a means of increasing walking behavior, few have incorporated all of these key features or assessed maintenance of behavior change. Objective The objective of our study was to investigate the effect of a 12-week pedometer step goal walking program individually tailored to baseline step counts, combined with an interactive support website for step counts, health parameters and motivation over 12 and 24 weeks. Methods Low active participants (mean [SD] 46.2 [11.2] years) were randomly assigned to the Stepwise (SW) intervention group (n=49) or a comparison (CP) group (n=48). SW received a pedometer, step goal walking program and access to the SW website (containing interactive self-monitoring and goal feedback tools, motivational messages and action and coping planning strategies). CP received a pedometer and locally available physical activity information. Step counts, BMI, resting heart rate, blood pressure and glucose, cholesterol and triglyceride levels, psychological well-being, perceived health, self-efficacy and self-determined motivation were measured at baseline, 12 and 24 weeks. Results Linear mixed model analysis found that both groups’ step counts increased from baseline to week 12 (β = 11,002, CI 5739-16,266, P<.001) and 24 (β = 6810, CI 1190-12,431; P=.02). Group step counts were significantly different at week 24 with SW taking 8939 (CI 274-17604, P=.04) more steps compared to CP. Compared to baseline, both groups had improved triglyceride levels (0.14 mmol/L, CI -0.25 to -0.02, P=.02) at week 12, decreased diastolic blood pressure (4.22 mmHg, CI -6.73 to -1.72) at weeks 12 and 24 (3.17 mmHg, CI -5.55 to -0.78), improved positive (β = .21, CI 0.03-0.38, P=.02) and negative affect (β = -.15, CI -0.28 to -0.03, P=.02) at week 12, and perceived health at week 12

  16. Effect of intensive aerobic exercise on respiratory capacity and walking ability with chronic stroke patients: a randomized controlled pilot trial

    PubMed Central

    Bang, Dae-Hyouk; Son, Young-Lan

    2016-01-01

    [Purpose] To investigate the effects of intensive aerobic exercise on respiratory capacity and walking ability in chronic stroke patients. [Subjects and Methods] The subjects were randomly assigned to an experimental group (n=6) or a control group (n=6). Patients in the experimental group received intensive aerobic exercise for 30 minutes and traditional physical therapy once a day, five days a week, for four weeks. The control group received aerobic exercise for 30 minutes and traditional physical therapy for 30 minutes a day, five days a week, for four weeks. [Results] After the intervention, both groups showed significant improvements in the forced vital capacity, forced expiratory volume in one second, 10-meter walking test, and six-minute walking test over the baseline results. The comparison of the two groups after the intervention revealed that the experimental group showed more significant improvements in the forced vital capacity, forced expiratory volume in one second, and six-minute walking test. There was no significant difference in saturation pulse oximetry oxygen and 10-meter walking test between the groups. [Conclusion] The results of this study suggest that intensive aerobic exercise has a positive effect on respiratory capacity and walking endurance in patients with chronic stroke. PMID:27630438

  17. Loop-erased random walk on a percolation cluster: crossover from Euclidean to fractal geometry.

    PubMed

    Daryaei, E; Rouhani, S

    2014-06-01

    We study loop-erased random walk (LERW) on the percolation cluster, with occupation probability p ≥ p_{c}, in two and three dimensions. We find that the fractal dimensions of LERW_{p} are close to normal LERW in a Euclidean lattice, for all p>p_{c}. However, our results reveal that LERW on critical incipient percolation clusters is fractal with d_{f}=1.217 ± 0.002 for d=2 and 1.43 ± 0.02 for d=3, independent of the coordination number of the lattice. These values are consistent with the known values for optimal path exponents in strongly disordered media. We investigate how the behavior of the LERW_{p} crosses over from Euclidean to fractal geometry by gradually decreasing the value of the parameter p from 1 to p_{c}. For finite systems, two crossover exponents and a scaling relation can be derived. This work opens up a theoretical window regarding the diffusion process on fractal and random landscapes.

  18. Hausdorff and Packing Spectra, Large Deviations, and Free Energy for Branching Random Walks in

    NASA Astrophysics Data System (ADS)

    Attia, Najmeddine; Barral, Julien

    2014-10-01

    Consider an -valued branching random walk (BRW) on a supercritical Galton Watson tree. Without any assumption on the distribution of this BRW we compute, almost surely and simultaneously, the Hausdorff and packing dimensions of the level sets E( K) of infinite branches in the boundary of the tree (endowed with its standard metric) along which the averages of the BRW have a given closed connected set of limit points K. This goes beyond multifractal analysis, which only considers those level sets when K ranges in the set of singletons . We also give a 0-∞ law for the Hausdorff and packing measures of the level sets E({ α}), and compute the free energy of the associated logarithmically correlated random energy model in full generality. Moreover, our results complete the previous works on multifractal analysis by including the levels α which do not belong to the range of the gradient of the free energy. This covers in particular a situation that was until now badly understood, namely the case where a first order phase transition occurs. As a consequence of our study, we can also describe the whole singularity spectrum of Mandelbrot measures, as well as the associated free energy function (or L q -spectrum), when a first order phase transition occurs.

  19. Testing the imprint of nonstandard cosmologies on void profiles using Monte Carlo random walks

    NASA Astrophysics Data System (ADS)

    Achitouv, Ixandra

    2016-11-01

    Using Monte Carlo random walks of a log-normal distribution, we show how to qualitatively study void properties for nonstandard cosmologies. We apply this method to an f (R ) modified gravity model and recover the N -body simulation results of [1 I. Achitouv, M. Baldi, E. Puchwein, and J. Weller, Phys. Rev. D 93, 103522 (2016).] for the void profiles and their deviation from GR. This method can potentially be extended to study other properties of the large scale structures such as the abundance of voids or overdense environments. We also introduce a new way to identify voids in the cosmic web, using only a few measurements of the density fluctuations around random positions. This algorithm allows us to select voids with specific profiles and radii. As a consequence, we can target classes of voids with higher differences between f (R ) and standard gravity void profiles. Finally, we apply our void criteria to galaxy mock catalogues and discuss how the flexibility of our void finder can be used to reduce systematic errors when probing the growth rate in the galaxy-void correlation function.

  20. Effective pore-scale dispersion upscaling with a correlated continuous time random walk approach

    NASA Astrophysics Data System (ADS)

    Le Borgne, T.; Bolster, D.; Dentz, M.; de Anna, P.; Tartakovsky, A.

    2011-12-01

    We investigate the upscaling of dispersion from a pore-scale analysis of Lagrangian velocities. A key challenge in the upscaling procedure is to relate the temporal evolution of spreading to the pore-scale velocity field properties. We test the hypothesis that one can represent Lagrangian velocities at the pore scale as a Markov process in space. The resulting effective transport model is a continuous time random walk (CTRW) characterized by a correlated random time increment, here denoted as correlated CTRW. We consider a simplified sinusoidal wavy channel model as well as a more complex heterogeneous pore space. For both systems, the predictions of the correlated CTRW model, with parameters defined from the velocity field properties (both distribution and correlation), are found to be in good agreement with results from direct pore-scale simulations over preasymptotic and asymptotic times. In this framework, the nontrivial dependence of dispersion on the pore boundary fluctuations is shown to be related to the competition between distribution and correlation effects. In particular, explicit inclusion of spatial velocity correlation in the effective CTRW model is found to be important to represent incomplete mixing in the pore throats.

  1. Bloch-like waves in random-walk potentials based on supersymmetry

    PubMed Central

    Yu, Sunkyu; Piao, Xianji; Hong, Jiho; Park, Namkyoo

    2015-01-01

    Bloch's theorem was a major milestone that established the principle of bandgaps in crystals. Although it was once believed that bandgaps could form only under conditions of periodicity and long-range correlations for Bloch's theorem, this restriction was disproven by the discoveries of amorphous media and quasicrystals. While network and liquid models have been suggested for the interpretation of Bloch-like waves in disordered media, these approaches based on searching for random networks with bandgaps have failed in the deterministic creation of bandgaps. Here we reveal a deterministic pathway to bandgaps in random-walk potentials by applying the notion of supersymmetry to the wave equation. Inspired by isospectrality, we follow a methodology in contrast to previous methods: we transform order into disorder while preserving bandgaps. Our approach enables the formation of bandgaps in extremely disordered potentials analogous to Brownian motion, and also allows the tuning of correlations while maintaining identical bandgaps, thereby creating a family of potentials with ‘Bloch-like eigenstates'. PMID:26373616

  2. Field Line Random Walk in Isotropic Magnetic Turbulence up to Infinite Kubo Number

    NASA Astrophysics Data System (ADS)

    Sonsrettee, W.; Wongpan, P.; Ruffolo, D. J.; Matthaeus, W. H.; Chuychai, P.; Rowlands, G.

    2013-12-01

    In astrophysical plasmas, the magnetic field line random walk (FLRW) plays a key role in the transport of energetic particles. In the present, we consider isotropic magnetic turbulence, which is a reasonable model for interstellar space. Theoretical conceptions of the FLRW have been strongly influenced by studies of the limit of weak fluctuations (or a strong mean field) (e.g, Isichenko 1991a, b). In this case, the behavior of FLRW can be characterized by the Kubo number R = (b/B0)(l_∥ /l_ \\bot ) , where l∥ and l_ \\bot are turbulence coherence scales parallel and perpendicular to the mean field, respectively, and b is the root mean squared fluctuation field. In the 2D limit (R ≫ 1), there has been an apparent conflict between concepts of Bohm diffusion, which is based on the Corrsin's independence hypothesis, and percolative diffusion. Here we have used three non-perturbative analytic techniques based on Corrsin's independence hypothesis for B0 = 0 (R = ∞ ): diffusive decorrelation (DD), random ballistic decorrelation (RBD) and a general ordinary differential equation (ODE), and compared them with direct computer simulations. All the analytical models and computer simulations agree that isotropic turbulence for R = ∞ has a field line diffusion coefficient that is consistent with Bohm diffusion. Partially supported by the Thailand Research Fund, NASA, and NSF.

  3. Rehabilitating Walking Speed Poststroke With Treadmill-Based Interventions: A Systematic Review of Randomized Controlled Trials

    PubMed Central

    Charalambous, Charalambos C.; Bonilha, Heather Shaw; Kautz, Steven A.; Gregory, Chris M.; Bowden, Mark G.

    2015-01-01

    Background In the past several years, several randomized controlled trials (RCTs) have been reported regarding the efficacy of treadmill-based walking-specific rehabilitation programs, either individually (TT) or combined with body weight support (BWSTT), over control group therapies poststroke. No clear consensus exists as to whether treadmill-based interventions are superior in rehabilitating walking speed (WS) poststroke. Objective To review published RCTs examining TT and BWSTT poststroke and describe the effects on improving and retaining WS. Methods A systematic literature search in computerized databases was conducted to identify RCTs whose methodological quality was assessed with PEDro. Pre- and post-WS, change in WS, functional outcomes, and follow-up speed were extracted and calculated from each study. Additionally, statistical results of each study were examined, and the intragroup and intergroup effect sizes (ESintra and ESinter, respectively) were calculated. Results All studies (8 TT; 7 BWSTT) met the inclusion criteria, and their methodological quality was generally good, with a mean PEDro score 6.9/10. Of the 15 studies, 8 studies (4 TT; 4 BWSTT) reported intragroup significant increases of WS, whereas only 4 (4 TT) found superiority of treadmill interventions. Nine studies demonstrated large ESintra (4 TT; 5 BWSTT), yet only 3 showed large ESinter (1 TT; 2 BWSTT). Four studies (2 TT and 2 BWSTT) reported retention of gains in WS, regardless of intervention. Conclusions Treadmill-based interventions poststroke may increase and retain WS, but their universal superiority to other control group therapies has failed to be established. PMID:23764885

  4. Self-Avoiding Walks on the Random Lattice and the Random Hopping Model on a Cayley Tree

    NASA Astrophysics Data System (ADS)

    Kim, Yup

    Using a field theoretic method based on the replica trick, it is proved that the three-parameter renormalization group for an n-vector model with quenched randomness reduces to a two-parameter one in the limit n (--->) 0 which corresponds to self-avoiding walks (SAWs). This is also shown by the explicit calculation of the renormalization group recursion relations to second order in (epsilon). From this reduction we find that SAWs on the random lattice are in the same universality class as SAWs on the regular lattice. By analogy with the case of the n-vector model with cubic anisotropy in the limit n (--->) 1, the fixed-point structure of the n-vector model with randomness is analyzed in the SAW limit, so that a physical interpretation of the unphysical fixed point is given. Corrections of the values of critical exponents of the unphysical fixed point published previously is also given. Next we formulate an integral equation and recursion relations for the configurationally averaged one particle Green's function of the random hopping model on a Cayley tree of coordination number ((sigma) + 1). This formalism is tested by applying it successfully to the nonrandom model. Using this scheme for 1 << (sigma) < (INFIN) we calculate the density of states of this model with a Gaussian distribution of hopping matrix elements in the range of energy E('2) > E(,c)('2), where E(,c) is a critical energy described below. The singularity in the Green's function which occurs at energy E(,1)('(0)) for (sigma) = (INFIN) is shifted to complex energy E(,1) (on the unphysical sheet of energy E) for small (sigma)('-1). This calculation shows that the density of states is smooth function of energy E around the critical energy E(,c) = Re E(,1) in accord with Wegner's theorem. In this formulation the density of states has no sharp phase transition on the real axis of E because E(,1) has developed an imaginary part. Using the Lifschitz argument, we calculate the density of states near the

  5. 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.

  6. Multicomponent effective medium-correlated random walk theory for the diffusion of fluid mixtures through porous media.

    PubMed

    Bonilla, Mauricio R; Bhatia, Suresh K

    2012-01-10

    Molecular transport in nanoconfined spaces plays a key role in many emerging technologies for gas separation and storage, as well as in nanofluidics. The infiltration of fluid mixtures into the voids of porous frameworks having complex topologies is common place to these technologies, and optimizing their performance entails developing a deeper understanding of how the flow of these mixtures is affected by the morphology of the pore space, particularly its pore size distribution and pore connectivity. Although several techniques have been developed for the estimation of the effective diffusivity characterizing the transport of single fluids through porous materials, this is not the case for fluid mixtures, where the only alternatives rely on a time-consuming solution of the pore network equations or adaptations of the single fluid theories which are useful for a limited type of systems. In this paper, a hybrid multicomponent effective medium-correlated random walk theory for the calculation of the effective transport coefficients matrix of fluid mixtures diffusing through porous materials is developed. The theory is suitable for those systems in which component fluxes at the single pore level can be related to the potential gradients of the different species through linear flux laws and corresponds to a generalization of the classical single fluid effective medium theory for the analysis of random resistor networks. Comparison with simulation of the diffusion of binary CO(2)/H(2)S and ternary CO(2)/H(2)S/C(3)H(8) gas mixtures in membranes modeled as large networks of randomly oriented pores with both continuous and discrete pore size distributions demonstrates the power of the theory, which was tested using the well-known generalized Maxwell-Stefan model for surface diffusion at the single pore level.

  7. 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.

  8. 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.

  9. Characterizing gene sets using discriminative random walks with restart on heterogeneous biological networks

    PubMed Central

    Blatti, Charles; Sinha, Saurabh

    2016-01-01

    Motivation: Analysis of co-expressed gene sets typically involves testing for enrichment of different annotations or ‘properties’ such as biological processes, pathways, transcription factor binding sites, etc., one property at a time. This common approach ignores any known relationships among the properties or the genes themselves. It is believed that known biological relationships among genes and their many properties may be exploited to more accurately reveal commonalities of a gene set. Previous work has sought to achieve this by building biological networks that combine multiple types of gene–gene or gene–property relationships, and performing network analysis to identify other genes and properties most relevant to a given gene set. Most existing network-based approaches for recognizing genes or annotations relevant to a given gene set collapse information about different properties to simplify (homogenize) the networks. Results: We present a network-based method for ranking genes or properties related to a given gene set. Such related genes or properties are identified from among the nodes of a large, heterogeneous network of biological information. Our method involves a random walk with restarts, performed on an initial network with multiple node and edge types that preserve more of the original, specific property information than current methods that operate on homogeneous networks. In this first stage of our algorithm, we find the properties that are the most relevant to the given gene set and extract a subnetwork of the original network, comprising only these relevant properties. We then re-rank genes by their similarity to the given gene set, based on a second random walk with restarts, performed on the above subnetwork. We demonstrate the effectiveness of this algorithm for ranking genes related to Drosophila embryonic development and aggressive responses in the brains of social animals. Availability and Implementation: DRaWR was implemented as

  10. Molecular dynamics simulation for PBR pebble tracking simulation via a random walk approach using Monte Carlo simulation.

    PubMed

    Lee, Kyoung O; Holmes, Thomas W; Calderon, Adan F; Gardner, Robin P

    2012-05-01

    Using a Monte Carlo (MC) simulation, random walks were used for pebble tracking in a two-dimensional geometry in the presence of a biased gravity field. We investigated the effect of viscosity damping in the presence of random Gaussian fluctuations. The particle tracks were generated by Molecular Dynamics (MD) simulation for a Pebble Bed Reactor. The MD simulations were conducted in the interaction of noncohesive Hertz-Mindlin theory where the random walk MC simulation has a correlation with the MD simulation. This treatment can easily be extended to include the generation of transient gamma-ray spectra from a single pebble that contains a radioactive tracer. Then the inverse analysis thereof could be made to determine the uncertainty of the realistic measurement of transient positions of that pebble by any given radiation detection system designed for that purpose.

  11. 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.

  12. Application of random walk concept to the cyclic diffusion mechanisms for self-diffusion in intermetallic compounds

    NASA Astrophysics Data System (ADS)

    Tiwari, G. P.; Mehrotra, R. S.; Iijima, Y.

    2014-02-01

    Huntington-Elcock-McCombie (HEM) mechanism involving six consecutive and correlated jumps, a triple-defect mechanism (TDM) involving three correlated jumps and an anti-structure bridge (ASB) mechanism invoking the migration of an anti-structure atom are the three mechanisms currently in vogue to explain the self- and solute diffusion in intermetallic compounds. Among them, HEM and TDM are cyclic in nature. The HEM and TDM constitute the theme of the present article. The concept of random walk is applied to them and appropriate expressions for the diffusion coefficient are derived. These equations are then employed to estimate activation energies for self-diffusion via HEM and TDM processes and compared with the available experimental data on activation energy for self-diffusion in intermetallic compounds. The resulting activation energies do not favour HEM and TDM for the self-diffusion in intermetallic compounds. A comparison of the sum of experimentally determined activation energies for vacancy formation and migration with the activation energies for self-diffusion determined from radioactive tracer method favours the conventional monovacancy-mediated process for self-diffusion in intermetallic compounds.

  13. Motor Learning Versus StandardWalking Exercise in Older Adults with Subclinical Gait Dysfunction: A Randomized Clinical Trial

    PubMed Central

    Brach, Jennifer S.; Van Swearingen, Jessie M.; Perera, Subashan; Wert, David M.; Studenski, Stephanie

    2013-01-01

    Background Current exercise recommendationsfocus on endurance and strength, but rarely incorporate principles of motor learning. Motor learning exerciseis designed to address neurological aspects of movement. Motor learning exercise has not been evaluated in older adults with subclinical gait dysfunction. Objectives Tocompare motor learning versus standard exercise on measures of mobility and perceived function and disability. Design Single-blind randomized trial. Setting University research center. Participants Olderadults (n=40), mean age 77.1±6.0 years), who had normal walking speed (≥1.0 m/s) and impaired motor skill (Figure of 8 walk time > 8 s). Interventions The motor learning program (ML) incorporated goal-oriented stepping and walking to promote timing and coordination within the phases of the gait cycle. The standard program (S) employed endurance training by treadmill walking.Both included strength training and were offered twice weekly for one hour for 12 weeks. Measurements Primary outcomes included mobility performance (gait efficiency, motor skill in walking, gait speed, and walking endurance)and secondary outcomes included perceived function and disability (Late Life Function and Disability Instrument). Results 38 of 40 participants completed the trial (ML, n=18; S, n=20). ML improved more than Sin gait speed (0.13 vs. 0.05 m/s, p=0.008) and motor skill (−2.2 vs. −0.89 s, p<0.0001). Both groups improved in walking endurance (28.3 and 22.9m, but did not differ significantly p=0.14). Changes in gait efficiency and perceived function and disability were not different between the groups (p>0.10). Conclusion In older adults with subclinical gait dysfunction, motor learning exercise improved some parameters of mobility performance more than standard exercise. PMID:24219189

  14. Lévy flights and multifractality in quantum critical diffusion and in classical random walks on fractals.

    PubMed

    Kravtsov, V E; Yevtushenko, O M; Snajberk, P; Cuevas, E

    2012-08-01

    We employ the method of virial expansion to compute the retarded density correlation function (generalized diffusion propagator) in the critical random matrix ensemble in the limit of strong multifractality. We find that the long-range nature of the Hamiltonian is a common root of both multifractality and Lévy flights, which show up in the power-law intermediate- and long-distance behaviors, respectively, of the density correlation function. We review certain models of classical random walks on fractals and show the similarity of the density correlation function in them to that for the quantum problem described by the random critical long-range Hamiltonians.

  15. Effect of inspiratory muscle training on respiratory capacity and walking ability with subacute stroke patients: a randomized controlled pilot trial.

    PubMed

    Jung, Kyeong-Man; Bang, Dae-Hyouk

    2017-02-01

    [Purpose] To investigate the effects of inspiratory muscle training on respiratory capacity and walking ability in subacute stroke patients. [Subjects and Methods] The subjects were randomly assigned to an experimental group (n=6) or a control group (n=6). Patients in the experimental group received inspiratory muscle training for 30 minutes (six sets of five-minutes) and traditional physical therapy once a day, five days a week, for four weeks. The control group received aerobic exercise for 30 minutes and traditional physical therapy for 30 minutes a day, five days a week, for four weeks. [Results] After the intervention, both groups showed significant improvements in the forced vital capacity, forced expiratory volume in one second, 10-meter walking test, and six-minute walking test over the baseline results. There were significant between-group differences for the forced vital capacity, forced expiratory volume in one second, and six-minute walking test. No statistically significant differences were observed for measures of saturation pulse oximetry oxygen and 10-meter walking test between the groups. [Conclusion] These findings gave some indications that inspiratory muscle training may benefit in patients with subacute stroke, and it is feasible to be included in rehabilitation program with this population.

  16. Effect of inspiratory muscle training on respiratory capacity and walking ability with subacute stroke patients: a randomized controlled pilot trial

    PubMed Central

    Jung, Kyeong-Man; Bang, Dae-Hyouk

    2017-01-01

    [Purpose] To investigate the effects of inspiratory muscle training on respiratory capacity and walking ability in subacute stroke patients. [Subjects and Methods] The subjects were randomly assigned to an experimental group (n=6) or a control group (n=6). Patients in the experimental group received inspiratory muscle training for 30 minutes (six sets of five-minutes) and traditional physical therapy once a day, five days a week, for four weeks. The control group received aerobic exercise for 30 minutes and traditional physical therapy for 30 minutes a day, five days a week, for four weeks. [Results] After the intervention, both groups showed significant improvements in the forced vital capacity, forced expiratory volume in one second, 10-meter walking test, and six-minute walking test over the baseline results. There were significant between-group differences for the forced vital capacity, forced expiratory volume in one second, and six-minute walking test. No statistically significant differences were observed for measures of saturation pulse oximetry oxygen and 10-meter walking test between the groups. [Conclusion] These findings gave some indications that inspiratory muscle training may benefit in patients with subacute stroke, and it is feasible to be included in rehabilitation program with this population. PMID:28265169

  17. Large-scale identification of adverse drug reaction-related proteins through a random walk model

    PubMed Central

    Chen, Xiaowen; Shi, Hongbo; Yang, Feng; Yang, Lei; Lv, Yingli; Wang, Shuyuan; Dai, Enyu; Sun, Dianjun; Jiang, Wei

    2016-01-01

    Adverse drug reactions (ADRs) are responsible for drug failure in clinical trials and affect life quality of patients. The identification of ADRs during the early phases of drug development is an important task. Therefore, predicting potential protein targets eliciting ADRs is essential for understanding the pathogenesis of ADRs. In this study, we proposed a computational algorithm,Integrated Network for Protein-ADR relations (INPADR), to infer potential protein-ADR relations based on an integrated network. First, the integrated network was constructed by connecting the protein-protein interaction network and the ADR similarity network using known protein-ADR relations. Then, candidate protein-ADR relations were further prioritized by performing a random walk with restart on this integrated network. Leave-one-out cross validation was used to evaluate the ability of the INPADR. An AUC of 0.8486 was obtained, which was a significant improvement compared to previous methods. We also applied the INPADR to two ADRs to evaluate its accuracy. The results suggested that the INPADR is capable of finding novel protein-ADR relations. This study provides new insight to our understanding of ADRs. The predicted ADR-related proteins will provide a reference for preclinical safety pharmacology studies and facilitate the identification of ADRs during the early phases of drug development. PMID:27805066

  18. Socially informed random walks: incorporating group dynamics into models of population spread and growth

    PubMed Central

    Haydon, Daniel T; Morales, Juan M; Yott, Adelle; Jenkins, Deborah A; Rosatte, Rick; Fryxell, John M

    2008-01-01

    Simple correlated random walk (CRW) models are rarely sufficient to describe movement of animals over more than the shortest time scales. However, CRW approaches can be used to model more complex animal movement trajectories by assuming individuals move in one of several different behavioural or movement states, each characterized by a different CRW. The spatial and social context an individual experiences may influence the proportion of time spent in different movement states, with subsequent effects on its spatial distribution, survival and fecundity. While methods to study habitat influences on animal movement have been previously developed, social influences have been largely neglected. Here, we fit a ‘socially informed’ movement model to data from a population of over 100 elk (Cervus canadensis) reintroduced into a new environment, radio-collared and subsequently tracked over a 4-year period. The analysis shows how elk move further when they are solitary than when they are grouped and incur a higher rate of mortality the further they move away from the release area. We use the model to show how the spatial distribution and growth rate of the population depend on the balance of fission and fusion processes governing the group structure of the population. The results are briefly discussed with respect to the design of species reintroduction programmes. PMID:18270158

  19. Path statistics, memory, and coarse-graining of continuous-time random walks on networks.

    PubMed

    Manhart, Michael; Kion-Crosby, Willow; Morozov, Alexandre V

    2015-12-07

    Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs.

