Numerical modelling of random walk one-dimensional diffusion
International Nuclear Information System (INIS)
Vamos, C.; Suciu, N.; Peculea, M.
1996-01-01
The evolution of a particle which moves on a discrete one-dimensional lattice, according to a random walk low, approximates better the diffusion process smaller the steps of the spatial lattice and time are. For a sufficiently large assembly of particles one can assume that their relative frequency at lattice knots approximates the distribution function of the diffusion process. This assumption has been tested by simulating on computer two analytical solutions of the diffusion equation: the Brownian motion and the steady state linear distribution. To evaluate quantitatively the similarity between the numerical and analytical solutions we have used a norm given by the absolute value of the difference of the two solutions. Also, a diffusion coefficient at any lattice knots and moment of time has been calculated, by using the numerical solution both from the diffusion equation and the particle flux given by Fick's low. The difference between diffusion coefficient of analytical solution and the spatial lattice mean coefficient of numerical solution constitutes another quantitative indication of the similarity of the two solutions. The results obtained show that the approximation depends first on the number of particles at each knot of the spatial lattice. In conclusion, the random walk is a microscopic process of the molecular dynamics type which permits simulations precision of the diffusion processes with given precision. The numerical method presented in this work may be useful both in the analysis of real experiments and for theoretical studies
On a class of one-dimensional random walks
O.J. Boxma (Onno); V.I. Lotov
1995-01-01
textabstractnoindent This paper studies a one-dimensional Markov chain ${X_n,n=0,1,dots$ that satisfies the recurrence relation $X_n = max(0, X_{n-1 + eta_n^{(m) )$ if $X_{n-1 =m leq a$; for $X_{n-1 > a$ it satisfies the same relation with $eta_n^{(m)$ replaced by $xi_n$. Here ${ eta_n^{(m) $ and ${
One-dimensional random walk of nanosized liquid Pb inclusions on dislocations in Al
DEFF Research Database (Denmark)
Johnson, E.; Levinsen, M.T.; Steenstrup, S.
2004-01-01
to and perpendicular to the dislocations respectively. Movements parallel to the dislocation lines display properties of partially confined one-dimensional random walks where smaller inclusions can be seen to move over distances that are many times their own sizes. In contrast, the trajectories perpendicular...
Intermittent random walks for an optimal search strategy: one-dimensional case
International Nuclear Information System (INIS)
Oshanin, G; Wio, H S; Lindenberg, K; Burlatsky, S F
2007-01-01
We study the search kinetics of an immobile target by a concentration of randomly moving searchers. The object of the study is to optimize the probability of detection within the constraints of our model. The target is hidden on a one-dimensional lattice in the sense that searchers have no a priori information about where it is, and may detect it only upon encounter. The searchers perform random walks in discrete time n = 0,1,2,...,N, where N is the maximal time the search process is allowed to run. With probability α the searchers step on a nearest-neighbour, and with probability (1-α) they leave the lattice and stay off until they land back on the lattice at a fixed distance L away from the departure point. The random walk is thus intermittent. We calculate the probability P N that the target remains undetected up to the maximal search time N, and seek to minimize this probability. We find that P N is a non-monotonic function of α, and show that there is an optimal choice α opt (N) of α well within the intermittent regime, 0 opt (N) N can be orders of magnitude smaller compared to the 'pure' random walk cases α = 0 and α = 1
Regularity of the Speed of Biased Random Walk in a One-Dimensional Percolation Model
Gantert, Nina; Meiners, Matthias; Müller, Sebastian
2018-03-01
We consider biased random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. Axelson-Fisk and Häggström established for this model a phase transition for the asymptotic linear speed \\overline{v} of the walk. Namely, there exists some critical value λ c>0 such that \\overline{v}>0 if λ \\in (0,λ c) and \\overline{v}=0 if λ ≥ λ c. We show that the speed \\overline{v} is continuous in λ on (0,∞) and differentiable on (0,λ c/2). Moreover, we characterize the derivative as a covariance. For the proof of the differentiability of \\overline{v} on (0,λ c/2), we require and prove a central limit theorem for the biased random walk. Additionally, we prove that the central limit theorem fails to hold for λ ≥ λ c/2.
Recurrence and Polya Number of General One-Dimensional Random Walks
International Nuclear Information System (INIS)
Zhang Xiaokun; Wan Jing; Lu Jingju; Xu Xinping
2011-01-01
The recurrence properties of random walks can be characterized by Polya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random walk on a line, in which at each time step the walker can move to the left or right with probabilities l and r, or remain at the same position with probability o (l + r + o = 1). We calculate Polya number P of this model and find a simple expression for P as, P = 1 - Δ, where Δ is the absolute difference of l and r (Δ = |l - r|). We prove this rigorous expression by the method of creative telescoping, and our result suggests that the walk is recurrent if and only if the left-moving probability l equals to the right-moving probability r. (general)
Avena, L.; Hollander, den W.Th.F.; Redig, F.H.J.
2009-01-01
Consider a one-dimensional shift-invariant attractive spin-ip system in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on vacant sites has a local drift to the left. In [2] we proved a law
Avena, L.; Hollander, den W.Th.F.; Redig, F.H.J.
2010-01-01
Consider a one-dimensional shift-invariant attractive spin-flip system in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on vacant sites has a local drift to the left. In previous work we
International Nuclear Information System (INIS)
Cocco, S; Monasson, R
2009-01-01
We consider the Sinai model, in which a random walker moves in a random quenched potential V, and ask the following questions: 1. how can the quenched potential V be inferred from the observations of one or more realizations of the random motion? 2. how many observations (walks) are required to make a reliable inference, that is, to be able to distinguish between two similar but distinct potentials, V 1 and V 2 ? We show how question 1 can be easily solved within the Bayesian framework. In addition, we show that the answer to question 2 is, in general, intimately connected to the calculation of the survival probability of a fictitious walker in a potential W defined from V 1 and V 2 , with partial absorption at sites where V 1 and V 2 do not coincide. For the one-dimensional Sinai model, this survival probability can be analytically calculated, in excellent agreement with numerical simulations.
Hilário, M.; Hollander, den W.Th.F.; Sidoravicius, V.; Soares dos Santos, R.; Teixeira, A.
2014-01-01
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density ¿¿(0,8). At each step the random walk performs a nearest-neighbour jump, moving to
Stopping time of a one-dimensional bounded quantum walk
International Nuclear Information System (INIS)
Luo Hao; Zhang Peng; Zhan Xiang; Xue Peng
2016-01-01
The stopping time of a one-dimensional bounded classical random walk (RW) is defined as the number of steps taken by a random walker to arrive at a fixed boundary for the first time. A quantum walk (QW) is a non-trivial generalization of RW, and has attracted a great deal of interest from researchers working in quantum physics and quantum information. In this paper, we develop a method to calculate the stopping time for a one-dimensional QW. Using our method, we further compare the properties of stopping time for QW and RW. We find that the mean value of the stopping time is the same for both of these problems. However, for short times, the probability for a walker performing a QW to arrive at the boundary is larger than that for a RW. This means that, although the mean stopping time of a quantum and classical walker are the same, the quantum walker has a greater probability of arriving at the boundary earlier than the classical walker. (paper)
Quantum logic using correlated one-dimensional quantum walks
Lahini, Yoav; Steinbrecher, Gregory R.; Bookatz, Adam D.; Englund, Dirk
2018-01-01
Quantum Walks are unitary processes describing the evolution of an initially localized wavefunction on a lattice potential. The complexity of the dynamics increases significantly when several indistinguishable quantum walkers propagate on the same lattice simultaneously, as these develop non-trivial spatial correlations that depend on the particle's quantum statistics, mutual interactions, initial positions, and the lattice potential. We show that even in the simplest case of a quantum walk on a one dimensional graph, these correlations can be shaped to yield a complete set of compact quantum logic operations. We provide detailed recipes for implementing quantum logic on one-dimensional quantum walks in two general cases. For non-interacting bosons—such as photons in waveguide lattices—we find high-fidelity probabilistic quantum gates that could be integrated into linear optics quantum computation schemes. For interacting quantum-walkers on a one-dimensional lattice—a situation that has recently been demonstrated using ultra-cold atoms—we find deterministic logic operations that are universal for quantum information processing. The suggested implementation requires minimal resources and a level of control that is within reach using recently demonstrated techniques. Further work is required to address error-correction.
One-dimensional quantum walk with a moving boundary
International Nuclear Information System (INIS)
Kwek, Leong Chuan; Setiawan
2011-01-01
Quantum walks are interesting models with potential applications to quantum algorithms and physical processes such as photosynthesis. In this paper, we study two models of one-dimensional quantum walks, namely, quantum walks with a moving absorbing wall and quantum walks with one stationary and one moving absorbing wall. For the former, we calculate numerically the survival probability, the rate of change of average position, and the rate of change of standard deviation of the particle's position in the long time limit for different wall velocities. Moreover, we also study the asymptotic behavior and the dependence of the survival probability on the initial particle's state. While for the latter, we compute the absorption probability of the right stationary wall for different velocities and initial positions of the left wall boundary. The results for these two models are compared with those obtained for the classical model. The difference between the results obtained for the quantum and classical models can be attributed to the difference in the probability distributions.
Randomized random walk on a random walk
International Nuclear Information System (INIS)
Lee, P.A.
1983-06-01
This paper discusses generalizations of the model introduced by Kehr and Kunter of the random walk of a particle on a one-dimensional chain which in turn has been constructed by a random walk procedure. The superimposed random walk is randomised in time according to the occurrences of a stochastic point process. The probability of finding the particle in a particular position at a certain instant is obtained explicitly in the transform domain. It is found that the asymptotic behaviour for large time of the mean-square displacement of the particle depends critically on the assumed structure of the basic random walk, giving a diffusion-like term for an asymmetric walk or a square root law if the walk is symmetric. Many results are obtained in closed form for the Poisson process case, and these agree with those given previously by Kehr and Kunter. (author)
Localization in a one-dimensional spatially correlated random potential
International Nuclear Information System (INIS)
Kasner, M.; Weller, W.
1986-01-01
The motion of an electron in a random one-dimensional spatially correlated potential is investigated. The spatial correlation is generated by a Markov chain. It is shown that the influence of the spatial correlation can be described by means of oscillating vertices usually neglected in the Berezinskii diagram technique. Correlation mainly leads to an increase of the localization length in comparison with an uncorrelated potential. However, there is a region of the parameter, where the localization decreases. (author)
Creating cat states in one-dimensional quantum walks using delocalized initial states
International Nuclear Information System (INIS)
Zhang, Wei-Wei; Gao, Fei; Goyal, Sandeep K; Sanders, Barry C; Simon, Christoph
2016-01-01
Cat states are coherent quantum superpositions of macroscopically distinct states and are useful for understanding the boundary between the classical and the quantum world. Due to their macroscopic nature, cat states are difficult to prepare in physical systems. We propose a method to create cat states in one-dimensional quantum walks using delocalized initial states of the walker. Since the quantum walks can be performed on any quantum system, our proposal enables a platform-independent realization of the cat states. We further show that the linear dispersion relation of the effective quantum walk Hamiltonian, which governs the dynamics of the delocalized states, is responsible for the formation of the cat states. We analyze the robustness of these states against environmental interactions and present methods to control and manipulate the cat states in the photonic implementation of quantum walks. (paper)
Limitations of discrete-time quantum walk on a one-dimensional infinite chain
Lin, Jia-Yi; Zhu, Xuanmin; Wu, Shengjun
2018-04-01
How well can we manipulate the state of a particle via a discrete-time quantum walk? We show that the discrete-time quantum walk on a one-dimensional infinite chain with coin operators that are independent of the position can only realize product operators of the form eiξ A ⊗1p, which cannot change the position state of the walker. We present a scheme to construct all possible realizations of all the product operators of the form eiξ A ⊗1p. When the coin operators are dependent on the position, we show that the translation operators on the position can not be realized via a DTQW with coin operators that are either the identity operator 1 or the Pauli operator σx.
Diffusion in one dimensional random medium and hyperbolic Brownian motion
International Nuclear Information System (INIS)
Comtet, A.; Monthus, C.; Paris-6 Univ., 75
1995-03-01
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. This relationship is analyzed in detail and various distributions are studied using stochastic calculus and functional integration. (author) 17 refs
Survival probability in a one-dimensional quantum walk on a trapped lattice
International Nuclear Information System (INIS)
Goenuelol, Meltem; Aydiner, Ekrem; Shikano, Yutaka; Muestecaplioglu, Oezguer E
2011-01-01
The dynamics of the survival probability of quantum walkers on a one-dimensional lattice with random distribution of absorbing immobile traps is investigated. The survival probability of quantum walkers is compared with that of classical walkers. It is shown that the time dependence of the survival probability of quantum walkers has a piecewise stretched exponential character depending on the density of traps in numerical and analytical observations. The crossover between the quantum analogues of the Rosenstock and Donsker-Varadhan behavior is identified.
Random isotropic one-dimensional XY-model
Gonçalves, L. L.; Vieira, A. P.
1998-01-01
The 1D isotropic s = ½XY-model ( N sites), with random exchange interaction in a transverse random field is considered. The random variables satisfy bimodal quenched distributions. The solution is obtained by using the Jordan-Wigner fermionization and a canonical transformation, reducing the problem to diagonalizing an N × N matrix, corresponding to a system of N noninteracting fermions. The calculations are performed numerically for N = 1000, and the field-induced magnetization at T = 0 is obtained by averaging the results for the different samples. For the dilute case, in the uniform field limit, the magnetization exhibits various discontinuities, which are the consequence of the existence of disconnected finite clusters distributed along the chain. Also in this limit, for finite exchange constants J A and J B, as the probability of J A varies from one to zero, the saturation field is seen to vary from Γ A to Γ B, where Γ A(Γ B) is the value of the saturation field for the pure case with exchange constant equal to J A(J B) .
Pseudo-Random Sequences Generated by a Class of One-Dimensional Smooth Map
Wang, Xing-Yuan; Qin, Xue; Xie, Yi-Xin
2011-08-01
We extend a class of a one-dimensional smooth map. We make sure that for each desired interval of the parameter the map's Lyapunov exponent is positive. Then we propose a novel parameter perturbation method based on the good property of the extended one-dimensional smooth map. We perturb the parameter r in each iteration by the real number xi generated by the iteration. The auto-correlation function and NIST statistical test suite are taken to illustrate the method's randomness finally. We provide an application of this method in image encryption. Experiments show that the pseudo-random sequences are suitable for this application.
Pseudo-Random Sequences Generated by a Class of One-Dimensional Smooth Map
International Nuclear Information System (INIS)
Wang Xing-Yuan; Qin Xue; Xie Yi-Xin
2011-01-01
We extend a class of a one-dimensional smooth map. We make sure that for each desired interval of the parameter the map's Lyapunov exponent is positive. Then we propose a novel parameter perturbation method based on the good property of the extended one-dimensional smooth map. We perturb the parameter r in each iteration by the real number x i generated by the iteration. The auto-correlation function and NIST statistical test suite are taken to illustrate the method's randomness finally. We provide an application of this method in image encryption. Experiments show that the pseudo-random sequences are suitable for this application. (general)
Expectation-based approach for one-dimensional randomly disordered phononic crystals
International Nuclear Information System (INIS)
Wu, Feng; Gao, Qiang; Xu, Xiaoming; Zhong, Wanxie
2014-01-01
An expectation-based approach to the statistical theorem is proposed for the one-dimensional randomly disordered phononic crystal. In the proposed approach, the expectations of the random eigenstates of randomly disordered phononic crystals are investigated. In terms of the expectations of the random eigenstates, the wave propagation and localization phenomenon in the random phononic crystal could be understood in a statistical perspective. Using the proposed approach, it is proved that for a randomly disordered phononic crystal, the Bloch theorem holds in the perspective of expectation. A one-dimensional randomly disordered binary phononic crystal consisting of two materials with the random geometry size or random physical parameter is addressed by using the proposed approach. From the result, it can be observed that with the increase of the disorder degree, the localization of the expectations of the eigenstates is strengthened. The effect of the random disorder on the eigenstates at higher frequencies is more significant than that at lower frequencies. Furthermore, after introducing the random disorder into phononic crystals, some random divergent eigenstates are changed to localized eigenstates in expectation sense.
Observation of quasiperiodic dynamics in a one-dimensional quantum walk of single photons in space
Xue, Peng; Qin, Hao; Tang, Bao; Sanders, Barry C.
2014-05-01
We realize the quasi-periodic dynamics of a quantum walker over 2.5 quasi-periods by realizing the walker as a single photon passing through a quantum-walk optical-interferometer network. We introduce fully controllable polarization-independent phase shifters in each optical path to realize arbitrary site-dependent phase shifts, and employ large clear-aperture beam displacers, while maintaining high-visibility interference, to enable 10 quantum-walk steps to be reached. By varying the half-wave-plate setting, we control the quantum-coin bias thereby observing a transition from quasi-periodic dynamics to ballistic diffusion.
The lace expansion approach to ballistic behaviour for one-dimensional weakly self-avoiding walks
Hofstad, van der R.W.
2001-01-01
We prove ballistic behaviour in dimension one fora model of weakly self-avoiding walks where loops of length m are penalized by a factor e -ß/mp with p¿ [0, 1] and ß sufficiently large. Furthermore, we prove that the fluctuations around the linear drift satisfy a centrallimit theorem. The proof uses
A comparison of random walks in dependent random environments
Scheinhardt, Willem R.W.; Kroese, Dirk
2015-01-01
Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the actual evaluation of various characteristics of such processes has received relatively little attention. This paper develops new methodology for the exact computation of the drift in such
Odagaki, Takashi; Kasuya, Keisuke
2017-09-01
Using the Monte Carlo simulation, we investigate a memory-impaired self-avoiding walk on a square lattice in which a random walker marks each of sites visited with a given probability p and makes a random walk avoiding the marked sites. Namely, p = 0 and p = 1 correspond to the simple random walk and the self-avoiding walk, respectively. When p> 0, there is a finite probability that the walker is trapped. We show that the trap time distribution can well be fitted by Stacy's Weibull distribution b(a/b){a+1}/{b}[Γ({a+1}/{b})]-1x^a\\exp(-a/bx^b)} where a and b are fitting parameters depending on p. We also find that the mean trap time diverges at p = 0 as p- α with α = 1.89. In order to produce sufficient number of long walks, we exploit the pivot algorithm and obtain the mean square displacement and its Flory exponent ν(p) as functions of p. We find that the exponent determined for 1000 step walks interpolates both limits ν(0) for the simple random walk and ν(1) for the self-avoiding walk as [ ν(p) - ν(0) ] / [ ν(1) - ν(0) ] = pβ with β = 0.388 when p ≪ 0.1 and β = 0.0822 when p ≫ 0.1. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
International Nuclear Information System (INIS)
Hu Dongsheng; Xiong Shijie
2002-01-01
We investigate the transport properties and Andreev reflection in one-dimensional (1D) systems with randomly doped superconducting grains. The superconducting grains are described by the Bogoliubov-de Gene Hamiltonian and the conductance is calculated by using the transfer matrix method and Landauer-Buettiker formula. It is found that although the quasiparticle states are localized due to the randomness and the low dimensionality, the conductance is still kept finite in the thermodynamical limit due to the Andreev reflection. We also investigate the effect of correlation of disorder in such systems and the results show the delocalization of quasiparticle states and suppression of Andreev reflection in a wide energy window
Relation between random walks and quantum walks
Boettcher, Stefan; Falkner, Stefan; Portugal, Renato
2015-05-01
Based on studies of four specific networks, we conjecture a general relation between the walk dimensions dw of discrete-time random walks and quantum walks with the (self-inverse) Grover coin. In each case, we find that dw of the quantum walk takes on exactly half the value found for the classical random walk on the same geometry. Since walks on homogeneous lattices satisfy this relation trivially, our results for heterogeneous networks suggest that such a relation holds irrespective of whether translational invariance is maintained or not. To develop our results, we extend the renormalization-group analysis (RG) of the stochastic master equation to one with a unitary propagator. As in the classical case, the solution ρ (x ,t ) in space and time of this quantum-walk equation exhibits a scaling collapse for a variable xdw/t in the weak limit, which defines dw and illuminates fundamental aspects of the walk dynamics, e.g., its mean-square displacement. We confirm the collapse for ρ (x ,t ) in each case with extensive numerical simulation. The exact values for dw themselves demonstrate that RG is a powerful complementary approach to study the asymptotics of quantum walks that weak-limit theorems have not been able to access, such as for systems lacking translational symmetries beyond simple trees.
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
2017-02-09
Feb 9, 2017 ... Abstract. In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamil- tonians are generators of time translations. Then an attempt has been made to ...
Scattering of electromagnetic wave by the layer with one-dimensional random inhomogeneities
Kogan, Lev; Zaboronkova, Tatiana; Grigoriev, Gennadii., IV.
A great deal of attention has been paid to the study of probability characteristics of electro-magnetic waves scattered by one-dimensional fluctuations of medium dielectric permittivity. However, the problem of a determination of a density of a probability and average intensity of the field inside the stochastically inhomogeneous medium with arbitrary extension of fluc-tuations has not been considered yet. It is the purpose of the present report to find and to analyze the indicated functions for the plane electromagnetic wave scattered by the layer with one-dimensional fluctuations of permittivity. We assumed that the length and the amplitude of individual fluctuations as well the interval between them are random quantities. All of indi-cated fluctuation parameters are supposed as independent random values possessing Gaussian distribution. We considered the stationary time cases both small-scale and large-scale rarefied inhomogeneities. Mathematically such problem can be reduced to the solution of integral Fred-holm equation of second kind for Hertz potential (U). Using the decomposition of the field into the series of multiply scattered waves we obtained the expression for a probability density of the field of the plane wave and determined the moments of the scattered field. We have shown that all odd moments of the centered field (U-¡U¿) are equal to zero and the even moments depend on the intensity. It was obtained that the probability density of the field possesses the Gaussian distribution. The average field is small compared with the standard fluctuation of scattered field for all considered cases of inhomogeneities. The value of average intensity of the field is an order of a standard of fluctuations of field intensity and drops with increases the inhomogeneities length in the case of small-scale inhomogeneities. The behavior of average intensity is more complicated in the case of large-scale medium inhomogeneities. The value of average intensity is the
Generalized random sequential adsorption of polydisperse mixtures on a one-dimensional lattice
International Nuclear Information System (INIS)
Lončarević, I; Budinski-Petković, Lj; Vrhovac, S B; Belić, A
2010-01-01
Generalized random sequential adsorption (RSA) of polydisperse mixtures of k-mers on a one-dimensional lattice is studied numerically by means of Monte Carlo simulations. The kinetics of the deposition process of mixtures is studied for the irreversible case, for adsorption–desorption processes and for the case where adsorption, desorption and diffusion are present simultaneously. We concentrate here on the influence of the number of mixture components and the length of the k-mers making up the mixture on the temporal behavior of the coverage fraction θ(t). The approach of the coverage θ(t) to the jamming limit θ jam in the case of irreversible RSA is found to be exponential, θ jam -θ(t)∝ exp(-t/σ), not only for a whole mixture, but also for the individual components. For the reversible deposition of polydisperse mixtures, we find that after the initial 'jamming', a stretched exponential growth of the coverage θ(t) towards the equilibrium state value θ eq occurs, i.e., θ eq -θ(t)∝ exp[-(t/τ) β ]. The characteristic timescale τ is found to decrease with the desorption probability P des . When adsorption, desorption and diffusion occur simultaneously, the coverage of a mixture always reaches an equilibrium value θ eq , but there is a significant difference in temporal evolution between the coverage with diffusion and that without
Topology determines force distributions in one-dimensional random spring networks
Heidemann, Knut M.; Sageman-Furnas, Andrew O.; Sharma, Abhinav; Rehfeldt, Florian; Schmidt, Christoph F.; Wardetzky, Max
2018-02-01
Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N ,z ) . Despite the universal properties of such (N ,z ) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.
Lawler, Gregory F.; Ferreras, José A. Trujillo
2004-01-01
The Brownian loop soup introduced in Lawler and Werner (2004) is a Poissonian realization from a sigma-finite measure on unrooted loops. This measure satisfies both conformal invariance and a restriction property. In this paper, we define a random walk loop soup and show that it converges to the Brownian loop soup. In fact, we give a strong approximation result making use of the strong approximation result of Koml\\'os, Major, and Tusn\\'ady. To make the paper self-contained, we include a proof...
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.
On the conductivity of a one-dimensional system of interacting fermions in a random potential
International Nuclear Information System (INIS)
Apel, W.
1981-01-01
A one-dimensional system of interacting fermions in an external potential is studied. The problem was for this purpose transformed to two classical models of statistical mechanics in two dimensions in which occasionally results were found in complementary ranges of the interaction constants of the fermion system. The conductivity appeared as a simple correlation function in both classical models. It was shown that the interaction in a one-dimensional polluted fermion system can cause an isolator-metal transition. (orig./HSI) [de
Velocity and Dispersion for a Two-Dimensional Random Walk
International Nuclear Information System (INIS)
Li Jinghui
2009-01-01
In the paper, we consider the transport of a two-dimensional random walk. The velocity and the dispersion of this two-dimensional random walk are derived. It mainly show that: (i) by controlling the values of the transition rates, the direction of the random walk can be reversed; (ii) for some suitably selected transition rates, our two-dimensional random walk can be efficient in comparison with the one-dimensional random walk. Our work is motivated in part by the challenge to explain the unidirectional transport of motor proteins. When the motor proteins move at the turn points of their tracks (i.e., the cytoskeleton filaments and the DNA molecular tubes), some of our results in this paper can be used to deal with the problem. (general)
Analytic results for asymmetric random walk with exponential transition probabilities
International Nuclear Information System (INIS)
Gutkowicz-Krusin, D.; Procaccia, I.; Ross, J.
1978-01-01
We present here exact analytic results for a random walk on a one-dimensional lattice with asymmetric, exponentially distributed jump probabilities. We derive the generating functions of such a walk for a perfect lattice and for a lattice with absorbing boundaries. We obtain solutions for some interesting moment properties, such as mean first passage time, drift velocity, dispersion, and branching ratio for absorption. The symmetric exponential walk is solved as a special case. The scaling of the mean first passage time with the size of the system for the exponentially distributed walk is determined by the symmetry and is independent of the range
A Novel Algorithm of Quantum Random Walk in Server Traffic Control and Task Scheduling
Directory of Open Access Journals (Sweden)
Dong Yumin
2014-01-01
Full Text Available A quantum random walk optimization model and algorithm in network cluster server traffic control and task scheduling is proposed. In order to solve the problem of server load balancing, we research and discuss the distribution theory of energy field in quantum mechanics and apply it to data clustering. We introduce the method of random walk and illuminate what the quantum random walk is. Here, we mainly research the standard model of one-dimensional quantum random walk. For the data clustering problem of high dimensional space, we can decompose one m-dimensional quantum random walk into m one-dimensional quantum random walk. In the end of the paper, we compare the quantum random walk optimization method with GA (genetic algorithm, ACO (ant colony optimization, and SAA (simulated annealing algorithm. In the same time, we prove its validity and rationality by the experiment of analog and simulation.