  20. Context-free pairs of groups II — Cuts, tree sets, and random walks

    PubMed Central

    Woess, Wolfgang

    2012-01-01

    This is a continuation of the study, begun by Ceccherini-Silberstein and Woess (2009) [5], of context-free pairs of groups and the related context-free graphs in the sense of Muller and Schupp (1985) [22]. The graphs under consideration are Schreier graphs of a subgroup of some finitely generated group, and context-freeness relates to a tree-like structure of those graphs. Instead of the cones of Muller and Schupp (1985) [22] (connected components resulting from deletion of finite balls with respect to the graph metric), a more general approach to context-free graphs is proposed via tree sets consisting of cuts of the graph, and associated structure trees. The existence of tree sets with certain “good” properties is studied. With a tree set, a natural context-free grammar is associated. These investigations of the structure of context free pairs, resp. graphs are then applied to study random walk asymptotics via complex analysis. In particular, a complete proof of the local limit theorem for return probabilities on any virtually free group is given, as well as on Schreier graphs of a finitely generated subgoup of a free group. This extends, respectively completes, the significant work of Lalley (1993, 2001) [18,20]. PMID:22267873

  1. Subdiffusive random walk in a membrane system: the generalized method of images approach

    NASA Astrophysics Data System (ADS)

    Kosztołowicz, Tadeusz

    2015-10-01

    Using two random walk models in a system with a thin membrane we find the Green’s functions describing various kinds of diffusion in this system; the membrane is treated here as a thin, partially permeable wall. The models differ in the assumptions concerning how the particle is stopped or reflected by the membrane when the particle’s attempts to pass through it fail. We show that the Green’s functions obtained for both models are equivalent with the exception of the values of these functions at the membranes’ surfaces. As examples we present the Green’s functions for a membrane system in which subdiffusion or slow subdiffusion occurs and we briefly discuss the properties of the functions. We also show that the Green’s functions can be obtained by means of the generalized method of images. Within this method, the Green’s functions appear to be a combination of the Green’s functions derived for a homogeneous system without a membrane by means of the rules presented in this paper. Additionally, the obtained Green’s functions are used to derive a boundary condition at the membrane. It is shown that the condition contains a specific term which can be interpreted as a ‘memory term’ depending on the kind of diffusion occurring in the system which is generated by the membrane.

  2. Memory-induced anomalous dynamics in a minimal random walk model

    NASA Astrophysics Data System (ADS)

    Harbola, Upendra; Kumar, Niraj; Lindenberg, Katja

    2014-08-01

    A discrete-time dynamics of a non-Markovian random walker is analyzed using a minimal model where memory of the past drives the present dynamics. In recent work [N. Kumar et al., Phys. Rev. E 82, 021101 (2010), 10.1103/PhysRevE.82.021101] we proposed a model that exhibits asymptotic superdiffusion, normal diffusion, and subdiffusion with the sweep of a single parameter. Here we propose an even simpler model, with minimal options for the walker: either move forward or stay at rest. We show that this model can also give rise to diffusive, subdiffusive, and superdiffusive dynamics at long times as a single parameter is varied. We show that in order to have subdiffusive dynamics, the memory of the rest states must be perfectly correlated with the present dynamics. We show explicitly that if this condition is not satisfied in a unidirectional walk, the dynamics is only either diffusive or superdiffusive (but not subdiffusive) at long times.

  3. Natural Organic Matter Transport Modeling with a Continuous Time Random Walk Approach

    PubMed Central

    McInnis, Daniel P.; Bolster, Diogo; Maurice, Patricia A.

    2014-01-01

    Abstract In transport experiments through columns packed with naturally Fe/Al oxide-coated quartz sand, breakthrough curves (BTCs) of natural organic matter (NOM) displayed strong and persistent power law tailing that could not be described by the classical advection–dispersion equation. Tailing was not observed in BTCs for a nonreactive tracer (sulforhodamine B); therefore, the anomalous transport is attributed to diverse adsorptive behavior of the polydisperse NOM sample rather than to physical heterogeneity of the porous medium. NOM BTC tailing became more pronounced with decreases in pH and increases in ionic strength, conditions previously shown to be associated with enhanced preferential adsorption of intermediate to high molecular weight NOM components. Drawing from previous work on anomalous solute transport, we develop an approach to model NOM transport within the framework of a continuous time random walk (CTRW) and show that under all conditions examined, the CTRW model is able to capture tailing of NOM BTCs by accounting for differences in transport rates of NOM fractions through a distribution of effective retardation factors. These results demonstrate the importance of considering effects of adsorptive fractionation on NOM mobility, and illustrate the ability of the CTRW model to describe transport of a multicomponent solute. PMID:24596449

  4. Upscaling solute transport in naturally fractured porous media with the continuous time random walk method

    SciTech Connect

    Geiger, S.; Cortis, A.; Birkholzer, J.T.

    2010-04-01

    Solute transport in fractured porous media is typically 'non-Fickian'; that is, it is characterized by early breakthrough and long tailing and by nonlinear growth of the Green function-centered second moment. This behavior is due to the effects of (1) multirate diffusion occurring between the highly permeable fracture network and the low-permeability rock matrix, (2) a wide range of advection rates in the fractures and, possibly, the matrix as well, and (3) a range of path lengths. As a consequence, prediction of solute transport processes at the macroscale represents a formidable challenge. Classical dual-porosity (or mobile-immobile) approaches in conjunction with an advection-dispersion equation and macroscopic dispersivity commonly fail to predict breakthrough of fractured porous media accurately. It was recently demonstrated that the continuous time random walk (CTRW) method can be used as a generalized upscaling approach. Here we extend this work and use results from high-resolution finite element-finite volume-based simulations of solute transport in an outcrop analogue of a naturally fractured reservoir to calibrate the CTRW method by extracting a distribution of retention times. This procedure allows us to predict breakthrough at other model locations accurately and to gain significant insight into the nature of the fracture-matrix interaction in naturally fractured porous reservoirs with geologically realistic fracture geometries.

  5. Path statistics, memory, and coarse-graining of continuous-time random walks on networks

    PubMed Central

    Kion-Crosby, Willow; Morozov, Alexandre V.

    2015-01-01

    Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs. PMID:26646868

  6. Random walk with nonuniform angular distribution biased by an external periodic pulse

    NASA Astrophysics Data System (ADS)

    Acharyya, Aranyak

    2016-11-01

    We studied the motion of a random walker in two dimensions with nonuniform angular distribution biased by an external periodic pulse. Here, we analytically calculated the mean square displacement (end-to-end distance of a walk after n time steps), without bias and with bias. We determined the average x-component of the final displacement of the walker. Interestingly, we noted that for a particular periodicity of the bias, this average x-component of the final displacement becomes approximately zero. The average y-component of the final displacement is found to be zero for any perodicity of the bias, and its reason can be attributed to the nature of the probability density function of the angle (subtended by the displacement vector with the x-axis). These analytical results are also supported by computer simulations. The present study may be thought of as a model for arresting the bacterial motion (along a preferred direction) by an external periodic bias. This article will be useful for undergraduate students of physics, statistics and biology as an example of an interdisciplinary approach to understand a way to control bacterial motion.

  7. Statistical analysis of cell migration in 3D using the anisotropic persistent random walk model.

    PubMed

    Wu, Pei-Hsun; Giri, Anjil; Wirtz, Denis

    2015-03-01

    Cell migration through 3D extracellular matrices (ECMs) is crucial to the normal development of tissues and organs and in disease processes, yet adequate analytical tools to characterize 3D migration are lacking. The motility of eukaryotic cells on 2D substrates in the absence of gradients has long been described using persistent random walks (PRWs). Recent work shows that 3D migration is anisotropic and features an exponential mean cell velocity distribution, rendering the PRW model invalid. Here we present a protocol for the analysis of 3D cell motility using the anisotropic PRW model. The software, which is implemented in MATLAB, enables statistical profiling of experimentally observed 2D and 3D cell trajectories, and it extracts the persistence and speed of cells along primary and nonprimary directions and an anisotropic index of migration. Basic computer skills and experience with MATLAB software are recommended for successful use of the protocol. This protocol is highly automated and fast, taking <30 min to analyze trajectory data per biological condition.

  8. D Fluid Deformation and Mixing via a Continuous Time Random Walk

    NASA Astrophysics Data System (ADS)

    Lester, D. R.; Dentz, M.; Le Borgne, T.; de Barros, F.

    2015-12-01

    Fluid stretching and deformation as quantified by the fluid deformation gradient tensor directly controls mixing of diffusive species in both chaotic and non-chaotic, 2D and 3D flows at the pore- and Darcy scales. Indeed, recent advances [LeBorgne et. al. PRL, 110, 204501, 2013] in the prediction of mixing and scalar dissipation require the distribution of fluid deformation rates as quantitative inputs. However, these measures are often difficult to link to medium properties or statistical heterogeneity controls. To advance this problem, we present a novel Continuous Time Random Walk (CTRW) to model stochastic evolution of the 3D fluid deformation tensor in a Protean (streamline) coordinate frame. This approach allows topological constraints imposed by the flow kinematics to be naturally obeyed, and furthermore flow features that generate non-Fickian transport can be clearly elucidated. For simple flows, this framework allows the distribution of deformation rates (and hence mixing) to be expressed in terms of heterogenenity controls, and for more complex flows, this approach clearly identifies what flow features govern anomalous transport and how their statistics can be measured as model inputs.

  9. Biased random walk in spatially embedded networks with total cost constraint

    NASA Astrophysics Data System (ADS)

    Niu, Rui-Wu; Pan, Gui-Jun

    2016-11-01

    We investigate random walk with a bias toward a target node in spatially embedded networks with total cost restriction introduced by Li et al. (2010). Precisely, The network is built from a two-dimension regular lattice to be improved by adding long-range shortcuts with probability P(rij) ∼rij-α, where rij is the Manhattan distance between sites i and j, and α is a variable exponent, the total length of the long-range connections is restricted. Bias is represented as a probability p of the packet or particle to travel at every hop toward the node which has the smallest Manhattan distance to the target node. By studying the mean first passage time (MFPT) for different exponent log < l > , we find that the best transportation condition is obtained with an exponent α = d + 1(d = 2) for all p. The special phenomena can be possibly explained by the theory of information entropy, we find that when α = d + 1(d = 2) , the spatial network with total cost restriction becomes an optimal network which has a maximum information entropy. In addition, the scaling of the MFPT with the size of the network is also investigated, and finds that the scaling of the MFPT with L follows a linear distribution for all p > 0.

  10. Fluctuations around equilibrium laws in ergodic continuous-time random walks.

    PubMed

    Schulz, Johannes H P; Barkai, Eli

    2015-06-01

    We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.

  11. Backward jump continuous-time random walk: An application to market trading

    NASA Astrophysics Data System (ADS)

    Gubiec, Tomasz; Kutner, Ryszard

    2010-10-01

    The backward jump modification of the continuous-time random walk model or the version of the model driven by the negative feedback was herein derived for spatiotemporal continuum in the context of a share price evolution on a stock exchange. In the frame of the model, we described stochastic evolution of a typical share price on a stock exchange with a moderate liquidity within a high-frequency time scale. The model was validated by satisfactory agreement of the theoretical velocity autocorrelation function with its empirical counterpart obtained for the continuous quotation. This agreement is mainly a result of a sharp backward correlation found and considered in this article. This correlation is a reminiscence of such a bid-ask bounce phenomenon where backward price jump has the same or almost the same length as preceding jump. We suggested that this correlation dominated the dynamics of the stock market with moderate liquidity. Although assumptions of the model were inspired by the market high-frequency empirical data, its potential applications extend beyond the financial market, for instance, to the field covered by the Le Chatelier-Braun principle of contrariness.

  12. Laplacian normalization and random walk on heterogeneous networks for disease-gene prioritization.

    PubMed

    Zhao, Zhi-Qin; Han, Guo-Sheng; Yu, Zu-Guo; Li, Jinyan

    2015-08-01

    Random walk on heterogeneous networks is a recently emerging approach to effective disease gene prioritization. Laplacian normalization is a technique capable of normalizing the weight of edges in a network. We use this technique to normalize the gene matrix and the phenotype matrix before the construction of the heterogeneous network, and also use this idea to define the transition matrices of the heterogeneous network. Our method has remarkably better performance than the existing methods for recovering known gene-phenotype relationships. The Shannon information entropy of the distribution of the transition probabilities in our networks is found to be smaller than the networks constructed by the existing methods, implying that a higher number of top-ranked genes can be verified as disease genes. In fact, the most probable gene-phenotype relationships ranked within top 3 or top 5 in our gene lists can be confirmed by the OMIM database for many cases. Our algorithms have shown remarkably superior performance over the state-of-the-art algorithms for recovering gene-phenotype relationships. All Matlab codes can be available upon email request.

  13. Random Walks in Anderson's Garden: A Journey from Cuprates to Cooper Pair Insulators and Beyond

    NASA Astrophysics Data System (ADS)

    Baskaran, G.

    Anderson's Garden is a drawing presented to Philip W. Anderson on the eve of his 60th birthday celebration, in 1983, by a colleague (author unknown). This cartoon (Fig. 1) succinctly depicts some of Anderson's pre-1983 works. As an avid reader of Anderson's papers, a random walk in Anderson's garden had become a part of my routine since graduate school days. This was of immense help and prepared me for a wonderful collaboration with Anderson on the theory of high-Tc cuprates and quantum spin liquids at Princeton. Here I narrate this story, ending with a brief summary of my ongoing theoretical efforts to extend Anderson's RVB theory for superconductivity to encompass the recently observed high-temperature (Tc ~ 203K) superconductivity in solid H2S at pressure ~200GPa. In H2S molecule, four valence electrons form two saturated covalent bonds, H-S-H. These bond singlets are confined Cooper pairs close to chemical potential. Solid H2S is a Cooper pair insulator. Pressure changes the structure and not the number of valence electrons. Bond singlet pairing tendency continues and new S-S and H-H bonds are formed. S-S bonds are mostly saturated. However, hydrogen sublattice has unsaturated H-H bonds. It prepares ground for a RVB superconducting state.

  14. Backward jump continuous-time random walk: an application to market trading.

    PubMed

    Gubiec, Tomasz; Kutner, Ryszard

    2010-10-01

    The backward jump modification of the continuous-time random walk model or the version of the model driven by the negative feedback was herein derived for spatiotemporal continuum in the context of a share price evolution on a stock exchange. In the frame of the model, we described stochastic evolution of a typical share price on a stock exchange with a moderate liquidity within a high-frequency time scale. The model was validated by satisfactory agreement of the theoretical velocity autocorrelation function with its empirical counterpart obtained for the continuous quotation. This agreement is mainly a result of a sharp backward correlation found and considered in this article. This correlation is a reminiscence of such a bid-ask bounce phenomenon where backward price jump has the same or almost the same length as preceding jump. We suggested that this correlation dominated the dynamics of the stock market with moderate liquidity. Although assumptions of the model were inspired by the market high-frequency empirical data, its potential applications extend beyond the financial market, for instance, to the field covered by the Le Chatelier-Braun principle of contrariness.

  15. Dispersion in porous media, continuous-time random walks, and percolation.

    PubMed

    Sahimi, Muhammad

    2012-01-01

    A promising approach to the modeling of anomalous (non-Gaussian) dispersion in flow through heterogeneous porous media is the continuous-time random walk (CTRW) method. In such a formula on the waiting time distribution ψ(t) is usually assumed to be given by ψ(t)∼t-1-α, with α fitted to the experimental data. The exponent α is also related to the power-law growth of the mean-square displacement of the solute with the time t ∼ tζ. Invoking percolation and using a scaling analysis, we relate α to the geometrical exponents of percolation (ν, β, and βB) as well as the exponents μ and e that characterize the power-law behavior of the effective conductivity and permeability of porous media near the percolation threshold. We then explain the cause of the nonuniversality of α in terms of the nonuniversality of μ and e in continuum systems, and in percolation models with long-range correlations, and propose bounds for it. The results are consistent with the experimental data, both at the laboratory and field scales.

  16. Quasi-Stationary Regime of a Branching Random Walk in Presence of an Absorbing Wall

    NASA Astrophysics Data System (ADS)

    Simon, Damien; Derrida, Bernard

    2008-04-01

    A branching random walk in presence of an absorbing wall moving at a constant velocity v undergoes a phase transition as the velocity v of the wall varies. Below the critical velocity v c , the population has a non-zero survival probability and when the population survives its size grows exponentially. We investigate the histories of the population conditioned on having a single survivor at some final time T. We study the quasi-stationary regime for v< v c when T is large. To do so, one can construct a modified stochastic process which is equivalent to the original process conditioned on having a single survivor at final time T. We then use this construction to show that the properties of the quasi-stationary regime are universal when v→ v c . We also solve exactly a simple version of the problem, the exponential model, for which the study of the quasi-stationary regime can be reduced to the analysis of a single one-dimensional map.

  17. Identifying and Analyzing Novel Epilepsy-Related Genes Using Random Walk with Restart Algorithm

    PubMed Central

    Guo, Wei; Shang, Dong-Mei; Cao, Jing-Hui; Feng, Kaiyan; Wang, ShaoPeng

    2017-01-01

    As a pathological condition, epilepsy is caused by abnormal neuronal discharge in brain which will temporarily disrupt the cerebral functions. Epilepsy is a chronic disease which occurs in all ages and would seriously affect patients' personal lives. Thus, it is highly required to develop effective medicines or instruments to treat the disease. Identifying epilepsy-related genes is essential in order to understand and treat the disease because the corresponding proteins encoded by the epilepsy-related genes are candidates of the potential drug targets. In this study, a pioneering computational workflow was proposed to predict novel epilepsy-related genes using the random walk with restart (RWR) algorithm. As reported in the literature RWR algorithm often produces a number of false positive genes, and in this study a permutation test and functional association tests were implemented to filter the genes identified by RWR algorithm, which greatly reduce the number of suspected genes and result in only thirty-three novel epilepsy genes. Finally, these novel genes were analyzed based upon some recently published literatures. Our findings implicate that all novel genes were closely related to epilepsy. It is believed that the proposed workflow can also be applied to identify genes related to other diseases and deepen our understanding of the mechanisms of these diseases. PMID:28255556

  18. An analytical correlated random walk model and its application to understand subdiffusion in crowded environment

    NASA Astrophysics Data System (ADS)

    Hasnain, Sabeeha; Bandyopadhyay, Pradipta

    2015-09-01

    Subdiffusion in crowded environment such as movement of macromolecule in a living cell has often been observed experimentally. The primary reason for subdiffusion is volume exclusion by the crowder molecules. However, other effects such as hydrodynamic interaction may also play an important role. Although there are a large number of computer simulation studies on understanding molecular crowding, there is a lack of theoretical models that can be connected to both experiment and simulation. In the current work, we have formulated a one-dimensional correlated random walk model by connecting this to the motion in a crowded environment. We have found the exact solution of the probability distribution function of the model by solving it analytically. The parameters of our model can be obtained either from simulation or experiment. It has been shown that this analytical model captures some of the general features of diffusion in crowded environment as given in the previous literature and its prediction for transient subdiffusion closely matches the observations of a previous study of computer simulation of Escherichia coli cytoplasm. It is likely that this model will open up more development of theoretical models in this area.

  19. Sharp Trapping Boundaries in the Random Walk of Interplanetary Magnetic Field Lines

    NASA Astrophysics Data System (ADS)

    Ruffolo, D.; Chuychai, P.; Meechai, J.; Pongkitiwanichkul, P.; Kimpraphan, N.; Matthaeus, W. H.; Rowlands, G.

    2004-05-01

    Although magnetic field lines in space are believed to undergo a diffusive random walk in the long-distance limit, observed dropouts of solar energetic particles, as well as computer simulations, indicate sharply defined filaments in which interplanetary magnetic field lines have been temporarily trapped. We identify mechanisms that can explain such sharp boundaries in the framework of 2D+slab turbulence, a model that provides a good explanation of solar wind turbulence spectra and the parallel transport of solar energetic particles. Local trapping boundaries (LTBs) are empirically defined as trajectories of 2D turbulence where the mean 2D field is a local maximum. In computer simulations, the filaments (or ``islands'' in the two dimensions perpendicular to the mean field) that are most resistant to slab diffusion correspond closely to the mathematically defined LTBs, that is, there is a mathematical prescription for defining the trapping regions. Furthermore, we provide computational evidence and a theoretical explanation that strong 2D turbulence can inhibit diffusion due to the slab component. Therefore, while these filaments are basically defined by the small-scale topology of 2D turbulence, there can be sharp trapping boundaries where the 2D field is strongest. This work was supported by the Thailand Research Fund, the Rachadapisek Sompoj Fund of Chulalongkorn University, and NASA Grant NAG5-11603. G.R. thanks Mahidol University for its hospitality and the Thailand Commission for Higher Education for travel support.

  20. Finite current stationary states of random walks on one-dimensional lattices with aperiodic disorder

    NASA Astrophysics Data System (ADS)

    Miki, Hiroshi

    2016-11-01

    Stationary states of random walks with finite induced drift velocity on one-dimensional lattices with aperiodic disorder are investigated by scaling analysis. Three aperiodic sequences, the Thue-Morse (TM), the paperfolding (PF), and the Rudin-Shapiro (RS) sequences, are used to construct the aperiodic disorder. These are binary sequences, composed of two symbols A and B, and the ratio of the number of As to that of Bs converges to unity in the infinite sequence length limit, but their effects on diffusional behavior are different. For the TM model, the stationary distribution is extended, as in the case without current, and the drift velocity is independent of the system size. For the PF model and the RS model, as the system size increases, the hierarchical and fractal structure and the localized structure, respectively, are broken by a finite current and changed to an extended distribution if the system size becomes larger than a certain threshold value. Correspondingly, the drift velocity is saturated in a large system while in a small system it decreases as the system size increases.

  1. Magnetic Field Line Random Walk in Isotropic Turbulence with Varying Mean Field

    NASA Astrophysics Data System (ADS)

    Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.; Rowlands, G.; Vyas, S.

    2016-08-01

    In astrophysical plasmas, the magnetic field line random walk (FLRW) plays an important role in guiding particle transport. The FLRW behavior is scaled by the Kubo number R=(b/{B}0)({{\\ell }}\\parallel /{{\\ell }}\\perp ) for rms magnetic fluctuation b, large-scale mean field {{\\boldsymbol{B}}}0, and coherence scales parallel ({{\\ell }}\\parallel ) and perpendicular ({{\\ell }}\\perp ) to {{\\boldsymbol{B}}}0. Here we use a nonperturbative analytic framework based on Corrsin’s hypothesis, together with direct computer simulations, to examine the R-scaling of the FLRW for varying B 0 with finite b and isotropic fluctuations with {{\\ell }}\\parallel /{{\\ell }}\\perp =1, instead of the well-studied route of varying {{\\ell }}\\parallel /{{\\ell }}\\perp for b \\ll {B}0. The FLRW for isotropic magnetic fluctuations is also of astrophysical interest regarding transport processes in the interstellar medium. With a mean field, fluctuations may have variance anisotropy, so we consider limiting cases of isotropic variance and transverse variance (with b z = 0). We obtain analytic theories, and closed-form solutions for extreme cases. Padé approximants are provided to interpolate all versions of theory and simulations to any B 0. We demonstrate that, for isotropic turbulence, Corrsin-based theories generally work well, and with increasing R there is a transition from quasilinear to Bohm diffusion. This holds even with b z = 0, when different routes to R\\to ∞ are mathematically equivalent; in contrast with previous studies, we find that a Corrsin-based theory with random ballistic decorrelation works well even up to R = 400, where the effects of trapping are barely perceptible in simulation results.

  2. MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD

    SciTech Connect

    Sonsrettee, W.; Ruffolo, D.; Snodin, A. P.; Wongpan, P.; Subedi, P.; Matthaeus, W. H.; Chuychai, P. E-mail: david.ruf@mahidol.ac.th E-mail: pat.wongpan@postgrad.otago.ac.nz E-mail: prasub@udel.edu

    2015-01-01

    In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B {sub 0})(ℓ{sub ∥}/ℓ ) for rms magnetic fluctuation b, large-scale mean field B {sub 0}, and parallel and perpendicular coherence scales ℓ{sub ∥} and ℓ , respectively. Here we examine the FLRW when R → ∞ by taking B {sub 0} → 0 for finite b{sub z} (fluctuation component along B {sub 0}), which differs from the well-studied route with b{sub z} = 0 or b{sub z} << B {sub 0} as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B {sub 0} = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k {sup –1} or k {sup –2} moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B {sub 0} → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.

  3. A stochastic simulation framework for the prediction of strategic noise mapping and occupational noise exposure using the random walk approach.

    PubMed

    Han, Lim Ming; Haron, Zaiton; Yahya, Khairulzan; Bakar, Suhaimi Abu; Dimon, Mohamad Ngasri

    2015-01-01

    Strategic noise mapping provides important information for noise impact assessment and noise abatement. However, producing reliable strategic noise mapping in a dynamic, complex working environment is difficult. This study proposes the implementation of the random walk approach as a new stochastic technique to simulate noise mapping and to predict the noise exposure level in a workplace. A stochastic simulation framework and software, namely RW-eNMS, were developed to facilitate the random walk approach in noise mapping prediction. This framework considers the randomness and complexity of machinery operation and noise emission levels. Also, it assesses the impact of noise on the workers and the surrounding environment. For data validation, three case studies were conducted to check the accuracy of the prediction data and to determine the efficiency and effectiveness of this approach. The results showed high accuracy of prediction results together with a majority of absolute differences of less than 2 dBA; also, the predicted noise doses were mostly in the range of measurement. Therefore, the random walk approach was effective in dealing with environmental noises. It could predict strategic noise mapping to facilitate noise monitoring and noise control in the workplaces.