Topics in random walks in random environment
International Nuclear Information System (INIS)
Sznitman, A.-S.
2004-01-01
Over the last twenty-five years random motions in random media have been intensively investigated and some new general methods and paradigms have by now emerged. Random walks in random environment constitute one of the canonical models of the field. However in dimension bigger than one they are still poorly understood and many of the basic issues remain to this day unresolved. The present series of lectures attempt to give an account of the progresses which have been made over the last few years, especially in the study of multi-dimensional random walks in random environment with ballistic behavior. (author)
Random walk through fractal environments
International Nuclear Information System (INIS)
Isliker, H.; Vlahos, L.
2003-01-01
We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D F of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D F ≤2 can thus be considered as defective Levy walks. The distribution of jump increments for D F >2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D F F >2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations
Efficient search by optimized intermittent random walks
International Nuclear Information System (INIS)
Oshanin, Gleb; Lindenberg, Katja; Wio, Horacio S; Burlatsky, Sergei
2009-01-01
We study the kinetics for the search of an immobile target by randomly moving searchers that detect it only upon encounter. The searchers perform intermittent random walks on a one-dimensional lattice. Each searcher can step on a nearest neighbor site with probability α or go off lattice with probability 1 - α to move in a random direction until it lands back on the lattice at a fixed distance L away from the departure point. Considering α and L as optimization parameters, we seek to enhance the chances of successful detection by minimizing the probability P N that the target remains undetected up to the maximal search time N. We show that even in this simple model, a number of very efficient search strategies can lead to a decrease of P N by orders of magnitude upon appropriate choices of α and L. We demonstrate that, in general, such optimal intermittent strategies are much more efficient than Brownian searches and are as efficient as search algorithms based on random walks with heavy-tailed Cauchy jump-length distributions. In addition, such intermittent strategies appear to be more advantageous than Levy-based ones in that they lead to more thorough exploration of visited regions in space and thus lend themselves to parallelization of the search processes.
Reserves Represented by Random Walks
International Nuclear Information System (INIS)
Filipe, J A; Ferreira, M A M; Andrade, M
2012-01-01
The reserves problem is studied through models based on Random Walks. Random walks are a classical particular case in the analysis of stochastic processes. They do not appear only to study reserves evolution models. They are also used to build more complex systems and as analysis instruments, in a theoretical feature, of other kind of systems. In this work by studying the reserves, the main objective is to see and guarantee that pensions funds get sustainable. Being the use of these models considering this goal a classical approach in the study of pensions funds, this work concluded about the problematic of reserves. A concrete example is presented.
Static and dynamic properties of frictional phenomena in a one-dimensional system with randomness
International Nuclear Information System (INIS)
Kawaguchi, T.; Matsukawa, H.
1997-01-01
Static and dynamic frictional phenomena at the interface with random impurities are investigated in a two-chain model with incommensurate structure. Static frictional force is caused by the impurity pinning and/or by the pinning due to the regular potential, which is responsible for the breaking of analyticity transition for impurity-free cases. It is confirmed that the static frictional force is always finite in the presence of impurities, in contrast to the impurity-free system. The nature of impurity pinning is discussed in connection with that in density waves. The kinetic frictional force of a steady sliding state is also investigated numerically. The relationship between the sliding velocity dependence of the kinetic frictional force and the strength of impurity potential is discussed. copyright 1997 The American Physical Society
Dynamical correlations for vicious random walk with a wall
International Nuclear Information System (INIS)
Nagao, Taro
2003-01-01
A one-dimensional system of nonintersecting Brownian particles is constructed as the diffusion scaling limit of Fisher's vicious random walk model. N Brownian particles start from the origin at time t=0 and undergo mutually avoiding motion until a finite time t=T. Dynamical correlation functions among the walkers are exactly evaluated in the case with a wall at the origin. Taking an asymptotic limit N→∞, we observe discontinuous transitions in the dynamical correlations. It is further shown that the vicious walk model with a wall is equivalent to a parametric random matrix model describing the crossover between the Bogoliubov-deGennes universality classes
Understanding deterministic diffusion by correlated random walks
International Nuclear Information System (INIS)
Klages, R.; Korabel, N.
2002-01-01
Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control parameter. Here we propose a systematic scheme of how to approximate deterministic diffusion coefficients of this kind in terms of correlated random walks. We apply this approach to two simple examples which are a one-dimensional map on the line and the periodic Lorentz gas. Starting from suitable Green-Kubo formulae we evaluate hierarchies of approximations for their parameter-dependent diffusion coefficients. These approximations converge exactly yielding a straightforward interpretation of the structure of these irregular diffusion coefficients in terms of dynamical correlations. (author)
International Nuclear Information System (INIS)
Yan Zhizhong; Zhang Chuanzeng; Wang Yuesheng
2011-01-01
The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor, which is calculated by the plane-wave-based transfer-matrix method. By treating the random disorder and aperiodicity as the deviation from the periodicity in a special way, three kinds of aperiodic phononic crystals that have normally distributed random disorder, Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered and the band structures are characterized using localization factors. Besides, as a special case, we analyze the band gap properties of a periodic planar layered composite containing a periodic array of square inclusions. The transmission coefficients based on eigen-mode matching theory are also calculated and the results show the same behaviors as the localization factor does. In the case of random disorders, the localization degree of the normally distributed random disorder is larger than that of the uniformly distributed random disorder although the eigenstates are both localized no matter what types of random disorders, whereas, for the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with the quasi-periodic (Fibonacci) sequence not present in the results of the Rudin-Shapiro sequence.
Thermophoresis as persistent random walk
International Nuclear Information System (INIS)
Plyukhin, A.V.
2009-01-01
In a simple model of a continuous random walk a particle moves in one dimension with the velocity fluctuating between +v and -v. If v is associated with the thermal velocity of a Brownian particle and allowed to be position dependent, the model accounts readily for the particle's drift along the temperature gradient and recovers basic results of the conventional thermophoresis theory.
Random walk through fractal environments
Isliker, H.; Vlahos, L.
2002-01-01
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is ...
Nezhadhaghighi, Mohsen Ghasemi
2017-08-01
Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.
Nezhadhaghighi, Mohsen Ghasemi
2017-08-01
Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Random walks, random fields, and disordered systems
Černý, Jiří; Kotecký, Roman
2015-01-01
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a mod...
Subdiffusivity of a random walk among a Poisson system of moving traps on ${\\mathbb Z}$
Athreya, Siva; Drewitz, Alexander; Sun, Rongfeng
2016-01-01
We consider a random walk among a Poisson system of moving traps on ${\\mathbb Z}$. In earlier work [DGRS12], 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 th...
Random walks on reductive groups
Benoist, Yves
2016-01-01
The classical theory of Random Walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
Random walks and diffusion on networks
Masuda, Naoki; Porter, Mason A.; Lambiotte, Renaud
2017-11-01
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.
Kiefer, Thomas; Villanueva, Guillermo; Brugger, Jürgen
2009-08-01
In this study we investigate electrical conduction in finite rectangular random resistor networks in quasione and two dimensions far away from the percolation threshold p(c) by the use of a bond percolation model. Various topologies such as parallel linear chains in one dimension, as well as square and triangular lattices in two dimensions, are compared as a function of the geometrical aspect ratio. In particular we propose a linear approximation for conduction in two-dimensional systems far from p(c), which is useful for engineering purposes. We find that the same scaling function, which can be used for finite-size scaling of percolation thresholds, also applies to describe conduction away from p(c). This is in contrast to the quasi-one-dimensional case, which is highly nonlinear. The qualitative analysis of the range within which the linear approximation is legitimate is given. A brief link to real applications is made by taking into account a statistical distribution of the resistors in the network. Our results are of potential interest in fields such as nanostructured or composite materials and sensing applications.
Locally Perturbed Random Walks with Unbounded Jumps
Paulin, Daniel; Szász, Domokos
2010-01-01
In \\cite{SzT}, D. Sz\\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \\ge 2$. The extension of their result to finite range random walks is straightforward. Here, however, we are interested in the situation when the random walk has unbounded range. Concretely we generalize the statement of \\cite{SzT} to unbounded random walks whose jump distribution belongs to th...
Winning quick and dirty: the greedy random walk
International Nuclear Information System (INIS)
Ben-Naim, E; Redner, S
2004-01-01
As a strategy to complete games quickly, we investigate one-dimensional random walks where the step length increases deterministically upon each return to the origin. When the step length after the kth return equals k, the displacement of the walk x grows linearly in time. Asymptotically, the probability distribution of displacements is a purely exponentially decaying function of |x|/t. The probability E(t, L) for the walk to escape a bounded domain of size L at time t decays algebraically in the long-time limit, E(t, L) ∼ L/t 2 . Consequently, the mean escape time (t) ∼ Lln L, while (t n ) ∼ L 2n-1 for n > 1. Corresponding results are derived when the step length after the kth return scales as k α for α > 0
Chemical Continuous Time Random Walks
Aquino, T.; Dentz, M.
2017-12-01
Traditional methods for modeling solute transport through heterogeneous media employ Eulerian schemes to solve for solute concentration. More recently, Lagrangian methods have removed the need for spatial discretization through the use of Monte Carlo implementations of Langevin equations for solute particle motions. While there have been recent advances in modeling chemically reactive transport with recourse to Lagrangian methods, these remain less developed than their Eulerian counterparts, and many open problems such as efficient convergence and reconstruction of the concentration field remain. We explore a different avenue and consider the question: In heterogeneous chemically reactive systems, is it possible to describe the evolution of macroscopic reactant concentrations without explicitly resolving the spatial transport? Traditional Kinetic Monte Carlo methods, such as the Gillespie algorithm, model chemical reactions as random walks in particle number space, without the introduction of spatial coordinates. The inter-reaction times are exponentially distributed under the assumption that the system is well mixed. In real systems, transport limitations lead to incomplete mixing and decreased reaction efficiency. We introduce an arbitrary inter-reaction time distribution, which may account for the impact of incomplete mixing. This process defines an inhomogeneous continuous time random walk in particle number space, from which we derive a generalized chemical Master equation and formulate a generalized Gillespie algorithm. We then determine the modified chemical rate laws for different inter-reaction time distributions. We trace Michaelis-Menten-type kinetics back to finite-mean delay times, and predict time-nonlocal macroscopic reaction kinetics as a consequence of broadly distributed delays. Non-Markovian kinetics exhibit weak ergodicity breaking and show key features of reactions under local non-equilibrium.
Random Walks with Anti-Correlated Steps
Wagner, Dirk; Noga, John
2005-01-01
We conjecture the expected value of random walks with anti-correlated steps to be exactly 1. We support this conjecture with 2 plausibility arguments and experimental data. The experimental analysis includes the computation of the expected values of random walks for steps up to 22. The result shows the expected value asymptotically converging to 1.
Brownian Optimal Stopping and Random Walks
International Nuclear Information System (INIS)
Lamberton, D.
2002-01-01
One way to compute the value function of an optimal stopping problem along Brownian paths consists of approximating Brownian motion by a random walk. We derive error estimates for this type of approximation under various assumptions on the distribution of the approximating random walk
Record statistics of a strongly correlated time series: random walks and Lévy flights
Godrèche, Claude; Majumdar, Satya N.; Schehr, Grégory
2017-08-01
We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few years, it was indeed realized that random walks are a very useful ‘laboratory’ to test the effects of correlations on the record statistics. We start with the simple one-dimensional random walk with symmetric jumps (both continuous and discrete) and discuss in detail the statistics of the number of records, as well as of the ages of the records, i.e. the lapses of time between two successive record breaking events. Then we review the results that were obtained for a wide variety of random walk models, including random walks with a linear drift, continuous time random walks, constrained random walks (like the random walk bridge) and the case of multiple independent random walkers. Finally, we discuss further observables related to records, like the record increments, as well as some questions raised by physical applications of record statistics, like the effects of measurement error and noise.
A comparison of random walks in dependent random environments
Scheinhardt, Willem R.W.; Kroese, Dirk
We provide exact computations for the drift of random walks in dependent random environments, including $k$-dependent and moving average environments. We show how the drift can be characterized and evaluated using Perron–Frobenius theory. Comparing random walks in various dependent environments, we
Elements of random walk and diffusion processes
Ibe, Oliver C
2013-01-01
Presents an important and unique introduction to random walk theory Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic
Iterated random walks with shape prior
DEFF Research Database (Denmark)
Pujadas, Esmeralda Ruiz; Kjer, Hans Martin; Piella, Gemma
2016-01-01
the parametric probability density function. Then, random walks is performed iteratively aligning the prior with the current segmentation in every iteration. We tested the proposed approach with natural and medical images and compared it with the latest techniques with random walks and shape priors......We propose a new framework for image segmentation using random walks where a distance shape prior is combined with a region term. The shape prior is weighted by a confidence map to reduce the influence of the prior in high gradient areas and the region term is computed with k-means to estimate....... The experiments suggest that this method gives promising results for medical and natural images....
The random walk model of intrafraction movement
International Nuclear Information System (INIS)
Ballhausen, H; Reiner, M; Kantz, S; Belka, C; Söhn, M
2013-01-01
The purpose of this paper is to understand intrafraction movement as a stochastic process driven by random external forces. The hypothetically proposed three-dimensional random walk model has significant impact on optimal PTV margins and offers a quantitatively correct explanation of experimental findings. Properties of the random walk are calculated from first principles, in particular fraction-average population density distributions for displacements along the principal axes. When substituted into the established optimal margin recipes these fraction-average distributions yield safety margins about 30% smaller as compared to the suggested values from end-of-fraction Gaussian fits. Stylized facts of a random walk are identified in clinical data, such as the increase of the standard deviation of displacements with the square root of time. Least squares errors in the comparison to experimental results are reduced by about 50% when accounting for non-Gaussian corrections from the random walk model. (paper)
The random walk model of intrafraction movement.
Ballhausen, H; Reiner, M; Kantz, S; Belka, C; Söhn, M
2013-04-07
The purpose of this paper is to understand intrafraction movement as a stochastic process driven by random external forces. The hypothetically proposed three-dimensional random walk model has significant impact on optimal PTV margins and offers a quantitatively correct explanation of experimental findings. Properties of the random walk are calculated from first principles, in particular fraction-average population density distributions for displacements along the principal axes. When substituted into the established optimal margin recipes these fraction-average distributions yield safety margins about 30% smaller as compared to the suggested values from end-of-fraction gaussian fits. Stylized facts of a random walk are identified in clinical data, such as the increase of the standard deviation of displacements with the square root of time. Least squares errors in the comparison to experimental results are reduced by about 50% when accounting for non-gaussian corrections from the random walk model.
Quantum random walks using quantum accelerator modes
International Nuclear Information System (INIS)
Ma, Z.-Y.; Burnett, K.; D'Arcy, M. B.; Gardiner, S. A.
2006-01-01
We discuss the use of high-order quantum accelerator modes to achieve an atom optical realization of a biased quantum random walk. We first discuss how one can create coexistent quantum accelerator modes, and hence how momentum transfer that depends on the atoms' internal state can be achieved. When combined with microwave driving of the transition between the states, a different type of atomic beam splitter results. This permits the realization of a biased quantum random walk through quantum accelerator modes
Simulation of random walks in field theory
International Nuclear Information System (INIS)
Rensburg, E.J.J. van
1988-01-01
The numerical simulation of random walks is considered using the Monte Carlo method previously proposed. The algorithm is tested and then generalised to generate Edwards random walks. The renormalised masses of the Edwards model are calculated and the results are compared with those obtained from a simple perturbation theory calculation for small values of the bare coupling constant. The efficiency of this algorithm is discussed and compared with an alternative approach. (author)
Many random walks are faster than one
Czech Academy of Sciences Publication Activity Database
Alon, N.; Avin, Ch.; Koucký, Michal; Kozma, G.; Lotker, Z.; Tuttle, M.R.
2011-01-01
Roč. 20, č. 4 (2011), s. 481-502 ISSN 0963-5483 R&D Projects: GA ČR GP201/07/P276; GA ČR GA201/05/0124 Institutional research plan: CEZ:AV0Z10190503 Keywords : multiple random walks * parallel random walks Subject RIV: BA - General Mathematics Impact factor: 0.778, year: 2011 http://journals.cambridge.org/ action /displayAbstract?fromPage=online&aid=8280727
Tempered stable laws as random walk limits
Chakrabarty, Arijit; Meerschaert, Mark M.
2010-01-01
Stable laws can be tempered by modifying the L\\'evy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk models that converge to a tempered stable law under a triangular array scheme. Since tempered stable laws and processes are useful in statistical physics, these random walk models can provide a basic physical model for the underlying physical phenomena.
Pedestrian Walking Behavior Revealed through a Random Walk Model
Directory of Open Access Journals (Sweden)
Hui Xiong
2012-01-01
Full Text Available This paper applies method of continuous-time random walks for pedestrian flow simulation. In the model, pedestrians can walk forward or backward and turn left or right if there is no block. Velocities of pedestrian flow moving forward or diffusing are dominated by coefficients. The waiting time preceding each jump is assumed to follow an exponential distribution. To solve the model, a second-order two-dimensional partial differential equation, a high-order compact scheme with the alternating direction implicit method, is employed. In the numerical experiments, the walking domain of the first one is two-dimensional with two entrances and one exit, and that of the second one is two-dimensional with one entrance and one exit. The flows in both scenarios are one way. Numerical results show that the model can be used for pedestrian flow simulation.
Random walk of passive tracers among randomly moving obstacles
Gori, Matteo; Donato, Irene; Floriani, Elena; Nardecchia, Ilaria; Pettini, Marco
2016-01-01
Background: This study is mainly motivated by the need of understanding how the diffusion behaviour of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target. Method: By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random en...
Random walks and polygons in tight confinement
International Nuclear Information System (INIS)
Diao, Y; Ernst, C; Ziegler, U
2014-01-01
We discuss the effect of confinement on the topology and geometry of tightly confined random walks and polygons. Here the walks and polygons are confined in a sphere of radius R ≥ 1/2 and the polygons are equilateral with n edges of unit length. We illustrate numerically that for a fixed length of random polygons the knotting probability increases to one as the radius decreases to 1/2. We also demonstrate that for random polygons (walks) the curvature increases to πn (π(n – 1)) as the radius approaches 1/2 and that the torsion decreases to ≈ πn/3 (≈ π(n – 1)/3). In addition we show the effect of length and confinement on the average crossing number of a random polygon
Scaling Argument of Anisotropic Random Walk
International Nuclear Information System (INIS)
Xu Bingzhen; Jin Guojun; Wang Feifeng
2005-01-01
In this paper, we analytically discuss the scaling properties of the average square end-to-end distance (R 2 ) for anisotropic random walk in D-dimensional space (D≥2), and the returning probability P n (r 0 ) for the walker into a certain neighborhood of the origin. We will not only give the calculating formula for (R 2 ) and P n (r 0 ), but also point out that if there is a symmetric axis for the distribution of the probability density of a single step displacement, we always obtain (R p erpendicular n 2 )∼n, where perpendicular refers to the projections of the displacement perpendicular to each symmetric axes of the walk; in D-dimensional space with D symmetric axes perpendicular to each other, we always have (R n 2 )∼n and the random walk will be like a purely random motion; if the number of inter-perpendicular symmetric axis is smaller than the dimensions of the space, we must have (R n 2 )∼n 2 for very large n and the walk will be like a ballistic motion. It is worth while to point out that unlike the isotropic random walk in one and two dimensions, which is certain to return into the neighborhood of the origin, generally there is only a nonzero probability for the anisotropic random walker in two dimensions to return to the neighborhood.
Coupled continuous time-random walks in quenched random environment
Magdziarz, M.; Szczotka, W.
2018-02-01
We introduce a coupled continuous-time random walk with coupling which is characteristic for Lévy walks. Additionally we assume that the walker moves in a quenched random environment, i.e. the site disorder at each lattice point is fixed in time. We analyze the scaling limit of such a random walk. We show that for large times the behaviour of the analyzed process is exactly the same as in the case of uncoupled quenched trap model for Lévy flights.
Mesoscopic description of random walks on combs
Méndez, Vicenç; Iomin, Alexander; Campos, Daniel; Horsthemke, Werner
2015-12-01
Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic method to obtain their transport properties. The random walk along the branches may be biased, and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone. We analyze the overall diffusion properties along the backbone and find normal diffusion, anomalous diffusion, and stochastic localization (diffusion failure), respectively, depending on the characteristics of the continuous time random walk along the branches, and compare our analytical results with stochastic simulations.
Random walks of oriented particles on fractals
International Nuclear Information System (INIS)
Haber, René; Prehl, Janett; Hoffmann, Karl Heinz; Herrmann, Heiko
2014-01-01
Random walks of point particles on fractals exhibit subdiffusive behavior, where the anomalous diffusion exponent is smaller than one, and the corresponding random walk dimension is larger than two. This is due to the limited space available in fractal structures. Here, we endow the particles with an orientation and analyze their dynamics on fractal structures. In particular, we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation, which are modeled using an appropriate move class. These interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure. A surprising finding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features. (paper)
Quantum random-walk search algorithm
International Nuclear Information System (INIS)
Shenvi, Neil; Whaley, K. Birgitta; Kempe, Julia
2003-01-01
Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speedup over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random-walk architecture that provides such a speedup. It will be shown that this algorithm performs an oracle search on a database of N items with O(√(N)) calls to the oracle, yielding a speedup similar to other quantum search algorithms. It appears that the quantum random-walk formulation has considerable flexibility, presenting interesting opportunities for development of other, possibly novel quantum algorithms
Path probabilities of continuous time random walks
International Nuclear Information System (INIS)
Eule, Stephan; Friedrich, Rudolf
2014-01-01
Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman–Kac formulae. (paper)
Directory of Open Access Journals (Sweden)
Min-Jhong Gu
2014-08-01
Full Text Available This article describes the development of a suite of programs that is capable of simulating the radiation properties of a random rough surface (RRS. The fundamental approach involves the generation, by fast Fourier transform (FFT built with rigorous finite difference time domain (FDTD, as the theoretical basis for the simulation of a bidirectional reflectance distribution function (BRDF of the RRS. The results are compared with the measurements and modeling of existing work to verify the feasibility of customized programming. It was found that the results of this study were a better match to the measurement data than those achieved in other modeling work.
Random walk with memory enhancement and decay
Tan, Zhi-Jie; Zou, Xian-Wu; Huang, Sheng-You; Zhang, Wei; Jin, Zhun-Zhi
2002-04-01
A model of random walk with memory enhancement and decay was presented on the basis of the characteristics of the biological intelligent walks. In this model, the movement of the walker is determined by the difference between the remaining information at the jumping-out site and jumping-in site. The amount of the memory information si(t) at a site i is enhanced with the increment of visiting times to that site, and decays with time t by the rate e-βt, where β is the memory decay exponent. When β=0, there exists a transition from Brownian motion (BM) to the compact growth of walking trajectory with the density of information energy u increasing. But for β>0, this transition does not appear and the walk with memory enhancement and decay can be considered as the BM of the mass center of the cluster composed of remembered sites in the late stage.
Random walk centrality for temporal networks
International Nuclear Information System (INIS)
Rocha, Luis E C; Masuda, Naoki
2014-01-01
Nodes can be ranked according to their relative importance within a network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based on random walks, for example the PageRank, have focused on static structures. However, several realistic networks are indeed dynamic, meaning that their structure changes in time. In this paper, we propose a centrality measure for temporal networks based on random walks under periodic boundary conditions that we call TempoRank. It is known that, in static networks, the stationary density of the random walk is proportional to the degree or the strength of a node. In contrast, we find that, in temporal networks, the stationary density is proportional to the in-strength of the so-called effective network, a weighted and directed network explicitly constructed from the original sequence of transition matrices. The stationary density also depends on the sojourn probability q, which regulates the tendency of the walker to stay in the node, and on the temporal resolution of the data. We apply our method to human interaction networks and show that although it is important for a node to be connected to another node with many random walkers (one of the principles of the PageRank) at the right moment, this effect is negligible in practice when the time order of link activation is included. (paper)
Random walk centrality for temporal networks
Rocha, Luis E. C.; Masuda, Naoki
2014-06-01
Nodes can be ranked according to their relative importance within a network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based on random walks, for example the PageRank, have focused on static structures. However, several realistic networks are indeed dynamic, meaning that their structure changes in time. In this paper, we propose a centrality measure for temporal networks based on random walks under periodic boundary conditions that we call TempoRank. It is known that, in static networks, the stationary density of the random walk is proportional to the degree or the strength of a node. In contrast, we find that, in temporal networks, the stationary density is proportional to the in-strength of the so-called effective network, a weighted and directed network explicitly constructed from the original sequence of transition matrices. The stationary density also depends on the sojourn probability q, which regulates the tendency of the walker to stay in the node, and on the temporal resolution of the data. We apply our method to human interaction networks and show that although it is important for a node to be connected to another node with many random walkers (one of the principles of the PageRank) at the right moment, this effect is negligible in practice when the time order of link activation is included.
International Nuclear Information System (INIS)
Lyo, S.K.
1986-01-01
The frequency-dependent electrical conductivity is studied in a nearest-neighbor-hopping linear lattice with disordered site energies and barrier heights in the presence of a uniform static electric field, allowing for detailed balance between random rates. Exact expressions are obtained for the conductivity for both high and low frequencies. The results reduce to those obtained by previous authors in the absence of site-energy disorder. However, the latter is found to alter the character of the frequency dependence of the conductivity significantly at low frequencies. In this case the conductivity is expanded as sigma(ω) = sigma 0 +isigma 1 ω-sigma 2 ω 2 -isigma 3 ω 3 +.... We find that sigma 1 is nonvanishing only if both site energies and barrier heights are disordered and that sigma 2 is positive when the fluctuations in site energies are small compared with the thermal energy but becomes negative in the opposite regime. The ac response is found to vanish [i.e., sigma(ω) = 0 for ωnot =0] in the absence of disorder in barrier heights
Directory of Open Access Journals (Sweden)
Nattagit Jiteurtragool
2018-02-01
Full Text Available The search for generation approaches to robust chaos has received considerable attention due to potential applications in cryptography or secure communications. This paper is of interest regarding a 1-D sigmoidal chaotic map, which has never been distinctly investigated. This paper introduces a generic form of the sigmoidal chaotic map with three terms, i.e., xn+1 = ∓AfNL(Bxn ± Cxn ± D, where A, B, C, and D are real constants. The unification of modified sigmoid and hyperbolic tangent (tanh functions reveals the existence of a “unified sigmoidal chaotic map” generically fulfilling the three terms, with robust chaos partially appearing in some parameter ranges. A simplified generic form, i.e., xn+1 = ∓fNL(Bxn ± Cxn, through various S-shaped functions, has recently led to the possibility of linearization using (i hardtanh and (ii signum functions. This study finds a linearized sigmoidal chaotic map that potentially offers robust chaos over an entire range of parameters. Chaos dynamics are described in terms of chaotic waveforms, histogram, cobweb plots, fixed point, Jacobian, and a bifurcation structure diagram based on Lyapunov exponents. As a practical example, a true random bit generator using the linearized sigmoidal chaotic map is demonstrated. The resulting output is evaluated using the NIST SP800-22 test suite and TestU01.