  4. Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk

    NASA Astrophysics Data System (ADS)

    Schütz, Gunter M.; Trimper, Steffen

    2004-10-01

    We consider a discrete-time random walk where the random increment at time step t depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition and on the memory parameter p . At a critical value pc(1)=1/2 where memory effects vanish there is a transition from a weakly localized regime [where the walker (elephant) returns to its starting point] to an escape regime. Inside the escape regime there is a second critical value where the random walk becomes superdiffusive. The probability distribution is shown to be governed by a non-Markovian Fokker-Planck equation with hopping rates that depend both on time and on the starting position of the walk. On large scales the memory organizes itself into an effective harmonic oscillator potential for the random walker with a time-dependent spring constant k=(2p-1)/t . The solution of this problem is a Gaussian distribution with time-dependent mean and variance which both depend on the initiation of the process.

  5. A comparison of network sampling designs for a hidden population of drug users: Random walk vs. respondent-driven sampling.

    PubMed

    Bell, David C; Erbaugh, Elizabeth B; Serrano, Tabitha; Dayton-Shotts, Cheryl A; Montoya, Isaac D

    2017-02-01

    Both random walk and respondent-driven sampling (RDS) exploit social networks and may reduce biases introduced by earlier methods for sampling from hidden populations. Although RDS has become much more widely used by social researchers than random walk (RW), there has been little discussion of the tradeoffs in choosing RDS over RW. This paper compares experiences of implementing RW and RDS to recruit drug users to a network-based study in Houston, Texas. Both recruitment methods were implemented over comparable periods of time, with the same population, by the same research staff. RDS methods recruited more participants with less strain on staff. However, participants recruited through RW were more forthcoming than RDS participants in helping to recruit members of their social networks. Findings indicate that, dependent upon study goals, researchers' choice of design may influence participant recruitment, participant commitment, and impact on staff, factors that may in turn affect overall study success.

  6. Estimating the causal effect of randomization versus treatment preference in a doubly randomized preference trial.

    PubMed

    Marcus, Sue M; Stuart, Elizabeth A; Wang, Pei; Shadish, William R; Steiner, Peter M

    2012-06-01

    Although randomized studies have high internal validity, generalizability of the estimated causal effect from randomized clinical trials to real-world clinical or educational practice may be limited. We consider the implication of randomized assignment to treatment, as compared with choice of preferred treatment as it occurs in real-world conditions. Compliance, engagement, or motivation may be better with a preferred treatment, and this can complicate the generalizability of results from randomized trials. The doubly randomized preference trial (DRPT) is a hybrid randomized and nonrandomized design that allows for estimation of the causal effect of randomization versus treatment preference. In the DRPT, individuals are first randomized to either randomized assignment or choice assignment. Those in the randomized assignment group are then randomized to treatment or control, and those in the choice group receive their preference of treatment versus control. Using the potential outcomes framework, we apply the algebra of conditional independence to show how the DRPT can be used to derive an unbiased estimate of the causal effect of randomization versus preference for each of the treatment and comparison conditions. Also, we show how these results can be implemented using full matching on the propensity score. The methodology is illustrated with a DRPT of introductory psychology students who were randomized to randomized assignment or preference of mathematics versus vocabulary training. We found a small to moderate benefit of preference versus randomization with respect to the mathematics outcome for those who received mathematics training.

  7. SU-D-201-06: Random Walk Algorithm Seed Localization Parameters in Lung Positron Emission Tomography (PET) Images

    SciTech Connect

    Soufi, M; Asl, A Kamali; Geramifar, P

    2015-06-15

    Purpose: The objective of this study was to find the best seed localization parameters in random walk algorithm application to lung tumor delineation in Positron Emission Tomography (PET) images. Methods: PET images suffer from statistical noise and therefore tumor delineation in these images is a challenging task. Random walk algorithm, a graph based image segmentation technique, has reliable image noise robustness. Also its fast computation and fast editing characteristics make it powerful for clinical purposes. We implemented the random walk algorithm using MATLAB codes. The validation and verification of the algorithm have been done by 4D-NCAT phantom with spherical lung lesions in different diameters from 20 to 90 mm (with incremental steps of 10 mm) and different tumor to background ratios of 4:1 and 8:1. STIR (Software for Tomographic Image Reconstruction) has been applied to reconstruct the phantom PET images with different pixel sizes of 2×2×2 and 4×4×4 mm{sup 3}. For seed localization, we selected pixels with different maximum Standardized Uptake Value (SUVmax) percentages, at least (70%, 80%, 90% and 100%) SUVmax for foreground seeds and up to (20% to 55%, 5% increment) SUVmax for background seeds. Also, for investigation of algorithm performance on clinical data, 19 patients with lung tumor were studied. The resulted contours from algorithm have been compared with nuclear medicine expert manual contouring as ground truth. Results: Phantom and clinical lesion segmentation have shown that the best segmentation results obtained by selecting the pixels with at least 70% SUVmax as foreground seeds and pixels up to 30% SUVmax as background seeds respectively. The mean Dice Similarity Coefficient of 94% ± 5% (83% ± 6%) and mean Hausdorff Distance of 1 (2) pixels have been obtained for phantom (clinical) study. Conclusion: The accurate results of random walk algorithm in PET image segmentation assure its application for radiation treatment planning and

  8. Random Walk and Graph Cut for Co-Segmentation of Lung Tumor on PET-CT Images.

    PubMed

    Ju, Wei; Xiang, Dehui; Xiang, Deihui; Zhang, Bin; Wang, Lirong; Kopriva, Ivica; Chen, Xinjian

    2015-12-01

    Accurate lung tumor delineation plays an important role in radiotherapy treatment planning. Since the lung tumor has poor boundary in positron emission tomography (PET) images and low contrast in computed tomography (CT) images, segmentation of tumor in the PET and CT images is a challenging task. In this paper, we effectively integrate the two modalities by making fully use of the superior contrast of PET images and superior spatial resolution of CT images. Random walk and graph cut method is integrated to solve the segmentation problem, in which random walk is utilized as an initialization tool to provide object seeds for graph cut segmentation on the PET and CT images. The co-segmentation problem is formulated as an energy minimization problem which is solved by max-flow/min-cut method. A graph, including two sub-graphs and a special link, is constructed, in which one sub-graph is for the PET and another is for CT, and the special link encodes a context term which penalizes the difference of the tumor segmentation on the two modalities. To fully utilize the characteristics of PET and CT images, a novel energy representation is devised. For the PET, a downhill cost and a 3D derivative cost are proposed. For the CT, a shape penalty cost is integrated into the energy function which helps to constrain the tumor region during the segmentation. We validate our algorithm on a data set which consists of 18 PET-CT images. The experimental results indicate that the proposed method is superior to the graph cut method solely using the PET or CT is more accurate compared with the random walk method, random walk co-segmentation method, and non-improved graph cut method.

  9. Comparison of training methods to improve walking in persons with chronic spinal cord injury: a randomized clinical trial

    PubMed Central

    Alexeeva, Natalia; Sames, Carol; Jacobs, Patrick L.; Hobday, Lori; DiStasio, Marcello M.; Mitchell, Sarah A.; Calancie, Blair

    2011-01-01

    Objective To compare two forms of device-specific training – body-weight-supported (BWS) ambulation on a fixed track (TRK) and BWS ambulation on a treadmill (TM) – to comprehensive physical therapy (PT) for improving walking speed in persons with chronic, motor-incomplete spinal cord injury (SCI). Methods Thirty-five adult subjects with a history of chronic SCI (>1 year; AIS ‘C’ or ‘D’) participated in a 13-week (1 hour/day; 3 days per week) training program. Subjects were randomized into one of the three training groups. Subjects in the two BWS groups trained without the benefit of additional input from a physical therapist or gait expert. For each training session, performance values and heart rate were monitored. Pre- and post-training maximal 10-m walking speed, balance, muscle strength, fitness, and quality of life were assessed in each subject. Results All three training groups showed significant improvement in maximal walking speed, muscle strength, and psychological well-being. A significant improvement in balance was seen for PT and TRK groups but not for subjects in the TM group. In all groups, post-training measures of fitness, functional independence, and perceived health and vitality were unchanged. Conclusions Our results demonstrate that persons with chronic, motor-incomplete SCI can improve walking ability and psychological well-being following a concentrated period of ambulation therapy, regardless of training method. Improvement in walking speed was associated with improved balance and muscle strength. In spite of the fact that we withheld any formal input of a physical therapist or gait expert from subjects in the device-specific training groups, these subjects did just as well as subjects receiving comprehensive PT for improving walking speed and strength. It is likely that further modest benefits would accrue to those subjects receiving a combination of device-specific training with input from a physical therapist or gait expert to

  10. Random Walk Graph Laplacian-Based Smoothness Prior for Soft Decoding of JPEG Images

    NASA Astrophysics Data System (ADS)

    Liu, Xianming; Cheung, Gene; Wu, Xiaolin; Zhao, Debin

    2017-02-01

    Given the prevalence of JPEG compressed images, optimizing image reconstruction from the compressed format remains an important problem. Instead of simply reconstructing a pixel block from the centers of indexed DCT coefficient quantization bins (hard decoding), soft decoding reconstructs a block by selecting appropriate coefficient values within the indexed bins with the help of signal priors. The challenge thus lies in how to define suitable priors and apply them effectively. In this paper, we combine three image priors---Laplacian prior for DCT coefficients, sparsity prior and graph-signal smoothness prior for image patches---to construct an efficient JPEG soft decoding algorithm. Specifically, we first use the Laplacian prior to compute a minimum mean square error (MMSE) initial solution for each code block. Next, we show that while the sparsity prior can reduce block artifacts, limiting the size of the over-complete dictionary (to lower computation) would lead to poor recovery of high DCT frequencies. To alleviate this problem, we design a new graph-signal smoothness prior (desired signal has mainly low graph frequencies) based on the left eigenvectors of the random walk graph Laplacian matrix (LERaG). Compared to previous graph-signal smoothness priors, LERaG has desirable image filtering properties with low computation overhead. We demonstrate how LERaG can facilitate recovery of high DCT frequencies of a piecewise smooth (PWS) signal via an interpretation of low graph frequency components as relaxed solutions to normalized cut in spectral clustering. Finally, we construct a soft decoding algorithm using the three signal priors with appropriate prior weights. Experimental results show that our proposal outperforms state-of-the-art soft decoding algorithms in both objective and subjective evaluations noticeably.

  11. Random Walk Graph Laplacian-Based Smoothness Prior for Soft Decoding of JPEG Images.

    PubMed

    Liu, Xianming; Cheung, Gene; Wu, Xiaolin; Zhao, Debin

    2017-02-01

    Given the prevalence of joint photographic experts group (JPEG) compressed images, optimizing image reconstruction from the compressed format remains an important problem. Instead of simply reconstructing a pixel block from the centers of indexed discrete cosine transform (DCT) coefficient quantization bins (hard decoding), soft decoding reconstructs a block by selecting appropriate coefficient values within the indexed bins with the help of signal priors. The challenge thus lies in how to define suitable priors and apply them effectively. In this paper, we combine three image priors-Laplacian prior for DCT coefficients, sparsity prior, and graph-signal smoothness prior for image patches-to construct an efficient JPEG soft decoding algorithm. Specifically, we first use the Laplacian prior to compute a minimum mean square error initial solution for each code block. Next, we show that while the sparsity prior can reduce block artifacts, limiting the size of the overcomplete dictionary (to lower computation) would lead to poor recovery of high DCT frequencies. To alleviate this problem, we design a new graph-signal smoothness prior (desired signal has mainly low graph frequencies) based on the left eigenvectors of the random walk graph Laplacian matrix (LERaG). Compared with the previous graph-signal smoothness priors, LERaG has desirable image filtering properties with low computation overhead. We demonstrate how LERaG can facilitate recovery of high DCT frequencies of a piecewise smooth signal via an interpretation of low graph frequency components as relaxed solutions to normalized cut in spectral clustering. Finally, we construct a soft decoding algorithm using the three signal priors with appropriate prior weights. Experimental results show that our proposal outperforms the state-of-the-art soft decoding algorithms in both objective and subjective evaluations noticeably.

  12. Directional Migration of Recirculating Lymphocytes through Lymph Nodes via Random Walks

    PubMed Central

    Thomas, Niclas; Matejovicova, Lenka; Srikusalanukul, Wichat; Shawe-Taylor, John; Chain, Benny

    2012-01-01

    Naive T lymphocytes exhibit extensive antigen-independent recirculation between blood and lymph nodes, where they may encounter dendritic cells carrying cognate antigen. We examine how long different T cells may spend in an individual lymph node by examining data from long term cannulation of blood and efferent lymphatics of a single lymph node in the sheep. We determine empirically the distribution of transit times of migrating T cells by applying the Least Absolute Shrinkage & Selection Operator () or regularised to fit experimental data describing the proportion of labelled infused cells in blood and efferent lymphatics over time. The optimal inferred solution reveals a distribution with high variance and strong skew. The mode transit time is typically between 10 and 20 hours, but a significant number of cells spend more than 70 hours before exiting. We complement the empirical machine learning based approach by modelling lymphocyte passage through the lymph node . On the basis of previous two photon analysis of lymphocyte movement, we optimised distributions which describe the transit times (first passage times) of discrete one dimensional and continuous (Brownian) three dimensional random walks with drift. The optimal fit is obtained when drift is small, i.e. the ratio of probabilities of migrating forward and backward within the node is close to one. These distributions are qualitatively similar to the inferred empirical distribution, with high variance and strong skew. In contrast, an optimised normal distribution of transit times (symmetrical around mean) fitted the data poorly. The results demonstrate that the rapid recirculation of lymphocytes observed at a macro level is compatible with predominantly randomised movement within lymph nodes, and significant probabilities of long transit times. We discuss how this pattern of migration may contribute to facilitating interactions between low frequency T cells and antigen presenting cells carrying cognate

  13. Are the variability properties of the Kepler AGN light curves consistent with a damped random walk?

    NASA Astrophysics Data System (ADS)

    Kasliwal, Vishal P.; Vogeley, Michael S.; Richards, Gordon T.

    2015-08-01

    We test the consistency of active galactic nuclei (AGN) optical flux variability with the damped random walk (DRW) model. Our sample consists of 20 multiquarter Kepler AGN light curves including both Type 1 and 2 Seyferts, radio-loud and -quiet AGN, quasars, and blazars. Kepler observations of AGN light curves offer a unique insight into the variability properties of AGN light curves because of the very rapid (11.6-28.6 min) and highly uniform rest-frame sampling combined with a photometric precision of 1 part in 105 over a period of 3.5 yr. We categorize the light curves of all 20 objects based on visual similarities and find that the light curves fall into five broad categories. We measure the first-order structure function of these light curves and model the observed light curve with a general broken power-law power spectral density (PSD) characterized by a short-time-scale power-law index γ and turnover time-scale τ. We find that less than half the objects are consistent with a DRW and observe variability on short time-scales (˜2 h). The turnover time-scale τ ranges from ˜10-135 d. Interesting structure function features include pronounced dips on rest-frame time-scales ranging from 10-100 d and varying slopes on different time-scales. The range of observed short-time-scale PSD slopes and the presence of dip and varying slope features suggests that the DRW model may not be appropriate for all AGN. We conclude that AGN variability is a complex phenomenon that requires a more sophisticated statistical treatment.

  14. Anisotropy of the monomer random walk in a polymer melt: local-order and connectivity effects

    NASA Astrophysics Data System (ADS)

    Bernini, S.; Leporini, D.

    2016-05-01

    The random walk of a bonded monomer in a polymer melt is anisotropic due to local order and bond connectivity. We investigate both effects by molecular-dynamics simulations on melts of fully-flexible linear chains ranging from dimers (M  =  2) up to entangled polymers (M  =  200). The corresponding atomic liquid is also considered a reference system. To disentangle the influence of the local geometry and the bond arrangements, and to reveal their interplay, we define suitable measures of the anisotropy emphasising either the former or the latter aspect. Connectivity anisotropy, as measured by the correlation between the initial bond orientation and the direction of the subsequent monomer displacement, shows a slight enhancement due to the local order at times shorter than the structural relaxation time. At intermediate times—when the monomer displacement is comparable to the bond length—a pronounced peak and then decays slowly as t -1/2, becoming negligible when the displacement is as large as about five bond lengths, i.e. about four monomer diameters or three Kuhn lengths. Local-geometry anisotropy, as measured by the correlation between the initial orientation of a characteristic axis of the Voronoi cell and the subsequent monomer dynamics, is affected at shorter times than the structural relaxation time by the cage shape with antagonistic disturbance by the connectivity. Differently, at longer times, the connectivity favours the persistence of the local-geometry anisotropy, which vanishes when the monomer displacement exceeds the bond length. Our results strongly suggest that the sole consideration of the local order is not enough to understand the microscopic origin of the rattling amplitude of the trapped monomer in the cage of the neighbours.

  15. Directed random walks and constraint programming reveal active pathways in hepatocyte growth factor signaling.

    PubMed

    Kittas, Aristotelis; Delobelle, Aurélien; Schmitt, Sabrina; Breuhahn, Kai; Guziolowski, Carito; Grabe, Niels

    2016-01-01

    An effective means to analyze mRNA expression data is to take advantage of established knowledge from pathway databases, using methods such as pathway-enrichment analyses. However, pathway databases are not case-specific and expression data could be used to infer gene-regulation patterns in the context of specific pathways. In addition, canonical pathways may not always describe the signaling mechanisms properly, because interactions can frequently occur between genes in different pathways. Relatively few methods have been proposed to date for generating and analyzing such networks, preserving the causality between gene interactions and reasoning over the qualitative logic of regulatory effects. We present an algorithm (MCWalk) integrated with a logic programming approach, to discover subgraphs in large-scale signaling networks by random walks in a fully automated pipeline. As an exemplary application, we uncover the signal transduction mechanisms in a gene interaction network describing hepatocyte growth factor-stimulated cell migration and proliferation from gene-expression measured with microarray and RT-qPCR using in-house perturbation experiments in a keratinocyte-fibroblast co-culture. The resulting subgraphs illustrate possible associations of hepatocyte growth factor receptor c-Met nodes, differentially expressed genes and cellular states. Using perturbation experiments and Answer Set programming, we are able to select those which are more consistent with the experimental data. We discover key regulator nodes by measuring the frequency with which they are traversed when connecting signaling between receptors and significantly regulated genes and predict their expression-shift consistently with the measured data. The Java implementation of MCWalk is publicly available under the MIT license at: https://bitbucket.org/akittas/biosubg.

  16. Multiscale modeling of interwoven Kevlar fibers based on random walk to predict yarn structural response

    NASA Astrophysics Data System (ADS)

    Recchia, Stephen

    Kevlar is the most common high-end plastic filament yarn used in body armor, tire reinforcement, and wear resistant applications. Kevlar is a trade name for an aramid fiber. These are fibers in which the chain molecules are highly oriented along the fiber axis, so the strength of the chemical bond can be exploited. The bulk material is extruded into filaments that are bound together into yarn, which may be chorded with other materials as in car tires, woven into a fabric, or layered in an epoxy to make composite panels. The high tensile strength to low weight ratio makes this material ideal for designs that decrease weight and inertia, such as automobile tires, body panels, and body armor. For designs that use Kevlar, increasing the strength, or tenacity, to weight ratio would improve performance or reduce cost of all products that are based on this material. This thesis computationally and experimentally investigates the tenacity and stiffness of Kevlar yarns with varying twist ratios. The test boundary conditions were replicated with a geometrically accurate finite element model, resulting in a customized code that can reproduce tortuous filaments in a yarn was developed. The solid model geometry capturing filament tortuosity was implemented through a random walk method of axial geometry creation. A finite element analysis successfully recreated the yarn strength and stiffness dependency observed during the tests. The physics applied in the finite element model was reproduced in an analytical equation that was able to predict the failure strength and strain dependency of twist ratio. The analytical solution can be employed to optimize yarn design for high strength applications.

  17. From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

    NASA Astrophysics Data System (ADS)

    Bodin, Jacques

    2015-03-01

    In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

  18. The importance of being atomic: Ecological invasions as random walks instead of waves.

    PubMed

    Reluga, Timothy C

    2016-12-01

    Invasions are one of the most easily identified spatial phenomena in ecology, and have inspired a rich variety of theories for ecologists' and naturalists' consideration. However, a number of arguments over the sensitivities of invasion rates to stochasticity, density-dependence, dimension, and discreteness persist in the literature. The standard mathematical approach to invasions is based on Fisher's analysis of traveling waves solutions for the spread of an advantageous allele. In this paper, we exploit an alternative theory based on Ellner's premise that species invasions are best interpreted not as waves, but as random walks, and that the discreteness of living organisms is fundamentally important. Using a density-dependent invasion model in a stationary environment with indivisible (atomic) individuals where reproduction and dispersal are stochastic and independent, we show 4 key properties of Ellner's invasions previously suggested by simulation analysis: (1) greater spatial dispersal stochasticity quickens invasions, (2) greater demographic stochasticity slows invasions, (3) negative density-dependence slows invasions, and (4) greater temporal dispersal stochasticity quickens invasions. We prove the first three results by using generating functions and stochastic-dominance methods to rank furthest-forward dispersal distributions. The fourth result is proven in the special case of atomless theory, but remains an open conjecture in atomic theory. In addition, we explain why, unlike atomless invasions, an infinitely wide atomic invasion in two-dimensions can travel faster than a finite-width invasion and a one-dimensional invasion. The paper concludes with a classification of invasion dynamics based on dispersal kernel tails.

  19. Performance of Random Effects Model Estimators under Complex Sampling Designs

    ERIC Educational Resources Information Center

    Jia, Yue; Stokes, Lynne; Harris, Ian; Wang, Yan

    2011-01-01

    In this article, we consider estimation of parameters of random effects models from samples collected via complex multistage designs. Incorporation of sampling weights is one way to reduce estimation bias due to unequal probabilities of selection. Several weighting methods have been proposed in the literature for estimating the parameters of…

  20. Estimation of Quasi-Stiffness of the Human Hip in the Stance Phase of Walking

    PubMed Central

    Shamaei, Kamran; Sawicki, Gregory S.; Dollar, Aaron M.

    2013-01-01

    This work presents a framework for selection of subject-specific quasi-stiffness of hip orthoses and exoskeletons, and other devices that are intended to emulate the biological performance of this joint during walking. The hip joint exhibits linear moment-angular excursion behavior in both the extension and flexion stages of the resilient loading-unloading phase that consists of terminal stance and initial swing phases. Here, we establish statistical models that can closely estimate the slope of linear fits to the moment-angle graph of the hip in this phase, termed as the quasi-stiffness of the hip. Employing an inverse dynamics analysis, we identify a series of parameters that can capture the nearly linear hip quasi-stiffnesses in the resilient loading phase. We then employ regression analysis on experimental moment-angle data of 216 gait trials across 26 human adults walking over a wide range of gait speeds (0.75–2.63 m/s) to obtain a set of general-form statistical models that estimate the hip quasi-stiffnesses using body weight and height, gait speed, and hip excursion. We show that the general-form models can closely estimate the hip quasi-stiffness in the extension (R2 = 92%) and flexion portions (R2 = 89%) of the resilient loading phase of the gait. We further simplify the general-form models and present a set of stature-based models that can estimate the hip quasi-stiffness for the preferred gait speed using only body weight and height with an average error of 27% for the extension stage and 37% for the flexion stage. PMID:24349136

  1. Estimating the Causal Effect of Randomization versus Treatment Preference in a Doubly Randomized Preference Trial

    ERIC Educational Resources Information Center

    Marcus, Sue M.; Stuart, Elizabeth A.; Wang, Pei; Shadish, William R.; Steiner, Peter M.

    2012-01-01

    Although randomized studies have high internal validity, generalizability of the estimated causal effect from randomized clinical trials to real-world clinical or educational practice may be limited. We consider the implication of randomized assignment to treatment, as compared with choice of preferred treatment as it occurs in real-world…

  2. The metabolic cost of changing walking speeds is significant, implies lower optimal speeds for shorter distances, and increases daily energy estimates.

    PubMed

    Seethapathi, Nidhi; Srinivasan, Manoj

    2015-09-01

    Humans do not generally walk at constant speed, except perhaps on a treadmill. Normal walking involves starting, stopping and changing speeds, in addition to roughly steady locomotion. Here, we measure the metabolic energy cost of walking when changing speed. Subjects (healthy adults) walked with oscillating speeds on a constant-speed treadmill, alternating between walking slower and faster than the treadmill belt, moving back and forth in the laboratory frame. The metabolic rate for oscillating-speed walking was significantly higher than that for constant-speed walking (6-20% cost increase for ±0.13-0.27 m s(-1) speed fluctuations). The metabolic rate increase was correlated with two models: a model based on kinetic energy fluctuations and an inverted pendulum walking model, optimized for oscillating-speed constraints. The cost of changing speeds may have behavioural implications: we predicted that the energy-optimal walking speed is lower for shorter distances. We measured preferred human walking speeds for different walking distances and found people preferred lower walking speeds for shorter distances as predicted. Further, analysing published daily walking-bout distributions, we estimate that the cost of changing speeds is 4-8% of daily walking energy budget.

  3. Electron random walk and collisional crossover in a gas in presence of electromagnetic waves and magnetostatic fields

    NASA Astrophysics Data System (ADS)

    Bhattacharjee, Sudeep; Dey, Indranuj; Paul, Samit

    2013-04-01

    This paper deals with random walk of electrons and collisional crossover in a gas evolving toward a plasma, in presence of electromagnetic (EM) waves and magnetostatic (B) fields, a fundamental subject of importance in areas requiring generation and confinement of wave assisted plasmas. In presence of EM waves and B fields, the number of collisions N suffered by an electron with neutral gas atoms while diffusing out of the volume during the walk is significantly modified when compared to the conventional field free square law diffusion; N =1.5(Λ /λ)2, where Λ is the characteristic diffusion length and λ is the mean free path. There is a distinct crossover and a time scale associated with the transition from the elastic to inelastic collisions dominated regime, which can accurately predict the breakdown time (τc) and the threshold electric field (EBD) for plasma initiation. The essential features of cyclotron resonance manifested as a sharp drop in τc, lowering of EBD and enhanced electron energy gain is well reproduced in the constrained random walk.

  4. Changes in work affect in response to lunchtime walking in previously physically inactive employees: A randomized trial.

    PubMed

    Thøgersen-Ntoumani, C; Loughren, E A; Kinnafick, F-E; Taylor, I M; Duda, J L; Fox, K R

    2015-12-01

    Physical activity may regulate affective experiences at work, but controlled studies are needed and there has been a reliance on retrospective accounts of experience. The purpose of the present study was to examine the effect of lunchtime walks on momentary work affect at the individual and group levels. Physically inactive employees (N = 56; M age = 47.68; 92.86% female) from a large university in the UK were randomized to immediate treatment or delayed treatment (DT). The DT participants completed both a control and intervention period. During the intervention period, participants partook in three weekly 30-min lunchtime group-led walks for 10 weeks. They completed twice daily affective reports at work (morning and afternoon) using mobile phones on two randomly chosen days per week. Multilevel modeling was used to analyze the data. Lunchtime walks improved enthusiasm, relaxation, and nervousness at work, although the pattern of results differed depending on whether between-group or within-person analyses were conducted. The intervention was effective in changing some affective states and may have broader implications for public health and workplace performance.

  5. Improved estimation of random vibration loads in launch vehicles

    NASA Technical Reports Server (NTRS)

    Mehta, R.; Erwin, E.; Suryanarayan, S.; Krishna, Murali M. R.

    1993-01-01

    Random vibration induced load is an important component of the total design load environment for payload and launch vehicle components and their support structures. The current approach to random vibration load estimation is based, particularly at the preliminary design stage, on the use of Miles' equation which assumes a single degree-of-freedom (DOF) system and white noise excitation. This paper examines the implications of the use of multi-DOF system models and response calculation based on numerical integration using the actual excitation spectra for random vibration load estimation. The analytical study presented considers a two-DOF system and brings out the effects of modal mass, damping and frequency ratios on the random vibration load factor. The results indicate that load estimates based on the Miles' equation can be significantly different from the more accurate estimates based on multi-DOF models.

  6. Combining motivational and volitional strategies to promote unsupervised walking in patients with fibromyalgia: study protocol for a randomized controlled trial

    PubMed Central

    2014-01-01

    Background Fibromyalgia patients are often advised to engage in regular low- to moderate-intensity physical exercise. The need of fibromyalgia patients to walk has been stressed in previous research. Behavioral self-regulation theories suggest that a combination of motivational aspects (to develop or strengthen a behavioral intention: Theory of Planned Behavior) and volitional aspects (engagement of intention in behavior: implementation intentions) is more effective than a single intervention. In this paper, we describe a protocol for identifying the motivational processes (using the Theory of Planned Behavior) involved in the practice of walking (phase I) and for studying the efficacy of an intervention that combines motivational and volitional contents to enhance the acquisition and continuation of this exercise behavior (phase II). The paper also shows the characteristics of eligible individuals (women who do not walk) and ineligible populations (women who walk or do not walk because of comorbidity without medical recommendation to walk). Both groups consist of members of any of four patients’ associations in Spain who are between 18 and 70 years of age and meet the London Fibromyalgia Epidemiology Study Screening Questionnaire criteria for fibromyalgia. Furthermore, using this study protocol, we will explore the characteristics of participants (eligible women who agreed to participate in the study) and nonparticipants (eligible women who refused to participate). Methods/design Two studies will be conducted: Phase I will be a cross-sectional study, and phase II will be a triple-blind, randomized longitudinal study with two treatment groups and one active control group. The questionnaires were sent to a total of 2,227 members of four patients’ associations in Spain. A total of 920 participants with fibromyalgia returned the questionnaires, and 582 were ultimately selected to participate. Discussion The first data gathered have allowed us to identify the

  7. Diffusion of epicenters of earthquake aftershocks, Omori's law, and generalized continuous-time random walk models.

    PubMed

    Helmstetter, A; Sornette, D

    2002-12-01

    The epidemic-type aftershock sequence (ETAS) model is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power-law decay approximately 1/t(1+theta) of seismicity after an earthquake) and Gutenberg-Richter law (power-law distribution of earthquake energies). In order to describe also the space distribution of seismicity, we use in addition a power-law distribution approximately 1/r(1+mu) of distances between triggered and triggering earthquakes. The ETAS model has been studied for the last two decades to model real seismicity catalogs and to obtain short-term probabilistic forecasts. Here, we present a mapping between the ETAS model and a class of CTRW (continuous time random walk) models, based on the identification of their corresponding master equations. This mapping allows us to use the wealth of results previously obtained on anomalous diffusion of CTRW. After translating into the relevant variable for the ETAS model, we provide a classification of the different regimes of diffusion of seismic activity triggered by a mainshock. Specifically, we derive the relation between the average distance between aftershocks and the mainshock as a function of the time from the mainshock and of the joint probability distribution of the times and locations of the aftershocks. The different regimes are fully characterized by the two exponents theta and mu. Our predictions are checked by careful numerical simulations. We stress the distinction between the "bare" Omori law describing the seismic rate activated directly by a mainshock and the "renormalized" Omori law taking into account all possible cascades from mainshocks to aftershocks of aftershock of aftershock, and so on. In particular, we predict that seismic diffusion or subdiffusion occurs and should be observable only when the observed Omori exponent is less than 1, because this signals the operation of the renormalization of the bare Omori law, also at the

  8. On random walk de Lévy aplicado aos mapas de variâncias

    NASA Astrophysics Data System (ADS)

    Klafke, J. C.

    2003-08-01

    Uma pergunta que surge ao nos confrontarmos com os mapas de variâncias, ou s-Maps [Klafke, J. C. "Estudo da Difusão Caótica em Ressonâncias Asteroidais", Tese de Doutorado, IAG/USP, 2002] diz respeito ao conteúdo físico de tais representações do espaço de fase. Ou seja, o que representa as variâncias das ações obtidas para uma determinada condição inicial e como relacioná-las com o tempo de difusão das órbitas, supondo-se que estas de fato estejam envolvidas em um processo difusivo? Para discutirmos essa questão, lançamos mão da modelagem dos processos estocásticos subjacentes às variâncias determinadas e implementamos uma série de simulações do tipo Monte Carlo a partir das informações registradas nos s-Maps calculados para algumas ressonâncias asteroidais bem estudadas (p.ex. 3: 1, 2: 1 e 3: 2). Para tanto, temos usado uma função de densidade de probabilidade gaussiana ao definir os n passos que permitirão estabelecer uma relação direta entre o Mapa de Difusão e o Mapa de Variâncias. Contudo, os resultados obtidos até agora tem subestimado o tempo de difusão esperado para os fenômenos conhecidos. Tal se deve ao fato de que, no processo difusivo real, é possível existirem passos de comprimento consideravelmente maiores que a média estabelecida pelas distribuições gaussiana ou normal, sobretudo quando se cruza uma região caótica. Neste trabalho, apresentamos os resultados comparativos de simulações de Monte Carlo com base no random walk de Lévy [Klafter, J. et al. 2002. "Beyond Brownian motion", Phys. Today, Feb, 33-39.], o qual possibilita passos esporádicos de comprimento acima do valor médio (saltos) permitindo estabelecer uma escala de tempo mais próxima da esperada para a difusão.

  9. Limitations on the recovery of the true AGN variability parameters using damped random walk modeling

    NASA Astrophysics Data System (ADS)

    Kozłowski, Szymon

    2017-01-01

    Context. The damped random walk (DRW) stochastic process is nowadays frequently used to model aperiodic light curves of active galactic nuclei (AGNs). A number of correlations between the DRW model parameters, the signal decorrelation timescale and amplitude, and the physical AGN parameters, such as the black hole mass or luminosity, have been reported. Aims: We are interested in whether or not it is plausible to correctly measure the DRW parameters from a typical ground-based survey, and, in particular, in how accurate the recovered DRW parameters are compared to the input ones. Methods: By means of Monte Carlo simulations of AGN light curves, we studied the impact of the light curve length, the source magnitude (the photometric properties of a survey), cadence, and additional light (e.g., from a host galaxy) on the DRW model parameters. Results: The most significant finding is that currently existing surveys are going to return unconstrained DRW decorrelation timescales, because typical rest-frame data do not probe long enough timescales or the white noise part of the power spectral density for DRW. The experiment length must be at least ten times longer than the true DRW decorrelation timescale, being presumably in the vicinity of one year, thus meaning the necessity for AGN light curves measuring a minimum of 10 years (rest-frame). The DRW timescales for sufficiently long light curves are typically weakly biased, and the exact bias depends on the fitting method and used priors. The DRW amplitude is mostly affected by the photometric noise (the source magnitude or the signal-to-noise ratio), cadence, and the AGN host light. Conclusions: Because the DRW parameters appear to be incorrectly determined from typically existing data, the reported correlations of the DRW variability and physical AGN parameters from other works seem unlikely to be correct. In particular, the anti-correlation of the DRW decorrelation timescale with redshift is a manifestation of the

  10. Estimates of Random Error in Satellite Rainfall Averages

    NASA Technical Reports Server (NTRS)

    Bell, Thomas L.; Kundu, Prasun K.

    2003-01-01

    Satellite rain estimates are most accurate when obtained with microwave instruments on low earth-orbiting satellites. Estimation of daily or monthly total areal rainfall, typically of interest to hydrologists and climate researchers, is made difficult, however, by the relatively poor coverage generally available from such satellites. Intermittent coverage by the satellites leads to random "sampling error" in the satellite products. The inexact information about hydrometeors inferred from microwave data also leads to random "retrieval errors" in the rain estimates. In this talk we will review approaches to quantitative estimation of the sampling error in area/time averages of satellite rain retrievals using ground-based observations, and methods of estimating rms random error, both sampling and retrieval, in averages using satellite measurements themselves.

  11. Walking speed estimation using foot-mounted inertial sensors: comparing machine learning and strap-down integration methods.

    PubMed

    Mannini, Andrea; Sabatini, Angelo Maria

    2014-10-01

    In this paper we implemented machine learning (ML) and strap-down integration (SDI) methods and analyzed them for their capability of estimating stride-by-stride walking speed. Walking speed was computed by dividing estimated stride length by stride time using data from a foot mounted inertial measurement unit. In SDI methods stride-by-stride walking speed estimation was driven by detecting gait events using a hidden Markov model (HMM) based method (HMM-based SDI); alternatively, a threshold-based gait event detector was investigated (threshold-based SDI). In the ML method a linear regression model was developed for stride length estimation. Whereas the gait event detectors were a priori fixed without training, the regression model was validated with leave-one-subject-out cross-validation. A subject-specific regression model calibration was also implemented to personalize the ML method. Healthy adults performed over-ground walking trials at natural, slower-than-natural and faster-than-natural speeds. The ML method achieved a root mean square estimation error of 2.0% and 4.2%, with and without personalization, against 2.0% and 3.1% by HMM-based SDI and threshold-based SDI. In spite that the results achieved by the two approaches were similar, the ML method, as compared with SDI methods, presented lower intra-subject variability and higher inter-subject variability, which was reduced by personalization.

  12. Radiation breakage of DNA: a model based on random-walk chromatin structure

    NASA Technical Reports Server (NTRS)

    Ponomarev, A. L.; Sachs, R. K.

    2001-01-01

    Monte Carlo computer software, called DNAbreak, has recently been developed to analyze observed non-random clustering of DNA double strand breaks in chromatin after exposure to densely ionizing radiation. The software models coarse-grained configurations of chromatin and radiation tracks, small-scale details being suppressed in order to obtain statistical results for larger scales, up to the size of a whole chromosome. We here give an analytic counterpart of the numerical model, useful for benchmarks, for elucidating the numerical results, for analyzing the assumptions of a more general but less mechanistic "randomly-located-clusters" formalism, and, potentially, for speeding up the calculations. The equations characterize multi-track DNA fragment-size distributions in terms of one-track action; an important step in extrapolating high-dose laboratory results to the much lower doses of main interest in environmental or occupational risk estimation. The approach can utilize the experimental information on DNA fragment-size distributions to draw inferences about large-scale chromatin geometry during cell-cycle interphase.

  13. Analysis of Individual Social-ecological Mediators and Moderators and Their Ability to Explain Effect of a Randomized Neighborhood Walking Intervention

    PubMed Central

    Michael, Yvonne L; Carlson, Nichole E

    2009-01-01

    Background Using data from the SHAPE trial, a randomized 6-month neighborhood-based intervention designed to increase walking activity among older adults, this study identified and analyzed social-ecological factors mediating and moderating changes in walking activity. Methods Three potential mediators (social cohesion, walking efficacy, and perception of neighborhood problems) and minutes of brisk walking were assessed at baseline, 3-months, and 6-months. One moderator, neighborhood walkability, was assessed using an administrative GIS database. The mediating effect of change in process variables on change in brisk walking was tested using a product-of-coefficients test, and we evaluated the moderating effect of neighborhood walkability on change in brisk walking by testing the significance of the interaction between walkability and intervention status. Results Only one of the hypothesized mediators, walking efficacy, explained the intervention effect (product of the coefficients (95% CI) = 8.72 (2.53, 15.56). Contrary to hypotheses, perceived neighborhood problems appeared to suppress the intervention effects (product of the coefficients (95% CI = -2.48, -5.6, -0.22). Neighborhood walkability did not moderate the intervention effect. Conclusion Walking efficacy may be an important mediator of lay-lead walking interventions for sedentary older adults. Social-ecologic theory-based analyses can support clinical interventions to elucidate the mediators and moderators responsible for producing intervention effects. PMID:19643024

  14. Neighborhood walkability, fear and risk of falling and response to walking promotion: The Easy Steps to Health 12-month randomized controlled trial

    PubMed Central

    Merom, D.; Gebel, K.; Fahey, P.; Astell-Burt, T.; Voukelatos, A.; Rissel, C.; Sherrington, C.

    2015-01-01

    In older adults the relationships between health, fall-related risk factors, perceived neighborhood walkability, walking behavior and intervention impacts are poorly understood. To determine whether: i) health and fall-related risk factors were associated with perceptions of neighborhood walkability; ii) perceived environmental attributes, and fall-related risk factors predicted change in walking behavior at 12 months; and iii) perceived environmental attributes and fall-related risk factors moderated the effect of a self-paced walking program on walking behavior. Randomized trial on walking and falls conducted between 2009 and 2012 involving 315 community-dwelling inactive adults ≥ 65 years living in Sydney, Australia. Measures were: mobility status, fall history, injurious fall and fear of falling (i.e., fall-related risk factors), health status, walking self-efficacy and 11 items from the neighborhood walkability scale and planned walking ≥ 150 min/week at 12 months. Participants with poorer mobility, fear of falling, and poor health perceived their surroundings as less walkable. Walking at 12 months was significantly greater in “less greenery” (AOR = 3.3, 95% CI: 1.11–9.98) and “high traffic” (AOR = 1.98, 95% CI: 1.00–3.91) neighborhoods. The intervention had greater effects in neighborhoods perceived to have poorer pedestrian infrastructure (p for interaction = 0.036). Low perceived walkability was shaped by health status and did not appear to be a barrier to walking behavior. There appears to be a greater impact of, and thus, need for, interventions to encourage walking in environments perceived not to have supportive walking infrastructure. Future studies on built environments and walking should gather information on fall-related risk factors to better understand how these characteristics interact. PMID:26844140

  15. An Application of the Random Walk Model to Proper Motions of Coronal Bright Points from SDO Data

    NASA Astrophysics Data System (ADS)

    Skokić, I.; Sudar, D.; Saar, S. H.; Brajša, R.; Poljančić-Beljan, I.

    Atmospheric Imaging Assembly (AIA) images from the Solar Dynamics Observatory (SDO) were used to follow the motions of coronal bright points (CBPs) in the period 1 January - 19 May 2011 with a cadence of 10 minutes. This resulted in a data set of 80966 CBPs with measured lifetimes and mean velocities which were used in a random walk model to calculate the diffusion coefficient, D. The results show that D has a value of ≈260 km^2 s^{-1} for CBPs with lifetime below 6 hours, decreasing to ≈170 km^2 s^{-1} for lifetimes above 12 hours, with a mean value of ≈230 km^2 s^{-1}.

  16. An analytical method for disentangling the roles of adhesion and crowding for random walk models on a crowded lattice

    NASA Astrophysics Data System (ADS)

    Ellery, Adam J.; Baker, Ruth E.; Simpson, Matthew J.

    2016-10-01

    Migration of cells and molecules in vivo is affected by interactions with obstacles. These interactions can include crowding effects, as well as adhesion/repulsion between the motile cell/molecule and the obstacles. Here we present an analytical framework that can be used to separately quantify the roles of crowding and adhesion/repulsion using a lattice-based random walk model. Our method leads to an exact calculation of the long time Fickian diffusivity, and avoids the need for computationally expensive stochastic simulations.

  17. A randomized controlled trial of telephone-mentoring with home-based walking preceding rehabilitation in COPD

    PubMed Central

    Cameron-Tucker, Helen Laura; Wood-Baker, Richard; Joseph, Lyn; Walters, Julia A; Schüz, Natalie; Walters, E Haydn

    2016-01-01

    Purpose With the limited reach of pulmonary rehabilitation (PR) and low levels of daily physical activity in chronic obstructive pulmonary disease (COPD), a need exists to increase daily exercise. This study evaluated telephone health-mentoring targeting home-based walking (tele-rehab) compared to usual waiting time (usual care) followed by group PR. Patients and methods People with COPD were randomized to tele-rehab (intervention) or usual care (controls). Tele-rehab delivered by trained nurse health-mentors supported participants’ home-based walking over 8–12 weeks. PR, delivered to both groups simultaneously, included 8 weeks of once-weekly education and self-management skills, with separate supervised exercise. Data were collected at three time-points: baseline (TP1), before (TP2), and after (TP3) PR. The primary outcome was change in physical capacity measured by 6-minute walk distance (6MWD) with two tests performed at each time-point. Secondary outcomes included changes in self-reported home-based walking, health-related quality of life, and health behaviors. Results Of 65 recruits, 25 withdrew before completing PR. Forty attended a median of 6 (4) education sessions. Seventeen attended supervised exercise (5±2 sessions). Between TP1 and TP2, there was a statistically significant increase in the median 6MWD of 12 (39.1) m in controls, but no change in the tele-rehab group. There were no significant changes in 6MWD between other time-points or groups, or significant change in any secondary outcomes. Participants attending supervised exercise showed a nonsignificant improvement in 6MWD, 12.3 (71) m, while others showed no change, 0 (33) m. The mean 6MWD was significantly greater, but not clinically meaningful, for the second test compared to the first at all time-points. Conclusion Telephone-mentoring for home-based walking demonstrated no benefit to exercise capacity. Two 6-minute walking tests at each time-point may not be necessary. Supervised exercise

  18. Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable

    ERIC Educational Resources Information Center

    du Toit, Stephen H. C.; Cudeck, Robert

    2009-01-01

    A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…

  19. An optimized Kalman filter for the estimate of trunk orientation from inertial sensors data during treadmill walking.

    PubMed

    Mazzà, Claudia; Donati, Marco; McCamley, John; Picerno, Pietro; Cappozzo, Aurelio

    2012-01-01

    The aim of this study was the fine tuning of a Kalman filter with the intent to provide optimal estimates of lower trunk orientation in the frontal and sagittal planes during treadmill walking at different speeds using measured linear acceleration and angular velocity components represented in a local system of reference. Data were simultaneously collected using both an inertial measurement unit (IMU) and a stereophotogrammetric system from three healthy subjects walking on a treadmill at natural, slow and fast speeds. These data were used to estimate the parameters of the Kalman filter that minimized the difference between the trunk orientations provided by the filter and those obtained through stereophotogrammetry. The optimized parameters were then used to process the data collected from a further 15 healthy subjects of both genders and different anthropometry performing the same walking tasks with the aim of determining the robustness of the filter set up. The filter proved to be very robust. The root mean square values of the differences between the angles estimated through the IMU and through stereophotogrammetry were lower than 1.0° and the correlation coefficients between the corresponding curves were greater than 0.91. The proposed filter design can be used to reliably estimate trunk lateral and frontal bending during walking from inertial sensor data. Further studies are needed to determine the filter parameters that are most suitable for other motor tasks.

  20. Determining global mean-first-passage time of random walks on Vicsek fractals using eigenvalues of Laplacian matrices.

    PubMed

    Zhang, Zhongzhi; Wu, Bin; Zhang, Hongjuan; Zhou, Shuigeng; Guan, Jihong; Wang, Zhigang

    2010-03-01

    The family of Vicsek fractals is one of the most important and frequently studied regular fractal classes, and it is of considerable interest to understand the dynamical processes on this treelike fractal family. In this paper, we investigate discrete random walks on the Vicsek fractals, with the aim to obtain the exact solutions to the global mean-first-passage time (GMFPT), defined as the average of first-passage time (FPT) between two nodes over the whole family of fractals. Based on the known connections between FPTs, effective resistance, and the eigenvalues of graph Laplacian, we determine implicitly the GMFPT of the Vicsek fractals, which is corroborated by numerical results. The obtained closed-form solution shows that the GMFPT approximately grows as a power-law function with system size (number of all nodes), with the exponent lies between 1 and 2. We then provide both the upper bound and lower bound for GMFPT of general trees, and show that the leading behavior of the upper bound is the square of system size and the dominating scaling of the lower bound varies linearly with system size. We also show that the upper bound can be achieved in linear chains and the lower bound can be reached in star graphs. This study provides a comprehensive understanding of random walks on the Vicsek fractals and general treelike networks.

  1. Prioritization of rheumatoid arthritis risk subpathways based on global immune subpathway interaction network and random walk strategy.

    PubMed

    Lv, Wenhua; Wang, Qiuyu; Chen, He; Jiang, Yongshuai; Zheng, Jiajia; Shi, Miao; Xu, Yanjun; Han, Junwei; Li, Chunquan; Zhang, Ruijie

    2015-11-01

    The initiation and development of rheumatoid arthritis (RA) is closely related to mutual dysfunction of multiple pathways. Furthermore, some similar molecular mechanisms are shared between RA and other immune diseases. Therefore it is vital to reveal the molecular mechanism of RA through searching for subpathways of immune diseases and investigating the crosstalk effect among subpathways. Here we exploited an integrated approach combining both construction of a subpathway-subpathway interaction network and a random walk strategy to prioritize RA risk subpathways. Our research can be divided into three parts: (1) acquisition of risk genes and identification of risk subpathways of 85 immune diseases by using subpathway-lenient distance similarity (subpathway-LDS) method; (2) construction of a global immune subpathway interaction (GISI) network with subpathways identified by subpathway-LDS; (3) optimization of RA risk subpathways by random walk strategy based on GISI network. The results showed that our method could effectively identify RA risk subpathways, such as MAPK signaling pathway, prostate cancer pathway and chemokine signaling pathway. The integrated strategy considering crosstalk between immune subpathways significantly improved the effect of risk subpathway identification. With the development of GWAS, our method will provide insight into exploring molecular mechanisms of immune diseases and might be a promising approach for studying other diseases.

  2. Exact two-point resistance, and the simple random walk on the complete graph minus N edges

    SciTech Connect

    Chair, Noureddine

    2012-12-15

    An analytical approach is developed to obtain the exact expressions for the two-point resistance and the total effective resistance of the complete graph minus N edges of the opposite vertices. These expressions are written in terms of certain numbers that we introduce, which we call the Bejaia and the Pisa numbers; these numbers are the natural generalizations of the bisected Fibonacci and Lucas numbers. The correspondence between random walks and the resistor networks is then used to obtain the exact expressions for the first passage and mean first passage times on this graph. - Highlights: Black-Right-Pointing-Pointer We obtain exact formulas for the two-point resistance of the complete graph minus N edges. Black-Right-Pointing-Pointer We obtain also the total effective resistance of this graph. Black-Right-Pointing-Pointer We modified Schwatt's formula on trigonometrical power sum to suit our computations. Black-Right-Pointing-Pointer We introduced the generalized bisected Fibonacci and Lucas numbers: the Bejaia and the Pisa numbers. Black-Right-Pointing-Pointer The first passage and mean first passage times of the random walks have exact expressions.

  3. A seed-expanding method based on random walks for community detection in networks with ambiguous community structures

    PubMed Central

    Su, Yansen; Wang, Bangju; Zhang, Xingyi

    2017-01-01

    Community detection has received a great deal of attention, since it could help to reveal the useful information hidden in complex networks. Although most previous modularity-based and local modularity-based community detection algorithms could detect strong communities, they may fail to exactly detect several weak communities. In this work, we define a network with clear or ambiguous community structures based on the types of its communities. A seed-expanding method based on random walks is proposed to detect communities for networks, especially for the networks with ambiguous community structures. We identify local maximum degree nodes, and detect seed communities in a network. Then, the probability of a node belonging to each community is calculated based on the total probability model and random walks, and each community is expanded by repeatedly adding the node which is most likely to belong to it. Finally, we use the community optimization method to ensure that each node is in a community. Experimental results on both computer-generated and real-world networks demonstrate that the quality of the communities detected by the proposed algorithm is superior to the- state-of-the-art algorithms in the networks with ambiguous community structures. PMID:28157183

  4. A seed-expanding method based on random walks for community detection in networks with ambiguous community structures

    NASA Astrophysics Data System (ADS)

    Su, Yansen; Wang, Bangju; Zhang, Xingyi

    2017-02-01

    Community detection has received a great deal of attention, since it could help to reveal the useful information hidden in complex networks. Although most previous modularity-based and local modularity-based community detection algorithms could detect strong communities, they may fail to exactly detect several weak communities. In this work, we define a network with clear or ambiguous community structures based on the types of its communities. A seed-expanding method based on random walks is proposed to detect communities for networks, especially for the networks with ambiguous community structures. We identify local maximum degree nodes, and detect seed communities in a network. Then, the probability of a node belonging to each community is calculated based on the total probability model and random walks, and each community is expanded by repeatedly adding the node which is most likely to belong to it. Finally, we use the community optimization method to ensure that each node is in a community. Experimental results on both computer-generated and real-world networks demonstrate that the quality of the communities detected by the proposed algorithm is superior to the- state-of-the-art algorithms in the networks with ambiguous community structures.