Random walk term weighting for information retrieval
DEFF Research Database (Denmark)
Blanco, R.; Lioma, Christina
2007-01-01
We present a way of estimating term weights for Information Retrieval (IR), using term co-occurrence as a measure of dependency between terms.We use the random walk graph-based ranking algorithm on a graph that encodes terms and co-occurrence dependencies in text, from which we derive term weights...
Random walks in Euclidean space
Varjú, Péter Pál
2012-01-01
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove a local limit theorem under a suitable moment condition and a necessary non-degeneracy condition. Under stronger hypothesis, we prove a limit theorem on a wide range of scales: between e^(-cl^(1/4)) and l^(1/2), where l is the number of steps.
RANDOM WALK HYPOTHESIS IN FINANCIAL MARKETS
Directory of Open Access Journals (Sweden)
Nicolae-Marius JULA
2017-05-01
Full Text Available Random walk hypothesis states that the stock market prices do not follow a predictable trajectory, but are simply random. If you are trying to predict a random set of data, one should test for randomness, because, despite the power and complexity of the used models, the results cannot be trustworthy. There are several methods for testing these hypotheses and the use of computational power provided by the R environment makes the work of the researcher easier and with a cost-effective approach. The increasing power of computing and the continuous development of econometric tests should give the potential investors new tools in selecting commodities and investing in efficient markets.
Random walk of passive tracers among randomly moving obstacles.
Gori, Matteo; Donato, Irene; Floriani, Elena; Nardecchia, Ilaria; Pettini, Marco
2016-04-14
This study is mainly motivated by the need of understanding how the diffusion behavior of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target. By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle among randomly moving and interacting obstacles. The relevant physical quantity which is worked out is the diffusion coefficient of the passive tracer which is computed as a function of the average inter-obstacles distance. The results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its motion can be considerably slowed down.
Continuous time quantum random walks in free space
Eichelkraut, Toni; Vetter, Christian; Perez-Leija, Armando; Christodoulides, Demetrios; Szameit, Alexander
2014-05-01
We show theoretically and experimentally that two-dimensional continuous time coherent random walks are possible in free space, that is, in the absence of any external potential, by properly tailoring the associated initial wave function. These effects are experimentally demonstrated using classical paraxial light. Evidently, the usage of classical beams to explore the dynamics of point-like quantum particles is possible since both phenomena are mathematically equivalent. This in turn makes our approach suitable for the realization of random walks using different quantum particles, including electrons and photons. To study the spatial evolution of a wavefunction theoretically, we consider the one-dimensional paraxial wave equation (i∂z +1/2 ∂x2) Ψ = 0 . Starting with the initially localized wavefunction Ψ (x , 0) = exp [ -x2 / 2σ2 ] J0 (αx) , one can show that the evolution of such Gaussian-apodized Bessel envelopes within a region of validity resembles the probability pattern of a quantum walker traversing a uniform lattice. In order to generate the desired input-field in our experimental setting we shape the amplitude and phase of a collimated light beam originating from a classical HeNe-Laser (633 nm) utilizing a spatial light modulator.
Curvature of random walks and random polygons in confinement
International Nuclear Information System (INIS)
Diao, Y; Ernst, C; Montemayor, A; Ziegler, U
2013-01-01
The purpose of this paper is to study the curvature of equilateral random walks and polygons that are confined in a sphere. Curvature is one of several basic geometric properties that can be used to describe random walks and polygons. We show that confinement affects curvature quite strongly, and in the limit case where the confinement diameter equals the edge length the unconfined expected curvature value doubles from π/2 to π. To study curvature a simple model of an equilateral random walk in spherical confinement in dimensions 2 and 3 is introduced. For this simple model we derive explicit integral expressions for the expected value of the total curvature in both dimensions. These expressions are functions that depend only on the radius R of the confinement sphere. We then show that the values obtained by numeric integration of these expressions agrees with numerical average curvature estimates obtained from simulations of random walks. Finally, we compare the confinement effect on curvature of random walks with random polygons. (paper)
Random walk and the heat equation
Lawler, Gregory F
2010-01-01
The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation by considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equation and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. The first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For exa...
Random walk generated by random permutations of {1, 2, 3, ..., n + 1}
International Nuclear Information System (INIS)
Oshanin, G; Voituriez, R
2004-01-01
We study properties of a non-Markovian random walk X (n) l , l = 0, 1, 2, ..., n, evolving in discrete time l on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the rise-and-descent sequences characterizing random permutations π of [n + 1] = {1, 2, 3, ..., n + 1}. We determine exactly the probability of finding the end-point X n = X (n) n of the trajectory of such a permutation-generated random walk (PGRW) at site X, and show that in the limit n → ∞ it converges to a normal distribution with a smaller, compared to the conventional Polya random walk, diffusion coefficient. We formulate, as well, an auxiliary stochastic process whose distribution is identical to the distribution of the intermediate points X (n) l , l < n, which enables us to obtain the probability measure of different excursions and to define the asymptotic distribution of the number of 'turns' of the PGRW trajectories
Dilemma Produced by Infinity of a Random Walk
International Nuclear Information System (INIS)
Li Jing-Hui
2015-01-01
We report a dilemma produced by the infinity of a random walk moving along a two-dimensional space sidestep. For this random walk, our investigation shows that using a different model can lead to a different diffusion coefficient of the random walk, which is produced by the infinity of the random walk. The result obtained by us in the present work can serve as a warning to us when we build the models to investigate the corresponding scientific problems. (paper)
Malicet, Dominique
2017-12-01
In this paper, we study random walks {g_n=f_{n-1}\\ldots f_0} on the group Homeo ( S 1) of the homeomorphisms of the circle, where the homeomorphisms f k are chosen randomly, independently, with respect to a same probability measure {ν}. We prove that under the only condition that there is no probability measure invariant by {ν}-almost every homeomorphism, the random walk almost surely contracts small intervals. It generalizes what has been known on this subject until now, since various conditions on {ν} were imposed in order to get the phenomenon of contractions. Moreover, we obtain the surprising fact that the rate of contraction is exponential, even in the lack of assumptions of smoothness on the f k 's. We deduce various dynamical consequences on the random walk ( g n ): finiteness of ergodic stationary measures, distribution of the trajectories, asymptotic law of the evaluations, etc. The proof of the main result is based on a modification of the Ávila-Viana's invariance principle, working for continuous cocycles on a space fibred in circles.
Quantum random walks and their convergence to Evans–Hudson ...
Indian Academy of Sciences (India)
Quantum dynamical semigroup; Evans–Hudson flow; quantum random walk. 1. Introduction. The aim of this article is to investigate convergence of random walks on von Neumann algebra to Evans–Hudson flows. Here the random walks and Evans–Hudson flows are gene- ralizations of classical Markov chains and Markov ...
Dynamic random walks theory and applications
Guillotin-Plantard, Nadine
2006-01-01
The aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer science, mathematical physics and finance. Each chapter contains didactical material as well as more advanced technical sections. Few appendices will help refreshing memories (if necessary!).· New probabilistic model, new results in probability theory· Original applications in computer science· Applications in mathematical physics· Applications in finance
Weak limits for quantum random walks
International Nuclear Information System (INIS)
Grimmett, Geoffrey; Janson, Svante; Scudo, Petra F.
2004-01-01
We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With X n denoting position at time n, we show that X n /n converges weakly as n→∞ to a certain distribution which is absolutely continuous and of bounded support. The proof is rigorous and makes use of Fourier transform methods. This approach simplifies and extends certain preceding derivations valid in one dimension that make use of combinatorial and path integral methods
A Random Walk Picture of Basketball
Gabel, Alan; Redner, Sidney
2012-02-01
We analyze NBA basketball play-by-play data and found that scoring is well described by a weakly-biased, anti-persistent, continuous-time random walk. The time between successive scoring events follows an exponential distribution, with little memory between events. We account for a wide variety of statistical properties of scoring, such as the distribution of the score difference between opponents and the fraction of game time that one team is in the lead.
Random walks on generalized Koch networks
International Nuclear Information System (INIS)
Sun, Weigang
2013-01-01
For deterministically growing networks, it is a theoretical challenge to determine the topological properties and dynamical processes. In this paper, we study random walks on generalized Koch networks with features that include an initial state that is a globally connected network to r nodes. In each step, every existing node produces m complete graphs. We then obtain the analytical expressions for first passage time (FPT), average return time (ART), i.e. the average of FPTs for random walks from node i to return to the starting point i for the first time, and average sending time (AST), defined as the average of FPTs from a hub node to all other nodes, excluding the hub itself with regard to network parameters m and r. For this family of Koch networks, the ART of the new emerging nodes is identical and increases with the parameters m or r. In addition, the AST of our networks grows with network size N as N ln N and also increases with parameter m. The results obtained in this paper are the generalizations of random walks for the original Koch network. (paper)
Random walk to a nonergodic equilibrium concept
Bel, G.; Barkai, E.
2006-01-01
Random walk models, such as the trap model, continuous time random walks, and comb models, exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this paper a nonergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. We show that when conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics. In the ergodic phase the distribution function of the occupation times approaches a δ function centered on the value predicted based on standard Boltzmann-Gibbs statistics. The relation of our work to single-molecule experiments is briefly discussed.
Spin, statistics, and geometry of random walks
International Nuclear Information System (INIS)
Jaroszewicz, T.; Kurzepa, P.S.
1991-01-01
The authors develop and unify two complementary descriptions of propagation of spinning particles: the directed random walk representation and the spin factor approach. Working in an arbitrary number of dimensions D, they first represent the Dirac propagator in terms of a directed random walk. They then derive the general and explicit form of the gauge connection describing parallel transport of spin and investigate the resulting quantum-mechanical problem of a particle moving on a sphere in the field of a nonabelian SO(D-1) monopole. This construction, generalizing Polyakov's results, enables them to prove the equivalence of the random walk and path-integral (spin factor) representation. As an alternative, they construct and discuss various Wess-Zumino-Witten forms of the spin factor. They clarify the role played by the coupling between the particle's spin and translational degrees of freedom in establishing the geometrical properties of particle's paths in spacetime. To this end, they carefully define and evaluate Hausdorff dimensions of bosonic and fermionic sample paths, in the covariant as well as nonrelativistic formulations. Finally, as an application of the developed formalism, they give an intuitive spacetime interpretation of chiral anomalies in terms of the geometry of fermion trajectories
Randomness at the root of things 1: Random walks
Ogborn, Jon; Collins, Simon; Brown, Mick
2003-09-01
This is the first of a pair of articles about randomness in physics. In this article, we use some variations on the idea of a `random walk' to consider first the path of a particle in Brownian motion, and then the random variation to be expected in radioactive decay. The arguments are set in the context of the general importance of randomness both in physics and in everyday life. We think that the ideas could usefully form part of students' A-level work on random decay and quantum phenomena, as well as being good for their general education. In the second article we offer a novel and simple approach to Poisson sequences.
A random walk model to evaluate autism
Moura, T. R. S.; Fulco, U. L.; Albuquerque, E. L.
2018-02-01
A common test administered during neurological examination in children is the analysis of their social communication and interaction across multiple contexts, including repetitive patterns of behavior. Poor performance may be associated with neurological conditions characterized by impairments in executive function, such as the so-called pervasive developmental disorders (PDDs), a particular condition of the autism spectrum disorders (ASDs). Inspired in these diagnosis tools, mainly those related to repetitive movements and behaviors, we studied here how the diffusion regimes of two discrete-time random walkers, mimicking the lack of social interaction and restricted interests developed for children with PDDs, are affected. Our model, which is based on the so-called elephant random walk (ERW) approach, consider that one of the random walker can learn and imitate the microscopic behavior of the other with probability f (1 - f otherwise). The diffusion regimes, measured by the Hurst exponent (H), is then obtained, whose changes may indicate a different degree of autism.
Quantum chemistry by random walk: Higher accuracy
International Nuclear Information System (INIS)
Anderson, J.B.
1980-01-01
The random walk method of solving the Schroedinger equation is extended to allow the calculation of eigenvalues of atomic and molecular systems with higher accuracy. The combination of direct calculation of the difference delta between a true wave function psi and a trial wave function psi/sub o/ with importance sampling greatly reduces systematic and statistical error. The method is illustrated with calculations for ground-state hydrogen and helium atoms using trial wave functions from variational calculations. The energies obtained are 20 to 100 times more accurate than those of the corresponding variational calculations
One-Dimensionality and Whiteness
Calderon, Dolores
2006-01-01
This article is a theoretical discussion that links Marcuse's concept of one-dimensional society and the Great Refusal with critical race theory in order to achieve a more robust interrogation of whiteness. The author argues that in the context of the United States, the one-dimensionality that Marcuse condemns in "One-Dimensional Man" is best…
Random walks on a fluctuating lattice: A renormalization group approach applied in one dimension
International Nuclear Information System (INIS)
Levermore, C.D.; Nadler, W.; Stein, D.L.
1995-01-01
We study the problem of a random walk on a lattice in which bonds connecting nearest-neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to solve for the effective diffusive behavior at long times. For one-dimensional lattices we obtain better quantitative agreement with simulation data than earlier effective medium results. Our technique works in principle in any dimension, although the amount of computation required rises with the dimensionality of the lattice
Generating random walks and polygons with stiffness in confinement
International Nuclear Information System (INIS)
Diao, Y; Ernst, C; Saarinen, S; Ziegler, U
2015-01-01
The purpose of this paper is to explore ways to generate random walks and polygons in confinement with a bias toward stiffness. Here the stiffness refers to the curvature angle between two consecutive edges along the random walk or polygon. The stiffer the walk (polygon), the smaller this angle on average. Thus random walks and polygons with an elevated stiffness have lower than expected curvatures. The authors introduced and studied several generation algorithms with a stiffness parameter s>0 that regulates the expected curvature angle at a given vertex in which the random walks and polygons are generated one edge at a time using conditional probability density functions. Our generating algorithms also allow the generation of unconfined random walks and polygons with any desired mean curvature angle. In the case of random walks and polygons confined in a sphere of fixed radius, we observe that, as expected, stiff random walks or polygons are more likely to be close to the confinement boundary. The methods developed here require that the random walks and random polygons be rooted at the center of the confinement sphere. (paper)
Limit theorems for random walks on a strip in subdiffusive regimes
International Nuclear Information System (INIS)
Dolgopyat, D; Goldsheid, I
2013-01-01
We study the asymptotic behaviour of occupation times of a transient random walk (RW) in a quenched random environment (RE) on a strip in a subdiffusive regime. The asymptotic behaviour of hitting times, which is a more traditional object of study, is exactly the same. As a particular case, we solve a long standing problem of describing the asymptotic behaviour of a RW with bounded jumps on a one-dimensional lattice. Our technique results from the development of ideas from our previous work (Dolgopyat and Goldsheid 2012 Commun. Math. Phys. 315 241–77) on the simple RWs in RE and those used in Bolthausen and Goldsheid (2000 Commun. Math. Phys. 214 429–47; 2008 Commun. Math. Phys. 278 253–88) and Goldsheid (2008 Probab. Theory Relat. Fields 141 471–511) for the study of random walks on a strip. (paper)
Heterogeneous continuous-time random walks
Grebenkov, Denis S.; Tupikina, Liubov
2018-01-01
We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.
Asymptotic Properties of Multistate Random Walks. I. Theory
Roerdink, J.B.T.M.; Shuler, K.E.
1985-01-01
A calculation is presented of the long-time behavior of various random walk properties (moments, probability of return to the origin, expected number of distinct sites visited) for multistate random walks on periodic lattices. In particular, we consider inhomogeneous periodic lattices, consisting of
How edge-reinforced random walk arises naturally
Rolles, S.W.W.
2003-01-01
We give a characterization of a modified edge-reinforced random walk in terms of certain partially exchangeable sequences. In particular, we obtain a characterization of an edge-reinforced random walk (introduced by Coppersmith and Diaconis) on a 2-edge-connected graph. Modifying the notion of
Girold, Sébastien; Rousseau, Jérome; Le Gal, Magalie; Coudeyre, Emmanuel; Le Henaff, Jacqueline
2017-07-01
With Nordic walking, or walking with poles, one can travel a greater distance and at a higher rate than with walking without poles, but whether the activity is beneficial for patients with cardiovascular disease is unknown. This randomized controlled trial was undertaken to determine whether Nordic walking was more effective than walking without poles on walk distance to support rehabilitation training for patients with acute coronary syndrome (ACS) and peripheral arterial occlusive disease (PAOD). Patients were recruited in a private specialized rehabilitation centre for cardiovascular diseases. The entire protocol, including patient recruitment, took place over 2 months, from September to October 2013. We divided patients into 2 groups: Nordic Walking Group (NWG, n=21) and Walking Group without poles (WG, n=21). All patients followed the same program over 4 weeks, except for the walk performed with or without poles. The main outcome was walk distance on the 6-min walk test. Secondary outcomes were maximum heart rate during exercise and walk distance and power output on a treadmill stress test. We included 42 patients (35 men; mean age 57.2±11 years and BMI 26.5±4.5kg/m 2 ). At the end of the training period, both groups showed improved walk distance on the 6-min walk test and treatment stress test as well as power on the treadmill stress test (PNordic walking training appeared more efficient than training without poles for increasing walk distance on the 6-min walk test for patients with ACS and PAOD. Copyright © 2017. Published by Elsevier Masson SAS.
On Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment
International Nuclear Information System (INIS)
Cao Xiaofeng; Deng Zongwei; Yang Chunbin
2008-01-01
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. We assume that the variation of the number of active sites has three possibilities in each update: to increase by 1 with probability f 1 , to decrease by 1 with probability f 2 , or remain unchanged with probability 1-f 1 -f 2 . This mimics the dynamics in the system. Power-law distributions of the lifetime are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions.
Random walk in dynamically disordered chains: Poisson white noise disorder
International Nuclear Information System (INIS)
Hernandez-Garcia, E.; Pesquera, L.; Rodriguez, M.A.; San Miguel, M.
1989-01-01
Exact solutions are given for a variety of models of random walks in a chain with time-dependent disorder. Dynamic disorder is modeled by white Poisson noise. Models with site-independent (global) and site-dependent (local) disorder are considered. Results are described in terms of an affective random walk in a nondisordered medium. In the cases of global disorder the effective random walk contains multistep transitions, so that the continuous limit is not a diffusion process. In the cases of local disorder the effective process is equivalent to usual random walk in the absence of disorder but with slower diffusion. Difficulties associated with the continuous-limit representation of random walk in a disordered chain are discussed. In particular, the authors consider explicit cases in which taking the continuous limit and averaging over disorder sources do not commute
International Nuclear Information System (INIS)
Lu Dawei; Peng Xinhua; Du Jiangfeng; Zhu Jing; Zou Ping; Yu Yihua; Zhang Shanmin; Chen Qun
2010-01-01
An important quantum search algorithm based on the quantum random walk performs an oracle search on a database of N items with O(√(phN)) calls, yielding a speedup similar to the Grover quantum search algorithm. The algorithm was implemented on a quantum information processor of three-qubit liquid-crystal nuclear magnetic resonance (NMR) in the case of finding 1 out of 4, and the diagonal elements' tomography of all the final density matrices was completed with comprehensible one-dimensional NMR spectra. The experimental results agree well with the theoretical predictions.
Efficient sampling of complex network with modified random walk strategies
Xie, Yunya; Chang, Shuhua; Zhang, Zhipeng; Zhang, Mi; Yang, Lei
2018-02-01
We present two novel random walk strategies, choosing seed node (CSN) random walk and no-retracing (NR) random walk. Different from the classical random walk sampling, the CSN and NR strategies focus on the influences of the seed node choice and path overlap, respectively. Three random walk samplings are applied in the Erdös-Rényi (ER), Barabási-Albert (BA), Watts-Strogatz (WS), and the weighted USAir networks, respectively. Then, the major properties of sampled subnets, such as sampling efficiency, degree distributions, average degree and average clustering coefficient, are studied. The similar conclusions can be reached with these three random walk strategies. Firstly, the networks with small scales and simple structures are conducive to the sampling. Secondly, the average degree and the average clustering coefficient of the sampled subnet tend to the corresponding values of original networks with limited steps. And thirdly, all the degree distributions of the subnets are slightly biased to the high degree side. However, the NR strategy performs better for the average clustering coefficient of the subnet. In the real weighted USAir networks, some obvious characters like the larger clustering coefficient and the fluctuation of degree distribution are reproduced well by these random walk strategies.
Continuous-time random walks with reset events. Historical background and new perspectives
Montero, Miquel; Masó-Puigdellosas, Axel; Villarroel, Javier
2017-09-01
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.
Continuous-time quantum random walks require discrete space
International Nuclear Information System (INIS)
Manouchehri, K; Wang, J B
2007-01-01
Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks
Continuous-time quantum random walks require discrete space
Manouchehri, K.; Wang, J. B.
2007-11-01
Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks.
Variational data assimilation using targetted random walks
Cotter, S. L.
2011-02-15
The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis. In either of these scenarios, it can be important to assess uncertainties in the assimilated state. Ideally, it is desirable to have complete information concerning the Bayesian posterior distribution for unknown state given data. We show that complete computational probing of this posterior distribution is now within the reach in the offline situation. We introduce a Markov chain-Monte Carlo (MCMC) method which enables us to directly sample from the Bayesian posterior distribution on the unknown functions of interest given observations. Since we are aware that these methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however, more sophisticated MCMC methods are available which exploit derivative information. For simplicity of exposition, we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number flow in a two-dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces. © 2011 John Wiley & Sons, Ltd.
Record statistics of financial time series and geometric random walks.
Sabir, Behlool; Santhanam, M S
2014-09-01
The study of record statistics of correlated series in physics, such as random walks, is gaining momentum, and several analytical results have been obtained in the past few years. In this work, we study the record statistics of correlated empirical data for which random walk models have relevance. We obtain results for the records statistics of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent α lying in the range 1.5≤α≤1.8. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that obtained from empirical stock data.
A scaling law for random walks on networks
Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick
2014-10-01
The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.
Chaos, periodic chaos, and the random-walk problem
International Nuclear Information System (INIS)
Kozak, J.J.; Musho, M.K.; Hatlee, M.D.
1982-01-01
The authors have studied whether numerically generated sequences from the logistic parabola f/sub b/(x) = 4bx(1-x) with b,xelement of[0,1], for values of b above the Feigenbaum critical value b/sub infinity/, are truly chaotic or whether they are periodic but with exceedingly large periods and very long transients. Using the logistic parabola the authors calculate via Monte Carlo simulation the average walk length for trapping on a one-dimensional lattice with a centrosymmetric trap. Comparison with exact results suggests that the only ''truly chaotic'' sequence is the one for which b = 1
The Random-Walk Hypothesis on the Indian Stock Market
Ankita Mishra; Vinod Mishra; Russell Smyth
2014-01-01
This study tests the random walk hypothesis for the Indian stock market. Using 19 years of monthly data on six indices from the National Stock Exchange (NSE) and the Bombay Stock Exchange (BSE), this study applies three different unit root tests with two structural breaks to analyse the random walk hypothesis. We find that unit root tests that allow for two structural breaks alone are not able to reject the unit root null; however, a recently developed unit root test that simultaneously accou...
Eich, H-J; Mach, H; Werner, C; Hesse, S
2004-09-01
To evaluate the immediate and long-term effects of aerobic treadmill plus Bobath walking training in subacute stroke survivors compared with Bobath walking training alone. Randomized controlled trial. Rehabilitation unit. Fifty patients, first-time supratentorial stroke, stroke interval less than six weeks, Barthel Index (0-100) from 50 to 80, able to walk a minimum distance of 12 m with either intermittent help or stand-by while walking, cardiovascular stable, minimum 50 W in the bicycle ergometry, randomly allocated to two groups, A and B. Group A 30 min of treadmill training, harness secured and minimally supported according to patients' needs, and 30 min of physiotherapy, every workday for six weeks, speed and inclination of the treadmill were adjusted to achieve a heart rate of HR: (Hrmax-HRrest)*0.6+HRrest; in group B 60 min of daily physiotherapy for six weeks. Primary outcome variables were the absolute improvement of walking velocity (m/s) and capacity (m), secondary were gross motor function including walking ability (score out of 13) and walking quality (score out of 41), blindly assessed before and after the intervention, and at follow-up three months later. Patients tolerated the aerobic training well with no side-effects, significantly greater improvement of walking velocity and capacity both at study end (p =0.001 versus p =0.002) and at follow-up (p Bobath walking training in moderately affected stroke patients was better than Bobath walking training alone with respect to the improvement of walking velocity and capacity. The treatment approach is recommended in patients meeting the inclusion criteria. A multicentre trial should follow to strengthen the evidence.
Convergence of a random walk method for the Burgers equation
International Nuclear Information System (INIS)
Roberts, S.
1985-10-01
In this paper we consider a random walk algorithm for the solution of Burgers' equation. The algorithm uses the method of fractional steps. The non-linear advection term of the equation is solved by advecting ''fluid'' particles in a velocity field induced by the particles. The diffusion term of the equation is approximated by adding an appropriate random perturbation to the positions of the particles. Though the algorithm is inefficient as a method for solving Burgers' equation, it does model a similar method, the random vortex method, which has been used extensively to solve the incompressible Navier-Stokes equations. The purpose of this paper is to demonstrate the strong convergence of our random walk method and so provide a model for the proof of convergence for more complex random walk algorithms; for instance, the random vortex method without boundaries
Gatto, Riccardo
2017-12-01
This article considers the random walk over Rp, with p ≥ 2, where a given particle starts at the origin and moves stepwise with uniformly distributed step directions and step lengths following a common distribution. Step directions and step lengths are independent. The case where the number of steps of the particle is fixed and the more general case where it follows an independent continuous time inhomogeneous counting process are considered. Saddlepoint approximations to the distribution of the distance from the position of the particle to the origin are provided. Despite the p-dimensional nature of the random walk, the computations of the saddlepoint approximations are one-dimensional and thus simple. Explicit formulae are derived with dimension p = 3: for uniformly and exponentially distributed step lengths, for fixed and for Poisson distributed number of steps. In these situations, the high accuracy of the saddlepoint approximations is illustrated by numerical comparisons with Monte Carlo simulation. 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.
Fayolle, Guy; Malyshev, Vadim
2017-01-01
This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts. Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows spec...
Roerdink, J.B.T.M.; Shuler, K.E.
1985-01-01
The previously developed formalism for the calculation of asymptotic properties of multistate random walks is used to study random walks on several inhomogeneous periodic lattices, where the periodically repeated unit cell contains a number of inequivalent sites, as well as on lattices with a random
Random walks in the quarter-plane: invariant measures and performance bounds
Chen, Y.
2015-01-01
This monograph focuses on random walks in the quarter-plane. Such random walks are frequently used to model queueing systems and the invariant measure of a random walk is of major importance in studying the performance of these systems. In special cases the invariant measure of a random walk can be
Adaptive random walks on the class of Web graphs
Tadić, B.
2001-09-01
We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [B. Tadić, Physica A 293, 273 (2001)], and are characterized by a pair of power-law distributions of out- and in-degree for each value of the parameter β, which measures the degree of rewiring in the graph. The walker adapts its move strategy according to locally available information both on out-degree of the visited node and in-degree of target node. A standard random walk, on the other hand, uses the out-degree only. We compute the distribution of connected subgraphs visited by an ensemble of walkers, the average access time and survival probability of the walks. We discuss these properties of the walk dynamics relative to the changes in the global graph structure when the control parameter β is varied. For β≥ 3, corresponding to the world-wide Web, the access time of the walk to a given level of hierarchy on the graph is much shorter compared to the standard random walk on the same graph. By reducing the amount of rewiring towards rigidity limit β↦βc≲ 0.1, corresponding to the range of naturally occurring biochemical networks, the survival probability of adaptive and standard random walk become increasingly similar. The adaptive random walk can be used as an efficient message-passing algorithm on this class of graphs for large degree of rewiring.
Search for Directed Networks by Different Random Walk Strategies
Zhu, Zi-Qi; Jin, Xiao-Ling; Huang, Zhi-Long
2012-03-01
A comparative study is carried out on the efficiency of five different random walk strategies searching on directed networks constructed based on several typical complex networks. Due to the difference in search efficiency of the strategies rooted in network clustering, the clustering coefficient in a random walker's eye on directed networks is defined and computed to be half of the corresponding undirected networks. The search processes are performed on the directed networks based on Erdös—Rényi model, Watts—Strogatz model, Barabási—Albert model and clustered scale-free network model. It is found that self-avoiding random walk strategy is the best search strategy for such directed networks. Compared to unrestricted random walk strategy, path-iteration-avoiding random walks can also make the search process much more efficient. However, no-triangle-loop and no-quadrangle-loop random walks do not improve the search efficiency as expected, which is different from those on undirected networks since the clustering coefficient of directed networks are smaller than that of undirected networks.
A New Random Walk for Replica Detection in WSNs
Aalsalem, Mohammed Y.; Saad, N. M.; Hossain, Md. Shohrab; Atiquzzaman, Mohammed; Khan, Muhammad Khurram
2016-01-01
Wireless Sensor Networks (WSNs) are vulnerable to Node Replication attacks or Clone attacks. Among all the existing clone detection protocols in WSNs, RAWL shows the most promising results by employing Simple Random Walk (SRW). More recently, RAND outperforms RAWL by incorporating Network Division with SRW. Both RAND and RAWL have used SRW for random selection of witness nodes which is problematic because of frequently revisiting the previously passed nodes that leads to longer delays, high expenditures of energy with lower probability that witness nodes intersect. To circumvent this problem, we propose to employ a new kind of constrained random walk, namely Single Stage Memory Random Walk and present a distributed technique called SSRWND (Single Stage Memory Random Walk with Network Division). In SSRWND, single stage memory random walk is combined with network division aiming to decrease the communication and memory costs while keeping the detection probability higher. Through intensive simulations it is verified that SSRWND guarantees higher witness node security with moderate communication and memory overheads. SSRWND is expedient for security oriented application fields of WSNs like military and medical. PMID:27409082
A New Random Walk for Replica Detection in WSNs.
Aalsalem, Mohammed Y; Khan, Wazir Zada; Saad, N M; Hossain, Md Shohrab; Atiquzzaman, Mohammed; Khan, Muhammad Khurram
2016-01-01
Wireless Sensor Networks (WSNs) are vulnerable to Node Replication attacks or Clone attacks. Among all the existing clone detection protocols in WSNs, RAWL shows the most promising results by employing Simple Random Walk (SRW). More recently, RAND outperforms RAWL by incorporating Network Division with SRW. Both RAND and RAWL have used SRW for random selection of witness nodes which is problematic because of frequently revisiting the previously passed nodes that leads to longer delays, high expenditures of energy with lower probability that witness nodes intersect. To circumvent this problem, we propose to employ a new kind of constrained random walk, namely Single Stage Memory Random Walk and present a distributed technique called SSRWND (Single Stage Memory Random Walk with Network Division). In SSRWND, single stage memory random walk is combined with network division aiming to decrease the communication and memory costs while keeping the detection probability higher. Through intensive simulations it is verified that SSRWND guarantees higher witness node security with moderate communication and memory overheads. SSRWND is expedient for security oriented application fields of WSNs like military and medical.
First steps in random walks from tools to applications
Klafter, J
2011-01-01
The name ""random walk"" for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of ""Nature"". The same year, a similar problem was formulated by Albert Einstein in one of his Annus Mirabilis works. Even earlier such a problem was posed by Louis Bachelier in his thesis devoted to the theory of financial speculations in 1900. Nowadays the theory of random walks has proved useful in physics andchemistry (diffusion, reactions, mixing in flows), economics, biology (from animal spread to motion of subcel
Maximal Increments of Local Time of a Random Walk
Jain, Naresh C.; Pruitt, William E.
1987-01-01
Let $(S_j)$ be a lattice random walk, i.e., $S_j = X_1 + \\cdots + X_j$, where $X_1, X_2,\\ldots$ are independent random variables with values in $\\mathbb{Z}$ and common nondegenerate distribution $F$. Let $\\{t_n\\}$ be a nondecreasing sequence of positive integers, $t_n \\leq n$, and $L^\\ast_n = \\max_{0\\leq j\\leq n-t_n}(L_{j+t_n} - L_j)$, where $L_n = \\sum^n_{j=1}1_{\\{0\\}}(S_j)$, the number of times zero is visited by the random walk by time $n$. Assuming that the random walk is recurrent and sa...
Decoherence in optimized quantum random-walk search algorithm
International Nuclear Information System (INIS)
Zhang Yu-Chao; Bao Wan-Su; Wang Xiang; Fu Xiang-Qun
2015-01-01
This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative. (paper)
A random walk down Main Street
Directory of Open Access Journals (Sweden)
David Matthew Levinson
2016-08-01
Full Text Available US suburbs have often been characterized by their relatively low walk accessibility compared to more urban environments, and US urban environments have been char- acterized by low walk accessibility compared to cities in other countries. Lower overall density in the suburbs implies that activities, if spread out, would have a greater distance between them. But why should activities be spread out instead of developed contiguously? This brief research note builds a positive model for the emergence of contiguous development along “Main Street” to illustrate the trade-offs that result in the built environment we observe. It then suggests some policy interventions to place a “thumb on the scale” to choose which parcels will develop in which sequence to achieve socially preferred outcomes.
The use of random walk in field theory
International Nuclear Information System (INIS)
Brydges, D.
1984-01-01
Ferromagnetic spin systems and gauge theories where the gauge group is topologically a sphere, e.g. Z 2 , U(1) and SU(2) are related to the theory of random walk and random surfaces respectively. I survey some applications of this theme to the phi 4 field theories. (orig.)
Directory of Open Access Journals (Sweden)
William Hansen
2017-12-01
Full Text Available A striking difference between the folk-narrative genres of legend and folktale is how the human characters respond to supernatural, otherworldly, or uncanny beings such as ghosts, gods, dwarves, giants, trolls, talking animals, witches, and fairies. In legend the human actors respond with fear and awe, whereas in folktale they treat such beings as if they were ordinary and unremarkable. Since folktale humans treat all characters as belonging to a single realm, folklorists have described the world of the folktale as one-dimensional, in contrast to the two-dimensionality of the legend. The present investigation examines dimensionality in the third major genre of folk narrative: myth. Using the Greek and Hebrew myths of primordial paradise as sample narratives, the present essay finds—surprisingly—that the humans in these stories respond to the otherworldly one-dimensionally, as folktale characters do, and suggests an explanation for their behavior that is peculiar to the world of myth.
One dimensional reactor core model
International Nuclear Information System (INIS)
Kostadinov, V.; Stritar, A.; Radovo, M.; Mavko, B.
1984-01-01
The one dimensional model of neutron dynamic in reactor core was developed. The core was divided in several axial nodes. The one group neutron diffusion equation for each node is solved. Feedback affects of fuel and water temperatures is calculated. The influence of xenon, boron and control rods is included in cross section calculations for each node. The system of equations is solved implicitly. The model is used in basic principle Training Simulator of NPP Krsko. (author)
A generalized model via random walks for information filtering
International Nuclear Information System (INIS)
Ren, Zhuo-Ming; Kong, Yixiu; Shang, Ming-Sheng; Zhang, Yi-Cheng
2016-01-01
There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation. - Highlights: • We propose a generalized recommendation model employing the random walk dynamics. • The proposed model with single and hybrid of degree information is analyzed. • A strategy with the hybrid degree information improves precision of recommendation.
A generalized model via random walks for information filtering
Energy Technology Data Exchange (ETDEWEB)
Ren, Zhuo-Ming, E-mail: zhuomingren@gmail.com [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland); Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, ChongQing, 400714 (China); Kong, Yixiu [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland); Shang, Ming-Sheng, E-mail: msshang@cigit.ac.cn [Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, ChongQing, 400714 (China); Zhang, Yi-Cheng [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland)
2016-08-06
There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation. - Highlights: • We propose a generalized recommendation model employing the random walk dynamics. • The proposed model with single and hybrid of degree information is analyzed. • A strategy with the hybrid degree information improves precision of recommendation.
One dimensional model for polytypes
International Nuclear Information System (INIS)
Rosato, A.
1979-01-01
The general expression for the dispersion relation for a polyatomic one dimensional crystal obtained by the Laplace Transform Method is applied to materials with the fcc and hcp structures, both consisting of close-packed planes of atoms with the stacking sequence of plane ABC/ABC... and AB/AB... respectively. The expression is also applied to polytypes, that is materials caracterized by a stacking sequence with longer repeat unit. The effective mass is cast in a condensed form useful for further calculations. The results from this simple model are only qualitative. (Author) [pt
Application of continuous-time random walk to statistical arbitrage
Directory of Open Access Journals (Sweden)
Sergey Osmekhin
2015-01-01
Full Text Available An analytical statistical arbitrage strategy is proposed, where the distribution of the spread is modelled as a continuous-time random walk. Optimal boundaries, computed as a function of the mean and variance of the firstpassage time ofthe spread,maximises an objective function. The predictability of the trading strategy is analysed and contrasted for two forms of continuous-time random walk processes. We found that the waiting-time distribution has a significant impact on the prediction of the expected profit for intraday trading
Navigation by anomalous random walks on complex networks.
Weng, Tongfeng; Zhang, Jie; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan
2016-11-23
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks.
Navigation by anomalous random walks on complex networks
Weng, Tongfeng; Zhang, Jie; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan
2016-11-01
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks.
Directed self-avoiding walks in random media
International Nuclear Information System (INIS)
Santra, S. B.; Seitz, W. A.; Klein, D. J.
2001-01-01
Two types of directed self-avoiding walks (SAW's), namely, three-choice directed SAW and outwardly directed SAW, have been studied on infinite percolation clusters on the square lattice in two dimensions. The walks on the percolation clusters are generated via a Monte Carlo technique. The longitudinal extension R N and the transverse fluctuation W N have been measured as a function of the number of steps N. Slight swelling is observed in the longitudinal direction on the random lattices. A crossover from shrinking to swelling of the transverse fluctuations is found at a certain length N c of the walks. The exponents related to the transverse fluctuations are seen to be unchanged in the random media even as the percolation threshold is reached. The scaling function form of the extensions are verified
Metastability of Reversible Random Walks in Potential Fields
Landim, C.; Misturini, R.; Tsunoda, K.
2015-09-01
Let be an open and bounded subset of , and let be a twice continuously differentiable function. Denote by the discretization of , , and denote by the continuous-time, nearest-neighbor, random walk on which jumps from to at rate . We examine in this article the metastable behavior of among the wells of the potential F.
Adaptive importance sampling of random walks on continuous state spaces
International Nuclear Information System (INIS)
Baggerly, K.; Cox, D.; Picard, R.
1998-01-01
The authors consider adaptive importance sampling for a random walk with scoring in a general state space. Conditions under which exponential convergence occurs to the zero-variance solution are reviewed. These results generalize previous work for finite, discrete state spaces in Kollman (1993) and in Kollman, Baggerly, Cox, and Picard (1996). This paper is intended for nonstatisticians and includes considerable explanatory material
Random-walk diffusion and drying of porous materials
Mehrafarin, M.; Faghihi, M.
2001-12-01
Based on random-walk diffusion, a microscopic model for drying is proposed to explain the characteristic features of the drying-rate curve of porous materials. The constant drying-rate period is considered as a normal diffusion process. The transition to the falling-rate regime is attributed to the fractal nature of porous materials which results in crossover to anomalous diffusion.
Random walk loop soups and conformal loop ensembles
van de Brug, T.; Camia, F.; Lis, M.
2016-01-01
The random walk loop soup is a Poissonian ensemble of lattice loops; it has been extensively studied because of its connections to the discrete Gaussian free field, but was originally introduced by Lawler and Trujillo Ferreras as a discrete version of the Brownian loop soup of Lawler and Werner, a
The Dickey-Fuller test for exponential random walks
Davies, P.L.; Krämer, W.
2003-01-01
A common test in econometrics is the Dickey–Fuller test, which is based on the test statistic . We investigate the behavior of the test statistic if the data yt are given by an exponential random walk exp(Zt) where Zt = Zt-1 + [sigma][epsilon]t and the [epsilon]t are independent and identically
Simulating intrafraction prostate motion with a random walk model
Directory of Open Access Journals (Sweden)
Tobias Pommer, PhD
2017-07-01
Conclusions: Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during delivery of radiation therapy.
Numerical solution of field theories using random walks
International Nuclear Information System (INIS)
Barnes, T.; Daniell, G.J.
1985-01-01
We show how random walks in function space can be employed to evaluate field theoretic vacuum expectation values numerically. Specific applications which we study are the two-point function, mass gap, magnetization and classical solutions. This technique offers the promise of faster calculations using less computer memory than current methods. (orig.)
Averaging in SU(2) open quantum random walk
International Nuclear Information System (INIS)
Ampadu Clement
2014-01-01
We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT
Averaging in SU(2) open quantum random walk
Clement, Ampadu
2014-03-01
We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.
Statistical shape model with random walks for inner ear segmentation
DEFF Research Database (Denmark)
Pujadas, Esmeralda Ruiz; Kjer, Hans Martin; Piella, Gemma
2016-01-01
is required. We propose a new framework for segmentation of micro-CT cochlear images using random walks combined with a statistical shape model (SSM). The SSM allows us to constrain the less contrasted areas and ensures valid inner ear shape outputs. Additionally, a topology preservation method is proposed...
Stability of reaction fronts in random walk simulations
Nagy, Noemi; Izsak, F.
A model of propagating reaction fronts is given for simple autocatalytic reactions and the stability of the propagating reaction fronts are studied in several numerical experiments. The corresponding random walk simulations - extending of a recent algorithm - make possible the simultaneous treatment
Random walks of a quantum particle on a circle
International Nuclear Information System (INIS)
Fjeldsoe, N.; Midtdal, J.; Ravndal, F.
1987-07-01
When the quantum planar rotor is put on a lattice, its dynamics can be approximated by random walks on a circle. This allows for fast and accurate Monto Carlo simulations to determine the topological charge of different configurations of the system and thereby the Θ-dependency of the lowest energy levels
Magnetic field line random walk in non-axisymmetric turbulence
International Nuclear Information System (INIS)
Tautz, R.C.; Lerche, I.
2011-01-01
Including a random component of a magnetic field parallel to an ambient field introduces a mean perpendicular motion to the average field line. This effect is normally not discussed because one customarily chooses at the outset to ignore such a field component in discussing random walk and diffusion of field lines. A discussion of the basic effect is given, indicating that any random magnetic field with a non-zero helicity will lead to such a non-zero perpendicular mean motion. Several exact analytic illustrations are given of the effect as well as a simple numerical illustration. -- Highlights: → For magnetic field line random walk all magnetic field components are important. → Non-vanishing magnetic helicity leads to mean perpendicular motion. → Analytically exact stream functions illustrate that the novel transverse effect exists.
Renewal theory for perturbed random walks and similar processes
Iksanov, Alexander
2016-01-01
This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration. Being of major importance in modern probability theory, both theoretical and applied, these objects have been used to model various phenomena in the natural sciences as well as in insurance and finance. The book also presents the many significant results and efficient techniques and methods that have been worked out in the last decade. The first chapter is devoted to perturbed random walks and discusses their asymptotic behavior and various functionals pertaining to them, including supremum and first-passage time. The second chapter examines perpetuities, presenting results on continuity of their distributions and the existence of moments, as well as weak convergence of divergent perpetuities. Focusing on random processes with immigration, the third chapter investigates the existence of moments, describes long-time behavior and discusses limit theorems, both with and without scaling. Chapters fou...
Amnestically Induced Persistence in Random Walks
Cressoni, J. C.; da Silva, Marco Antonio Alves; Viswanathan, G. M.
2007-02-01
We study how the Hurst exponent α depends on the fraction f of the total time t remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walker’s position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimer’s disease and other dementias.
Return probabilities for the reflected random walk on N_0
Essifi, R.; Peigné, M.
2015-01-01
Let \\((Y_n)\\) be a sequence of i.i.d. \\(\\mathbb{Z }\\)-valued random variables with law \\(\\mu \\). The reflected random walk \\((X_n)\\) is defined recursively by \\(X_0=x \\in \\mathbb{N }_0, X_{n+1}=\\vert X_n+Y_{n+1}\\vert \\). Under mild hypotheses on the law \\(\\mu \\), it is proved that, for any \\( y \\in
On reflexivity of random walks in a random environment on a metric space
International Nuclear Information System (INIS)
Rozikov, U.A.
2002-11-01
In this paper, we consider random walks in random environments on a countable metric space when jumps of the walks of the fractions are finite. The transfer probabilities of the random walk from x is an element of G (where G is the considering metric space) are defined by vector p(x) is an element of R k , k>1, where {p(x), x is an element of G} is the set of independent and indentically distributed random vectors. For the random walk, a sufficient condition of nonreflexivity is obtained. Examples for metric spaces Z d free groups and free product of finite numbers cyclic groups of the second order and some other metric spaces are considered. (author)
Random walk of the baryon number
International Nuclear Information System (INIS)
Kazaryan, A.M.; Khlebnikov, S.Y.; Shaposhnikov, M.E.
1989-01-01
A new approach is suggested for the anomalous nonconservation of baryon number in the electroweak theory at high temperatures. Arguments are presented in support of the idea that the baryon-number changing reactions may be viewed as random Markov processes. Making use of the general theory of Markov processes, the Fokker--Planck equation for the baryon-number distribution density is obtained and kinetic coefficients are calculated
Counting the corners of a random walk and its application to traffic flow
International Nuclear Information System (INIS)
Knorr, Florian; Schreckenberg, Michael
2012-01-01
We study a system with two types of interacting particles on a one-dimensional lattice. Particles of the first type, which we call ‘active’, are able to detect particles of the second type (called ‘passive’). By relating the problem to a discrete random walk in one dimension with a fixed number of steps we determine the fraction of active and detected particles for both open and periodic boundary conditions as well as for the case where passive particles interact with both or only one neighbors. In the random walk picture, where the two particles types stand for steps in opposite directions, passive particles are detected whenever the resulting path has a corner. For open boundary conditions, it turns out that a simple mean field approximation reproduces the exact result if the particles interact with one neighbor only. A practical application of this problem is heterogeneous traffic flow with communicating and non-communicating vehicles. In this context communicating vehicles can be thought of as active particles which can by front (and rear) sensors detect the vehicle ahead (and behind) although these vehicles do not actively share information. Therefore, we also present simulation results which show the validity of our analysis for real traffic flow. (paper)
Random Walks and Diffusions on Graphs and Databases An Introduction
Blanchard, Philippe
2011-01-01
Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.
Random walks, critical phenomena, and triviality in quantum field theory
International Nuclear Information System (INIS)
Fernandez, R.; Froehlich, J.; Sokal, A.D.
1992-01-01
The subject of this book is equilibrium statistical mechanics - in particular the theory of critical phenomena - and quantum field theory. A general review of the theory of critical phenomena in spin systems, field theories, and random-walk and random-surface models is presented. Among the more technical topics treated in this book, the central theme is the use of random-walk representations as a tool to derive correlation inequalities. The consequences of these inequalities for critical-exponent theory and the triviality question in quantum field theory are expounded in detail. The book contains some previously unpublished results. It addresses both the researcher and the graduate student in modern statistical mechanics and quantum field theory. (orig.)
Spherically symmetric random walks. II. Dimensionally dependent critical behavior
International Nuclear Information System (INIS)
Bender, C.M.; Boettcher, S.; Meisinger, P.N.
1996-01-01
A recently developed model of random walks on a D-dimensional hyperspherical lattice, where D is not restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state distributions of random walkers are obtained for all dimensions D approx-gt 0 by solving a discrete eigenvalue problem. These distributions exhibit dimensionally dependent critical behavior as a function of the birth rate. This remarkably simple model exhibits a second-order phase transition with a universal, nontrivial critical exponent for all dimensions D approx-gt 0. copyright 1996 The American Physical Society
Reheating-volume measure for random-walk inflation
International Nuclear Information System (INIS)
Winitzki, Sergei
2008-01-01
The recently proposed 'reheating-volume' (RV) measure promises to solve the long-standing problem of extracting probabilistic predictions from cosmological multiverse scenarios involving eternal inflation. I give a detailed description of the new measure and its applications to generic models of eternal inflation of random-walk type. For those models I derive a general formula for RV-regulated probability distributions that is suitable for numerical computations. I show that the results of the RV cutoff in random-walk type models are always gauge invariant and independent of the initial conditions at the beginning of inflation. In a toy model where equal-time cutoffs lead to the 'youngness paradox', the RV cutoff yields unbiased results that are distinct from previously proposed measures.
Biasing the random walk of a molecular motor
Energy Technology Data Exchange (ETDEWEB)
Astumian, R Dean [Department of Physics, University of Maine, Orono, ME 04469-5709 (United States)
2005-11-30
Biomolecular motors are often described in mechanical terms, with analogy to cars, turbines, judo throws, levers, etc. It is important to remember however that because of their small size, and because of the aqueous environment in which molecular motors move, viscous drag and thermal noise dominate the inertial forces that drive macroscopic machines. The sequence of motions-conformational changes-by which a motor protein moves can best be described as a random walk, with transitions from one state to another occurring by thermal activation over energy barriers. In this paper I will address the question of how this random walk is biased by a non-equilibrium chemical reaction (ATP hydrolysis) so that the motor molecule moves preferentially (with almost unit certainty) in one direction, even when an external force is applied to drive it in the opposite direction. I will also discuss how these 'soft matter' motors can achieve thermodynamic efficiencies of nearly 100%.
Biasing the random walk of a molecular motor
International Nuclear Information System (INIS)
Astumian, R Dean
2005-01-01
Biomolecular motors are often described in mechanical terms, with analogy to cars, turbines, judo throws, levers, etc. It is important to remember however that because of their small size, and because of the aqueous environment in which molecular motors move, viscous drag and thermal noise dominate the inertial forces that drive macroscopic machines. The sequence of motions-conformational changes-by which a motor protein moves can best be described as a random walk, with transitions from one state to another occurring by thermal activation over energy barriers. In this paper I will address the question of how this random walk is biased by a non-equilibrium chemical reaction (ATP hydrolysis) so that the motor molecule moves preferentially (with almost unit certainty) in one direction, even when an external force is applied to drive it in the opposite direction. I will also discuss how these 'soft matter' motors can achieve thermodynamic efficiencies of nearly 100%
A generalized model via random walks for information filtering
Ren, Zhuo-Ming; Kong, Yixiu; Shang, Ming-Sheng; Zhang, Yi-Cheng
2016-08-01
There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation.
Decay times in one-dimensional chains
International Nuclear Information System (INIS)
Van den Broeck, C.; Bouten, M.
1986-01-01
The authors calculate the average residence time tau for a particle performing a random walk over a chain of N neighboring sites i = 1,..., N, with decay rates λ/sub i/ depending on the location of the particle in the chain. Exact results are given for some particular cases, while bounds on tau are given for specific initial conditions. In the continuum limit, various results from the literature are recovered or improved upon
Limit distributions of random walks on stochastic matrices
Indian Academy of Sciences (India)
condition that μm(P) > 0 for some positive integer m (as opposed to just 1, instead of m, considered in [1]), where μm is the ...... Limit distributions of random walks. 611. PROPOSITION 3.2. Let f be as introduced before Proposition 3.1. The probability distribution λ is the image of π by the map b ↦→ f (b). In other words, λ = ∑.
Random walks on semaphore codes and delay de Bruijn semigroups
Rhodes, John; Schilling, Anne; Silva, Pedro V.
2015-01-01
© 2016 World Scientific Publishing Company. We develop a new approach to random walks on de Bruijn graphs over the alphabet A through right congruences on A k , defined using the natural right action of A + . A major role is played by special right congruences, which correspond to semaphore codes and allow an easier computation of the hitting time. We show how right congruences can be approximated by special right congruences.
Autocatalytic polymerization generates persistent random walk of crawling cells.