  5. Effects on Balance and Walking with the CoDuSe Balance Exercise Program in People with Multiple Sclerosis: A Multicenter Randomized Controlled Trial

    PubMed Central

    von Koch, Lena

    2016-01-01

    Background. Balance and walking impairments are frequent in people with multiple sclerosis (MS). Objective. The aim was to investigate the effects of a group-based balance exercise program targeting core stability, dual tasking, and sensory strategies (CoDuSe) on balance, postural sway, walking, perceived walking limitations, and balance confidence. Design. A single-blinded randomized multicenter trial. No intervention was given to controls. Participants. People with MS able to walk 100 meters but unable to maintain tandem stance ≥30 seconds. Eighty-seven participants were randomized to intervention or control. Intervention. The 60-minute CoDuSe group program, twice weekly for seven weeks, supervised by physical therapists. Measurements. Primary outcome was dynamic balance (Berg Balance Scale (BBS)). Secondary outcomes were postural sway, walking (Timed-Up and Go test; Functional Gait Assessment (FGA)), MS Walking Scale, and Activities-specific Balance Confidence (ABC) Scale. Assessments were performed before and after (week 8) the intervention. Results. 73 participants fulfilled the study. There were significant differences between the intervention and the control groups in change in the BBS and in the secondary measures: postural sway with eyes open, FGA, MS Walking Scale, and ABC scale in favor of the intervention. Conclusions. The seven-week CoDuSe program improved dynamic balance more than no intervention. PMID:28042485

  6. Lasso adjustments of treatment effect estimates in randomized experiments

    PubMed Central

    Bloniarz, Adam; Liu, Hanzhong; Zhang, Cun-Hui; Sekhon, Jasjeet S.; Yu, Bin

    2016-01-01

    We provide a principled way for investigators to analyze randomized experiments when the number of covariates is large. Investigators often use linear multivariate regression to analyze randomized experiments instead of simply reporting the difference of means between treatment and control groups. Their aim is to reduce the variance of the estimated treatment effect by adjusting for covariates. If there are a large number of covariates relative to the number of observations, regression may perform poorly because of overfitting. In such cases, the least absolute shrinkage and selection operator (Lasso) may be helpful. We study the resulting Lasso-based treatment effect estimator under the Neyman–Rubin model of randomized experiments. We present theoretical conditions that guarantee that the estimator is more efficient than the simple difference-of-means estimator, and we provide a conservative estimator of the asymptotic variance, which can yield tighter confidence intervals than the difference-of-means estimator. Simulation and data examples show that Lasso-based adjustment can be advantageous even when the number of covariates is less than the number of observations. Specifically, a variant using Lasso for selection and ordinary least squares (OLS) for estimation performs particularly well, and it chooses a smoothing parameter based on combined performance of Lasso and OLS. PMID:27382153

  7. Estimating random signal parameters from noisy images with nuisance parameters

    PubMed Central

    Whitaker, Meredith Kathryn; Clarkson, Eric; Barrett, Harrison H.

    2008-01-01

    In a pure estimation task, an object of interest is known to be present, and we wish to determine numerical values for parameters that describe the object. This paper compares the theoretical framework, implementation method, and performance of two estimation procedures. We examined the performance of these estimators for tasks such as estimating signal location, signal volume, signal amplitude, or any combination of these parameters. The signal is embedded in a random background to simulate the effect of nuisance parameters. First, we explore the classical Wiener estimator, which operates linearly on the data and minimizes the ensemble mean-squared error. The results of our performance tests indicate that the Wiener estimator can estimate amplitude and shape once a signal has been located, but is fundamentally unable to locate a signal regardless of the quality of the image. Given these new results on the fundamental limitations of Wiener estimation, we extend our methods to include more complex data processing. We introduce and evaluate a scanning-linear estimator that performs impressively for location estimation. The scanning action of the estimator refers to seeking a solution that maximizes a linear metric, thereby requiring a global-extremum search. The linear metric to be optimized can be derived as a special case of maximum a posteriori (MAP) estimation when the likelihood is Gaussian and a slowly varying covariance approximation is made. PMID:18545527

  8. [Estimation of energy expenditure and the validity of pitch counting during walking and jogging by piezoelectric materials].

    PubMed

    Yoshida, T; Udo, M; Mizuno, C; Yamanaka, H; Tasaka, I

    1992-09-01

    The purpose of the present study was to assess the validity of Piezo-electric accelerometer for estimating energy expenditure in walking and jogging. Energy consumption by oxygen uptake was determined during steady state level of treadmill walking at the speed of 60, 80 and 100 m/min and jogging at the speed of 100, 120, 140, and 160 m/min for 10 subjects. There was a highly significant correlation between the energy consumption and the estimated energy expenditure by an accelerometer despite the attached position (r = 0.912 at the waist, r = 0.915 at the chest, P < 0.001), which suggests accurate estimating energy expenditure in the field.

  9. Tactile and proprioceptive sensory stimulation modifies estimation of walking distance but not upright gait stability: a pilot study

    PubMed Central

    Paolucci, Teresa; Piccinini, Giulia; Paolucci, Stefano; Spadini, Ennio; Saraceni, Vincenzo Maria; Morone, Giovanni

    2015-01-01

    [Purpose] Recently, there has been growing interest in the somatosensory system, but little data exist on the interaction between dynamic postural control and the somatosensory system. The purpose of this study was to determine whether a training program, based on tactile and proprioceptive sensory stimulation of the trunk with the use of perceptual surfaces, improved the estimation of walking distance by healthy subjects, the ability to walk toward a memorized distance without vision, and whether it increases upright gait stability. [Subjects and Methods] Ten healthy subjects with a mean age of 31.9 ± 2.5 years were enrolled and participated in 10 daily sessions of perceptive training using perceptual surfaces, for 45 minutes each session. An experimental indoor test measured the subjects’ ability to perceive walking distances to a memorized target in an indoor environment. [Results] After treatment, the distances that were traversed were closer to the target than before treatment. Trunk acceleration did not differ significantly between pre- and post-training and did not increase significantly after training. [Conclusion] Treatment with perceptual surfaces stimulating the trunk midline improves the estimation of walking distance and modifies proprioceptive gait patterns, allowing various corrective strategies to be implemented during ambulation. PMID:26644695

  10. Split-belt walking adaptation recalibrates sensorimotor estimates of leg speed but not position or force

    PubMed Central

    Vazquez, Alejandro; Statton, Matthew A.; Busgang, Stefanie A.

    2015-01-01

    Motor learning during reaching not only recalibrates movement but can also lead to small but consistent changes in the sense of arm position. Studies have suggested that this sensory effect may be the result of recalibration of a forward model that associates motor commands with their sensory consequences. Here we investigated whether similar perceptual changes occur in the lower limbs after learning a new walking pattern on a split-belt treadmill—a task that critically involves proprioception. Specifically, we studied how this motor learning task affects perception of leg speed during walking, perception of leg position during standing or walking, and perception of contact force during stepping. Our results show that split-belt adaptation leads to robust motor aftereffects and alters the perception of leg speed during walking. This is specific to the direction of walking that was trained during adaptation (i.e., backward or forward). The change in leg speed perception accounts for roughly half of the observed motor aftereffect. In contrast, split-belt adaptation does not alter the perception of leg position during standing or walking and does not change the perception of stepping force. Our results demonstrate that there is a recalibration of a sensory percept specific to the domain of the perturbation that was applied during walking (i.e., speed but not position or force). Furthermore, the motor and sensory consequences of locomotor adaptation may be linked, suggesting overlapping mechanisms driving changes in the motor and sensory domains. PMID:26424576

  11. A polymer, random walk model for the size-distribution of large DNA fragments after high linear energy transfer radiation

    NASA Technical Reports Server (NTRS)

    Ponomarev, A. L.; Brenner, D.; Hlatky, L. R.; Sachs, R. K.

    2000-01-01

    DNA double-strand breaks (DSBs) produced by densely ionizing radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. Stochastic DSB clustering at large scales, from > 100 Mbp down to < 0.01 Mbp, is modeled using computer simulations and analytic equations. A random-walk, coarse-grained polymer model for chromatin is combined with a simple track structure model in Monte Carlo software called DNAbreak and is applied to data on alpha-particle irradiation of V-79 cells. The chromatin model neglects molecular details but systematically incorporates an increase in average spatial separation between two DNA loci as the number of base-pairs between the loci increases. Fragment-size distributions obtained using DNAbreak match data on large fragments about as well as distributions previously obtained with a less mechanistic approach. Dose-response relations, linear at small doses of high linear energy transfer (LET) radiation, are obtained. They are found to be non-linear when the dose becomes so large that there is a significant probability of overlapping or close juxtaposition, along one chromosome, for different DSB clusters from different tracks. The non-linearity is more evident for large fragments than for small. The DNAbreak results furnish an example of the RLC (randomly located clusters) analytic formalism, which generalizes the broken-stick fragment-size distribution of the random-breakage model that is often applied to low-LET data.

  12. Statistics of Persistent Events in the Binomial Random Walk: Will the Drunken Sailor Hit the Sober Man?

    NASA Astrophysics Data System (ADS)

    Bauer, M.; Godrèche, C.; Luck, J. M.

    1999-09-01

    The statistics of persistent events, recently introduced in the context of phase ordering dynamics, is investigated in the case of the one-dimensional lattice random walk in discrete time. We determine the survival probability of the random walker in the presence of an obstacle moving ballistically with velocity v, i.e., the probability that the random walker remains up to time n on the left of the obstacle. Three regimes are to be considered for the long-time behavior of this probability, according to the sign of the difference between v and the drift velocity V¯ of the random walker. In one of these regimes ( v> V¯), the survival probability has a nontrivial limit at long times which is discontinuous at all rational values of v. An algebraic approach allows us to compute these discontinuities as well as several related quantities. The mathematical structure underlying the solvability of this model combines elementary number theory, algebraic functions, and algebraic curves defined over the rationals.

  13. Cover estimation and payload location using Markov random fields

    NASA Astrophysics Data System (ADS)

    Quach, Tu-Thach

    2014-02-01

    Payload location is an approach to find the message bits hidden in steganographic images, but not necessarily their logical order. Its success relies primarily on the accuracy of the underlying cover estimators and can be improved if more estimators are used. This paper presents an approach based on Markov random field to estimate the cover image given a stego image. It uses pairwise constraints to capture the natural two-dimensional statistics of cover images and forms a basis for more sophisticated models. Experimental results show that it is competitive against current state-of-the-art estimators and can locate payload embedded by simple LSB steganography and group-parity steganography. Furthermore, when combined with existing estimators, payload location accuracy improves significantly.

  14. Direct measurement of the dynamics of hole hopping in extended DNA G-tracts. An unbiased random walk.

    PubMed

    Conron, Sarah M Mickley; Thazhathveetil, Arun K; Wasielewski, Michael R; Burin, Alexander L; Lewis, Frederick D

    2010-10-20

    We report the measurement of distance- and temperature-dependent rate constants for charge separation in capped hairpins in which a stilbene hole acceptor and hole donor are separated by A(3)G(n) diblock polypurine sequences consisting of 3 adenines and 1-19 guanines. The longer diblock systems obey the simplest model for an unbiased random walk, providing a direct measurement of k(hop) = 4.3 × 10(9) s(-1) for a single reversible G-to-G hole hopping step, somewhat faster than the value of 1.2 × 10(9) s(-1) calculated for A-tract hole hopping. The temperature dependence for hopping in A(3)G(13) provides values of E(act) = 2.8 kcal/mol and A = 7 × 10(9) s(-1), consistent with a weakly activated, conformationally gated process.

  15. Random walk approach to spin dynamics in a two-dimensional electron gas with spin-orbit coupling

    SciTech Connect

    Yang, Luyi; Orenstein, J.; Lee, Dung-Hai

    2010-09-27

    We introduce and solve a semiclassical random walk (RW) model that describes the dynamics of spin polarization waves in zinc-blende semiconductor quantum wells. We derive the dispersion relations for these waves, including the Rashba, linear and cubic Dresselhaus spin-orbit interactions, as well as the effects of an electric field applied parallel to the spin polarization wave vector. In agreement with calculations based on quantum kinetic theory [P. Kleinert and V. V. Bryksin, Phys. Rev. B 76, 205326 (2007)], the RW approach predicts that spin waves acquire a phase velocity in the presence of the field that crosses zero at a nonzero wave vector, q{sub 0}. In addition, we show that the spin-wave decay rate is independent of field at q{sub 0} but increases as (q-q{sub 0}){sup 2} for q {ne} q{sub 0}. These predictions can be tested experimentally by suitable transient spin grating experiments.

  16. A micro-scale random-walk model for radionuclide migration based on image analysis-derived modelling grids

    NASA Astrophysics Data System (ADS)

    Eberhard Falck, W.; Vokal, Vratko

    2010-01-01

    This paper describes the development of a random-walk transport model for the migration of radionuclides in hard-rocks at the grain scale. The physics of diffusion are reviewed and it is described how they are translated into the appropriate model algorithm. Further, the algorithm for recognising solid grain boundaries during the migration step is discussed. The model grid is derived from the analysis of images obtained by optical micro-photography and from autoradiography of hardrock samples impregnated with 14C-marked resins. Sample calculations for tracer-transport cases and simple reaction, i.e. precipitation cases are presented. It is envisaged to couple the code with a geochemical speciation code at a later stage.

  17. The non-random walk of stock prices: the long-term correlation between signs and sizes

    NASA Astrophysics Data System (ADS)

    La Spada, G.; Farmer, J. D.; Lillo, F.

    2008-08-01

    We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about 70%, and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-contemporaneous correlation between the signs and sizes of individual returns. We conjecture that this is related to the long-memory of transaction signs and the need to enforce market efficiency.

  18. Methods for a Randomized Trial of Weight-Supported Treadmill Training versus Conventional Training for Walking during Inpatient Rehabilitation after Incomplete Traumatic Spinal Cord Injury

    PubMed Central

    Dobkin, Bruce H.; Apple, David; Barbeau, Hugues; Basso, Michele; Behrman, Andrea; Deforge, Dan; Ditunno, John; Dudley, Gary; Elashoff, Robert; Fugate, Lisa; Harkema, Susan; Saulino, Michael; Scott, Michael

    2014-01-01

    The authors describe the rationale and methodology for the first prospective, multicenter, randomized clinical trial (RCT) of a task-oriented walking intervention for subjects during early rehabilitation for an acute traumatic spinal cord injury (SCI). The experimental strategy, body weight–supported treadmill training (BWSTT), allows physical therapists to systematically train patients to walk on a treadmill at increasing speeds typical of community ambulation with increasing weight bearing. The therapists provide verbal and tactile cues to facilitate the kinematic, kinetic, and temporal features of walking. Subjects were randomly assigned to a conventional therapy program for mobility versus the same intensity and duration of a combination of BWSTT and over-ground locomotor retraining. Subjects had an incomplete SCI (American Spinal Injury Association grades B, C, and D) from C-4 to T-10 (upper motoneuron group) or from T-11 to L-3 (lower motoneuron group). Within 8 weeks of a SCI, 146 subjects were entered for 12 weeks of intervention. The 2 single-blinded primary outcome measures are the level of independence for ambulation and, for those who are able to walk, the maximal speed for walking 50 feet, tested 6 and 12 months after randomization. The trial’s methodology offers a model for the feasibility of translating neuroscientific experiments into a RCT to develop evidence-based rehabilitation practices. PMID:14503436

  19. Random walk of processive, quantum dot-labeled myosin Va molecules within the actin cortex of COS-7 cells.

    PubMed

    Nelson, Shane R; Ali, M Yusuf; Trybus, Kathleen M; Warshaw, David M

    2009-07-22

    Myosin Va (myoVa) is an actin-based intracellular cargo transporter. In vitro experiments have established that a single myoVa moves processively along actin tracks, but less is known about how this motor operates within cells. Here we track the movement of a quantum dot (Qdot)-labeled myoVa HMM in COS-7 cells using total internal reflectance fluorescence microscopy. This labeling approach is unique in that it allows myoVa, instead of its cargo, to be tracked. Single-particle analysis showed short periods (random nature of the trajectories represents processive myoVa motors undergoing a random walk through the dense and randomly oriented cortical actin network.

  20. Random Walk of Processive, Quantum Dot-Labeled Myosin Va Molecules within the Actin Cortex of COS-7 Cells

    PubMed Central

    Nelson, Shane R.; Ali, M. Yusuf; Trybus, Kathleen M.; Warshaw, David M.

    2009-01-01

    Abstract Myosin Va (myoVa) is an actin-based intracellular cargo transporter. In vitro experiments have established that a single myoVa moves processively along actin tracks, but less is known about how this motor operates within cells. Here we track the movement of a quantum dot (Qdot)-labeled myoVa HMM in COS-7 cells using total internal reflectance fluorescence microscopy. This labeling approach is unique in that it allows myoVa, instead of its cargo, to be tracked. Single-particle analysis showed short periods (≤0.5 s) of ATP-sensitive linear motion. The mean velocity of these trajectories was 604 nm/s and independent of the number of myoVa molecules attached to the Qdot. With high time (16.6 ms) and spatial (15 nm) resolution imaging, Qdot-labeled myoVa moved with sequential 75 nm steps per head, at a rate of 16 s−1, similarly to myoVa in vitro. Monte Carlo modeling suggests that the random nature of the trajectories represents processive myoVa motors undergoing a random walk through the dense and randomly oriented cortical actin network. PMID:19619465

  1. Step-Detection and Adaptive Step-Length Estimation for Pedestrian Dead-Reckoning at Various Walking Speeds Using a Smartphone

    PubMed Central

    Ho, Ngoc-Huynh; Truong, Phuc Huu; Jeong, Gu-Min

    2016-01-01

    We propose a walking distance estimation method based on an adaptive step-length estimator at various walking speeds using a smartphone. First, we apply a fast Fourier transform (FFT)-based smoother on the acceleration data collected by the smartphone to remove the interference signals. Then, we analyze these data using a set of step-detection rules in order to detect walking steps. Using an adaptive estimator, which is based on a model of average step speed, we accurately obtain the walking step length. To evaluate the accuracy of the proposed method, we examine the distance estimation for four different distances and three speed levels. The experimental results show that the proposed method significantly outperforms conventional estimation methods in terms of accuracy. PMID:27598171

  2. Stochastic modeling of short-term exposure close to an air pollution source in a naturally ventilated room: an autocorrelated random walk method.

    PubMed

    Cheng, Kai-Chung; Acevedo-Bolton, Viviana; Jiang, Ruo-Ting; Klepeis, Neil E; Ott, Wayne R; Kitanidis, Peter K; Hildemann, Lynn M

    2014-01-01

    For an actively emitting source such as cooking or smoking, indoor measurements have shown a strong "proximity effect" within 1 m. The significant increase in both the magnitude and variation of concentration near a source is attributable to transient high peaks that occur sporadically-and these "microplumes" cause great uncertainty in estimating personal exposure. Recent field studies in naturally ventilated rooms show that close-proximity concentrations are approximately lognormally distributed. We use the autocorrelated random walk method to represent the time-varying directionality of indoor emissions, thereby predicting the time series and frequency distributions of concentrations close to an actively emitting point source. The predicted 5-min concentrations show good agreement with measurements from a point source of CO in a naturally ventilated house-the measured and predicted frequency distributions at 0.5- and 1-m distances are similar and approximately lognormal over a concentration range spanning three orders of magnitude. By including the transient peak concentrations, this random airflow modeling method offers a way to more accurately assess acute exposure levels for cases where well-defined airflow patterns in an indoor space are not available.

  3. Estimation of Parameters from Discrete Random Nonstationary Time Series

    NASA Astrophysics Data System (ADS)

    Takayasu, H.; Nakamura, T.

    For the analysis of nonstationary stochastic time series we introduce a formulation to estimate the underlying time-dependent parameters. This method is designed for random events with small numbers that are out of the applicability range of the normal distribution. The method is demonstrated for numerical data generated by a known system, and applied to time series of traffic accidents, batting average of a baseball player and sales volume of home electronics.

  4. Quantum walk computation

    SciTech Connect

    Kendon, Viv

    2014-12-04

    Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. Recent results showing quantum walks are “universal for quantum computation” relate to algorithms, to be run on quantum computers. We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer.

  5. Colloidal Dancers: Designing networks of DNA-functionalized colloids for non-random walks

    NASA Astrophysics Data System (ADS)

    Gehrels, Emily W.; Rogers, W. Benjamin; Zeravcic, Zorana; Manoharan, Vinothan N.

    2014-03-01

    We present experimental developments of a system of DNA-functionalized colloidal particles with the goal of creating directed motion (`dancing') along patterned substrates in response to temperature cycling. We take advantage of toehold exchange in the design of the DNA sequences that mediate the colloidal interactions to produce broadened, flat, or even re-entrant binding and unbinding transitions between the particles and substrate. Using this new freedom of design, we devise systems where, by thermal ratcheting, we can externally control the direction of motion and sequence of steps of the colloidal dancer. In comparison to DNA-based walkers, which move autonomously and whose motion is controlled by the substrate, our colloidal dancers respond to external driving, and their motion can be controlled in situ. Our use of DNA-functionalized colloidal particles instead of pure DNA systems also enables walking on the mesoscale in contrast to the molecular length scales previously demonstrated, allowing for the future prospect of directed transport over larger distances.

  6. Can Nonexperimental Estimates Replicate Estimates Based on Random Assignment in Evaluations of School Choice? A Within-Study Comparison

    ERIC Educational Resources Information Center

    Bifulco, Robert

    2012-01-01

    The ability of nonexperimental estimators to match impact estimates derived from random assignment is examined using data from the evaluation of two interdistrict magnet schools. As in previous within-study comparisons, nonexperimental estimates differ from estimates based on random assignment when nonexperimental estimators are implemented…

  7. Logical-Rule Models of Classification Response Times: A Synthesis of Mental-Architecture, Random-Walk, and Decision-Bound Approaches

    ERIC Educational Resources Information Center

    Fific, Mario; Little, Daniel R.; Nosofsky, Robert M.

    2010-01-01

    We formalize and provide tests of a set of logical-rule models for predicting perceptual classification response times (RTs) and choice probabilities. The models are developed by synthesizing mental-architecture, random-walk, and decision-bound approaches. According to the models, people make independent decisions about the locations of stimuli…

  8. Random walk, zonation and the food searching strategy of Terebralia palustris (Mollusca, Potamididae) in Kenya

    NASA Astrophysics Data System (ADS)

    Vannini, Marco; Cannicci, Stefano; Mrabu, Elisha; Rorandelli, Rocco; Fratini, Sara

    2008-12-01

    Terebralia palustris is a common mud-whelk present at a particularly high density in all Indo-West Pacific mangroves. Young snails feed on nothing but mud while larger specimens are able to feed on fallen leaves too. In Kenya (Mida Creek) under the canopy, competition for mangrove leaves can be very high due to the high density of Sesarmidae crabs. On open exposed muddy platforms, no Sesarmidae occur but the leaf density is very low because the leaves are only randomly present as they are deposited and removed twice a day by the tide. However, the snail density is always very high, raising the question as to whether the snails use a special searching strategy to optimize their resource finding rather than a purely random movement. By analyzing the snails' movements on a uniform area at different levels and comparing them with simulated random paths, we could show that the snails' movements are not purely random. The distribution of different size classes of T. palustris in Mida Creek was known to be quite odd: the same simulation approach suggests that the zonation asymmetry could reasonably be due to the stochastic recruitment of juveniles in space and time and maintained by a substantial long-lasting spatial inertia.

  9. Random Walks on a Simple Cubic Lattice, the Multinomial Theorem, and Configurational Properties of Polymers

    ERIC Educational Resources Information Center

    Hladky, Paul W.