Sambeth, R; Baumgaertner, A
2001-05-28
The autocatalytic polymerization kinetics of the cytoskeletal actin network provides the basic mechanism for a persistent random walk of a crawling cell. It is shown that network remodeling by branching processes near the cell membrane is essential for the bimodal spatial stability of the network which induces a spontaneous breaking of isotropic cell motion. Details of the phenomena are analyzed using a simple polymerization model studied by analytical and simulation methods.
Simulating intrafraction prostate motion with a random walk model.
Pommer, Tobias; Oh, Jung Hun; Munck Af Rosenschöld, Per; Deasy, Joseph O
2017-01-01
Prostate motion during radiation therapy (ie, intrafraction motion) can cause unwanted loss of radiation dose to the prostate and increased dose to the surrounding organs at risk. A compact but general statistical description of this motion could be useful for simulation of radiation therapy delivery or margin calculations. We investigated whether prostate motion could be modeled with a random walk model. Prostate motion recorded during 548 radiation therapy fractions in 17 patients was analyzed and used for input in a random walk prostate motion model. The recorded motion was categorized on the basis of whether any transient excursions (ie, rapid prostate motion in the anterior and superior direction followed by a return) occurred in the trace and transient motion. This was separately modeled as a large step in the anterior/superior direction followed by a returning large step. Random walk simulations were conducted with and without added artificial transient motion using either motion data from all observed traces or only traces without transient excursions as model input, respectively. A general estimate of motion was derived with reasonable agreement between simulated and observed traces, especially during the first 5 minutes of the excursion-free simulations. Simulated and observed diffusion coefficients agreed within 0.03, 0.2 and 0.3 mm 2 /min in the left/right, superior/inferior, and anterior/posterior directions, respectively. A rapid increase in variance at the start of observed traces was difficult to reproduce and seemed to represent the patient's need to adjust before treatment. This could be estimated somewhat using artificial transient motion. Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during
From elongated spanning trees to vicious random walks
Gorsky, A.; Nechaev, S.; Poghosyan, V. S.; Priezzhev, V. B.
2012-01-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of the paths are grouped in a fashion a $k$--leg watermelon. For large distance $r$ between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as $r^{-\
First-passage exponents of multiple random walks
International Nuclear Information System (INIS)
Ben-Naim, E; Krapivsky, P L
2010-01-01
We investigate first-passage statistics of an ensemble of N noninteracting random walks on a line. Starting from a configuration in which all particles are located in the positive half-line, we study S n (t), the probability that the nth rightmost particle remains in the positive half-line up to time t. This quantity decays algebraically, S n (t)∼t -β n , in the long-time limit. Interestingly, there is a family of nontrivial first-passage exponents, β 1 2 N-1 ; the only exception is the two-particle case where β 1 = 1/3. In the N → ∞ limit, however, the exponents attain a scaling form, β n (N) → β(z) with z=(n-N/2)/√N. We also demonstrate that the smallest exponent decays exponentially with N. We deduce these results from first-passage kinetics of a random walk in an N-dimensional cone and confirm them using numerical simulations. Additionally, we investigate the family of exponents that characterizes leadership statistics of multiple random walks and find that in this case, the cone provides an excellent approximation.
A random walk rule for phase I clinical trials.
Durham, S D; Flournoy, N; Rosenberger, W F
1997-06-01
We describe a family of random walk rules for the sequential allocation of dose levels to patients in a dose-response study, or phase I clinical trial. Patients are sequentially assigned the next higher, same, or next lower dose level according to some probability distribution, which may be determined by ethical considerations as well as the patient's response. It is shown that one can choose these probabilities in order to center dose level assignments unimodally around any target quantile of interest. Estimation of the quantile is discussed; the maximum likelihood estimator and its variance are derived under a two-parameter logistic distribution, and the maximum likelihood estimator is compared with other nonparametric estimators. Random walk rules have clear advantages: they are simple to implement, and finite and asymptotic distribution theory is completely worked out. For a specific random walk rule, we compute finite and asymptotic properties and give examples of its use in planning studies. Having the finite distribution theory available and tractable obviates the need for elaborate simulation studies to analyze the properties of the design. The small sample properties of our rule, as determined by exact theory, compare favorably to those of the continual reassessment method, determined by simulation.
Random walk theory and exchange rate dynamics in transition economies
Directory of Open Access Journals (Sweden)
Gradojević Nikola
2010-01-01
Full Text Available This paper investigates the validity of the random walk theory in the Euro-Serbian dinar exchange rate market. We apply Andrew Lo and Archie MacKinlay's (1988 conventional variance ratio test and Jonathan Wright's (2000 non-parametric ranks and signs based variance ratio tests to the daily Euro/Serbian dinar exchange rate returns using the data from January 2005 - December 2008. Both types of variance ratio tests overwhelmingly reject the random walk hypothesis over the data span. To assess the robustness of our findings, we examine the forecasting performance of a non-linear, nonparametric model in the spirit of Francis Diebold and James Nason (1990 and find that it is able to significantly improve upon the random walk model, thus confirming the existence of foreign exchange market imperfections in a small transition economy such as Serbia. In the last part of the paper, we conduct a comparative study on how our results relate to those of other transition economies in the region.
Ant-inspired density estimation via random walks.
Musco, Cameron; Su, Hsin-Hao; Lynch, Nancy A
2017-10-03
Many ant species use distributed population density estimation in applications ranging from quorum sensing, to task allocation, to appraisal of enemy colony strength. It has been shown that ants estimate local population density by tracking encounter rates: The higher the density, the more often the ants bump into each other. We study distributed density estimation from a theoretical perspective. We prove that a group of anonymous agents randomly walking on a grid are able to estimate their density within a small multiplicative error in few steps by measuring their rates of encounter with other agents. Despite dependencies inherent in the fact that nearby agents may collide repeatedly (and, worse, cannot recognize when this happens), our bound nearly matches what would be required to estimate density by independently sampling grid locations. From a biological perspective, our work helps shed light on how ants and other social insects can obtain relatively accurate density estimates via encounter rates. From a technical perspective, our analysis provides tools for understanding complex dependencies in the collision probabilities of multiple random walks. We bound the strength of these dependencies using local mixing properties of the underlying graph. Our results extend beyond the grid to more general graphs, and we discuss applications to size estimation for social networks, density estimation for robot swarms, and random walk-based sampling for sensor networks.
On the pertinence to Physics of random walks induced by random dynamical systems: a survey
International Nuclear Information System (INIS)
Petritis, Dimitri
2016-01-01
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 (( S_a)_a , ( p_a)_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 p_a (x) , the transformation S_a and evolve to S_a (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. (paper)
A one-dimensional stochastic approach to the study of cyclic voltammetry with adsorption effects
Energy Technology Data Exchange (ETDEWEB)
Samin, Adib J. [The Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19" t" h Avenue, Columbus, Ohio 43210 (United States)
2016-05-15
In this study, a one-dimensional stochastic model based on the random walk approach is used to simulate cyclic voltammetry. The model takes into account mass transport, kinetics of the redox reactions, adsorption effects and changes in the morphology of the electrode. The model is shown to display the expected behavior. Furthermore, the model shows consistent qualitative agreement with a finite difference solution. This approach allows for an understanding of phenomena on a microscopic level and may be useful for analyzing qualitative features observed in experimentally recorded signals.
A one-dimensional stochastic approach to the study of cyclic voltammetry with adsorption effects
International Nuclear Information System (INIS)
Samin, Adib J.
2016-01-01
In this study, a one-dimensional stochastic model based on the random walk approach is used to simulate cyclic voltammetry. The model takes into account mass transport, kinetics of the redox reactions, adsorption effects and changes in the morphology of the electrode. The model is shown to display the expected behavior. Furthermore, the model shows consistent qualitative agreement with a finite difference solution. This approach allows for an understanding of phenomena on a microscopic level and may be useful for analyzing qualitative features observed in experimentally recorded signals.
Social aggregation in pea aphids: experiment and random walk modeling.
Directory of Open Access Journals (Sweden)
Christa Nilsen
Full Text Available From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid's nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control.
History dependent quantum random walks as quantum lattice gas automata
Energy Technology Data Exchange (ETDEWEB)
Shakeel, Asif, E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu; Love, Peter J., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu [Department of Physics, Haverford College, Haverford, Pennsylvania 19041 (United States); Meyer, David A., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu [Department of Mathematics, University of California/San Diego, La Jolla, California 92093-0112 (United States)
2014-12-15
Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the history information arise naturally as geometrical degrees of freedom on the lattice.
Conditioned random walks and interaction-driven condensation
International Nuclear Information System (INIS)
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. (paper)
Karpatkin, Herb; Cohen, Evan T; Rzetelny, Adam; Parrott, J Scott; Breismeister, Breanne; Hartman, Ryan; Luu, Ronald; Napolione, Danielle
2015-07-01
Fatigue is a common, disabling symptom experienced by persons with multiple sclerosis (MS). Evidence shows that intermittent exercise is associated in improved performance and negligible fatigue. The purpose of this study was to examine whether subjects with MS walk greater distances with less fatigue under intermittent (INT) or continuous (CONT) walking condition. Twenty-seven subjects with MS (median Extended Disability Severity Scale 3.5, interquartile range 1.6) walked in the CONT (ie, 6 uninterrupted minutes) and INT (ie, three 2-minute walking bouts) conditions in a randomized crossover. Distance was measured for the entire 6-minute walking period and each 2-minute increment. Fatigue was measured as the difference in a visual analog scale of fatigue (ΔVAS-F) immediately preceding and following each trial. Participants walked greater distances in the INT condition compared to the CONT condition (P = 0.005). There was a significant interaction of walking condition and time (P walked in the INT condition changed across time. ΔVAS-F was significantly lower in the INT condition than in the CONT condition (P = 0.036). Subjects with MS walked farther, and with less fatigue, when walking intermittently rather than continuously. Persons with MS may be able to tolerate a greater dose of walking training if the walking bouts are intermittent. Further study to determine the benefits of a walking exercise program using intermittent walking is recommended.Video Abstract available for additional insights from the authors (Supplemental Digital Content 1, http://links.lww.com/JNPT/A103).
Intermittent random walks: transport regimes and implications on search strategies
International Nuclear Information System (INIS)
Gomez Portillo, Ignacio; Campos, Daniel; Méndez, Vicenç
2011-01-01
We construct a transport model for particles that alternate rests of random duration and flights with random velocities. The model provides a balance equation for the mesoscopic particle density obtained from the continuous-time random walk framework. By assuming power laws for the distributions of waiting times and flight durations (for any velocity distribution with finite moments) we have found that the model can yield all the transport regimes ranging from subdiffusion to ballistic depending on the values of the characteristic exponents of the distributions. In addition, if the exponents satisfy a simple relationship it is shown how the competition between the tails of the distributions gives rise to a diffusive transport. Finally, we explore how the details of this intermittent transport process affect the success probability in an optimal search problem where an individual searcher looks for a target distributed (heterogeneously) in space. All the results are conveniently checked with numerical simulations
Why the null matters: statistical tests, random walks and evolution.
Sheets, H D; Mitchell, C E
2001-01-01
A number of statistical tests have been developed to determine what type of dynamics underlie observed changes in morphology in evolutionary time series, based on the pattern of change within the time series. The theory of the 'scaled maximum', the 'log-rate-interval' (LRI) method, and the Hurst exponent all operate on the same principle of comparing the maximum change, or rate of change, in the observed dataset to the maximum change expected of a random walk. Less change in a dataset than expected of a random walk has been interpreted as indicating stabilizing selection, while more change implies directional selection. The 'runs test' in contrast, operates on the sequencing of steps, rather than on excursion. Applications of these tests to computer generated, simulated time series of known dynamical form and various levels of additive noise indicate that there is a fundamental asymmetry in the rate of type II errors of the tests based on excursion: they are all highly sensitive to noise in models of directional selection that result in a linear trend within a time series, but are largely noise immune in the case of a simple model of stabilizing selection. Additionally, the LRI method has a lower sensitivity than originally claimed, due to the large range of LRI rates produced by random walks. Examination of the published results of these tests show that they have seldom produced a conclusion that an observed evolutionary time series was due to directional selection, a result which needs closer examination in light of the asymmetric response of these tests.
Discrete random walk models for space-time fractional diffusion
International Nuclear Information System (INIS)
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-01-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order α is part of (0,2] and skewness θ (moduleθ≤{α,2-α}), and the first-order time derivative with a Caputo derivative of order β is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation
Random walk on a population of random walkers
International Nuclear Information System (INIS)
Agliari, E; Burioni, R; Cassi, D; Neri, F M
2008-01-01
We consider a population of N labelled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label X(t) of the walker carrying the excitation at time t can be viewed as a stochastic process, where the transition probabilities are a stochastic process themselves. Upon mapping onto two simpler processes, the quantities characterizing X(t) can be calculated in the limit of long times and low walkers density. The results are compared with numerical simulations. Several different topologies for the substrate underlying diffusion are considered
How fast does a random walk cover a torus?
Grassberger, Peter
2017-07-01
We present high statistics simulation data for the average time that a random walk needs to cover completely a two-dimensional torus of size L ×L . They confirm the mathematical prediction that ˜(LlnL ) 2 for large L , but the prefactor seems to deviate significantly from the supposedly exact result 4 /π derived by Dembo et al. [Ann. Math. 160, 433 (2004), 10.4007/annals.2004.160.433], if the most straightforward extrapolation is used. On the other hand, we find that this scaling does hold for the time TN (t )=1(L ) at which the average number of yet unvisited sites is 1, as also predicted previously. This might suggest (wrongly) that and TN (t )=1(L ) scale differently, although the distribution of rescaled cover times becomes sharp in the limit L →∞ . But our results can be reconciled with those of Dembo et al. by a very slow and nonmonotonic convergence of /(LlnL ) 2 , as had been indeed proven by Belius et al. [Probab. Theory Relat. Fields 167, 461 (2017), 10.1007/s00440-015-0689-6] for Brownian walks, and was conjectured by them to hold also for lattice walks.
Knots and Random Walks in Vibrated Granular Chains
International Nuclear Information System (INIS)
Ben-Naim, E.; Daya, Z. A.; Vorobieff, P.; Ecke, R. E.
2001-01-01
We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard-core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with theoretical values
Correlation effects in a discrete quantum random walk
International Nuclear Information System (INIS)
Stang, J B; Rezakhani, A T; Sanders, B C
2009-01-01
We introduce memory-dependent discrete-time quantum random walk models by adding uncorrelated memory terms and also by modifying the Hamiltonian of the walker to include couplings with memory-keeping agents. We next study numerically the correlation effects in these models. We also propose a correlation exponent as a relevant and promising tool for investigation of correlation or memory (hence non-Markovian) effects. Our analysis can easily be applied to more realistic models in which different regimes may emerge because of competition between different underlying physical mechanisms
Time-delayed fronts from biased random walks
International Nuclear Information System (INIS)
Fort, Joaquim; Pujol, Toni
2007-01-01
We generalize a previous model of time-delayed reaction-diffusion fronts (Fort and Mendez 1999 Phys. Rev. Lett. 82 867) to allow for a bias in the microscopic random walk of particles or individuals. We also present a second model which takes the time order of events (diffusion and reproduction) into account. As an example, we apply them to the human invasion front across the USA in the 19th century. The corrections relative to the previous model are substantial. Our results are relevant to physical and biological systems with anisotropic fronts, including particle diffusion in disordered lattices, population invasions, the spread of epidemics, etc
Universality in random-walk models with birth and death
International Nuclear Information System (INIS)
Bender, C.M.; Boettcher, S.; Meisinger, P.N.
1995-01-01
Models of random walks are considered in which walkers are born at one site and die at all other sites. Steady-state distributions of walkers exhibit dimensionally dependent critical behavior as a function of the birth rate. Exact analytical results for a hyperspherical lattice yield a second-order phase transition with a nontrivial critical exponent for all positive dimensions D≠2, 4. Numerical studies of hypercubic and fractal lattices indicate that these exact results are universal. This work elucidates the adsorption transition of polymers at curved interfaces. copyright 1995 The American Physical Society
Random-walk simulation of selected aspects of dissipative collisions
International Nuclear Information System (INIS)
Toeke, J.; Gobbi, A.; Matulewicz, T.
1984-11-01
Internuclear thermal equilibrium effects and shell structure effects in dissipative collisions are studied numerically within the framework of the model of stochastic exchanges by applying the random-walk technique. Effective blocking of the drift through the mass flux induced by the temperature difference, while leaving the variances of the mass distributions unaltered is found possible, provided an internuclear potential barrier is present. Presence of the shell structure is found to lead to characteristic correlations between the consecutive exchanges. Experimental evidence for the predicted effects is discussed. (orig.)
The Random Walk Model Based on Bipartite Network
Directory of Open Access Journals (Sweden)
Zhang Man-Dun
2016-01-01
Full Text Available With the continuing development of the electronic commerce and growth of network information, there is a growing possibility for citizens to be confused by the information. Though the traditional technology of information retrieval have the ability to relieve the overload of information in some extent, it can not offer a targeted personality service based on user’s interests and activities. In this context, the recommendation algorithm arose. In this paper, on the basis of conventional recommendation, we studied the scheme of random walk based on bipartite network and the application of it. We put forward a similarity measurement based on implicit feedback. In this method, a uneven character vector is imported(the weight of item in the system. We put forward a improved random walk pattern which make use of partial or incomplete neighbor information to create recommendation information. In the end, there is an experiment in the real data set, the recommendation accuracy and practicality are improved. We promise the reality of the result of the experiment
Do MENA stock market returns follow a random walk process?
Directory of Open Access Journals (Sweden)
Salim Lahmiri
2013-01-01
Full Text Available In this research, three variance ratio tests: the standard variance ratio test, the wild bootstrap multiple variance ratio test, and the non-parametric rank scores test are adopted to test the random walk hypothesis (RWH of stock markets in Middle East and North Africa (MENA region using most recent data from January 2010 to September 2012. The empirical results obtained by all three econometric tests show that the RWH is strongly rejected for Kuwait, Tunisia, and Morocco. However, the standard variance ratio test and the wild bootstrap multiple variance ratio test reject the null hypothesis of random walk in Jordan and KSA, while non-parametric rank scores test do not. We may conclude that Jordan and KSA stock market are weak efficient. In sum, the empirical results suggest that return series in Kuwait, Tunisia, and Morocco are predictable. In other words, predictable patterns that can be exploited in these markets still exit. Therefore, investors may make profits in such less efficient markets.
A Random Walk Approach to Query Informative Constraints for Clustering.
Abin, Ahmad Ali
2017-08-09
This paper presents a random walk approach to the problem of querying informative constraints for clustering. The proposed method is based on the properties of the commute time, that is the expected time taken for a random walk to travel between two nodes and return, on the adjacency graph of data. Commute time has the nice property of that, the more short paths connect two given nodes in a graph, the more similar those nodes are. Since computing the commute time takes the Laplacian eigenspectrum into account, we use this property in a recursive fashion to query informative constraints for clustering. At each recursion, the proposed method constructs the adjacency graph of data and utilizes the spectral properties of the commute time matrix to bipartition the adjacency graph. Thereafter, the proposed method benefits from the commute times distance on graph to query informative constraints between partitions. This process iterates for each partition until the stop condition becomes true. Experiments on real-world data show the efficiency of the proposed method for constraints selection.
An explicit semantic relatedness measure based on random walk
Directory of Open Access Journals (Sweden)
HU Sihui
2016-10-01
Full Text Available The semantic relatedness calculation of open domain knowledge network is a significant issue.In this paper,pheromone strategy is drawn from the thought of ant colony algorithm and is integrated into the random walk which is taken as the basic framework of calculating the semantic relatedness degree.The pheromone distribution is taken as a criterion of determining the tightness degree of semantic relatedness.A method of calculating semantic relatedness degree based on random walk is proposed and the exploration process of calculating the semantic relatedness degree is presented in a dominant way.The method mainly contains Path Select Model(PSM and Semantic Relatedness Computing Model(SRCM.PSM is used to simulate the path selection of ants and pheromone release.SRCM is used to calculate the semantic relatedness by utilizing the information returned by ants.The result indicates that the method could complete semantic relatedness calculation in linear complexity and extend the feasible strategy of semantic relatedness calculation.
Random-walk simulation of the Schrodinger equation: H+3
International Nuclear Information System (INIS)
Anderson, J.B.
1975-01-01
A simple random-walk method for obtaining ab initio solutions of the Schrodinger equation is examined in its application to the case of the molecular ion H + 3 in the equilateral triangle configuration with side length R=1.66 bohr. The method, which is based on the similarity of the Schrodinger equation and the diffusion equation, involves the random movement of imaginary particles (psips) in electron configuration space subject to a variable chance of multiplication or disappearance. The computation requirements for high accuracy in determining energies of H + 3 are greater than those of existing LCAO--MO--SCF--CI methods. For more complex molecular systems the method may be competitive. (auth)
Basic physics of one-dimensional metals
International Nuclear Information System (INIS)
Emery, V.J.
1976-01-01
Largely nonmathematical qualitative lectures are given on the basic physics of nearly one-dimensional conductors. The main emphasis is placed on the properties of a purely one-dimensional electron gas. The effects of a real system having interchain coupling, impurities, a compressible lattice, lattice distortions and phonon anomalies are discussed
Random Walks in Stock Exchange Prices and the Vienna Stock Exchange
Huber, Peter
1995-01-01
This paper uses the multiple variance ratio test procedure developed by Chow and Denning (1993) to test for a random walk of stock returns on the Austrian Stock Exchange. I find that with daily data the test rejects the random walk hypothesis at all conventional significance levels for each and every title and for both indeces tested. Individual shares, however, do seem to follow a random walk when weekly returns are considered, while the hypothesis is rejected for both indices. Dieser Art...
Some Tests of Random Walk Hypothesis for Bulgarian Foreign Exchange Rates
Nikolai Gueorguiev
1993-01-01
The objective of this paper is to check if the exchange rate in newly emerged, relatively thin foreign exchange markets, follows a random walk pattern. The findings of the current study cast doubts on random walk presence in Bulgarian exchange rates against major international currencies. It turns out that the series of daily returns are stationary but correlated and therefore can be modelled better by higher-order ARIMA processes than by random walk.
International Nuclear Information System (INIS)
Pfingsten, W.
1996-01-01
Safety assessments for radioactive waste repositories require a detailed knowledge of physical, chemical, hydrological, and geological processes for long time spans. In the past, individual models for hydraulics, transport, or geochemical processes were developed more or less separately to great sophistication for the individual processes. Such processes are especially important in the near field of a waste repository. Attempts have been made to couple at least two individual processes to get a more adequate description of geochemical systems. These models are called coupled codes; they couple predominantly a multicomponent transport model with a chemical reaction model. Here reactive transport is modeled by the sequentially coupled code MCOTAC that couples one-dimensional advective, dispersive, and diffusive transport with chemical equilibrium complexation and precipitation/dissolution reactions in a porous medium. Transport, described by a random walk of multispecies particles, and chemical equilibrium calculations are solved separately, coupled only by an exchange term. The modular-structured code was applied to incongruent dissolution of hydrated silicate gels, to movement of multiple solid front systems, and to an artificial, numerically difficult heterogeneous redox problem. These applications show promising features with respect to applicability to relevant problems and possibilities of extensions
The average inter-crossing number of equilateral random walks and polygons
International Nuclear Information System (INIS)
Diao, Y; Dobay, A; Stasiak, A
2005-01-01
In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is a = 3ln2/8 ∼ 0.2599. In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance ρ apart and ρ is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of ρ. Our simulation result shows that the model in fact works very well for the entire range of ρ. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well
Complex networks: when random walk dynamics equals synchronization
International Nuclear Information System (INIS)
Kriener, Birgit; Anand, Lishma; Timme, Marc
2012-01-01
Synchrony prevalently emerges from the interactions of coupled dynamical units. For simple systems such as networks of phase oscillators, the asymptotic synchronization process is assumed to be equivalent to a Markov process that models standard diffusion or random walks on the same network topology. In this paper, we analytically derive the conditions for such equivalence for networks of pulse-coupled oscillators, which serve as models for neurons and pacemaker cells interacting by exchanging electric pulses or fireflies interacting via light flashes. We find that the pulse synchronization process is less simple, but there are classes of, e.g., network topologies that ensure equivalence. In particular, local dynamical operators are required to be doubly stochastic. These results provide a natural link between stochastic processes and deterministic synchronization on networks. Tools for analyzing diffusion (or, more generally, Markov processes) may now be transferred to pin down features of synchronization in networks of pulse-coupled units such as neural circuits. (paper)
Scattering quantum random-walk search with errors
International Nuclear Information System (INIS)
Gabris, A.; Kiss, T.; Jex, I.
2007-01-01
We analyze the realization of a quantum-walk search algorithm in a passive, linear optical network. The specific model enables us to consider the effect of realistic sources of noise and losses on the search efficiency. Photon loss uniform in all directions is shown to lead to the rescaling of search time. Deviation from directional uniformity leads to the enhancement of the search efficiency compared to uniform loss with the same average. In certain cases even increasing loss in some of the directions can improve search efficiency. We show that while we approach the classical limit of the general search algorithm by introducing random phase fluctuations, its utility for searching is lost. Using numerical methods, we found that for static phase errors the averaged search efficiency displays a damped oscillatory behavior that asymptotically tends to a nonzero value
Information filtering via biased random walk on coupled social network.
Nie, Da-Cheng; Zhang, Zi-Ke; Dong, Qiang; Sun, Chongjing; Fu, Yan
2014-01-01
The recommender systems have advanced a great deal in the past two decades. However, most researchers focus their attentions on mining the similarities among users or objects in recommender systems and overlook the social influence which plays an important role in users' purchase process. In this paper, we design a biased random walk algorithm on coupled social networks which gives recommendation results based on both social interests and users' preference. Numerical analyses on two real data sets, Epinions and Friendfeed, demonstrate the improvement of recommendation performance by taking social interests into account, and experimental results show that our algorithm can alleviate the user cold-start problem more effectively compared with the mass diffusion and user-based collaborative filtering methods.
A random walk in the land of precompound decay
International Nuclear Information System (INIS)
Akkermans, J.M.
1982-09-01
Several aspects of precompound-decay (preequilibrium) reactions, relevant for the application to fusion-reactor design, are considered. Preequilibrium angular distributions are discussed in the framework of the generalized exciton model. A critical discussion of the theory is given and various refinements are suggested. A comparison is made with experimental data on 14 MeV neutron-induced reactions for a large number of nuclides covering the whole mass range. The exciton model is further generalized to the description of multiparticle emission. Preequilibrium effects in multiple emission are investigated. Computational aspects of preequilibrium theory are examined whereby the exact solution for the mean exciton-state lifetimes is derived in closed form. A random-walk model of precompound decay is developed. The dynamics of the nuclear relaxation process and the fluctuations originating from its stochastic nature are studied in detail. Uncertainty calculations are presented for the exciton-state lifetimes and the emission cross-sections. (Auth.)