    2007-01-01

    Random-climb models enable undergraduate chemistry students to visualize polymer molecules, quantify their configurational properties, and relate molecular structure to a variety of physical properties. The model could serve as an introduction to more elaborate models of polymer molecules and could help in learning topics such as lattice models of…

  10. A Telehealth Intervention Using Nintendo Wii Fit Balance Boards and iPads to Improve Walking in Older Adults With Lower Limb Amputation (Wii.n.Walk): Study Protocol for a Randomized Controlled Trial

    PubMed Central

    Imam, Bita; Finlayson, Heather C; Eng, Janice J; Payne, Michael WC; Jarus, Tal; Goldsmith, Charles H; Mitchell, Ian M

    2014-01-01

    Background The number of older adults living with lower limb amputation (LLA) who require rehabilitation for improving their walking capacity and mobility is growing. Existing rehabilitation practices frequently fail to meet this demand. Nintendo Wii Fit may be a valuable tool to enable rehabilitation interventions. Based on pilot studies, we have developed “Wii.n.Walk”, an in-home telehealth Wii Fit intervention targeted to improve walking capacity in older adults with LLA. Objective The objective of this study is to determine whether the Wii.n.Walk intervention enhances walking capacity compared to an attention control group. Methods This project is a multi-site (Vancouver BC, London ON), parallel, evaluator-blind randomized controlled trial. Participants include community-dwelling older adults over the age of 50 years with unilateral transtibial or transfemoral amputation. Participants will be stratified by site and block randomized in triplets to either the Wii.n.Walk intervention or an attention control group employing the Wii Big Brain cognitive software. This trial will include both supervised and unsupervised phases. During the supervised phase, both groups will receive 40-minute sessions of supervised group training three times per week for a duration of 4 weeks. Participants will complete the first week of the intervention in groups of three at their local rehabilitation center with a trainer. The remaining 3 weeks will take place at participants’ homes using remote supervision by the trainer using Apple iPad technology. At the end of 4 weeks, the supervised period will end and the unsupervised period will begin. Participants will retain the Wii console and be encouraged to continue using the program for an additional 4 weeks’ duration. The primary outcome measure will be the “Two-Minute Walk Test” to measure walking capacity. Outcome measures will be evaluated for all participants at baseline, after the end of both the supervised and

  11. Estimation of foot trajectory during human walking by a wearable inertial measurement unit mounted to the foot.

    PubMed

    Kitagawa, Naoki; Ogihara, Naomichi

    2016-03-01

    To establish a supportive technology for reducing the risk of falling in older people, it is essential to clarify gait characteristics in elderly individuals that are possibly linked to the risk of falling during actual daily activities. In this study, we developed a system to monitor human gait in an outdoor environment using an inertial measurement unit consisting of a tri-axial accelerometer and tri-axial gyroscope. Step-by-step foot trajectories were estimated from the sensor unit attached to the dorsum of the foot. Specifically, stride length and foot clearance were calculated by integrating the gravity-compensated translational acceleration over time during the swing phase. Zero vertical velocity and displacement corrections were applied to obtain the final trajectory, assuming the slope of the walking surface is negligible. Short, normal, and long stride-length walking of 10 healthy participants was simultaneously measured using the proposed system and a conventional motion capture system to evaluate the accuracy of the estimated foot trajectory. Mean accuracy and precision were approximately 20 ± 50 mm, for stride length, and 2 ± 7 mm for foot clearance, indicating that the swing phase trajectory of the sensor unit attached to the foot was reconstructed more accurately and precisely using the proposed system than with previously published methods owing to the flat floor assumption. Although some methodological limitations certainly apply, this system will serve as a useful tool to monitor human walking during daily activities.

  12. Random walk of electrons in a gas in the presence of polarized electromagnetic waves: Genesis of a wave induced discharge

    NASA Astrophysics Data System (ADS)

    Bhattacharjee, Sudeep; Paul, Samit

    2009-10-01

    The average number of collisions N of seed electrons with neutral gas atoms during random walk in escaping from a given volume, in the presence of polarized electromagnetic waves, is found to vary as N =B(Λ /λ)2/[1+C(Λ /λ)]2, indicating a modification to the conventional field free square law N =A(Λ /λ)2, where Λ is the characteristic diffusion length and λ the mean free path. It is found that for the field free case A =1.5 if all the electrons originate at the center and is 1.25 if they are allowed to originate at any random point in the given volume. The B and C coefficients depend on the wave electric field and frequency. Predictions of true discharge initiation time τc can be made from the temporal evolution of seed electrons over a wide range of collision frequencies. For linearly polarized waves of 2.45 GHz and electric field in the range (0.6-1.0)×105 V/m, τc=5.5-1.6 ns for an unmagnetized microwave driven discharge at 1 Torr argon.

  13. Hybrid random walk-linear discriminant analysis method for unwrapping quantitative phase microscopy images of biological samples

    PubMed Central

    Kim, Diane N. H.; Teitell, Michael A.; Reed, Jason; Zangle, Thomas A.

    2015-01-01

    Abstract. Standard algorithms for phase unwrapping often fail for interferometric quantitative phase imaging (QPI) of biological samples due to the variable morphology of these samples and the requirement to image at low light intensities to avoid phototoxicity. We describe a new algorithm combining random walk-based image segmentation with linear discriminant analysis (LDA)-based feature detection, using assumptions about the morphology of biological samples to account for phase ambiguities when standard methods have failed. We present three versions of our method: first, a method for LDA image segmentation based on a manually compiled training dataset; second, a method using a random walker (RW) algorithm informed by the assumed properties of a biological phase image; and third, an algorithm which combines LDA-based edge detection with an efficient RW algorithm. We show that the combination of LDA plus the RW algorithm gives the best overall performance with little speed penalty compared to LDA alone, and that this algorithm can be further optimized using a genetic algorithm to yield superior performance for phase unwrapping of QPI data from biological samples. PMID:26305212

  14. Continuous-time random walk models of DNA electrophoresis in a post array: part I. Evaluation of existing models.

    PubMed

    Olson, Daniel W; Ou, Jia; Tian, Mingwei; Dorfman, Kevin D

    2011-02-01

    Several continuous-time random walk (CTRW) models exist to predict the dynamics of DNA in micropost arrays, but none of them quantitatively describes the separation seen in experiments or simulations. In Part I of this series, we examine the assumptions underlying these models by observing single molecules of λ DNA during electrophoresis in a regular, hexagonal array of oxidized silicon posts. Our analysis takes advantage of a combination of single-molecule videomicroscopy and previous Brownian dynamics simulations. Using a custom-tracking program, we automatically identify DNA-post collisions and thus study a large ensemble of events. Our results show that the hold-up time and the distance between collisions for consecutive collisions are uncorrelated. The distance between collisions is a random variable, but it can be smaller than the minimum value predicted by existing models of DNA transport in post arrays. The current CTRW models correctly predict the exponential decay in the probability density of the collision hold-up times, but they fail to account for the influence of finite-sized posts on short hold-up times. The shortcomings of the existing models identified here motivate the development of a new CTRW approach, which is presented in Part II of this series.

  15. Random Walks in the Presence of Absorbing Barriers in Parrondo's Games

    NASA Astrophysics Data System (ADS)

    Yang, Liu; Zheng, Kai-Xuan; Xie, Neng-Gang; Ye, Ye; Wang, Lu

    2015-10-01

    For a multi-agent spatial Parrondo's model that it is composed of games A and B, we use the discrete time Markov chains to derive the probability transition matrix. Then, we respectively deduce the stationary distribution for games A and B played individually and the randomized combination of game A + B. We notice that under a specific set of parameters, two absorbing states instead of a fixed stationary distribution exist in game B. However, the randomized game A + B can jump out of the absorbing states of game B and has a fixed stationary distribution because of the "agitating" role of game A. Moreover, starting at different initial states, we deduce the probabilities of absorption at the two absorbing barriers.

  16. Simple unified view of branching process statistics: Random walks in balanced logarithmic potentials

    NASA Astrophysics Data System (ADS)

    di Santo, Serena; Villegas, Pablo; Burioni, Raffaella; Muñoz, Miguel A.

    2017-03-01

    We revisit the problem of deriving the mean-field values of avalanche exponents in systems with absorbing states. These are well known to coincide with those of unbiased branching processes. Here we show that for at least four different universality classes (directed percolation, dynamical percolation, the voter model or compact directed percolation class, and the Manna class of stochastic sandpiles) this common result can be obtained by mapping the corresponding Langevin equations describing each of them into a random walker confined to the origin by a logarithmic potential. We report on the emergence of nonuniversal continuously varying exponent values stemming from the presence of small external driving - that might induce avalanche merging - that, to the best of our knowledge, has not been noticed in the past. Many of the other results derived here appear in the literature as independently derived for individual universality classes or for the branching process itself. Still, we believe that a simple and unified perspective as the one presented here can help (1) clarify the overall picture, (2) underline the superuniversality of the behavior as well as the dependence on external driving, and (3) avoid the common existing confusion between unbiased branching processes (equivalent to a random walker in a balanced logarithmic potential) and standard (unconfined) random walkers.

  17. The influence of a user-adaptive prosthetic knee across varying walking speeds: A randomized cross-over trial.

    PubMed

    Prinsen, E C; Nederhand, M J; Sveinsdóttir, H S; Prins, M R; van der Meer, F; Koopman, H F J M; Rietman, J S

    2017-01-01

    Previously conducted trials comparing the gait pattern of individuals with a transfemoral amputation using a user-adaptive and a non-microprocessor-controlled prosthetic knee (NMPK) found mixed and conflicting results. Few trials, however, have compared user-adaptive to non-adaptive prosthetic knees across different walking speeds. Because of the ability of variable damping, the effect of user-adaptive knees might be more pronounced at lower or higher walking speeds. Our aim was to compare the Rheo Knee II (a microprocessor-controlled prosthetic knee) with NMPKs across varying walking speeds. In addition, we studied compensatory mechanisms associated with non-optimal prosthetic knee kinematics, such as intact ankle vaulting and vertical acceleration of the pelvis. Nine persons with a transfemoral amputation or knee disarticulation were included and measured with their own NMPK and with the Rheo Knee II. Measurements were performed at three walking speeds: preferred walking speed, 70% preferred walking speed and 115% preferred walking speed. No differences on peak prosthetic knee flexion during swing were found between prosthetic knee conditions. In addition, prosthetic knee flexion increased significantly with walking speed for both prosthetic knee conditions. At 70% preferred walking speed we found that vaulting of the intact ankle was significantly decreased while walking with the Rheo Knee II compared to the NMPK condition (P=0.028). We did not find differences in peak vertical acceleration of the pelvis during initial and mid-swing of the prosthetic leg. In conclusion, comparison of walking with the Rheo Knee II to walking with a NMPK across different walking speeds showed limited differences in gait parameters.

  18. A proposal for the experimental detection of CSL induced random walk.

    PubMed

    Bera, Sayantani; Motwani, Bhawna; Singh, Tejinder P; Ulbricht, Hendrik

    2015-01-07

    Continuous Spontaneous Localization (CSL) is one possible explanation for dynamically induced collapse of the wave-function during a quantum measurement. The collapse is mediated by a stochastic non-linear modification of the Schrödinger equation. A consequence of the CSL mechanism is an extremely tiny violation of energy-momentum conservation, which can, in principle, be detected in the laboratory via the random diffusion of a particle induced by the stochastic collapse mechanism. In a paper in 2003, Collett and Pearle investigated the translational CSL diffusion of a sphere, and the rotational CSL diffusion of a disc, and showed that this effect dominates over the ambient environmental noise at low temperatures and extremely low pressures (about ten-thousandth of a pico-Torr). In the present paper, we revisit their analysis and argue that this stringent condition on pressure can be relaxed, and that the CSL effect can be seen at the pressure of about a pico-Torr. A similar analysis is provided for diffusion produced by gravity-induced decoherence, where the effect is typically much weaker than CSL. We also discuss the CSL induced random displacement of a quantum oscillator. Lastly, we propose possible experimental set-ups justifying that CSL diffusion is indeed measurable with the current technology.

  19. A proposal for the experimental detection of CSL induced random walk

    PubMed Central

    Bera, Sayantani; Motwani, Bhawna; Singh, Tejinder P.; Ulbricht, Hendrik

    2015-01-01

    Continuous Spontaneous Localization (CSL) is one possible explanation for dynamically induced collapse of the wave-function during a quantum measurement. The collapse is mediated by a stochastic non-linear modification of the Schrödinger equation. A consequence of the CSL mechanism is an extremely tiny violation of energy-momentum conservation, which can, in principle, be detected in the laboratory via the random diffusion of a particle induced by the stochastic collapse mechanism. In a paper in 2003, Collett and Pearle investigated the translational CSL diffusion of a sphere, and the rotational CSL diffusion of a disc, and showed that this effect dominates over the ambient environmental noise at low temperatures and extremely low pressures (about ten-thousandth of a pico-Torr). In the present paper, we revisit their analysis and argue that this stringent condition on pressure can be relaxed, and that the CSL effect can be seen at the pressure of about a pico-Torr. A similar analysis is provided for diffusion produced by gravity-induced decoherence, where the effect is typically much weaker than CSL. We also discuss the CSL induced random displacement of a quantum oscillator. Lastly, we propose possible experimental set-ups justifying that CSL diffusion is indeed measurable with the current technology. PMID:25563619

  20. Comparing Estimators of Microbiological Attributes by Random Subsamples

    NASA Astrophysics Data System (ADS)

    Li, M.; Adriaens, P.

    2005-12-01

    validation approach called bootstrapping, which randomly take a designed number of data points out of the data set, and examine the reproduction of their estimate by the rest of the data. The repeated random selection will be used to compare the M-scale model to the ordinary kriging, visualized quantitatively by quantile-quantile (Q-Q) plots and scatter plots. Estimates and uncertainties evaluated by the M-scale model will be compared using the random subsets, to examine the unbiasedness of the estimate as well as the appropriateness of the uncertainty evaluated. An additional comparison, using the dataset collected in Anacostia River, Washington D.C., can further be used to inform further applicability under sparsely sampled site. For a conclusive test, artificial datasets based on different scenario will then be generated, in order to examine the general performance and restriction of the models under different data distribution and spatial structures.

  1. Molecular motion in cell membranes: Analytic study of fence-hindered random walks

    NASA Astrophysics Data System (ADS)

    Kenkre, V. M.; Giuggioli, L.; Kalay, Z.

    2008-05-01

    A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G -protein coupled μ -opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.

  2. The implementation of a community-based aerobic walking program for mild to moderate knee osteoarthritis: A knowledge translation randomized controlled trial: Part II: Clinical outcomes

    PubMed Central

    2012-01-01

    Background Osteoarthritis (OA) is the most common joint disorder in the world, as it is appears to be prevalent among 80% of individuals over the age of 75. Although physical activities such as walking have been scientifically proven to improve physical function and arthritic symptoms, individuals with OA tend to adopt a sedentary lifestyle. There is therefore a need to improve knowledge translation in order to influence individuals to adopt effective self-management interventions, such as an adapted walking program. Methods A single-blind, randomized control trial was conducted. Subjects (n = 222) were randomized to one of three knowledge translation groups: 1) Walking and Behavioural intervention (WB) (18 males, 57 females) which included the supervised community-based aerobic walking program combined with a behavioural intervention and an educational pamphlet on the benefits of walking; 2) Walking intervention (W) (24 males, 57 females) wherein participants only received the supervised community-based aerobic walking program intervention and the educational pamphlet; 3) Self-directed control (C) (32 males, 52 females) wherein participants only received the educational pamphlet. One-way analyses of variance were used to test for differences in quality of life, adherence, confidence, and clinical outcomes among the study groups at each 3 month assessment during the 12-month intervention period and 6-month follow-up period. Results The clinical and quality of life outcomes improved among participants in each of the three comparative groups. However, there were few statistically significant differences observed for quality of life and clinical outcomes at long-term measurements at 12-months end of intervention and at 6- months post intervention (18-month follow-up). Outcome results varied among the three groups. Conclusion The three groups were equivalent when determining the effectiveness of knowledge uptake and improvements in quality of life and other

  3. Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice

    NASA Astrophysics Data System (ADS)

    Ellery, Adam J.; Baker, Ruth E.; Simpson, Matthew J.

    2016-05-01

    The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motion of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations.

  4. Validation of the English version of the Walking Estimated-Limitation Calculated by History (WELCH) questionnaire in patients with intermittent claudication.

    PubMed

    Tew, Garry A; Nawaz, Shah; Humphreys, Liam; Ouedraogo, Nafi; Abraham, Pierre

    2014-02-01

    The Walking Estimated-Limitation Calculated by History (WELCH) questionnaire has recently been proposed as a valid and simple instrument for assessing walking limitation in patients with intermittent claudication. The aim of this study was to validate an English version of the WELCH questionnaire in an English native population. Thirty-nine patients (ankle-brachial index 0.59 ± 0.16, age 65 ± 11 years, 82% male) completed an English version of the WELCH questionnaire. Maximum walking distance was measured objectively using the Gardner-Skinner treadmill test and the 6-minute walk test. The median WELCH score was 24 (9-39). Maximum walking distances were 412 m (149-675 m) for the treadmill test and 381 ± 88 m for the 6-minute walking test. The Spearman's correlation coefficient was ρ = 0.59 between the WELCH score and treadmill distance (p < 0.001) and ρ = 0.82 between the WELCH score and 6-minute walk distance (p < 0.001). These findings suggest that the English version of the WELCH questionnaire is a valid instrument for assessing walking impairment in patients with intermittent claudication.

  5. Spatially random models, estimation theory, and robot arm dynamics

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.

    1987-01-01

    Spatially random models provide an alternative to the more traditional deterministic models used to describe robot arm dynamics. These alternative models can be used to establish a relationship between the methodologies of estimation theory and robot dynamics. A new class of algorithms for many of the fundamental robotics problems of inverse and forward dynamics, inverse kinematics, etc. can be developed that use computations typical in estimation theory. The algorithms make extensive use of the difference equations of Kalman filtering and Bryson-Frazier smoothing to conduct spatial recursions. The spatially random models are very easy to describe and are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. The models can also be used to generate numerically the composite multibody system inertia matrix. This is done without resorting to the more common methods of deterministic modeling involving Lagrangian dynamics, Newton-Euler equations, etc. These methods make substantial use of human knowledge in derivation and minipulation of equations of motion for complex mechanical systems.

  6. Multiscale approach to pest insect monitoring: random walks, pattern formation, synchronization, and networks.

    PubMed

    Petrovskii, Sergei; Petrovskaya, Natalia; Bearup, Daniel

    2014-09-01

    Pest insects pose a significant threat to food production worldwide resulting in annual losses worth hundreds of billions of dollars. Pest control attempts to prevent pest outbreaks that could otherwise destroy a sward. It is good practice in integrated pest management to recommend control actions (usually pesticides application) only when the pest density exceeds a certain threshold. Accurate estimation of pest population density in ecosystems, especially in agro-ecosystems, is therefore very important, and this is the overall goal of the pest insect monitoring. However, this is a complex and challenging task; providing accurate information about pest abundance is hardly possible without taking into account the complexity of ecosystems' dynamics, in particular, the existence of multiple scales. In the case of pest insects, monitoring has three different spatial scales, each of them having their own scale-specific goal and their own approaches to data collection and interpretation. In this paper, we review recent progress in mathematical models and methods applied at each of these scales and show how it helps to improve the accuracy and robustness of pest population density estimation.

  7. Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks

    NASA Astrophysics Data System (ADS)

    Petrovskii, Sergei; Petrovskaya, Natalia; Bearup, Daniel

    2014-09-01

    Pest insects pose a significant threat to food production worldwide resulting in annual losses worth hundreds of billions of dollars. Pest control attempts to prevent pest outbreaks that could otherwise destroy a sward. It is good practice in integrated pest management to recommend control actions (usually pesticides application) only when the pest density exceeds a certain threshold. Accurate estimation of pest population density in ecosystems, especially in agro-ecosystems, is therefore very important, and this is the overall goal of the pest insect monitoring. However, this is a complex and challenging task; providing accurate information about pest abundance is hardly possible without taking into account the complexity of ecosystems' dynamics, in particular, the existence of multiple scales. In the case of pest insects, monitoring has three different spatial scales, each of them having their own scale-specific goal and their own approaches to data collection and interpretation. In this paper, we review recent progress in mathematical models and methods applied at each of these scales and show how it helps to improve the accuracy and robustness of pest population density estimation.

  8. An empirical evaluation of lightweight random walk based routing protocol in duty cycle aware wireless sensor networks.

    PubMed

    Mian, Adnan Noor; Fatima, Mehwish; Khan, Raees; Prakash, Ravi

    2014-01-01

    Energy efficiency is an important design paradigm in Wireless Sensor Networks (WSNs) and its consumption in dynamic environment is even more critical. Duty cycling of sensor nodes is used to address the energy consumption problem. However, along with advantages, duty cycle aware networks introduce some complexities like synchronization and latency. Due to their inherent characteristics, many traditional routing protocols show low performance in densely deployed WSNs with duty cycle awareness, when sensor nodes are supposed to have high mobility. In this paper we first present a three messages exchange Lightweight Random Walk Routing (LRWR) protocol and then evaluate its performance in WSNs for routing low data rate packets. Through NS-2 based simulations, we examine the LRWR protocol by comparing it with DYMO, a widely used WSN protocol, in both static and dynamic environments with varying duty cycles, assuming the standard IEEE 802.15.4 in lower layers. Results for the three metrics, that is, reliability, end-to-end delay, and energy consumption, show that LRWR protocol outperforms DYMO in scalability, mobility, and robustness, showing this protocol as a suitable choice in low duty cycle and dense WSNs.

  9. Global industrial impact coefficient based on random walk process and inter-country input-output table

    NASA Astrophysics Data System (ADS)

    Xing, Lizhi; Dong, Xianlei; Guan, Jun

    2017-04-01

    Input-output table is very comprehensive and detailed in describing the national economic system with lots of economic relationships, which contains supply and demand information among industrial sectors. The complex network, a theory and method for measuring the structure of complex system, can describe the structural characteristics of the internal structure of the research object by measuring the structural indicators of the social and economic system, revealing the complex relationship between the inner hierarchy and the external economic function. This paper builds up GIVCN-WIOT models based on World Input-Output Database in order to depict the topological structure of Global Value Chain (GVC), and assumes the competitive advantage of nations is equal to the overall performance of its domestic sectors' impact on the GVC. Under the perspective of econophysics, Global Industrial Impact Coefficient (GIIC) is proposed to measure the national competitiveness in gaining information superiority and intermediate interests. Analysis of GIVCN-WIOT models yields several insights including the following: (1) sectors with higher Random Walk Centrality contribute more to transmitting value streams within the global economic system; (2) Half-Value Ratio can be used to measure robustness of open-economy macroeconomics in the process of globalization; (3) the positive correlation between GIIC and GDP indicates that one country's global industrial impact could reveal its international competitive advantage.

  10. Correlated continuous time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics

    NASA Astrophysics Data System (ADS)

    Schulz, Johannes H. P.; Chechkin, Aleksei V.; Metzler, Ralf

    2013-11-01

    Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through scale-free forms of the jump length and/or waiting time distributions by virtue of the generalized central limit theorem. Here we present a modified version of recently proposed correlated CTRW processes, where we incorporate a power-law correlated noise on the level of both jump length and waiting time dynamics. We obtain a very general stochastic model, that encompasses key features of several paradigmatic models of anomalous diffusion: discontinuous, scale-free displacements as in Lévy flights, scale-free waiting times as in subdiffusive CTRWs, and the long-range temporal correlations of fractional Brownian motion (FBM). We derive the exact solutions for the single-time probability density functions and extract the scaling behaviours. Interestingly, we find that different combinations of the model parameters lead to indistinguishable shapes of the emerging probability density functions and identical scaling laws. Our model will be useful for describing recent experimental single particle tracking data that feature a combination of CTRW and FBM properties.

  11. Promoting walking as an adjunct intervention to group cognitive behavioral therapy for anxiety disorders--a pilot group randomized trial.

    PubMed

    Merom, Dafna; Phongsavan, Philayrath; Wagner, Renate; Chey, Tien; Marnane, Claire; Steel, Zachary; Silove, Derrick; Bauman, Adrian

    2008-08-01

    A group randomized trial of adding a home-based walking program to a standard group cognitive behavioral therapy (GCBT+EX) was compared with groups receiving GCBT and educational sessions (GCBT+ED). The study was implemented in an outpatient clinic providing GCBT for clients diagnosed with panic disorder, generalized anxiety disorder or social phobia. Pre- and post-treatment measures included the self-report depression, anxiety, and stress scale (DASS-21) and measures of physical activity. From January 2004 to May 2005, six groups were allocated to GCBT+EX (n=38) and five to GCBT+ED (n=36). Analysis of covariance for completed cases (GCBT+EX, n=21; GCBT+ED, n=20), adjusting for the group design, baseline DASS-21 scores, and anxiety diagnosis showed significant effect for GCBT+EX on depression, anxiety, and stress (regression coefficients=-6.21, -3.41, and -5.14, respectively, p<0.05) compared to the GCBT+ED. The potential of exercise interventions as adjunct to GCBT for anxiety disorder needs to be further explored.

  12. An Empirical Evaluation of Lightweight Random Walk Based Routing Protocol in Duty Cycle Aware Wireless Sensor Networks

    PubMed Central

    Fatima, Mehwish

    2014-01-01

    Energy efficiency is an important design paradigm in Wireless Sensor Networks (WSNs) and its consumption in dynamic environment is even more critical. Duty cycling of sensor nodes is used to address the energy consumption problem. However, along with advantages, duty cycle aware networks introduce some complexities like synchronization and latency. Due to their inherent characteristics, many traditional routing protocols show low performance in densely deployed WSNs with duty cycle awareness, when sensor nodes are supposed to have high mobility. In this paper we first present a three messages exchange Lightweight Random Walk Routing (LRWR) protocol and then evaluate its performance in WSNs for routing low data rate packets. Through NS-2 based simulations, we examine the LRWR protocol by comparing it with DYMO, a widely used WSN protocol, in both static and dynamic environments with varying duty cycles, assuming the standard IEEE 802.15.4 in lower layers. Results for the three metrics, that is, reliability, end-to-end delay, and energy consumption, show that LRWR protocol outperforms DYMO in scalability, mobility, and robustness, showing this protocol as a suitable choice in low duty cycle and dense WSNs. PMID:24696667

  13. A correction scheme for a simplified analytical random walk model algorithm of proton dose calculation in distal Bragg peak regions

    NASA Astrophysics Data System (ADS)

    Yao, Weiguang; Merchant, Thomas E.; Farr, Jonathan B.