Correlated continuous time random walk and option pricing
Lv, Longjin; Xiao, Jianbin; Fan, Liangzhong; Ren, Fuyao
2016-04-01
In this paper, we study a correlated continuous time random walk (CCTRW) with averaged waiting time, whose probability density function (PDF) is proved to follow stretched Gaussian distribution. Then, we apply this process into option pricing problem. Supposing the price of the underlying is driven by this CCTRW, we find this model captures the subdiffusive characteristic of financial markets. By using the mean self-financing hedging strategy, we obtain the closed-form pricing formulas for a European option with and without transaction costs, respectively. At last, comparing the obtained model with the classical Black-Scholes model, we find the price obtained in this paper is higher than that obtained from the Black-Scholes model. A empirical analysis is also introduced to confirm the obtained results can fit the real data well.
From elongated spanning trees to vicious random walks
Gorsky, A.; Nechaev, S.; Poghosyan, V. S.; Priezzhev, V. B.
2013-05-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of k paths (k is odd) along branches of trees or, equivalently, k loop-erased random walks. Starting and ending points of the paths are grouped such that they form a k-leg watermelon. For large distance r between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as r-ν log r with ν = (k2 - 1) / 2. Considering the spanning forest stretched along the meridian of this watermelon, we show that the two-dimensional k-leg loop-erased watermelon exponent ν is converting into the scaling exponent for the reunion probability (at a given point) of k (1 + 1)-dimensional vicious walkers, ν˜ =k2 / 2. At the end, we express the conjectures about the possible relation to integrable systems.
From elongated spanning trees to vicious random walks
International Nuclear Information System (INIS)
Gorsky, A.; Nechaev, S.; Poghosyan, V.S.; Priezzhev, V.B.
2013-01-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of k paths (k is odd) along branches of trees or, equivalently, k loop-erased random walks. Starting and ending points of the paths are grouped such that they form a k-leg watermelon. For large distance r between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as r −ν logr with ν=(k 2 −1)/2. Considering the spanning forest stretched along the meridian of this watermelon, we show that the two-dimensional k-leg loop-erased watermelon exponent ν is converting into the scaling exponent for the reunion probability (at a given point) of k(1+1)-dimensional vicious walkers, ν -tilde= k 2 /2. At the end, we express the conjectures about the possible relation to integrable systems
A random walk approach to stochastic neutron transport
International Nuclear Information System (INIS)
Mulatier, Clelia de
2015-01-01
One of the key goals of nuclear reactor physics is to determine the distribution of the neutron population within a reactor core. This population indeed fluctuates due to the stochastic nature of the interactions of the neutrons with the nuclei of the surrounding medium: scattering, emission of neutrons from fission events and capture by nuclear absorption. Due to these physical mechanisms, the stochastic process performed by neutrons is a branching random walk. For most applications, the neutron population considered is very large, and all physical observables related to its behaviour, such as the heat production due to fissions, are well characterised by their average values. Generally, these mean quantities are governed by the classical neutron transport equation, called linear Boltzmann equation. During my PhD, using tools from branching random walks and anomalous diffusion, I have tackled two aspects of neutron transport that cannot be approached by the linear Boltzmann equation. First, thanks to the Feynman-Kac backward formalism, I have characterised the phenomenon of 'neutron clustering' that has been highlighted for low-density configuration of neutrons and results from strong fluctuations in space and time of the neutron population. Then, I focused on several properties of anomalous (non-exponential) transport, that can model neutron transport in strongly heterogeneous and disordered media, such as pebble-bed reactors. One of the novel aspects of this work is that problems are treated in the presence of boundaries. Indeed, even though real systems are finite (confined geometries), most of previously existing results were obtained for infinite systems. (author) [fr
One-Dimensional Czedli-Type Islands
Horvath, Eszter K.; Mader, Attila; Tepavcevic, Andreja
2011-01-01
The notion of an island has surfaced in recent algebra and coding theory research. Discrete versions provide interesting combinatorial problems. This paper presents the one-dimensional case with finitely many heights, a topic convenient for student research.
Analytical solution of one dimensional temporally dependent ...
African Journals Online (AJOL)
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transfer of heat in fluids, flow through porous media, and the spread of ... In present paper, advection-dispersion equation is considered one dimensional longitudinal initially solute free semi- .... free. Thus initial and boundary conditions for eq.
Directory of Open Access Journals (Sweden)
Miguel eFERNANDEZ-DEL-OLMO
2014-09-01
Full Text Available 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. 22 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 Parkinson’s disease.
Factorizations of one-dimensional classical systems
International Nuclear Information System (INIS)
Kuru, Senguel; Negro, Javier
2008-01-01
A class of one-dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra. These two functions lead directly to two time-dependent integrals of motion from which the phase motions are derived algebraically. The systems so obtained constitute the classical analogues of the well known factorizable one-dimensional quantum mechanical systems
One-dimensional photonic crystal design
International Nuclear Information System (INIS)
Mee, Cornelis van der; Contu, Pietro; Pintus, Paolo
2010-01-01
In this article we present a method to determine the band spectrum, band gaps, and discrete energy levels, of a one-dimensional photonic crystal with localized impurities. For one-dimensional crystals with piecewise constant refractive indices we develop an algorithm to recover the refractive index distribution from the period map. Finally, we derive the relationship between the period map and the scattering matrix containing the information on the localized modes.
Diffusive transport in a one dimensional disordered potential involving correlations
International Nuclear Information System (INIS)
Monthus, C.; Paris-6 Univ., 75
1995-03-01
Transport properties of one dimensional Brownian diffusion under the influence of a quenched random force, distributed as a two-level Poisson process is discussed. Large time scaling laws of the position of the Brownian particle, and the probability distribution of the stationary flux going through a sample between two prescribed concentrations are studied. (author) 14 refs.; 3 figs
First-passage time asymptotics over moving boundaries for random walk bridges
Sloothaak, F.; Zwart, B.; Wachtel, V.
2017-01-01
We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with
Scaling Limit of Symmetric Random Walk in High-Contrast Periodic Environment
Piatnitski, A.; Zhizhina, E.
2017-11-01
The paper deals with the asymptotic properties of a symmetric random walk in a high contrast periodic medium in Z^d, d≥1. From the existing homogenization results it follows that under diffusive scaling the limit behaviour of this random walk need not be Markovian. The goal of this work is to show that if in addition to the coordinate of the random walk in Z^d we introduce an extra variable that characterizes the position of the random walk inside the period then the limit dynamics of this two-component process is Markov. We describe the limit process and observe that the components of the limit process are coupled. We also prove the convergence in the path space for the said random walk.
Dispersal of spores following a persistent random walk.
Bicout, D J; Sache, I
2003-03-01
A model of a persistent random walk is used to describe the transport and deposition of the spore dispersal process. In this model, the spore particle flies along straight line trajectories, with constant speed v, which are interrupted by scattering, originating from interaction of spores with the field and wind variations, which randomly change its direction. To characterize the spore dispersal gradients, we have derived analytical expressions of the deposition probability epsilon (r|v) of airborne spores as a function of the distance r from the spore source in an infinite free space and in a disk of radius R with an absorbing edge that mimics an agricultural field surrounded with fields of nonhost plants and bare land. It is found in the free space that epsilon (r|v) approximately e(-alphar/l), with alpha a function of l(d)/l, where l and l(d) are the scattering and deposition mean free paths, respectively. In the disk, however, epsilon (r|v) is an infinite series of Bessel functions and, exhibits three regimes: absorbing (Rl(d)).
The relationship between randomness and power-law distributed move lengths in random walk algorithms
Sakiyama, Tomoko; Gunji, Yukio-Pegio
2014-05-01
Recently, we proposed a new random walk algorithm, termed the REV algorithm, in which the agent alters the directional rule that governs it using the most recent four random numbers. Here, we examined how a non-bounded number, i.e., "randomness" regarding move direction, was important for optimal searching and power-law distributed step lengths in rule change. We proposed two algorithms: the REV and REV-bounded algorithms. In the REV algorithm, one of the four random numbers used to change the rule is non-bounded. In contrast, all four random numbers in the REV-bounded algorithm are bounded. We showed that the REV algorithm exhibited more consistent power-law distributed step lengths and flexible searching behavior.
One-dimensional Gromov minimal filling problem
International Nuclear Information System (INIS)
Ivanov, Alexandr O; Tuzhilin, Alexey A
2012-01-01
The paper is devoted to a new branch in the theory of one-dimensional variational problems with branching extremals, the investigation of one-dimensional minimal fillings introduced by the authors. On the one hand, this problem is a one-dimensional version of a generalization of Gromov's minimal fillings problem to the case of stratified manifolds. On the other hand, this problem is interesting in itself and also can be considered as a generalization of another classical problem, the Steiner problem on the construction of a shortest network connecting a given set of terminals. Besides the statement of the problem, we discuss several properties of the minimal fillings and state several conjectures. Bibliography: 38 titles.
A Monotonicity Result for the Range of a Perturbed Random Walk
Chen, Lung-Chi; Sun, Rongfeng
2012-01-01
We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of sites visited by the perturbed random walk up to time n is always larger than or equal to that for the unperturbed walk. This intriguing problem arises from the study of a particle among a Poisson system of moving traps with sub-diffusive trap motion. In pa...
Random Walk Particle Tracking For Multiphase Heat Transfer
Lattanzi, Aaron; Yin, Xiaolong; Hrenya, Christine
2017-11-01
As computing capabilities have advanced, direct numerical simulation (DNS) has become a highly effective tool for quantitatively predicting the heat transfer within multiphase flows. Here we utilize a hybrid DNS framework that couples the lattice Boltzmann method (LBM) to the random walk particle tracking (RWPT) algorithm. The main challenge of such a hybrid is that discontinuous fields pose a significant challenge to the RWPT framework and special attention must be given to the handling of interfaces. We derive a method for addressing discontinuities in the diffusivity field, arising at the interface between two phases. Analytical means are utilized to develop an interfacial tracer balance and modify the RWPT algorithm. By expanding the modulus of the stochastic (diffusive) step and only allowing a subset of the tracers within the high diffusivity medium to undergo a diffusive step, the correct equilibrium state can be restored (globally homogeneous tracer distribution). The new RWPT algorithm is implemented within the SUSP3D code and verified against a variety of systems: effective diffusivity of a static gas-solids mixture, hot sphere in unbounded diffusion, cooling sphere in unbounded diffusion, and uniform flow past a hot sphere.
Identifying diseases-related metabolites using random walk.
Hu, Yang; Zhao, Tianyi; Zhang, Ningyi; Zang, Tianyi; Zhang, Jun; Cheng, Liang
2018-04-11
Metabolites disrupted by abnormal state of human body are deemed as the effect of diseases. In comparison with the cause of diseases like genes, these markers are easier to be captured for the prevention and diagnosis of metabolic diseases. Currently, a large number of metabolic markers of diseases need to be explored, which drive us to do this work. The existing metabolite-disease associations were extracted from Human Metabolome Database (HMDB) using a text mining tool NCBO annotator as priori knowledge. Next we calculated the similarity of a pair-wise metabolites based on the similarity of disease sets of them. Then, all the similarities of metabolite pairs were utilized for constructing a weighted metabolite association network (WMAN). Subsequently, the network was utilized for predicting novel metabolic markers of diseases using random walk. Totally, 604 metabolites and 228 diseases were extracted from HMDB. From 604 metabolites, 453 metabolites are selected to construct the WMAN, where each metabolite is deemed as a node, and the similarity of two metabolites as the weight of the edge linking them. The performance of the network is validated using the leave one out method. As a result, the high area under the receiver operating characteristic curve (AUC) (0.7048) is achieved. The further case studies for identifying novel metabolites of diabetes mellitus were validated in the recent studies. In this paper, we presented a novel method for prioritizing metabolite-disease pairs. The superior performance validates its reliability for exploring novel metabolic markers of diseases.
Anomalous transport in turbulent plasmas and continuous time random walks
International Nuclear Information System (INIS)
Balescu, R.
1995-01-01
The possibility of a model of anomalous transport problems in a turbulent plasma by a purely stochastic process is investigated. The theory of continuous time random walks (CTRW's) is briefly reviewed. It is shown that a particular class, called the standard long tail CTRW's is of special interest for the description of subdiffusive transport. Its evolution is described by a non-Markovian diffusion equation that is constructed in such a way as to yield exact values for all the moments of the density profile. The concept of a CTRW model is compared to an exact solution of a simple test problem: transport of charged particles in a fluctuating magnetic field in the limit of infinite perpendicular correlation length. Although the well-known behavior of the mean square displacement proportional to t 1/2 is easily recovered, the exact density profile cannot be modeled by a CTRW. However, the quasilinear approximation of the kinetic equation has the form of a non-Markovian diffusion equation and can thus be generated by a CTRW
Stochastic calculus for uncoupled continuous-time random walks.
Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L
2009-06-01
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingale transform theorem, if the CTRW is a martingale, the Itō integral is a martingale too. It is shown how the definition of the stochastic integrals can be used to easily compute them by Monte Carlo simulation. The relations between a CTRW, its quadratic variation, its Stratonovich integral, and its Itō integral are highlighted by numerical calculations when the jumps in space of the CTRW have a symmetric Lévy alpha -stable distribution and its waiting times have a one-parameter Mittag-Leffler distribution. Remarkably, these distributions have fat tails and an unbounded quadratic variation. In the diffusive limit of vanishing scale parameters, the probability density of this kind of CTRW satisfies the space-time fractional diffusion equation (FDE) or more in general the fractional Fokker-Planck equation, which generalizes the standard diffusion equation, solved by the probability density of the Wiener process, and thus provides a phenomenologic model of anomalous diffusion. We also provide an analytic expression for the quadratic variation of the stochastic process described by the FDE and check it by Monte Carlo.
From elongated spanning trees to vicious random walks
Energy Technology Data Exchange (ETDEWEB)
Gorsky, A. [ITEP, B. Cheryomushkinskaya 25, 117218 Moscow (Russian Federation); Nechaev, S., E-mail: nechaev@lptms.u-psud.fr [LPTMS, Université Paris Sud, 91405 Orsay Cedex (France); P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 119991 Moscow (Russian Federation); Poghosyan, V.S. [Institute for Informatics and Automation Problems NAS of Armenia, 375044 Yerevan (Armenia); Priezzhev, V.B. [Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)
2013-05-01
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of k paths (k is odd) along branches of trees or, equivalently, k loop-erased random walks. Starting and ending points of the paths are grouped such that they form a k-leg watermelon. For large distance r between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as r{sup −ν}logr with ν=(k{sup 2}−1)/2. Considering the spanning forest stretched along the meridian of this watermelon, we show that the two-dimensional k-leg loop-erased watermelon exponent ν is converting into the scaling exponent for the reunion probability (at a given point) of k(1+1)-dimensional vicious walkers, ν{sup -tilde=}k{sup 2}/2. At the end, we express the conjectures about the possible relation to integrable systems.
Ordering kinetics in quasi-one-dimensional Ising-like systems
International Nuclear Information System (INIS)
Mueller, M.; Paul, W.
1993-01-01
Results are presented of a Monte Carlo simulation of the kinetics of ordering in the two-dimensional nearest-neighbor Ising model in an L x M geometry with two free boundaries of length M much-gt L. This model can be viewed as representing an adsorbant on a stepped surface with mean terrace width L. The authors follow the ordering kinetics after quenches to temperatures 0.25 ≤T/T c ≤1 starting from a random initial configuration at a coverage of Θ=0.5 in the corresponding lattice gas picture. The systems evolve in time according to a Glauber kinetics with nonconserved order parameter. The equilibrium structure is given by a one-dimensional sequence of ordered domains. The ordering process evolves from a short initial two-dimensional ordering process through a crossover region to a quasi-one-dimensional behavior. The whole process is diffusive (inverse half-width of the structure factor peak 1/Δq parallel ∝ √t), in contrast to a model proposed by Kawasaki et al., where an intermediate logarithmic growth law is expected. All results are completely describable in the picture of an annihilating random walk (ARW) of domain walls. 36 refs., 16 figs
Random walks on the braid group B3 and magnetic translations in hyperbolic geometry
International Nuclear Information System (INIS)
Voituriez, Raphaeel
2002-01-01
We study random walks on the three-strand braid group B 3 , and in particular compute the drift, or average topological complexity of a random braid, as well as the probability of trivial entanglement. These results involve the study of magnetic random walks on hyperbolic graphs (hyperbolic Harper-Hofstadter problem), what enables to build a faithful representation of B 3 as generalized magnetic translation operators for the problem of a quantum particle on the hyperbolic plane
The linking number and the writhe of uniform random walks and polygons in confined spaces
International Nuclear Information System (INIS)
Panagiotou, E; Lambropoulou, S; Millett, K C
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(n 2 ). 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(√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.
Sounds in one-dimensional superfluid helium
International Nuclear Information System (INIS)
Um, C.I.; Kahng, W.H.; Whang, E.H.; Hong, S.K.; Oh, H.G.; George, T.F.
1989-01-01
The temperature variations of first-, second-, and third-sound velocity and attenuation coefficients in one-dimensional superfluid helium are evaluated explicitly for very low temperatures and frequencies (ω/sub s/tau 2 , and the ratio of second sound to first sound becomes unity as the temperature decreases to absolute zero
QUASI-ONE DIMENSIONAL CLASSICAL FLUIDS
Directory of Open Access Journals (Sweden)
J.K.Percus
2003-01-01
Full Text Available We study the equilibrium statistical mechanics of simple fluids in narrow pores. A systematic expansion is made about a one-dimensional limit of this system. It starts with a density functional, constructed from projected densities, which depends upon projected one and two-body potentials. The nature of higher order corrections is discussed.
Highly conducting one-dimensional solids
Evrard, Roger; Doren, Victor
1979-01-01
Although the problem of a metal in one dimension has long been known to solid-state physicists, it was not until the synthesis of real one-dimensional or quasi-one-dimensional systems that this subject began to attract considerable attention. This has been due in part to the search for high temperature superconductivity and the possibility of reaching this goal with quasi-one-dimensional substances. A period of intense activity began in 1973 with the report of a measurement of an apparently divergent conduc tivity peak in TfF-TCNQ. Since then a great deal has been learned about quasi-one-dimensional conductors. The emphasis now has shifted from trying to find materials of very high conductivity to the many interesting problems of physics and chemistry involved. But many questions remain open and are still under active investigation. This book gives a review of the experimental as well as theoretical progress made in this field over the last years. All the chapters have been written by scientists who have ...
Remarks for one-dimensional fractional equations
Directory of Open Access Journals (Sweden)
Massimiliano Ferrara
2014-01-01
Full Text Available In this paper we study a class of one-dimensional Dirichlet boundary value problems involving the Caputo fractional derivatives. The existence of infinitely many solutions for this equations is obtained by exploiting a recent abstract result. Concrete examples of applications are presented.
Controlled size and one-dimensional growth
Indian Academy of Sciences (India)
875–881. c Indian Academy of Sciences. Synthesis of azamacrocycle stabilized palladium nanoparticles: Controlled size and one-dimensional growth. JEYARAMAN ATHILAKSHMI and DILLIP KUMAR CHAND. ∗. Department of Chemistry, Indian Institute of Technology Madras, Chennai 600036, India e-mail: dillip@iitm.ac.
DEFF Research Database (Denmark)
Visser, Andre
2008-01-01
The movement of plankton, either by turbulent mixing or their own inherent motility, can be simulated in a Lagrangian framework as a random walk. Validation of random walk simulations is essential. There is a continuum of mathematically valid stochastic integration schemes upon which random walk...
Kapadia, Naaz; Masani, Kei; Catharine Craven, B; Giangregorio, Lora M; Hitzig, Sander L; Richards, Kieva; Popovic, Milos R
2014-09-01
Multi-channel surface functional electrical stimulation (FES) for walking has been used to improve voluntary walking and balance in individuals with spinal cord injury (SCI). To investigate short- and long-term benefits of 16 weeks of thrice-weekly FES-assisted walking program, while ambulating on a body weight support treadmill and harness system, versus a non-FES exercise program, on improvements in gait and balance in individuals with chronic incomplete traumatic SCI, in a randomized controlled trial design. Individuals with traumatic and chronic (≥18 months) motor incomplete SCI (level C2 to T12, American Spinal Cord Injury Association Impairment Scale C or D) were recruited from an outpatient SCI rehabilitation hospital, and randomized to FES-assisted walking therapy (intervention group) or aerobic and resistance training program (control group). Outcomes were assessed at baseline, and after 4, 6, and 12 months. Gait, balance, spasticity, and functional measures were collected. Spinal cord independence measure (SCIM) mobility sub-score improved over time in the intervention group compared with the control group (baseline/12 months: 17.27/21.33 vs. 19.09/17.36, respectively). On all other outcome measures the intervention and control groups had similar improvements. Irrespective of group allocation walking speed, endurance, and balance during ambulation all improved upon completion of therapy, and majority of participants retained these gains at long-term follow-ups. Task-oriented training improves walking ability in individuals with incomplete SCI, even in the chronic stage. Further randomized controlled trials, involving a large number of participants are needed, to verify if FES-assisted treadmill training is superior to aerobic and strength training.
Self-Trapping Self-Repelling Random Walks
Grassberger, Peter
2017-10-01
Although the title seems self-contradictory, it does not contain a misprint. The model we study is a seemingly minor modification of the "true self-avoiding walk" model of Amit, Parisi, and Peliti in two dimensions. The walks in it are self-repelling up to a characteristic time T* (which depends on various parameters), but spontaneously (i.e., without changing any control parameter) become self-trapping after that. For free walks, T* is astronomically large, but on finite lattices the transition is easily observable. In the self-trapped regime, walks are subdiffusive and intermittent, spending longer and longer times in small areas until they escape and move rapidly to a new area. In spite of this, these walks are extremely efficient in covering finite lattices, as measured by average cover times.
Directional migration of recirculating lymphocytes through lymph nodes via random walks.
Directory of Open Access Journals (Sweden)
Niclas Thomas
Full Text Available 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 (LASSO or regularised S-LASSO 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 insilico. 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
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.
Walking adaptability therapy after stroke: study protocol for a randomized controlled trial.
Timmermans, Celine; Roerdink, Melvyn; van Ooijen, Marielle W; Meskers, Carel G; Janssen, Thomas W; Beek, Peter J
2016-08-26
Walking in everyday life requires the ability to adapt walking to the environment. This adaptability is often impaired after stroke, and this might contribute to the increased fall risk after stroke. To improve safe community ambulation, walking adaptability training might be beneficial after stroke. This study is designed to compare the effects of two interventions for improving walking speed and walking adaptability: treadmill-based C-Mill therapy (therapy with augmented reality) and the overground FALLS program (a conventional therapy program). We hypothesize that C-Mill therapy will result in better outcomes than the FALLS program, owing to its expected greater amount of walking practice. This is a single-center parallel group randomized controlled trial with pre-intervention, post-intervention, retention, and follow-up tests. Forty persons after stroke (≥3 months) with deficits in walking or balance will be included. Participants will be randomly allocated to either C-Mill therapy or the overground FALLS program for 5 weeks. Both interventions will incorporate practice of walking adaptability and will be matched in terms of frequency, duration, and therapist attention. Walking speed, as determined by the 10 Meter Walking Test, will be the primary outcome measure. Secondary outcome measures will pertain to walking adaptability (10 Meter Walking Test with context or cognitive dual-task and Interactive Walkway assessments). Furthermore, commonly used clinical measures to determine walking ability (Timed Up-and-Go test), walking independence (Functional Ambulation Category), balance (Berg Balance Scale), and balance confidence (Activities-specific Balance Confidence scale) will be used, as well as a complementary set of walking-related assessments. The amount of walking practice (the number of steps taken per session) will be registered using the treadmill's inbuilt step counter (C-Mill therapy) and video recordings (FALLS program). This process measure will
Transduction on Directed Graphs via Absorbing Random Walks.
De, Jaydeep; Zhang, Xiaowei; Lin, Feng; Cheng, Li
2017-08-11
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications.Different from existing research efforts that either only deal with undirected graphs or circumvent directionality by means of symmetrization, we propose a novel random walk approach on directed graphs using absorbing Markov chains, which can be regarded as maximizing the accumulated expected number of visits from the unlabeled transient states. Our algorithm is simple, easy to implement, and works with large-scale graphs on binary, multiclass, and multi-label prediction problems. Moreover, it is capable of preserving the graph structure even when the input graph is sparse and changes over time, as well as retaining weak signals presented in the directed edges. We present its intimate connections to a number of existing methods, including graph kernels, graph Laplacian based methods, and interestingly, spanning forest of graphs. Its computational complexity and the generalization error are also studied. Empirically our algorithm is systematically evaluated on a wide range of applications, where it has shown to perform competitively comparing to a suite of state-of-the-art methods. In particular, our algorithm is shown to work exceptionally well with large sparse directed graphs with e.g. millions of nodes and tens of millions of edges, where it significantly outperforms other state-of-the-art methods. In the dynamic graph setting involving insertion or deletion of nodes and edge-weight changes over time, it also allows efficient online updates that produce the same results as of the batch update counterparts.
Realization of Configurable One-Dimensional Reflectarray
2017-08-31
experiments show strong signatures of beam steering that are dependent upon graphene doping. This seed grant has allowed our team to establish the essential...based, one-dimensional reflectarrays. Several immediate improvements to the device design and process flow are essential to suppress specular...beam steering that are dependent upon graphene doping. This seed grant has allowed our team to establish the essential operating procedures (i.e
Movie Recommendation using Random Walks over the Contextual Graph
DEFF Research Database (Denmark)
Bogers, Toine
Recommender systems have become an essential tool in fighting information overload. However, the majority of recommendation algorithms focus only on using ratings information, while disregarding information about the context of the recommendation process. We present ContextWalk, a recommendation...
Covering Ground: Movement Patterns and Random Walk Behavior in Aquilonastra anomala Sea Stars.