    2016-10-01

    The lateral homogeneity assumption is used in most analytical algorithms for proton dose, such as the pencil-beam algorithms and our simplified analytical random walk model. To improve the dose calculation in the distal fall-off region in heterogeneous media, we analyzed primary proton fluence near heterogeneous media and propose to calculate the lateral fluence with voxel-specific Gaussian distributions. The lateral fluence from a beamlet is no longer expressed by a single Gaussian for all the lateral voxels, but by a specific Gaussian for each lateral voxel. The voxel-specific Gaussian for the beamlet of interest is calculated by re-initializing the fluence deviation on an effective surface where the proton energies of the beamlet of interest and the beamlet passing the voxel are the same. The dose improvement from the correction scheme was demonstrated by the dose distributions in two sets of heterogeneous phantoms consisting of cortical bone, lung, and water and by evaluating distributions in example patients with a head-and-neck tumor and metal spinal implants. The dose distributions from Monte Carlo simulations were used as the reference. The correction scheme effectively improved the dose calculation accuracy in the distal fall-off region and increased the gamma test pass rate. The extra computation for the correction was about 20% of that for the original algorithm but is dependent upon patient geometry.

  14. Records for the number of distinct sites visited by a random walk on the fully connected lattice

    NASA Astrophysics Data System (ADS)

    Turban, Loïc

    2015-11-01

    We consider a random walk on the fully connected lattice with N sites and study the time evolution of the number of distinct sites s visited by the walker on a subset with n sites. A record value v is obtained for s at a record time t when the walker visits a site of the subset for the first time. The record time t is a partial covering time when v\\lt n and a total covering time when v = n. The probability distributions for the number of records s, the record value v and the record (covering) time t, involving r-Stirling numbers, are obtained using generating function techniques. The mean values, variances and skewnesses are deduced from the generating functions. In the scaling limit the probability distributions for s and v lead to the same Gaussian density. The fluctuations of the record time t are also Gaussian at partial covering, when n-v={{O}}(n). They are distributed according to the type-I Gumbel extreme-value distribution at total covering, when v = n. A discrete sequence of generalized Gumbel distributions, indexed by n-v, is obtained at almost total covering, when n-v={{O}}(1). These generalized Gumbel distributions are crossing over to the Gaussian distribution when n - v increases.

  15. Correlation of electron transport and photocatalysis of nanocrystalline clusters studied by Monte-Carlo continuity random walking.

    PubMed

    Liu, Baoshun; Li, Ziqiang; Zhao, Xiujian

    2015-02-21

    In this research, Monte-Carlo Continuity Random Walking (MC-RW) model was used to study the relation between electron transport and photocatalysis of nano-crystalline (nc) clusters. The effects of defect energy disorder, spatial disorder of material structure, electron density, and interfacial transfer/recombination on the electron transport and the photocatalysis were studied. Photocatalytic activity is defined as 1/τ from a statistical viewpoint with τ being the electron average lifetime. Based on the MC-RW simulation, a clear physical and chemical "picture" was given for the photocatalytic kinetic analysis of nc-clusters. It is shown that the increase of defect energy disorder and material spatial structural disorder, such as the decrease of defect trap number, the increase of crystallinity, the increase of particle size, and the increase of inter-particle connection, can enhance photocatalytic activity through increasing electron transport ability. The increase of electron density increases the electron Fermi level, which decreases the activation energy for electron de-trapping from traps to extending states, and correspondingly increases electron transport ability and photocatalytic activity. Reducing recombination of electrons and holes can increase electron transport through the increase of electron density and then increases the photocatalytic activity. In addition to the electron transport, the increase of probability for electrons to undergo photocatalysis can increase photocatalytic activity through the increase of the electron interfacial transfer speed.

  16. Random walks based multi-image segmentation: Quasiconvexity results and GPU-based solutions

    PubMed Central

    Collins, Maxwell D.; Xu, Jia; Grady, Leo; Singh, Vikas

    2012-01-01

    We recast the Cosegmentation problem using Random Walker (RW) segmentation as the core segmentation algorithm, rather than the traditional MRF approach adopted in the literature so far. Our formulation is similar to previous approaches in the sense that it also permits Cosegmentation constraints (which impose consistency between the extracted objects from ≥ 2 images) using a nonparametric model. However, several previous nonparametric cosegmentation methods have the serious limitation that they require adding one auxiliary node (or variable) for every pair of pixels that are similar (which effectively limits such methods to describing only those objects that have high entropy appearance models). In contrast, our proposed model completely eliminates this restrictive dependence –the resulting improvements are quite significant. Our model further allows an optimization scheme exploiting quasiconvexity for model-based segmentation with no dependence on the scale of the segmented foreground. Finally, we show that the optimization can be expressed in terms of linear algebra operations on sparse matrices which are easily mapped to GPU architecture. We provide a highly specialized CUDA library for Cosegmentation exploiting this special structure, and report experimental results showing these advantages. PMID:25278742

  17. Random walk patterns of a soil bacterium in open and confined environments

    NASA Astrophysics Data System (ADS)

    Theves, M.; Taktikos, J.; Zaburdaev, V.; Stark, H.; Beta, C.

    2015-01-01

    We used microfluidic tools and high-speed time-lapse microscopy to record trajectories of the soil bacterium Pseudomonas putida in a confined environment with cells swimming in close proximity to a glass-liquid interface. While the general swimming pattern is preserved, when compared to swimming in the bulk fluid, our results show that cells in the presence of two solid boundaries display more frequent reversals in swimming direction and swim faster. Additionally, we observe that run segments are no longer straight and that cells swim on circular trajectories, which can be attributed to the hydrodynamic wall effect. Using the experimentally observed parameters together with a recently presented analytic model for a run-reverse random walker, we obtained additional insight on how the spreading behavior of a cell population is affected under confinement. While on short time scales, the mean square displacement of confined swimmers grows faster as compared to the bulk fluid case, our model predicts that for large times the situation reverses due to the strong increase in effective rotational diffusion.

  18. Random walks based multi-image segmentation: Quasiconvexity results and GPU-based solutions.

    PubMed

    Collins, Maxwell D; Xu, Jia; Grady, Leo; Singh, Vikas

    2012-01-01

    We recast the Cosegmentation problem using Random Walker (RW) segmentation as the core segmentation algorithm, rather than the traditional MRF approach adopted in the literature so far. Our formulation is similar to previous approaches in the sense that it also permits Cosegmentation constraints (which impose consistency between the extracted objects from ≥ 2 images) using a nonparametric model. However, several previous nonparametric cosegmentation methods have the serious limitation that they require adding one auxiliary node (or variable) for every pair of pixels that are similar (which effectively limits such methods to describing only those objects that have high entropy appearance models). In contrast, our proposed model completely eliminates this restrictive dependence -the resulting improvements are quite significant. Our model further allows an optimization scheme exploiting quasiconvexity for model-based segmentation with no dependence on the scale of the segmented foreground. Finally, we show that the optimization can be expressed in terms of linear algebra operations on sparse matrices which are easily mapped to GPU architecture. We provide a highly specialized CUDA library for Cosegmentation exploiting this special structure, and report experimental results showing these advantages.

  19. Consistent Estimation in Mendelian Randomization with Some Invalid Instruments Using a Weighted Median Estimator

    PubMed Central

    Bowden, Jack; Davey Smith, George; Haycock, Philip C.

    2016-01-01

    ABSTRACT Developments in genome‐wide association studies and the increasing availability of summary genetic association data have made application of Mendelian randomization relatively straightforward. However, obtaining reliable results from a Mendelian randomization investigation remains problematic, as the conventional inverse‐variance weighted method only gives consistent estimates if all of the genetic variants in the analysis are valid instrumental variables. We present a novel weighted median estimator for combining data on multiple genetic variants into a single causal estimate. This estimator is consistent even when up to 50% of the information comes from invalid instrumental variables. In a simulation analysis, it is shown to have better finite‐sample Type 1 error rates than the inverse‐variance weighted method, and is complementary to the recently proposed MR‐Egger (Mendelian randomization‐Egger) regression method. In analyses of the causal effects of low‐density lipoprotein cholesterol and high‐density lipoprotein cholesterol on coronary artery disease risk, the inverse‐variance weighted method suggests a causal effect of both lipid fractions, whereas the weighted median and MR‐Egger regression methods suggest a null effect of high‐density lipoprotein cholesterol that corresponds with the experimental evidence. Both median‐based and MR‐Egger regression methods should be considered as sensitivity analyses for Mendelian randomization investigations with multiple genetic variants. PMID:27061298

  20. From Random Walks to Brownian Motion, from Diffusion to Entropy: Statistical Principles in Introductory Physics

    NASA Astrophysics Data System (ADS)

    Reeves, Mark

    2014-03-01

    Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is dominant contribution of the entropy in driving important biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy) that enable students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce seemingly complex biological processes and structures to be described by tractable models that include deterministic processes and simple probabilistic inference. The students test these models in simulations and in laboratory experiments that are biologically relevant. The students are challenged to bridge the gap between statistical parameterization of their data (mean and standard deviation) and simple model-building by inference. This allows the students to quantitatively describe realistic cellular processes such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront ``random'' forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk

  1. Solutions of the integral equation of diffusion and the random walk model for continuous plumes and instantaneous puffs in the atmospheric boundary layer

    NASA Astrophysics Data System (ADS)

    Smith, F. B.; Thomson, D.

    1984-09-01

    The integral equation method is related to the random walk modelling that has proved so effective and popular in recent years. The I.E. method, by using simple probability techniques, avoids the inefficient determination of thousands of trajectories in order to build up concentration profiles. In fact it is so simple and efficient it can be run on a conventional programmable calculator. The method is applied to passive material being released from an elevated source within a neutrally stable surface layer over a uniform surface, and also to an instantaneous release when the effect of wind shear is examined. The latter scenario is also studied using random walk techniques and a comparison of the solutions obtained. Agreement is very good, although downwind spread is shown to be quite sensitive to gridlength size in the I.E. method.

  2. ON THE ESTIMATION OF RANDOM UNCERTAINTIES OF STAR FORMATION HISTORIES

    SciTech Connect

    Dolphin, Andrew E.

    2013-09-20

    The standard technique for measurement of random uncertainties of star formation histories (SFHs) is the bootstrap Monte Carlo, in which the color-magnitude diagram (CMD) is repeatedly resampled. The variation in SFHs measured from the resampled CMDs is assumed to represent the random uncertainty in the SFH measured from the original data. However, this technique systematically and significantly underestimates the uncertainties for times in which the measured star formation rate is low or zero, leading to overly (and incorrectly) high confidence in that measurement. This study proposes an alternative technique, the Markov Chain Monte Carlo (MCMC), which samples the probability distribution of the parameters used in the original solution to directly estimate confidence intervals. While the most commonly used MCMC algorithms are incapable of adequately sampling a probability distribution that can involve thousands of highly correlated dimensions, the Hybrid Monte Carlo algorithm is shown to be extremely effective and efficient for this particular task. Several implementation details, such as the handling of implicit priors created by parameterization of the SFH, are discussed in detail.

  3. Effect of Random Clustering on Surface Damage Density Estimates

    SciTech Connect

    Matthews, M J; Feit, M D

    2007-10-29

    Identification and spatial registration of laser-induced damage relative to incident fluence profiles is often required to characterize the damage properties of laser optics near damage threshold. Of particular interest in inertial confinement laser systems are large aperture beam damage tests (>1cm{sup 2}) where the number of initiated damage sites for {phi}>14J/cm{sup 2} can approach 10{sup 5}-10{sup 6}, requiring automatic microscopy counting to locate and register individual damage sites. However, as was shown for the case of bacteria counting in biology decades ago, random overlapping or 'clumping' prevents accurate counting of Poisson-distributed objects at high densities, and must be accounted for if the underlying statistics are to be understood. In this work we analyze the effect of random clumping on damage initiation density estimates at fluences above damage threshold. The parameter {psi} = a{rho} = {rho}/{rho}{sub 0}, where a = 1/{rho}{sub 0} is the mean damage site area and {rho} is the mean number density, is used to characterize the onset of clumping, and approximations based on a simple model are used to derive an expression for clumped damage density vs. fluence and damage site size. The influence of the uncorrected {rho} vs. {phi} curve on damage initiation probability predictions is also discussed.

  4. The Effect of Disorder on the Free-Energy for the Random Walk Pinning Model: Smoothing of the Phase Transition and Low Temperature Asymptotics

    NASA Astrophysics Data System (ADS)

    Berger, Quentin; Lacoin, Hubert

    2011-01-01

    We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in (Berger and Toninelli (Electron. J. Probab., to appear) and Birkner and Sun (Ann. Inst. Henri Poincaré Probab. Stat. 46:414-441, 2010; arXiv:0912.1663). Given a fixed realization of a random walk Y on ℤ d with jump rate ρ (that plays the role of the random medium), we modify the law of a random walk X on ℤ d with jump rate 1 by reweighting the paths, giving an energy reward proportional to the intersection time Lt(X,Y)=int0t {1}_{Xs=Ys} {d}s: the weight of the path under the new measure is exp ( βL t ( X, Y)), β∈ℝ. As β increases, the system exhibits a delocalization/localization transition: there is a critical value β c , such that if β> β c the two walks stick together for almost-all Y realizations. A natural question is that of disorder relevance, that is whether the quenched and annealed systems have the same behavior. In this paper we investigate how the disorder modifies the shape of the free energy curve: (1) We prove that, in dimension d≥3, the presence of disorder makes the phase transition at least of second order. This, in dimension d≥4, contrasts with the fact that the phase transition of the annealed system is of first order. (2) In any dimension, we prove that disorder modifies the low temperature asymptotic of the free energy.

  5. Guided random-walk calculation of energies and values of the 1Σg state of H2 in a magnetic field

    NASA Astrophysics Data System (ADS)

    Encinosa, Mario

    1999-03-01

    Energies and spatial observables for the 1Σg state of the hydrogen molecule in magnetic fields parallel to the proton-proton axis are calculated with a guided random-walk Feynman-Kac algorithm. We demonstrate that the accuracy of the results and simplicity of the method may provide it a viable alternative to large basis-set expansions for small molecules in applied fields.

  6. Quantum walk and potential application

    NASA Astrophysics Data System (ADS)

    Wang, J. B.; Douglas, B. L.

    2010-06-01

    Quantum walk represents a generalised version of the well-known classical random walk. Regardless of their apparent connection, the dynamics of quantum walk is often non-intuitive and far deviate from its classical counterpart. However, despite such potentially superior efficiency in quantum walks, it has yet to be applied to problems of practical importance. In this paper, we will give a brief introduction to quantum walks and discuss potential applications.

  7. Lévy walks

    NASA Astrophysics Data System (ADS)

    Zaburdaev, V.; Denisov, S.; Klafter, J.

    2015-04-01

    Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The Lévy-walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, biophysics, and behavioral science demonstrate that this particular type of random walk provides significant insight into complex transport phenomena. This review gives a self-consistent introduction to Lévy walks, surveys their existing applications, including latest advances, and outlines further perspectives.

  8. Criterion-Related Validity of the Distance- and Time-Based Walk/Run Field Tests for Estimating Cardiorespiratory Fitness: A Systematic Review and Meta-Analysis

    PubMed Central

    Mayorga-Vega, Daniel; Bocanegra-Parrilla, Raúl; Ornelas, Martha; Viciana, Jesús

    2016-01-01

    Objectives The main purpose of the present meta-analysis was to examine the criterion-related validity of the distance- and time-based walk/run tests for estimating cardiorespiratory fitness among apparently healthy children and adults. Materials and Methods Relevant studies were searched from seven electronic bibliographic databases up to August 2015 and through other sources. The Hunter-Schmidt’s psychometric meta-analysis approach was conducted to estimate the population criterion-related validity of the following walk/run tests: 5,000 m, 3 miles, 2 miles, 3,000 m, 1.5 miles, 1 mile, 1,000 m, ½ mile, 600 m, 600 yd, ¼ mile, 15 min, 12 min, 9 min, and 6 min. Results From the 123 included studies, a total of 200 correlation values were analyzed. The overall results showed that the criterion-related validity of the walk/run tests for estimating maximum oxygen uptake ranged from low to moderate (rp = 0.42–0.79), with the 1.5 mile (rp = 0.79, 0.73–0.85) and 12 min walk/run tests (rp = 0.78, 0.72–0.83) having the higher criterion-related validity for distance- and time-based field tests, respectively. The present meta-analysis also showed that sex, age and maximum oxygen uptake level do not seem to affect the criterion-related validity of the walk/run tests. Conclusions When the evaluation of an individual’s maximum oxygen uptake attained during a laboratory test is not feasible, the 1.5 mile and 12 min walk/run tests represent useful alternatives for estimating cardiorespiratory fitness. As in the assessment with any physical fitness field test, evaluators must be aware that the performance score of the walk/run field tests is simply an estimation and not a direct measure of cardiorespiratory fitness. PMID:26987118

  9. Estimating oxygen uptake and energy expenditure during treadmill walking by neural network analysis of easy-to-obtain inputs.

    PubMed

    Beltrame, Thomas; Amelard, Robert; Villar, Rodrigo; Shafiee, Mohammad J; Wong, Alexander; Hughson, Richard L

    2016-11-01

    The study of oxygen uptake (V̇o2) dynamics during walking exercise transitions adds valuable information regarding fitness. However, direct V̇o2 measurements are not practical for general population under realistic settings. Devices to measure V̇o2 are associated with elevated cost, uncomfortable use of a mask, need of trained technicians, and impossibility of long-term data collection. The objective of this study was to predict the V̇o2 dynamics from heart rate and inputs from the treadmill ergometer by a novel artificial neural network approach. To accomplish this, 10 healthy young participants performed one incremental and three moderate constant work rate treadmill walking exercises. The speed and grade used for the moderate-intensity protocol was related to 80% of the V̇o2 response at the gas exchange threshold estimated during the incremental exercise. The measured V̇o2 was used to train an artificial neural network to create an algorithm able to predict the V̇o2 based on easy-to-obtain inputs. The dynamics of the V̇o2 response during exercise transition were evaluated by exponential modeling. Within each participant, the predicted V̇o2 was strongly correlated to the measured V̇o2 ( = 0.97 ± 0.0) and presented a low bias (~0.2%), enabling the characterization of the V̇o2 dynamics during treadmill walking exercise. The proposed algorithm could be incorporated into smart devices and fitness equipment, making them suitable for tracking changes in aerobic fitness and physical health beyond the infrequent monitoring of patients during clinical interventions and rehabilitation programs.

  10. Kinetic study of the heterogeneous photocatalysis of porous nanocrystalline TiO₂ assemblies using a continuous random walk simulation.

    PubMed

    Liu, Baoshun; Zhao, Xiujian

    2014-10-28

    The continuous time random walk (CTRW) simulation was used to study the photocatalytic kinetics of nanocrystalline (nc)-TiO2 assemblies in this research. nc-TiO2 assemblies, such as nc-TiO2 porous films and nc-TiO2 hierarchical structures, are now widely used in photocatalysis. The nc-TiO2 assemblies have quasi-disordered networks consisting of many tiny nanoparticles, so the charge transport within them can be studied by CTRW simulation. We considered the experimental facts that the holes can be quickly trapped and transferred to organic species just after photogeneration, and the electrons transfer to O2 slowly and accumulate in the conduction band of TiO2, which is believed to be the rate-limiting process of the photocatalysis under low light intensity and low organic concentration. Due to the existence of numerous traps, the electron transport within the nc-TiO2 assemblies follows a multi-trapping (MT) mechanism, which significantly limits the electron diffusion speed. The electrons need to undergo several steps of MT transport before transferring to oxygen, so it is highly important that the electron transport in nc-TiO2 networks is determined for standard photocatalytic reactions. Based on the MT transport model, the transient decays of photocurrents during the photocatalytic oxidation of formic acid were studied by CTRW simulation, and are in good accordance with experiments. The steady state photocatalysis was also simulated. The effects of organic concentration, light intensity, temperature, and nc-TiO2 crystallinity on the photocatalytic kinetics were investigated, and were also consistent with the experimental results. Due to the agreement between the simulation and the experiments for both the transient and the steady state photocatalysis, the MT charge transport should be an important mechanism that controls the kinetics of recombination and photocatalysis in nc-TiO2 assemblies. Also, our research provides a new methodology to study the photocatalytic

  11. Theory of Random Walks.

    NASA Astrophysics Data System (ADS)

    Sokol, M.

    1996-11-01

    We develope a mathematical analysis derived from a simple vector-kick model of the evolution of a laser field due to strictly phase diffusion and having arbitrary average photon number barn. We write the exact-coupled, nonlinear equations in two dynamical variables, namely the magnitude of the new field E_0^' and the differential change in angle δ φ. A closed form approximate solution to find the variance in the tangent of phase, for small angles, has yielded the theoretical lower limit for large photon number √n=E_0>> 1. The exact solution to the variance in the tangent of phase angle δ φ was made possible by a trigonometric substitution method, and the transformed argument has been analyzed using residue calculus. There is a double-zero at z=0, simple-poles at z=± i, and double poles at z=± √(E0 +1)(E_0-1) i, in the Argand plane. The variance in the tangent of phase is found to be <(tan δφ)^2> = 2π(√(barn)/(barn-1) -1). An extension of this result would include effects due to amplification and saturation. The general result would include a regime of small photon numbers. Part C of program listing

  12. Angular Random Walk Estimation of a Time-Domain Switching Micromachined Gyroscope

    DTIC Science & Technology

    2016-10-19

    Wineglass to the Planets.” Proceedings of the 19th AAS/AIAA Space Flight Mechanics Meeting (AAS/AIAA 2009) (pp. 1157–1178). 8–12 February, Savannah...the Advanced Concepts and Applied Research Branch (Code 71730) and the Advanced Integrated Circuit Technology Branch (Code 55250), Space and Naval

  13. Supervised and non-supervised Nordic walking in the treatment of chronic low back pain: a single blind randomized clinical trial

    PubMed Central

    2010-01-01

    Background Active approaches including both specific and unspecific exercise are probably the most widely recommended treatment for patients with chronic low back pain but it is not known exactly which types of exercise provide the most benefit. Nordic Walking - power walking using ski poles - is a popular and fast growing type of exercise in Northern Europe that has been shown to improve cardiovascular metabolism. Until now, no studies have been performed to investigate whether Nordic Walking has beneficial effects in relation to back pain. Methods A total of 151 patients with low back and/or leg pain of greater than eight weeks duration were recruited from a hospital based outpatient back pain clinic. Patients continuing to have pain greater than three on the 11-point numeric rating scale after a multidisciplinary intervention were included. Fifteen patients were unable to complete the baseline evaluation and 136 patients were randomized to receive A) Nordic walking supervised by a specially trained instructor twice a week for eight weeks B) One-hour instruction in Nordic walking by a specially trained instructor followed by advice to perform Nordic walking at home as much as they liked for eight weeks or C) Individual oral information consisting of advice to remain active and about maintaining the daily function level that they had achieved during their stay at the backcenter. Primary outcome measures were pain and disability using the Low Back Pain Rating Scale, and functional limitation further assessed using the Patient Specific Function Scale. Furthermore, information on time off work, use of medication, and concurrent treatment for their low back pain was collected. Objective measurements of physical activity levels for the supervised and unsupervised Nordic walking groups were performed using accelerometers. Data were analyzed on an intention-to-treat basis. Results No mean differences were found between the three groups in relation to any of the outcomes

  14. Using global node-based velocity in random walk particle tracking in variably saturated porous media: application to contaminant leaching from road constructions

    NASA Astrophysics Data System (ADS)

    Park, Chan-Hee; Beyer, Christof; Bauer, Sebastian; Kolditz, Olaf

    2008-10-01

    Precise and efficient numerical simulation of transport processes in subsurface systems is a prerequisite for many site investigation or remediation studies. Random walk particle tracking (RWPT) methods have been introduced in the past to overcome numerical difficulties when simulating propagation processes in porous media such as advection-dominated mass transport. Crucial for the precision of RWPT methods is the accuracy of the numerically calculated ground water velocity field. In this paper, a global node-based method for velocity calculation is used, which was originally proposed by Yeh (Water Resour Res 7:1216-1225, 1981). This method is improved in three ways: (1) extension to unstructured grids, (2) significant enhancement of computational efficiency, and (3) extension to saturated (groundwater) as well as unsaturated systems (soil water). The novel RWPT method is tested with numerical benchmark examples from the literature and used in two field scale applications of contaminant transport in saturated and unsaturated ground water. To evaluate advective transport of the model, the accuracy of the velocity field is demonstrated by comparing several published results of particle pathlines or streamlines. Given the chosen test problem, the global node-based velocity estimation is found to be as accurate as the CK method (Cordes and Kinzelbach in Water Resour Res 28(11):2903-2911, 1992) but less accurate than the mixed or mixed-hybrid finite element methods for flow in highly heterogeneous media. To evaluate advective-diffusive transport, a transport problem studied by Hassan and Mohamed (J Hydrol 275(3-4):242-260, 2003) is investigated here and evaluated using different numbers of particles. The results indicate that the number of particles required for the given problem is decreased using the proposed method by about two orders of magnitude without losing accuracy of the concentration contours as compared to the published numbers.

  15. Sensor Data Fusion for Body State Estimation in a Bipedal Robot and Its Feedback Control Application for Stable Walking

    PubMed Central

    Chen, Ching-Pei; Chen, Jing-Yi; Huang, Chun-Kai; Lu, Jau-Ching; Lin, Pei-Chun

    2015-01-01

    We report on a sensor data fusion algorithm via an extended Kalman filter for estimating the spatial motion of a bipedal robot. Through fusing the sensory information from joint encoders, a 6-axis inertial measurement unit and a 2-axis inclinometer, the robot’s body state at a specific fixed position can be yielded. This position is also equal to the CoM when the robot is in the standing posture suggested by the detailed CAD model of the robot. In addition, this body state is further utilized to provide sensory information for feedback control on a bipedal robot with walking gait. The overall control strategy includes the proposed body state estimator as well as the damping controller, which regulates the body position state of the robot in real-time based on instant and historical position tracking errors. Moreover, a posture corrector for reducing unwanted torque during motion is addressed. The body state estimator and the feedback control structure are implemented in a child-size bipedal robot and the performance is experimentally evaluated. PMID:25734644

  16. Sensor data fusion for body state estimation in a bipedal robot and its feedback control application for stable walking.

    PubMed

    Chen, Ching-Pei; Chen, Jing-Yi; Huang, Chun-Kai; Lu, Jau-Ching; Lin, Pei-Chun

    2015-02-27

    We report on a sensor data fusion algorithm via an extended Kalman filter for estimating the spatial motion of a bipedal robot. Through fusing the sensory information from joint encoders, a 6-axis inertial measurement unit and a 2-axis inclinometer, the robot's body state at a specific fixed position can be yielded. This position is also equal to the CoM when the robot is in the standing posture suggested by the detailed CAD model of the robot. In addition, this body state is further utilized to provide sensory information for feedback control on a bipedal robot with walking gait. The overall control strategy includes the proposed body state estimator as well as the damping controller, which regulates the body position state of the robot in real-time based on instant and historical position tracking errors. Moreover, a posture corrector for reducing unwanted torque during motion is addressed. The body state estimator and the feedback control structure are implemented in a child-size bipedal robot and the performance is experimentally evaluated.

  17. Correcting treatment effect for treatment switching in randomized oncology trials with a modified iterative parametric estimation method.

    PubMed

    Zhang, Jin; Chen, Cong

    2016-09-20

    In randomized oncology trials, patients in the control arm are sometimes permitted to switch to receive experimental drug after disease progression. This is mainly due to ethical reasons or to reduce the patient dropout rate. While progression-free survival is not usually impacted by crossover, the treatment effect on overall survival can be highly confounded. The rank-preserving structural failure time (RPSFT) model and iterative parametric estimation (IPE) are the main randomization-based methods used to adjust for confounding in the analysis of overall survival. While the RPSFT has been extensively studied, the properties of the IPE have not been thoroughly examined and its application is not common. In this manuscript, we clarify the re-censoring algorithm needed for IPE estimation and incorporate it into a method we propose as modified IPE (MIPE). We compared the MIPE and RPSFT via extensive simulations and then walked through the analysis using the modified IPE in a real clinical trial. We provided practical guidance on bootstrap by examining the performance in estimating the variance and confidence interval for the MIPE. Our results indicate that the MIPE method with the proposed re-censoring rule is an attractive alternative to the RPSFT method. Copyright © 2016 John Wiley & Sons, Ltd.

  18. Anomalous stress diffusion, Omori's law and Continuous Time Random Walk in the 2010 Efpalion aftershock sequence (Corinth rift, Greece)

    NASA Astrophysics Data System (ADS)

    Michas, Georgios; Vallianatos, Filippos; Karakostas, Vassilios; Papadimitriou, Eleftheria; Sammonds, Peter

    2014-05-01

    Efpalion aftershock sequence occurred in January 2010, when an M=5.5 earthquake was followed four days later by another strong event (M=5.4) and numerous aftershocks (Karakostas et al., 2012). This activity interrupted a 15 years period of low to moderate earthquake occurrence in Corinth rift, where the last major event was the 1995 Aigion earthquake (M=6.2). Coulomb stress analysis performed in previous studies (Karakostas et al., 2012; Sokos et al., 2012; Ganas et al., 2013) indicated that the second major event and most of the aftershocks were triggered due to stress transfer. The aftershocks production rate decays as a power-law with time according to the modified Omori law (Utsu et al., 1995) with an exponent larger than one for the first four days, while after the occurrence of the second strong event the exponent turns to unity. We consider the earthquake sequence as a point process in time and space and study its spatiotemporal evolution considering a Continuous Time Random Walk (CTRW) model with a joint probability density function of inter-event times and jumps between the successive earthquakes (Metzler and Klafter, 2000). Jump length distribution exhibits finite variance, whereas inter-event times scale as a q-generalized gamma distribution (Michas et al., 2013) with a long power-law tail. These properties are indicative of a subdiffusive process in terms of CTRW. Additionally, the mean square displacement of aftershocks is constant with time after the occurrence of the first event, while it changes to a power-law with exponent close to 0.15 after the second major event, illustrating a slow diffusive process. During the first four days aftershocks cluster around the epicentral area of the second major event, while after that and taking as a reference the second event, the aftershock zone is migrating slowly with time to the west near the epicentral area of the first event. This process is much slower from what would be expected from normal diffusion, a

  19. Effects of an 8-Week Outdoor Brisk Walking Program on Fatigue in Hi-Tech Industry Employees: A Randomized Control Trial.

    PubMed

    Wu, Li-Ling; Wang, Kuo-Ming; Liao, Po-I; Kao, Yu-Hsiu; Huang, Yi-Ching

    2015-10-01

    Over 73% of hi-tech industry employees in Taiwan lack regular exercise. They are exposed to a highly variable and stressful work environment for extended periods of time, and may subsequently experience depression, detrimental to workers' physiological and mental health. In this cross-sectional survey, the authors explored the effect of an 8-week brisk walking program on the fatigue of employees in the hi-tech industry. The participants, from a hi-tech company in northern Taiwan, were randomly assigned to an experimental group (EG; 41 subjects, Mage = 33.34 ± 6.40) or control group (CG; 45 subjects, Mage = 29.40 ± 3.60). Following the 8-week brisk walking program, the EG showed significantly lower scores for subjective fatigue, working motivation, attention, and overall fatigue. The authors confirmed that the 8-week outdoor brisk walking program significantly improved the level of fatigue among employees of the hi-tech industry. The finding serves as an important reference for health authorities in Taiwan and provides awareness of workplace health promotion in the hi-tech industry.

  20. Home‐Based Walking Exercise in Peripheral Artery Disease: 12‐Month Follow‐up of the Goals Randomized Trial

    PubMed Central

    McDermott, Mary M.; Guralnik, Jack M.; Criqui, Michael H.; Ferrucci, Luigi; Zhao, Lihui; Liu, Kiang; Domanchuk, Kathryn; Spring, Bonnie; Tian, Lu; Kibbe, Melina; Liao, Yihua; Lloyd Jones, Donald; Rejeski, W. Jack

    2014-01-01

    Background We studied whether a 6‐month group‐mediated cognitive behavioral (GMCB) intervention for peripheral artery disease (PAD) participants, which promoted home‐based walking exercise, improved 6‐minute walk and other outcomes at 12‐month follow‐up, 6 months after completing the intervention, compared to a control group. Methods and Results We randomized PAD participants to a GMCB intervention or a control group. During phase I (months 1 to 6), the intervention used group support and self‐regulatory skills during weekly on‐site meetings to help participants adhere to home‐based exercise. The control group received weekly on‐site lectures on topics unrelated to exercise. Primary outcomes were measured at the end of phase I. During phase II (months 7 to 12), each group received telephone contact. Compared to controls, participants randomized to the intervention increased their 6‐minute walk distance from baseline to 12‐month follow‐up, (from 355.4 to 381.9 m in the intervention versus 353.1 to 345.6 m in the control group; mean difference=+34.1 m; 95% confidence interval [CI]=+14.6, +53.5; P<0.001) and their Walking Impairment Questionnaire (WIQ) speed score (from 36.1 to 46.5 in the intervention group versus 34.9 to 36.5 in the control group; mean difference =+8.8; 95% CI=+1.6, +16.1; P=0.018). Change in the WIQ distance score was not different between the 2 groups at 12‐month follow‐up (P=0.139). Conclusions A weekly on‐site GMCB intervention that promoted home‐based walking exercise intervention for people with PAD demonstrated continued benefit at 12‐month follow‐up, 6 months after the GMCB intervention was completed. Clinical Trial Registration URL: ClinicalTrials.gov. Unique identifier: NCT00693940. PMID:24850615

  1. Identifiability and Estimation in Random Translations of Marked Point Processes.

    DTIC Science & Technology

    1982-10-01

    inversion of the Laplace Transform Hermit* Distribution Parmetrc and Non- parametric Estimation 20 ABSTRACT ContInwue en reverse side If neeee ww ftn id... Parametric Estimation of h(.) and P(.) If h(.) and P(.) belong to a certain known family of functions with some unknown parameters, the expression (3...complex type of data is required and nothing can be learned about the arrival process. Non- Parametric Estimation of P(’) Let h(.) be a completely

  2. A comparison of energy expenditure estimates from the Actiheart and Actical physical activity monitors during low intensity activities, walking, and jogging.

    PubMed

    Spierer, David K; Hagins, Marshall; Rundle, Andrew; Pappas, Evangelos

    2011-04-01

    Combining accelerometry with heart rate monitoring has been suggested to improve energy estimates, however, it remains unclear whether the single, currently existing commercially available device combining these data streams (Actiheart) provides improved energy estimates compared to simpler and less expensive accelerometry-only devices. The purpose of this study was to compare the validity of the heart rate (HR), accelerometry (ACC), and combined ACC/HR estimates of the Actiheart to the ACC estimates of the Actical during low and moderate intensity activities. Twenty-seven participants (mean age 26.3 ± 7.3) wore an Actical, Actiheart and indirect calorimeter (K4b(2)) while performing card playing, sweeping, lifting weights, walking and jogging activities. All estimates tended to underestimate energy, sometimes by substantial amounts. Viewed across all activities studied, there was no significant difference in the ability of the waist-mounted Actical and torso-mounted Actiheart (ACC, HR, ACC/HR) estimates to predict energy expenditure. However, the Actiheart provided significantly better estimates than the Actical for the activities in which acceleration of the pelvis is not closely related to energy expenditure (card playing, sweeping, lifting weights) and the Actical provided significantly better estimates for level walking and level jogging. Similar to a previous study, the ACC component of the Actiheart was found to be the weakest predictor of energy suggesting it may be responsible for the failure of the combined ACC/HR estimate to equal or better the estimates derived solely from a waist mounted ACC device.

  3. Precision of recombination frequency estimates after random intermating with finite population sizes.

    PubMed

    Frisch, Matthias; Melchinger, Albrecht E

    2008-01-01

    Random intermating of F2 populations has been suggested for obtaining precise estimates of recombination frequencies between tightly linked loci. In a simulation study, sampling effects due to small population sizes in the intermating generations were found to abolish the advantages of random intermating that were reported in previous theoretical studies considering an infinite population size. We propose a mating scheme for intermating with planned crosses that yields more precise estimates than those under random intermating.

  4. T-cell motility in the early stages of the immune response modeled as a random walk amongst targets

    NASA Astrophysics Data System (ADS)

    Preston, S. P.; Waters, S. L.; Jensen, O. E.; Heaton, P. R.; Pritchard, D. I.

    2006-07-01

    The transport process by which a T cell makes high-frequency encounters with antigen-presenting cells following infection is an important element of adaptive immunity. Recent experimental work has allowed in vivo cell motility to be characterized in detail. On the basis of experimental data we develop a quantitative model for encounters between T cells and antigen-presenting cells. We model this as a transport-limited chemical reaction with the dynamics dependent on physical contact between randomly moving reactants. We use asymptotic methods to calculate a time distribution which characterizes the delay before a T cell is activated and use Monte Carlo simulations to verify the analysis. We find that the density of antigen-primed dendritic cells within the lymph node paracortex must be greater than 35cells/mm3 for a T cell to have a more than 50% chance of encountering a dendritic cell within 24h . This density is much larger than existing estimates based on calculations which neglect the transport process. We also use simulations to compare a T cell which re-orients isotropically with a T cell which turns according to an experimentally observed distribution and find that the effects of anisotropy on the solution are small.

  5. Walk on the wild side: estimating the global magnitude of visits to protected areas.

    PubMed

    Balmford, Andrew; Green, Jonathan M H; Anderson, Michael; Beresford, James; Huang, Charles; Naidoo, Robin; Walpole, Matt; Manica, Andrea

    2015-02-01

    How often do people visit the world's protected areas (PAs)? Despite PAs covering one-eighth of the land and being a major focus of nature-based recreation and tourism, we don't know. To address this, we compiled a globally-representative database of visits to PAs and built region-specific models predicting visit rates from PA size, local population size, remoteness, natural attractiveness, and national income. Applying these models to all but the very smallest of the world's terrestrial PAs suggests that together they receive roughly 8 billion (8 x 109) visits/y-of which more than 80% are in Europe and North America. Linking our region-specific visit estimates to valuation studies indicates that these visits generate approximately US $600 billion/y in direct in-country expenditure and US $250 billion/y in consumer surplus. These figures dwarf current, typically inadequate spending on conserving PAs. Thus, even without considering the many other ecosystem services that PAs provide to people, our findings underscore calls for greatly increased investment in their conservation.

  6. Walk on the Wild Side: Estimating the Global Magnitude of Visits to Protected Areas

    PubMed Central

    Balmford, Andrew; Green, Jonathan M. H.; Anderson, Michael; Beresford, James; Huang, Charles; Naidoo, Robin; Walpole, Matt; Manica, Andrea

    2015-01-01

    How often do people visit the world’s protected areas (PAs)? Despite PAs covering one-eighth of the land and being a major focus of nature-based recreation and tourism, we don’t know. To address this, we compiled a globally-representative database of visits to PAs and built region-specific models predicting visit rates from PA size, local population size, remoteness, natural attractiveness, and national income. Applying these models to all but the very smallest of the world’s terrestrial PAs suggests that together they receive roughly 8 billion (8 x 109) visits/y—of which more than 80% are in Europe and North America. Linking our region-specific visit estimates to valuation studies indicates that these visits generate approximately US $600 billion/y in direct in-country expenditure and US $250 billion/y in consumer surplus. These figures dwarf current, typically inadequate spending on conserving PAs. Thus, even without considering the many other ecosystem services that PAs provide to people, our findings underscore calls for greatly increased investment in their conservation. PMID:25710450

  7. On co-design of filter and fault estimator against randomly occurring nonlinearities and randomly occurring deception attacks

    NASA Astrophysics Data System (ADS)

    Hu, Jun; Liu, Steven; Ji, Donghai; Li, Shanqiang

    2016-07-01

    In this paper, the co-design problem of filter and fault estimator is studied for a class of time-varying non-linear stochastic systems subject to randomly occurring nonlinearities and randomly occurring deception attacks. Two mutually independent random variables obeying the Bernoulli distribution are employed to characterize the phenomena of the randomly occurring nonlinearities and randomly occurring deception attacks, respectively. By using the augmentation approach, the co-design problem of the robust filter and fault estimator is converted into the recursive filter design problem. A new compensation scheme is proposed such that, for both randomly occurring nonlinearities and randomly occurring deception attacks, an upper bound of the filtering error covariance is obtained and such an upper bound is minimized by properly designing the filter gain at each sampling instant. Moreover, the explicit form of the filter gain is given based on the solution to two Riccati-like difference equations. It is shown that the proposed co-design algorithm is of a recursive form that is suitable for online computation. Finally, a simulation example is given to illustrate the usefulness of the developed filtering approach.

  8. Image estimation using doubly stochastic gaussian random field models.

    PubMed

    Woods, J W; Dravida, S; Mediavilla, R

    1987-02-01

    The two-dimensional (2-D) doubly stochastic Gaussian (DSG) model was introduced by one of the authors to provide a complete model for spatial filters which adapt to the local structure in an image signal. Here we present the optimal estimator and 2-D fixed-lag smoother for this DSG model extending earlier work of Ackerson and Fu. As the optimal estimator has an exponentially growing state space, we investigate suboptimal estimators using both a tree and a decision-directed method. Experimental results are presented.

  9. Hazard Function Estimation with Cause-of-Death Data Missing at Random

    PubMed Central

    Wang, Qihua; Dinse, Gregg E.; Liu, Chunling

    2010-01-01

    Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data. PMID:22267874

  10. Estimating Independent Locally Shifted Random Utility Models for Ranking Data

    ERIC Educational Resources Information Center

    Lam, Kar Yin; Koning, Alex J.; Franses, Philip Hans

    2011-01-01

    We consider the estimation of probabilistic ranking models in the context of conjoint experiments. By using approximate rather than exact ranking probabilities, we avoided the computation of high-dimensional integrals. We extended the approximation technique proposed by Henery (1981) in the context of the Thurstone-Mosteller-Daniels model to any…

  11. Fractional Brownian Motion:. Theory and Application to DNA Walk

    NASA Astrophysics Data System (ADS)

    Lim, S. C.; Muniandy, S. V.

    2001-09-01

    This paper briefly reviews the theory of fractional Brownian motion (FBM) and its generalization to multifractional Brownian motion (MBM). FBM and MBM are applied to a biological system namely the DNA sequence. By considering a DNA sequence as a fractal random walk, it is possible to model the noncoding sequence of human retinoblastoma DNA as a discrete version of FBM. The average scaling exponent or Hurst exponent of the DNA walk is estimated to be H = 0.60 ± 0.05 using the monofractal R/S analysis. This implies that the mean square fluctuation of DNA walk belongs to anomalous superdiffusion type. We also show that the DNA landscape is not monofractal, instead one has multifractal DNA landscape. The empirical estimates of the Hurst exponent falls approximately within the range H ~ 0.62 - 0.72. We propose two multifractal models, namely the MBM and multiscale FBM to describe the existence of different Hurst exponents in DNA walk.

  12. Moving human full body and body parts detection, tracking, and applications on human activity estimation, walking pattern and face recognition

    NASA Astrophysics Data System (ADS)

    Chen, Hai-Wen; McGurr, Mike

    2016-05-01

    We have developed a new way for detection and tracking of human full-body and body-parts with color (intensity) patch morphological segmentation and adaptive thresholding for security surveillance cameras. An adaptive threshold scheme has been developed for dealing with body size changes, illumination condition changes, and cross camera parameter changes. Tests with the PETS 2009 and 2014 datasets show that we can obtain high probability of detection and low probability of false alarm for full-body. Test results indicate that our human full-body detection method can considerably outperform the current state-of-the-art methods in both detection performance and computational complexity. Furthermore, in this paper, we have developed several methods using color features for detection and tracking of human body-parts (arms, legs, torso, and head, etc.). For example, we have developed a human skin color sub-patch segmentation algorithm by first conducting a RGB to YIQ transformation and then applying a Subtractive I/Q image Fusion with morphological operations. With this method, we can reliably detect and track human skin color related body-parts such as face, neck, arms, and legs. Reliable body-parts (e.g. head) detection allows us to continuously track the individual person even in the case that multiple closely spaced persons are merged. Accordingly, we have developed a new algorithm to split a merged detection blob back to individual detections based on the detected head positions. Detected body-parts also allow us to extract important local constellation features of the body-parts positions and angles related to the full-body. These features are useful for human walking gait pattern recognition and human pose (e.g. standing or falling down) estimation for potential abnormal behavior and accidental event detection, as evidenced with our experimental tests. Furthermore, based on the reliable head (face) tacking, we have applied a super-resolution algorithm to enhance

  13. A combined exercise model for improving muscle strength, balance, walking distance, and motor agility in multiple sclerosis patients: A randomized clinical trial

    PubMed Central

    Sangelaji, Bahram; Kordi, Mohammadreza; Banihashemi, Farzaneh; Nabavi, Seyed Massood; Khodadadeh, Sara; Dastoorpoor, Maryam

    2016-01-01

    Background: Multiple sclerosis (MS) is a neurological disease with a variety of signs and symptoms. Exercise therapy has been shown to improve physical functions in MS. However, questions about an optimal exercise therapy remain. In this regard, we suggest a combined exercise therapy including aerobic and resistance exercises for MS patients. The study is designed to observe, test and compare the effects of proposed combined exercises on strength, balance, agility, fatigue, speed, and walking distance in people with mild to moderate MS [0 < expanded disability status scale (EDSS) < 5]. Methods: A total of 40 people with relapse-remitting MS (16 male, 0 < EDSS < 5) were randomized into one of the four groups (3 intervention and one control). The intervention consisted of various combinations of aerobic and resistance exercises with different repetition rates. Pre- and post-intervention scores of fatigue severity scale (FSS), timed up and go (TUG) test, 6-minute walk test (6MWT), 10- and 20-MWT, Berg balance scale (BBS), and one repetition maximum (1RM) test were recorded and analyzed. Results: For most tests, post-intervention values of the group 1, with 3-aerobic and 1-resistance exercises, were significantly higher compared to control group (P < 0.050). However, no significant progression was observed in the other two intervention groups. Conclusion: A combination of three aerobic exercises with one resistance exercise may result in improved balance, locomotion, and endurance in MS patients. PMID:27648171

  14. Effects of the DASH Diet and Walking on Blood Pressure in Patients With Type 2 Diabetes and Uncontrolled Hypertension: A Randomized Controlled Trial.

    PubMed

    Paula, Tatiana P; Viana, Luciana V; Neto, Alessandra T Z; Leitão, Cristiane B; Gross, Jorge L; Azevedo, Mirela J

    2015-11-01

    Data on the potential beneficial effects of combining diet and exercise on blood pressure (BP) are still scarce. A 4-week randomized controlled clinical trial was undertaken in 40 hypertensive patients with type 2 diabetes with uncontrolled blood pressure (BP) in office and daytime ambulatory BP monitoring (ABPM). Patients were assigned to follow a Dietary Approaches to Stop Hypertension (DASH) diet associated with advice to increase walking using a pedometer (intervention group) or a diet based on the American Diabetes Association recommendations (control group). The lifestyle intervention caused a greater ABPM (mm Hg) reduction in systolic 24-hour, diastolic 24-hour, nighttime systolic, daytime systolic, and daytime diastolic measurements than observed in the control group. In the intervention group there was a decrease in urinary sodium and an increase in urinary potassium, plasma aldosterone, and the number of steps per day (P<.05). The DASH diet and increased walking were associated with clinically significant reductions in ABPM values in hypertensive patients with type 2 diabetes.

  15. Estimation of treatment efficacy with complier average causal effects (CACE) in a randomized stepped wedge trial.

    PubMed

    Gruber, Joshua S; Arnold, Benjamin F; Reygadas, Fermin; Hubbard, Alan E; Colford, John M

    2014-05-01

    Complier average causal effects (CACE) estimate the impact of an intervention among treatment compliers in randomized trials. Methods used to estimate CACE have been outlined for parallel-arm trials (e.g., using an instrumental variables (IV) estimator) but not for other randomized study designs. Here, we propose a method for estimating CACE in randomized stepped wedge trials, where experimental units cross over from control conditions to intervention conditions in a randomized sequence. We illustrate the approach with a cluster-randomized drinking water trial conducted in rural Mexico from 2009 to 2011. Additionally, we evaluated the plausibility of assumptions required to estimate CACE using the IV approach, which are testable in stepped wedge trials but not in parallel-arm trials. We observed small increases in the magnitude of CACE risk differences compared with intention-to-treat estimates for drinking water contamination (risk difference (RD) = -22% (95% confidence interval (CI): -33, -11) vs. RD = -19% (95% CI: -26, -12)) and diarrhea (RD = -0.8% (95% CI: -2.1, 0.4) vs. RD = -0.1% (95% CI: -1.1, 0.9)). Assumptions required for IV analysis were probably violated. Stepped wedge trials allow investigators to estimate CACE with an approach that avoids the stronger assumptions required for CACE estimation in parallel-arm trials. Inclusion of CACE estimates in stepped wedge trials with imperfect compliance could enhance reporting and interpretation of the results of such trials.

  16. Probabilistic Estimation of Rare Random Collisions in 3 Space

    DTIC Science & Technology

    2009-03-01

    encouragement, and her unyielding belief in my ability to excel, were all crucial to my being able to complete this intense program . As much as this...Process Theory) . . . . . . . . . . . . . . . . . 3-8 3.3.3 Step 3: Probabilistic Estimation (Applying Nu- merical Integration ...are more likely to encounter object a than you are encounter with object b). This is the approach taken by the Bird/Wildlife Aircraft Strike Hazard

  17. Recursive state estimation for discrete time-varying stochastic nonlinear systems with randomly occurring deception attacks

    NASA Astrophysics Data System (ADS)

    Ding, Derui; Shen, Yuxuan; Song, Yan; Wang, Yongxiong

    2016-07-01

    This paper is concerned with the state estimation problem for a class of discrete time-varying stochastic nonlinear systems with randomly occurring deception attacks. The stochastic nonlinearity described by statistical means which covers several classes of well-studied nonlinearities as special cases is taken into discussion. The randomly occurring deception attacks are modelled by a set of random variables obeying Bernoulli distributions with given probabilities. The purpose of the addressed state estimation problem is to design an estimator with hope to minimize the upper bound for estimation error covariance at each sampling instant. Such an upper bound is minimized by properly designing the estimator gain. The proposed estimation scheme in the form of two Riccati-like difference equations is of a recursive form. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed scheme.

  18. Optimal volume Wegner estimate for random magnetic Laplacians on Z2

    NASA Astrophysics Data System (ADS)

    Hasler, David; Luckett, Daniel

    2013-03-01

    We consider a two dimensional magnetic Schrödinger operator on a square lattice with a spatially stationary random magnetic field. We prove a Wegner estimate with optimal volume dependence. The Wegner estimate holds around the spectral edges, and it implies Hölder continuity of the integrated density of states in this region. The proof is based on the Wegner estimate obtained in Erdős and Hasler ["Wegner estimate for random magnetic Laplacians on {{Z}}^2," Ann. Henri Poincaré 12, 1719-1731 (2012)], 10.1007/s00023-012-0177-9.

  19. Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation.

    PubMed

    Fulger, Daniel; Scalas, Enrico; Germano, Guido

    2008-02-01

    We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Lévy alpha -stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Lévy alpha -stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space- and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.

  20. State-Bound Estimation for Nonlinear Systems Using Randomized Mu-Analysis

    DTIC Science & Technology

    2014-04-30

    Jae-Hun Park, Ho J. Lee, Hong S. Min, and Seon-Dong Kim. The effects of geothermal heating on the East/Japan Sea circulation. J. Geophys. Res. Oceans...AFRL-AFOSR-UK-TR-2014-0020 State-bound estimation for nonlinear systems using randomized mu-analysis Jongrae Kim THE UNIVERSITY OF GLASGOW...COVERED (From – To) 28 February 2013 – 27 February 2014 4. TITLE AND SUBTITLE State-bound estimation for nonlinear systems using randomized mu