Lohmann, Amanda C; Evangelista, Dennis; Waldrop, Lindsay D; Mah, Christopher L; Hedrick, Tyson L
2016-10-01
The paths animals take while moving through their environments affect their likelihood of encountering food and other resources; thus, models of foraging behavior abound. To collect movement data appropriate for comparison with these models, we used time-lapse photography to track movements of a small, hardy, and easy-to-obtain organism, Aquilonastra anomala sea stars. We recorded the sea stars in a tank over many hours, with and without a food cue. With food present, they covered less distance, as predicted by theory; this strategy would allow them to remain near food. We then compared the paths of the sea stars to three common models of animal movement: Brownian motion, Lévy walks, and correlated random walks; we found that the sea stars' movements most closely resembled a correlated random walk. Additionally, we compared the search performance of models of Brownian motion, a Lévy walk, and a correlated random walk to that of a model based on the sea stars' movements. We found that the behavior of the modeled sea star walk was similar to that of the modeled correlated random walk and the Brownian motion model, but that the sea star walk was slightly more likely than the other walks to find targets at intermediate distances. While organisms are unlikely to follow an idealized random walk in all details, our data suggest that comparing the effectiveness of an organism's paths to those from theory can give insight into the organism's actual movement strategy. Finally, automated optical tracking of invertebrates proved feasible, and A. anomala was revealed to be a tractable, 2D-movement study system.
Random walks with shape prior for cochlea segmentation in ex vivo μCT
DEFF Research Database (Denmark)
Ruiz Pujadas, Esmeralda; Kjer, Hans Martin; Piella, Gemma
2016-01-01
Purpose Cochlear implantation is a safe and effective surgical procedure to restore hearing in deaf patients. However, the level of restoration achieved may vary due to differences in anatomy, implant type and surgical access. In order to reduce the variability of the surgical outcomes, we...... propose a new framework for cochlea segmentation in ex vivo μCT images using random walks where a distance-based shape prior is combined with a region term estimated by a Gaussian mixture model. The prior is also weighted by a confidence map to adjust its influence according to the strength of the image...... contour. Random walks is performed iteratively, and the prior mask is aligned in every iteration. Results We tested the proposed approach in ten μCT data sets and compared it with other random walks-based segmentation techniques such as guided random walks (Eslami et al. in Med Image Anal 17...
Mathematical conversations multicolor problems, problems in the theory of numbers, and random walks
Dynkin, E B
2006-01-01
Comprises Multicolor Problems, dealing with map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; Random Walks, addressing basic problems in probability theory. 1963 edition.
A Realization of a Quasi-Random Walk for Atoms in Time-Dependent Optical Potentials
Directory of Open Access Journals (Sweden)
Torsten Hinkel
2015-09-01
Full Text Available We consider the time dependent dynamics of an atom in a two-color pumped cavity, longitudinally through a side mirror and transversally via direct driving of the atomic dipole. The beating of the two driving frequencies leads to a time dependent effective optical potential that forces the atom into a non-trivial motion, strongly resembling a discrete random walk behavior between lattice sites. We provide both numerical and analytical analysis of such a quasi-random walk behavior.
Genetic Analysis of Daily Maximum Milking Speed by a Random Walk Model in Dairy Cows
DEFF Research Database (Denmark)
Karacaören, Burak; Janss, Luc; Kadarmideen, Haja
Data were obtained from dairy cows stationed at research farm ETH Zurich for maximum milking speed. The main aims of this paper are a) to evaluate if the Wood curve is suitable to model mean lactation curve b) to predict longitudinal breeding values by random regression and random walk models of ...... filter applications: random walk model could give online prediction of breeding values. Hence without waiting for whole lactation records, genetic evaluation could be made when the daily or monthly data is available......Data were obtained from dairy cows stationed at research farm ETH Zurich for maximum milking speed. The main aims of this paper are a) to evaluate if the Wood curve is suitable to model mean lactation curve b) to predict longitudinal breeding values by random regression and random walk models...... of maximum milking speed. Wood curve did not provide a good fit to the data set. Quadratic random regressions gave better predictions compared with the random walk model. However random walk model does not need to be evaluated for different orders of regression coefficients. In addition with the Kalman...
One-dimensional plasma simulation studies
International Nuclear Information System (INIS)
Friberg, Ari; Virtamo, Jorma
1976-01-01
Some basic plasma phenomena are studied by a one-dimensional electrostatic simulation code. A brief description of the code and its application to a test problem is given. The experiments carried out include Landau damping of an excited wave, particle retardation by smoothed field and beam-plasma instability. In each case, the set-up of the experiment is described and the results are compared with theoretical predictions. In the theoretical discussions, the oscillatory behaviour found in the Landau damping experiment is explained, an explicit formula for the particle retardation rate is derived and a rudimentary picture of the beam-plasma instability in terms of quasilinear theory is given. (author)
Solitons in one-dimensional antiferromagnetic chains
International Nuclear Information System (INIS)
Pires, A.S.T.; Talim, S.L.; Costa, B.V.
1989-01-01
We study the quantum-statistical mechanics, at low temperatures, of a one-dimensional antiferromagnetic Heisenberg model with two anisotropies. In the weak-coupling limit we determine the temperature dependences of the soliton energy and the soliton density. We have found that the leading correction to the sine-Gordon (SG) expression for the soliton density and the quantum soliton energy comes from the out-of-plane magnon mode, not present in the pure SG model. We also show that when an external magnetic field is applied, the chain supports a new type of kink, where the sublattices rotate in opposite directions
One-dimensional hypersonic phononic crystals.
Gomopoulos, N; Maschke, D; Koh, C Y; Thomas, E L; Tremel, W; Butt, H-J; Fytas, G
2010-03-10
We report experimental observation of a normal incidence phononic band gap in one-dimensional periodic (SiO(2)/poly(methyl methacrylate)) multilayer film at gigahertz frequencies using Brillouin spectroscopy. The band gap to midgap ratio of 0.30 occurs for elastic wave propagation along the periodicity direction, whereas for inplane propagation the system displays an effective medium behavior. The phononic properties are well captured by numerical simulations. The porosity in the silica layers presents a structural scaffold for the introduction of secondary active media for potential coupling between phonons and other excitations, such as photons and electrons.
Specificities of one-dimensional dissipative magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Popov, P. V., E-mail: popov.pv@mipt.ru [National Research Center Kurchatov Institute (Russian Federation)
2016-11-15
One-dimensional dynamics of a plane slab of cold (β ≪ 1) isothermal plasma accelerated by a magnetic field is studied in terms of the MHD equations with a finite constant conductivity. The passage to the limit β → 0 is analyzed in detail. It is shown that, at β = 0, the character of the solution depends substantially on the boundary condition for the electric field at the inner plasma boundary. The relationship between the boundary condition for the pressure at β > 0 and the conditions for the electric field at β = 0 is found. The stability of the solution against one-dimensional longitudinal perturbations is analyzed. It is shown that, in the limit β → 0, the stationary solution is unstable if the time during which the acoustic wave propagates across the slab is longer than the time of magnetic field diffusion. The growth rate and threshold of instability are determined, and results of numerical simulation of its nonlinear stage are presented.
Liang, Yingjie; Chen, Wen
2018-04-01
The mean squared displacement (MSD) of the traditional ultraslow diffusion is a logarithmic function of time. Recently, the continuous time random walk model is employed to characterize this ultraslow diffusion dynamics by connecting the heavy-tailed logarithmic function and its variation as the asymptotical waiting time density. In this study we investigate the limiting waiting time density of a general ultraslow diffusion model via the inverse Mittag-Leffler function, whose special case includes the traditional logarithmic ultraslow diffusion model. The MSD of the general ultraslow diffusion model is analytically derived as an inverse Mittag-Leffler function, and is observed to increase even more slowly than that of the logarithmic function model. The occurrence of very long waiting time in the case of the inverse Mittag-Leffler function has the largest probability compared with the power law model and the logarithmic function model. The Monte Carlo simulations of one dimensional sample path of a single particle are also performed. The results show that the inverse Mittag-Leffler waiting time density is effective in depicting the general ultraslow random motion.
Human mammary epithelial cells exhibit a bimodal correlated random walk pattern.
Potdar, Alka A; Jeon, Junhwan; Weaver, Alissa M; Quaranta, Vito; Cummings, Peter T
2010-03-10
Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells) that exist in multi-cellular organisms (humans) follow a bimodal correlated random walk (BCRW). Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases) each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation). Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.
Human mammary epithelial cells exhibit a bimodal correlated random walk pattern.
Directory of Open Access Journals (Sweden)
Alka A Potdar
2010-03-01
Full Text Available Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells that exist in multi-cellular organisms (humans follow a bimodal correlated random walk (BCRW.Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation.Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.
One-dimensional nanomaterials for energy storage
Chen, Cheng; Fan, Yuqi; Gu, Jianhang; Wu, Liming; Passerini, Stefano; Mai, Liqiang
2018-03-01
The search for higher energy density, safer, and longer cycling-life energy storage systems is progressing quickly. One-dimensional (1D) nanomaterials have a large length-to-diameter ratio, resulting in their unique electrical, mechanical, magnetic and chemical properties, and have wide applications as electrode materials in different systems. This article reviews the latest hot topics in applying 1D nanomaterials, covering both their synthesis and their applications. 1D nanomaterials can be grouped into the categories: carbon, silicon, metal oxides, and conducting polymers, and we structure our discussion accordingly. Then, we survey the unique properties and application of 1D nanomaterials in batteries and supercapacitors, and provide comments on the progress and advantages of those systems, paving the way for a better understanding of employing 1D nanomaterials for energy storage.
One-Dimensional Modelling of Internal Ballistics
Monreal-González, G.; Otón-Martínez, R. A.; Velasco, F. J. S.; García-Cascáles, J. R.; Ramírez-Fernández, F. J.
2017-10-01
A one-dimensional model is introduced in this paper for problems of internal ballistics involving solid propellant combustion. First, the work presents the physical approach and equations adopted. Closure relationships accounting for the physical phenomena taking place during combustion (interfacial friction, interfacial heat transfer, combustion) are deeply discussed. Secondly, the numerical method proposed is presented. Finally, numerical results provided by this code (UXGun) are compared with results of experimental tests and with the outcome from a well-known zero-dimensional code. The model provides successful results in firing tests of artillery guns, predicting with good accuracy the maximum pressure in the chamber and muzzle velocity what highlights its capabilities as prediction/design tool for internal ballistics.
Stability model for one-dimensional FRCs
International Nuclear Information System (INIS)
Schwarzmeier, J.L.; Hewitt, T.G.; Lewis, H.R.; Seyler, C.E.; Symon, K.R.
1982-01-01
The subject of transport near the separatrix in FRC devices is important for determining the performance to be expected from an FRC reactor or from FRC experiments. A computer code was constructed for studying the micro-stability properties of FRCs near the separatrix as a first step in obtaining quasilinear transport coefficients that can be used in a transport code. We consider collisionless ions and electrons, without an expansion in powers of a parameter, like the electron or ion gyroradius, and we approximate the equilibrium with an infinitely long axially and translationally symmetric equilibrium. Thus, in our equilibria, there are only an axial magnetic field and a radial electric field. Our equilibria are collisionless, two-species, diffuse-profile, one-dimensional, theta-pinch equilibria. We allow the possibility that there be a magnetic field null in order to be able to model FRC devices more realistically
One-Dimensional Photonic Crystal Superprisms
Ting, David
2005-01-01
Theoretical calculations indicate that it should be possible for one-dimensional (1D) photonic crystals (see figure) to exhibit giant dispersions known as the superprism effect. Previously, three-dimensional (3D) photonic crystal superprisms have demonstrated strong wavelength dispersion - about 500 times that of conventional prisms and diffraction gratings. Unlike diffraction gratings, superprisms do not exhibit zero-order transmission or higher-order diffraction, thereby eliminating cross-talk problems. However, the fabrication of these 3D photonic crystals requires complex electron-beam substrate patterning and multilayer thin-film sputtering processes. The proposed 1D superprism is much simpler in structural complexity and, therefore, easier to design and fabricate. Like their 3D counterparts, the 1D superprisms can exhibit giant dispersions over small spectral bands that can be tailored by judicious structure design and tuned by varying incident beam direction. Potential applications include miniature gas-sensing devices.
One dimensional systems with singular perturbations
International Nuclear Information System (INIS)
Alvarez, J J; Gadella, M; Nieto, L M; Glasser, L M; Lara, L P
2011-01-01
This paper discusses some one dimensional quantum models with singular perturbations. Eventually, a mass discontinuity is added at the points that support the singular perturbations. The simplest model includes an attractive singular potential with a mass jump both located at the origin. We study the form of the only bound state. Another model exhibits a hard core at the origin plus one or more repulsive deltas with mass jumps at the points supporting these deltas. We study the location and the multiplicity of these resonances for the case of one or two deltas and settle the basis for a generalization. Finally, we consider the harmonic oscillator and the infinite square well plus a singular potential at the origin. We see how the energy of bound states is affected by the singular perturbation.
Cohesive motion in one-dimensional flocking
International Nuclear Information System (INIS)
Dossetti, V
2012-01-01
A one-dimensional rule-based model for flocking, which combines velocity alignment and long-range centering interactions, is presented and studied. The induced cohesion in the collective motion of the self-propelled agents leads to unique group behavior that contrasts with previous studies. Our results show that the largest cluster of particles, in the condensed states, develops a mean velocity slower than the preferred one in the absence of noise. For strong noise, the system also develops a non-vanishing mean velocity, alternating its direction of motion stochastically. This allows us to address the directional switching phenomenon. The effects of different sources of stochasticity on the system are also discussed. (paper)
International Nuclear Information System (INIS)
Kiskis, J.; Narayanan, R.; Vranas, P.
1993-01-01
The authors study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments, the authors show that the critical exponent v describing the vanishing of the physical mass at the critical point is equal to v θ /d w , where d w is the Hausdorff dimension of the walk, and v θ = var-phi, where var-phi is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is var-phi/v for O(N) models. 3 refs
Walking improves sleep in individuals with cancer: a meta-analysis of randomized, controlled trials.
Chiu, Hsiao-Yean; Huang, Hui-Chuan; Chen, Pin-Yuan; Hou, Wen-Hsuan; Tsai, Pei-Shan
2015-03-01
To evaluate the effectiveness of walking exercise on sleep in people with cancer. Databases searched included China Knowledge Resource Integrated Database, CINAHL®, Cochrane Central Register of Controlled Trials, EMBASE, PsycINFO®, PubMed, Wanfang Data, and Web of Science. Nine randomized, controlled trials involving 599 patients were included. Most of the studies used moderate-intensity walking exercise. Overall, walking exercise significantly improved sleep in people with cancer (Hedges' g = –0.52). Moderator analyses showed that walking exercise alone and walking exercise combined with other forms of interventions yielded comparable effects on sleep improvement, and that the effect size did not differ among participants who were at different stages of cancer. The effect sizes for studies involving individuals with breast cancer and for studies including individuals with other types of cancer were similar. Moderate-intensity walking exercise is effective in improving sleep in individuals with cancer. The authors' findings support the inclusion of walking exercise into the multimodal approaches to managing sleep in people with cancer. Healthcare providers must convey the benefits of walking exercise to individuals with cancer who are suffering from sleep problems.
Diffusion coefficients for multi-step persistent random walks on lattices
International Nuclear Information System (INIS)
Gilbert, Thomas; Sanders, David P
2010-01-01
We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with a two-step memory on different classes of one-, two- and higher dimensional lattices.
Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications
Directory of Open Access Journals (Sweden)
Zhongtuan Zheng
2017-01-01
Full Text Available This paper investigates, both theoretically and numerically, preferential random walks (PRW on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW. Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.
Few quantum particles on one dimensional lattices
International Nuclear Information System (INIS)
Valiente Cifuentes, Manuel
2010-01-01
There is currently a great interest in the physics of degenerate quantum gases and low-energy few-body scattering due to the recent experimental advances in manipulation of ultracold atoms by light. In particular, almost perfect periodic potentials, called optical lattices, can be generated. The lattice spacing is fixed by the wavelength of the laser field employed and the angle betwen the pair of laser beams; the lattice depth, defining the magnitude of the different band gaps, is tunable within a large interval of values. This flexibility permits the exploration of different regimes, ranging from the ''free-electron'' picture, modified by the effective mass for shallow optical lattices, to the tight-binding regime of a very deep periodic potential. In the latter case, effective single-band theories, widely used in condensed matter physics, can be implemented with unprecedent accuracy. The tunability of the lattice depth is nowadays complemented by the use of magnetic Feshbach resonances which, at very low temperatures, can vary the relevant atom-atom scattering properties at will. Moreover, optical lattices loaded with gases of effectively reduced dimensionality are experimentally accessible. This is especially important for one spatial dimension, since most of the exactly solvable models in many-body quantum mechanics deal with particles on a line; therefore, experiments with one-dimensional gases serve as a testing ground for many old and new theories which were regarded as purely academic not so long ago. The physics of few quantum particles on a one-dimensional lattice is the topic of this thesis. Most of the results are obtained in the tight-binding approximation, which is amenable to exact numerical or analytical treatment. For the two-body problem, theoretical methods for calculating the stationary scattering and bound states are developed. These are used to obtain, in closed form, the two-particle solutions of both the Hubbard and extended Hubbard models
Few quantum particles on one dimensional lattices
Energy Technology Data Exchange (ETDEWEB)
Valiente Cifuentes, Manuel
2010-06-18
There is currently a great interest in the physics of degenerate quantum gases and low-energy few-body scattering due to the recent experimental advances in manipulation of ultracold atoms by light. In particular, almost perfect periodic potentials, called optical lattices, can be generated. The lattice spacing is fixed by the wavelength of the laser field employed and the angle betwen the pair of laser beams; the lattice depth, defining the magnitude of the different band gaps, is tunable within a large interval of values. This flexibility permits the exploration of different regimes, ranging from the ''free-electron'' picture, modified by the effective mass for shallow optical lattices, to the tight-binding regime of a very deep periodic potential. In the latter case, effective single-band theories, widely used in condensed matter physics, can be implemented with unprecedent accuracy. The tunability of the lattice depth is nowadays complemented by the use of magnetic Feshbach resonances which, at very low temperatures, can vary the relevant atom-atom scattering properties at will. Moreover, optical lattices loaded with gases of effectively reduced dimensionality are experimentally accessible. This is especially important for one spatial dimension, since most of the exactly solvable models in many-body quantum mechanics deal with particles on a line; therefore, experiments with one-dimensional gases serve as a testing ground for many old and new theories which were regarded as purely academic not so long ago. The physics of few quantum particles on a one-dimensional lattice is the topic of this thesis. Most of the results are obtained in the tight-binding approximation, which is amenable to exact numerical or analytical treatment. For the two-body problem, theoretical methods for calculating the stationary scattering and bound states are developed. These are used to obtain, in closed form, the two-particle solutions of both the Hubbard and
Richards, Elizabeth A; Ogata, Niwako; Cheng, Ching-Wei
2016-01-01
To facilitate physical activity (PA) adoption and maintenance, promotion of innovative population-level strategies that focus on incorporating moderate-intensity lifestyle PAs are needed. The purpose of this randomized controlled trial was to evaluate the Dogs, Physical Activity, and Walking intervention, a 3-month, social cognitive theory (SCT), e-mail-based PA intervention. In a longitudinal, repeated-measures design, 49 dog owners were randomly assigned to a control (n = 25) or intervention group (n = 24). The intervention group received e-mail messages (twice weekly for 4 weeks and weekly for 8 weeks) designed to influence SCT constructs of self-efficacy, self-regulation, outcome expectations and expectancies, and social support. At baseline and every 3 months through 1 year, participants completed self-reported questionnaires of individual, interpersonal, and PA variables. Linear mixed models were used to assess for significant differences in weekly minutes of dog walking and theoretical constructs between groups (intervention and control) across time. To test self-efficacy as a mediator of social support for dog walking, tests for mediation were conducted using the bootstrapping technique. With the exception of Month 9, participants in the intervention group accumulated significantly more weekly minutes of dog walking than the control group. On average, the intervention group accumulated 58.4 more minutes (SD = 18.1) of weekly dog walking than the control group (p dog walking. Results indicate that a simple SCT-based e-mail intervention is effective in increasing and maintaining an increase in dog walking among dog owners at 12-month follow-up. In light of these findings, it may be advantageous to design dog walking interventions that focus on increasing self-efficacy for dog walking by fostering social support.
A Non-Random Walk Down Hollywood Boulevard
DEFF Research Database (Denmark)
Lepori, Gabriele
affect (i.e. grief, proxied by the death of Hollywood Walk of Fame celebrities) on people’s willingness to invest in risky assets (proxied by the daily performance of the U.S. stock market). Using a sample of 1,374 celebrity deaths over the period 1926-2009 and controlling for seasonalities, economic....../environmental factors, and market liquidity, I find that the death of popular and beloved celebrities is immediately followed by a 16 basis point increase in stock returns, which is consistent with a rise in the net demand for risky instruments. I also find evidence that the size of this celebrity-death effect...
Evolution of the concentration PDF in random environments modeled by global random walk
Suciu, Nicolae; Vamos, Calin; Attinger, Sabine; Knabner, Peter
2013-04-01
The evolution of the probability density function (PDF) of concentrations of chemical species transported in random environments is often modeled by ensembles of notional particles. The particles move in physical space along stochastic-Lagrangian trajectories governed by Ito equations, with drift coefficients given by the local values of the resolved velocity field and diffusion coefficients obtained by stochastic or space-filtering upscaling procedures. A general model for the sub-grid mixing also can be formulated as a system of Ito equations solving for trajectories in the composition space. The PDF is finally estimated by the number of particles in space-concentration control volumes. In spite of their efficiency, Lagrangian approaches suffer from two severe limitations. Since the particle trajectories are constructed sequentially, the demanded computing resources increase linearly with the number of particles. Moreover, the need to gather particles at the center of computational cells to perform the mixing step and to estimate statistical parameters, as well as the interpolation of various terms to particle positions, inevitably produce numerical diffusion in either particle-mesh or grid-free particle methods. To overcome these limitations, we introduce a global random walk method to solve the system of Ito equations in physical and composition spaces, which models the evolution of the random concentration's PDF. The algorithm consists of a superposition on a regular lattice of many weak Euler schemes for the set of Ito equations. Since all particles starting from a site of the space-concentration lattice are spread in a single numerical procedure, one obtains PDF estimates at the lattice sites at computational costs comparable with those for solving the system of Ito equations associated to a single particle. The new method avoids the limitations concerning the number of particles in Lagrangian approaches, completely removes the numerical diffusion, and
Simulation of quantum systems with random walks: A new algorithm for charged systems
International Nuclear Information System (INIS)
Ceperley, D.
1983-01-01
Random walks with branching have been used to calculate exact properties of the ground state of quantum many-body systems. In this paper, a more general Green's function identity is derived which relates the potential energy, a trial wavefunction, and a trial density matrix to the rules of a branched random walk. It is shown that an efficient algorithm requires a good trial wavefunction, a good trial density matrix, and a good sampling of this density matrix. An accurate density matrix is constructed for Coulomb systems using the path integral formula. The random walks from this new algorithm diffuse through phase space an order of magnitude faster than the previous Green's Function Monte Carlo method. In contrast to the simple diffusion Monte Carlo algorithm, it is exact method. Representative results are presented for several molecules
One dimensional benchmark calculations using diffusion theory
International Nuclear Information System (INIS)
Ustun, G.; Turgut, M.H.
1986-01-01
This is a comparative study by using different one dimensional diffusion codes which are available at our Nuclear Engineering Department. Some modifications have been made in the used codes to fit the problems. One of the codes, DIFFUSE, solves the neutron diffusion equation in slab, cylindrical and spherical geometries by using 'Forward elimination- Backward substitution' technique. DIFFUSE code calculates criticality, critical dimensions and critical material concentrations and adjoint fluxes as well. It is used for the space and energy dependent neutron flux distribution. The whole scattering matrix can be used if desired. Normalisation of the relative flux distributions to the reactor power, plotting of the flux distributions and leakage terms for the other two dimensions have been added. Some modifications also have been made for the code output. Two Benchmark problems have been calculated with the modified version and the results are compared with BBD code which is available at our department and uses same techniques of calculation. Agreements are quite good in results such as k-eff and the flux distributions for the two cases studies. (author)
One-dimensional model of inertial pumping
Kornilovitch, Pavel E.; Govyadinov, Alexander N.; Markel, David P.; Torniainen, Erik D.
2013-02-01
A one-dimensional model of inertial pumping is introduced and solved. The pump is driven by a high-pressure vapor bubble generated by a microheater positioned asymmetrically in a microchannel. The bubble is approximated as a short-term impulse delivered to the two fluidic columns inside the channel. Fluid dynamics is described by a Newton-like equation with a variable mass, but without the mass derivative term. Because of smaller inertia, the short column refills the channel faster and accumulates a larger mechanical momentum. After bubble collapse the total fluid momentum is nonzero, resulting in a net flow. Two different versions of the model are analyzed in detail, analytically and numerically. In the symmetrical model, the pressure at the channel-reservoir connection plane is assumed constant, whereas in the asymmetrical model it is reduced by a Bernoulli term. For low and intermediate vapor bubble pressures, both models predict the existence of an optimal microheater location. The predicted net flow in the asymmetrical model is smaller by a factor of about 2. For unphysically large vapor pressures, the asymmetrical model predicts saturation of the effect, while in the symmetrical model net flow increases indefinitely. Pumping is reduced by nonzero viscosity, but to a different degree depending on the microheater location.
Diffusiophoresis in one-dimensional solute gradients
Energy Technology Data Exchange (ETDEWEB)
Ault, Jesse T. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Warren, Patrick B. [Unilever R& D Port Sunlight, Bebington (United Kingdom); Shin, Sangwoo [Univ. of Hawaii at Manoa, Honolulu, HI (United States); Stone, Howard A. [Princeton Univ., Princeton, NJ (United States)
2017-11-06
Here, the diffusiophoretic motion of suspended colloidal particles under one-dimensional solute gradients is solved using numerical and analytical techniques. Similarity solutions are developed for the injection and withdrawal dynamics of particles into semi-infinite pores. Furthermore, a method of characteristics formulation of the diffusion-free particle transport model is presented and integrated to realize particle trajectories. Analytical solutions are presented for the limit of small particle diffusiophoretic mobility Γ_{p} relative to the solute diffusivity D_{s} for particle motions in both semi-infinite and finite domains. Results confirm the build up of local maxima and minima in the propagating particle front dynamics. The method of characteristics is shown to successfully predict particle motions and the position of the particle front, although it fails to accurately predict suspended particle concentrations in the vicinity of sharp gradients, such as at the particle front peak seen in some injection cases, where particle diffusion inevitably plays an important role. Results inform the design of applications in which the use of applied solute gradients can greatly enhance particle injection into and withdrawal from pores.
Diffusiophoresis in one-dimensional solute gradients
International Nuclear Information System (INIS)
Ault, Jesse T.; Warren, Patrick B.; Shin, Sangwoo; Stone, Howard A.
2017-01-01
Here, the diffusiophoretic motion of suspended colloidal particles under one-dimensional solute gradients is solved using numerical and analytical techniques. Similarity solutions are developed for the injection and withdrawal dynamics of particles into semi-infinite pores. Furthermore, a method of characteristics formulation of the diffusion-free particle transport model is presented and integrated to realize particle trajectories. Analytical solutions are presented for the limit of small particle diffusiophoretic mobility Γ p relative to the solute diffusivity D s for particle motions in both semi-infinite and finite domains. Results confirm the build up of local maxima and minima in the propagating particle front dynamics. The method of characteristics is shown to successfully predict particle motions and the position of the particle front, although it fails to accurately predict suspended particle concentrations in the vicinity of sharp gradients, such as at the particle front peak seen in some injection cases, where particle diffusion inevitably plays an important role. Results inform the design of applications in which the use of applied solute gradients can greatly enhance particle injection into and withdrawal from pores.
Novel pseudo-random number generator based on quantum random walks
Yang, Yu-Guang; Zhao, Qian-Qian
2016-02-01
In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.
Novel pseudo-random number generator based on quantum random walks.
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.
High Dimensional Spectral Graph Theory and Non-backtracking Random Walks on Graphs
Kempton, Mark
This thesis has two primary areas of focus. First we study connection graphs, which are weighted graphs in which each edge is associated with a d-dimensional rotation matrix for some fixed dimension d, in addition to a scalar weight. Second, we study non-backtracking random walks on graphs, which are random walks with the additional constraint that they cannot return to the immediately previous state at any given step. Our work in connection graphs is centered on the notion of consistency, that is, the product of rotations moving from one vertex to another is independent of the path taken, and a generalization called epsilon-consistency. We present higher dimensional versions of the combinatorial Laplacian matrix and normalized Laplacian matrix from spectral graph theory, and give results characterizing the consistency of a connection graph in terms of the spectra of these matrices. We generalize several tools from classical spectral graph theory, such as PageRank and effective resistance, to apply to connection graphs. We use these tools to give algorithms for sparsification, clustering, and noise reduction on connection graphs. In non-backtracking random walks, we address the question raised by Alon et. al. concerning how the mixing rate of a non-backtracking random walk to its stationary distribution compares to the mixing rate for an ordinary random walk. Alon et. al. address this question for regular graphs. We take a different approach, and use a generalization of Ihara's Theorem to give a new proof of Alon's result for regular graphs, and to extend the result to biregular graphs. Finally, we give a non-backtracking version of Polya's Random Walk Theorem for 2-dimensional grids.
Aref, S
1982-01-01
A study of the migration of fourth stage larvae of the parasite Strongylus vulgaris in the intestinal arteries of the horse is presented. It is established, that the larvae migrate along the arteries in almost straight lines. It is suggested that this is primarily due to their ability to sense the curvature of the vessel wall, and not, as might have been expected, because of an ability to sense the direction of blood flow. A larva will sometimes alter its direction of motion when encountering a small off-branching artery. This behaviour suggests, that the migration of S. vulgaris larvae can be modeled as a one-dimensional discrete random walk on a long time scale. This model is simpler than any deterministic model and, in particular, does not require the existence of a predilection site. The available data is not, however, sufficient for a convincing, quantitative test of the model. The proposed reluctance of the larvae to bend into off-branching arteries is used to explain the crowding of larvae in the cranial mesenteric artery.
Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile
Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.
2012-09-01
Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.
Ding, Jian; Li, Li
2018-06-01
We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.
First-passage time asymptotics over moving boundaries for random walk bridges
Sloothaak, F.; Zwart, B.; Wachtel, V.
2017-01-01
We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent -1/2, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the re...
Emergence of an optimal search strategy from a simple random walk.
Sakiyama, Tomoko; Gunji, Yukio-Pegio
2013-09-06
In reports addressing animal foraging strategies, it has been stated that Lévy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths.
Pólya number and first return of bursty random walk: Rigorous solutions
Wan, J.; Xu, X. P.
2012-03-01
The recurrence properties of random walks can be characterized by Pólya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we investigate Pólya number and first return for bursty random walk on a line, in which the walk has different step size and moving probabilities. Using the concept of the Catalan number, we obtain exact results for first return probability, the average first return time and Pólya number for the first time. We show that Pólya number displays two different functional behavior when the walk deviates from the recurrent point. By utilizing the Lagrange inversion formula, we interpret our findings by transferring Pólya number to the closed-form solutions of an inverse function. We also calculate Pólya number using another approach, which corroborates our results and conclusions. Finally, we consider the recurrence properties and Pólya number of two variations of the bursty random walk model.
Fritschi, Juliette O; Brown, Wendy J; van Uffelen, Jannique G Z
2014-04-17
Physical activity is associated with better physical and mental health in older adults. Pole walking is a form of walking which may have additional health benefits in older adults, because of the addition of hand held poles, and consequent upper limb involvement. However, few studies have examined the potential additional effects of pole walking on physical and psychosocial health in older adults compared with walking. The aim of this study is to compare the effect of a pole walking program with the effects of a walking program, on physical and psychosocial wellbeing, in older adults in assisted living facilities. Sixty men and women from assisted living communities over 65 years will be recruited from senior retirement facilities and randomized into a group based, pole walking program, or walking program. The pole walking group will use the Exerstrider method of pole walking. Total duration of the programs is 12 weeks, with three sessions per week, building from 20 minute to 30 minute sessions.The primary outcome is physical function, as measured by items from the Seniors Fitness Test and hand grip strength. Secondary outcomes include, physical activity levels, sedentary behaviour, joint pain, and quality of life. All outcomes will be assessed before and after the programs, using valid and reliable measures. The study will add to the evidence base for the effects of pole walking, compared with walking, on physical and psychosocial health and physical function, in healthy older adults. This will improve understanding about the feasibility of pole walking programs and its specific benefits in this population. Australian New Zealand Clinical Trials Registry ACTRN12612001127897.
Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki
2018-03-01
We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2}). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3}) and the level sets of the Gaussian free field ({d≥ 3}). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.
Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs
International Nuclear Information System (INIS)
Salimi, S.; Jafarizadeh, M. A.
2009-01-01
In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product Cayley graphs (complete cycle, complete K n , charter and n-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as t → ∞ but for quantum state is not always satisfied. (general)
Nordic Walking and chronic low back pain: design of a randomized clinical trial
Directory of Open Access Journals (Sweden)
Hartvigsen Jan
2006-10-01
Full Text Available Abstract Background Low Back Pain is a major public health problem all over the western world. Active approaches including exercise in the treatment of low back pain results in better outcomes for patients, but it is not known exactly which types of back exercises are most beneficial or whether general physical activity provide similar benefits. Nordic Walking is a popular and fast growing type of exercise in Northern Europe. Initial studies have demonstrated that persons performing Nordic Walking are able to exercise longer and harder compared to normal walking thereby increasing their cardiovascular metabolism. Until now no studies have been performed to investigate whether Nordic Walking has beneficial effects in relation to low back pain. The primary aim of this study is to investigate whether supervised Nordic Walking can reduce pain and improve function in a population of chronic low back pain patients when compared to unsupervised Nordic Walking and advice to stay active. In addition we investigate whether there is an increase in the cardiovascular metabolism in persons performing supervised Nordic Walking compared to persons who are advised to stay active. Finally, we investigate whether there is a difference in compliance between persons receiving supervised Nordic Walking and persons doing unsupervised Nordic Walking. Methods One hundred and fifty patients with low back pain for at least eight weeks and referred to a specialized secondary sector outpatient back pain clinic are included in the study. After completion of the standard back centre treatment patients are randomized into one of three groups: A Nordic Walking twice a week for eight weeks under supervision of a specially trained instructor; B Unsupervised Nordic Walking for eight weeks after one training session with an instructor; C A one hour motivational talk including advice to stay active. Outcome measures are pain, function, overall health, cardiovascular ability and
Elliptic equation for random walks. Application to transport in microporous media
DEFF Research Database (Denmark)
Shapiro, Alexander
2007-01-01
We consider a process of random walks with arbitrary residence time distribution. We show that in many cases this process may not be described by the classical (Fick) parabolic diffusion equation, but an elliptic equation. An additional term proportional to the second time derivative takes into a...
Czech Academy of Sciences Publication Activity Database
Wiesner, Ivo; Wiesnerová, Dana
2010-01-01
Roč. 54, č. 2 (2010), s. 353-356 ISSN 0006-3134 R&D Projects: GA AV ČR 1QS500510566 Institutional research plan: CEZ:AV0Z50510513 Keywords : begonia germplasm identification * random walk * primary sequence analysis Subject RIV: EB - Genetics ; Molecular Biology Impact factor: 1.582, year: 2010
A note on the random walk theory of recoil movement in prolonged ion bombardment
International Nuclear Information System (INIS)
Koponen, Ismo
1994-01-01
A characteristic function is derived for the probability distribution of final positions of recoil atoms in prolonged ion bombardment of dense matter. The derivation is done within the framework of Poissonian random walk theory using a jump distribution, which is somewhat more general than those studied previously. ((orig.))
Cai, Bingjing; Wang, Haiying; Zheng, Huiru; Wang, Hui
2015-01-01
Systematic identification of protein complexes from protein-protein interaction networks (PPIs) is an important application of data mining in life science. Over the past decades, various new clustering techniques have been developed based on modelling PPIs as binary relations. Non-binary information of co-complex relations (prey/bait) in PPIs data derived from tandem affinity purification/mass spectrometry (TAP-MS) experiments has been unfairly disregarded. In this paper, we propose a Biased Random Walk based algorithm for detecting protein complexes from TAP-MS data, resulting in the random walk with restarting baits (RWRB). RWRB is developed based on Random walk with restart. The main contribution of RWRB is the incorporation of co-complex relations in TAP-MS PPI networks into the clustering process, by implementing a new restarting strategy during the process of random walk. Through experimentation on un-weighted and weighted TAP-MS data sets, we validated biological significance of our results by mapping them to manually curated complexes. Results showed that, by incorporating non-binary, co-membership information, significant improvement has been achieved in terms of both statistical measurements and biological relevance. Better accuracy demonstrates that the proposed method outperformed several state-of-the-art clustering algorithms for the detection of protein complexes in TAP-MS data.
Do exchange rates follow random walks? A variance ratio test of the ...
African Journals Online (AJOL)
The random-walk hypothesis in foreign-exchange rates market is one of the most researched areas, particularly in developed economies. However, emerging markets in sub-Saharan Africa have received little attention in this regard. This study applies Lo and MacKinlay's (1988) conventional variance ratio test and Wright's ...
The Hidden Flow Structure and Metric Space of Network Embedding Algorithms Based on Random Walks.
Gu, Weiwei; Gong, Li; Lou, Xiaodan; Zhang, Jiang
2017-10-13
Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a network, such as the clustering and linking prediction but also learns the latent vector representation of the nodes which provides theoretical support for a variety of applications, such as visualization, link prediction, node classification, and recommendation. As the latest progress of the research, several algorithms based on random walks have been devised. Although those algorithms have drawn much attention for their high scores in learning efficiency and accuracy, there is still a lack of theoretical explanation, and the transparency of those algorithms has been doubted. Here, we propose an approach based on the open-flow network model to reveal the underlying flow structure and its hidden metric space of different random walk strategies on networks. We show that the essence of embedding based on random walks is the latent metric structure defined on the open-flow network. This not only deepens our understanding of random- walk-based embedding algorithms but also helps in finding new potential applications in network embedding.
Random walks and a simple chirally invariant lattice Hamiltonian without fermion doubling
International Nuclear Information System (INIS)
Belyea, C.I.
1992-01-01
It is shown that there is a simple chirally-invariant lattice Hamiltonian for fermions which is doubling-free but non-Hermitian and which may be valuable in lattice Hamiltonian studies of quantum chromodynamics. A connection is established between the existence of random walk representations of spinor propagators and this doubling-free formulation, in analogy with Wilson fermions. 15 refs
Random Walk Model for the Growth of Monolayer in Dip Pen Nanolithography
International Nuclear Information System (INIS)
Kim, H; Ha, S; Jang, J
2013-01-01
By using a simple random-walk model, we simulate the growth of a self-assembled monolayer (SAM) pattern generated in dip pen nanolithography (DPN). In this model, the SAM pattern grows mainly via the serial pushing of molecules deposited from the tip. We examine various SAM patterns, such as lines, crosses, and letters by changing the tip scan speed.
National Research Council Canada - National Science Library
Durrett, Richard; Kesten, Harry; Spitzer, Frank
1991-01-01
..., made the transparency used in the printing process. STUDENTS OF FRANK SPITZERSTUDENTS OF FRANK SPITZER 1957 J. W. Lamperti, On the asymptotic behavior of recurrent and almostrecurrent events. 1964 W. W. Whitman, Some strong laws for random walks and Brownian motion. 1965 J. C. Mineka, The existence and uniqueness of positive solutions to the Wien...
Directory of Open Access Journals (Sweden)
Choon Sen Seah
2017-12-01
Full Text Available Microarray technology has become one of the elementary tools for researchers to study the genome of organisms. As the complexity and heterogeneity of cancer is being increasingly appreciated through genomic analysis, cancerous classification is an emerging important trend. Significant directed random walk is proposed as one of the cancerous classification approach which have higher sensitivity of risk gene prediction and higher accuracy of cancer classification. In this paper, the methodology and material used for the experiment are presented. Tuning parameter selection method and weight as parameter are applied in proposed approach. Gene expression dataset is used as the input datasets while pathway dataset is used to build a directed graph, as reference datasets, to complete the bias process in random walk approach. In addition, we demonstrate that our approach can improve sensitive predictions with higher accuracy and biological meaningful classification result. Comparison result takes place between significant directed random walk and directed random walk to show the improvement in term of sensitivity of prediction and accuracy of cancer classification.
Efficient tests for equivalence of hidden Markov processes and quantum random walks
U. Faigle; A. Schönhuth (Alexander)
2011-01-01
htmlabstractWhile two hidden Markov process (HMP) resp.~quantum random walk (QRW) parametrizations can differ from one another, the stochastic processes arising from them can be equivalent. Here a polynomial-time algorithm is presented which can determine equivalence of two HMP parametrizations
The supremuim of a negative drift random walk with dependent heavy-tailed steps
Mikosch, T; Smorodnitsky, G
Many important probabilistic models in queuing theory, insurance and finance deal with partial sums of a negative mean stationary process (a negative drift random walk), and the law of the supremum of such a process is used to calculate, depending on the context, the ruin probability, the steady
The invariant measure of random walks in the quarter-plane: respresentation in geometric terms
Chen, Y.; Boucherie, Richardus J.; Goseling, Jasper
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these linear combinations such that the resulting measure may
Continuous-time random walk as a guide to fractional Schroedinger equation
International Nuclear Information System (INIS)
Lenzi, E. K.; Ribeiro, H. V.; Mukai, H.; Mendes, R. S.
2010-01-01
We argue that the continuous-time random walk approach may be a useful guide to extend the Schroedinger equation in order to incorporate nonlocal effects, avoiding the inconsistencies raised by Jeng et al. [J. Math. Phys. 51, 062102 (2010)]. As an application, we work out a free particle in a half space, obtaining the time dependent solution by considering an arbitrary initial condition.
Necessary conditions for the invariant measure of a random walk to be a sum of geometric terms
Chen, Y.; Boucherie, Richardus J.; Goseling, Jasper
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as an infinite sum of geometric terms. We present necessary conditions for the invariant measure of a random walk to be a sum of geometric terms. We
Elavsky, Steriani; McAuley, Edward
2007-01-01
To examine the effects of walking and yoga on multidimensional self-esteem and roles played by self-efficacy, body composition, and physical activity (PA) in changes in esteem. Four-month randomized controlled exercise trial with three arms: walking, yoga, and control. Previously low-active middle-aged women (n=164; M age = 49.9; SD = 3.6). Structured and supervised walking program meeting three times per week for I hour and supervised yoga program meeting twice per week for 90 minutes. Body composition, fitness assessment, and battery of psychologic measures. Panel analysis within a structural equation modeling framework using Mplus 3.0. The walking and yoga interventions failed to enhance global or physical self-esteem but improved subdomain esteem relative to physical condition and strength (for walking) and body attractiveness (for both walking and yoga). Over time the effects of PA, self-efficacy, and body fat on changes in physical self-esteem and global esteem were mediated by changes in physical condition and body attractiveness subdomain esteem. Women reporting greater levels of self-efficacy and PA with lower body fat also reported greater enhancements in subdomain esteem. These results provide support for the hierarchic and multidimensional nature of self-esteem and indicate that middle-aged women may enhance certain aspects of physical self-esteem by participating in PA.
On the genealogy of branching random walks and of directed polymers
Derrida, Bernard; Mottishaw, Peter
2016-08-01
It is well known that the mean-field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite-size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks.
Brownian Motion Problem: Random Walk and Beyond -RE ...
Indian Academy of Sciences (India)
by their continuous bombardment by the surrounding molecules of much smaller size (Figure 1). This effect .... of continuous impacts of the randomly moving surround- ing molecules of the fluid (the 'npise'); (ii) these ..... ually increasing range of values due to integration and, thus, keeping it alive. Consequently, the observed ...
Directory of Open Access Journals (Sweden)
Burton Nicola W
2009-07-01
Full Text Available Abstract Background Interventions designed to increase workplace physical activity may not automatically reduce high volumes of sitting, a behaviour independently linked to chronic diseases such as obesity and type II diabetes. This study compared the impact two different walking strategies had on step counts and reported sitting times. Methods Participants were white-collar university employees (n = 179; age 41.3 ± 10.1 years; 141 women, who volunteered and undertook a standardised ten-week intervention at three sites. Pre-intervention step counts (Yamax SW-200 and self-reported sitting times were measured over five consecutive workdays. Using pre-intervention step counts, employees at each site were randomly allocated to a control group (n = 60; maintain normal behaviour, a route-based walking group (n = 60; at least 10 minutes sustained walking each workday or an incidental walking group (n = 59; walking in workday tasks. Workday step counts and reported sitting times were re-assessed at the beginning, mid- and endpoint of intervention and group mean± SD steps/day and reported sitting times for pre-intervention and intervention measurement points compared using a mixed factorial ANOVA; paired sample-t-tests were used for follow-up, simple effect analyses. Results A significant interactive effect (F = 3.5; p t = 3.9, p t = 2.5, p Conclusion Compared to controls, both route and incidental walking increased physical activity in white-collar employees. Our data suggests that workplace walking, particularly through incidental movement, also has the potential to decrease employee sitting times, but there is a need for on-going research using concurrent and objective measures of sitting, standing and walking.
Koschate, J; Drescher, U; Thieschäfer, L; Heine, O; Baum, K; Hoffmann, U
2016-12-01
This study aims to compare cardiorespiratory kinetics as a response to a standardised work rate protocol with pseudo-random binary sequences between cycling and walking in young healthy subjects. Muscular and pulmonary oxygen uptake (V̇O 2 ) kinetics as well as heart rate kinetics were expected to be similar for walking and cycling. Cardiac data and V̇O 2 of 23 healthy young subjects were measured in response to pseudo-random binary sequences. Kinetics were assessed applying time series analysis. Higher maxima of cross-correlation functions between work rate and the respective parameter indicate faster kinetics responses. Muscular V̇O 2 kinetics were estimated from heart rate and pulmonary V̇O 2 using a circulatory model. Muscular (walking vs. cycling [mean±SD in arbitrary units]: 0.40±0.08 vs. 0.41±0.08) and pulmonary V̇O 2 kinetics (0.35±0.06 vs. 0.35±0.06) were not different, although the time courses of the cross-correlation functions of pulmonary V̇O 2 showed unexpected biphasic responses. Heart rate kinetics (0.50±0.14 vs. 0.40±0.14; P=0.017) was faster for walking. Regarding the biphasic cross-correlation functions of pulmonary V̇O 2 during walking, the assessment of muscular V̇O 2 kinetics via pseudo-random binary sequences requires a circulatory model to account for cardio-dynamic distortions. Faster heart rate kinetics for walking should be considered by comparing results from cycle and treadmill ergometry. © Georg Thieme Verlag KG Stuttgart · New York.
Test of Random Walk Behavior in Karachi Stock Exchange
Directory of Open Access Journals (Sweden)
Muhammad Mudassar
2013-05-01
Full Text Available Study was carried out to check the random behavior of the Karachi Stock Exchange (KSE 100 Index during the period of past three financial years to know whether investors could generate abnormal profits during the period or otherwise. Tests used were Runs Test, ADF Test, PP Test and Autocorrelation Function Test. During the study it was found that the performance of KSE 100 Index remained in weak form of inefficiency and investors have been able to generate excessive returns on their investment most of the times.
Resonant scattering induced thermopower in one-dimensional disordered systems
Müller, Daniel; Smit, Wilbert J.; Sigrist, Manfred
2015-05-01
This study analyzes thermoelectric properties of a one-dimensional random conductor which shows localization effects and simultaneously includes resonant scatterers yielding sharp conductance resonances. These sharp features give rise to a distinct behavior of the Seebeck coefficient in finite systems and incorporate the degree of localization as a means to enhance thermoelectric performance, in principle. The model for noninteracting electrons is discussed within the Landauer-Büttiker formalism such that analytical treatment is possible for a wide range of properties, if a special averaging scheme is applied. The approximations in the averaging procedure are tested with numerical evaluations showing good qualitative agreement, with some limited quantitative disagreement. The validity of low-temperature Mott's formula is determined and a good approximation is developed for the intermediate temperature range. In both regimes the intricate interplay between Anderson localization due to disorder and conductance resonances of the disorder potential is analyzed.
Capillary condensation in one-dimensional irregular confinement.
Handford, Thomas P; Pérez-Reche, Francisco J; Taraskin, Sergei N
2013-07-01
A lattice-gas model with heterogeneity is developed for the description of fluid condensation in finite sized one-dimensional pores of arbitrary shape. Mapping to the random-field Ising model allows an exact solution of the model to be obtained at zero-temperature, reproducing the experimentally observed dependence of the amount of fluid adsorbed in the pore on external pressure. It is demonstrated that the disorder controls the sorption for long pores and can result in H2-type hysteresis. Finite-temperature Metropolis dynamics simulations support analytical findings in the limit of low temperatures. The proposed framework is viewed as a fundamental building block of the theory of capillary condensation necessary for reliable structural analysis of complex porous media from adsorption-desorption data.
Interacting Fermi gases in disordered one-dimensional lattices
International Nuclear Information System (INIS)
Xianlong, Gao; Polini, M.; Tosi, M. P.; Tanatar, B.
2006-01-01
Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subject to harmonic trapping exhibit intriguing compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a random potential on these ground-state phases. Within a density-functional scheme we show that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the compressibility at low density from quenching of percolation
Continuous-Time Random Walk with multi-step memory: an application to market dynamics
Gubiec, Tomasz; Kutner, Ryszard
2017-11-01
An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary number of successive jumps of the process while waiting times between jumps are considered as i.i.d. random variables. This dependence was established analyzing empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale. Then, it was justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model appeared exactly analytically solvable. Therefore, it enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus, the present research significantly extends capabilities of the CTRW formalism. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
MARCUSE’S ONE-DIMENSIONAL SOCIETY IN ONE-DIMENSIONAL MAN
Directory of Open Access Journals (Sweden)
MILOS RASTOVIC
2013-05-01
Full Text Available Nowadays, Marcuse’s main book One-Dimensional Man is almost obsolete, or rather passé. However, there are reasons to renew the reading of his book because of “the crisis of capitalism,” and the prevailing framework of technological domination in “advanced industrial society” in which we live today. “The new forms of control” in “advanced industrial societies” have replaced traditional methods of political and economic administration. The dominant structural element of “advanced industrial society” has become a technical and scientific apparatus of production and distribution of technology and administrative practice based on application of impersonal rules by a hierarchy of associating authorities. Technology has been liberated from the control of particular interests, and it has become the factor of domination in itself. Technological domination stems from the technical development of the productive apparatus that reproduces its ability into all spheres of social life (cultural, political, and economic. Based upon this consideration, in this paper, I will examine Marcuse’s ideas of “the new forms of control,” which creates a one–dimensional society. Marcuse’s fundamental thesis in One-Dimensional Man is that technological rationality is the most dominant factor in an “advanced industrial society,” which unites two earlier opposing forces of dissent: the bourgeoisie and the proletariat.
Correlated random walks induced by dynamical wavefunction collapse
Bedingham, Daniel
2015-03-01
Wavefunction collapse models modify Schrödinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a genuine physical process [PRA 42, 78 (1990)]. 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. Furthermore, the diffusions of two sufficiently nearby particles are positively correlated -- it is more likely that the particles diffuse in the same direction than would happen if they behaved independently [PRA 89, 032713 (2014)]. The use of this effect is proposed as an experimental test of wave function collapse models in which pairs of nanoparticles are simultaneously released from nearby traps and allowed a brief period of free fall. The random displacements of the particles are then measured. The experiment must be carried out at sufficiently low temperature and pressure 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 class of viable wavefunction collapse models. Work supported by the Templeton World Charity Foundation.
A random walk on water (Henry Darcy Medal Lecture)
Koutsoyiannis, D.
2009-04-01
Randomness and uncertainty had been well appreciated in hydrology and water resources engineering in their initial steps as scientific disciplines. However, this changed through the years and, following other geosciences, hydrology adopted a naïve view of randomness in natural processes. Such a view separates natural phenomena into two mutually exclusive types, random or stochastic, and deterministic. When a classification of a specific process into one of these two types fails, then a separation of the process into two different, usually additive, parts is typically devised, each of which may be further subdivided into subparts (e.g., deterministic subparts such as periodic and aperiodic or trends). This dichotomous logic is typically combined with a manichean perception, in which the deterministic part supposedly represents cause-effect relationships and thus is physics and science (the "good"), whereas randomness has little relationship with science and no relationship with understanding (the "evil"). Probability theory and statistics, which traditionally provided the tools for dealing with randomness and uncertainty, have been regarded by some as the "necessary evil" but not as an essential part of hydrology and geophysics. Some took a step further to banish them from hydrology, replacing them with deterministic sensitivity analysis and fuzzy-logic representations. Others attempted to demonstrate that irregular fluctuations observed in natural processes are au fond manifestations of underlying chaotic deterministic dynamics with low dimensionality, thus attempting to render probabilistic descriptions unnecessary. Some of the above recent developments are simply flawed because they make erroneous use of probability and statistics (which, remarkably, provide the tools for such analyses), whereas the entire underlying logic is just a false dichotomy. To see this, it suffices to recall that Pierre Simon Laplace, perhaps the most famous proponent of determinism in
An Experimental Study on Solute Transport in One-Dimensional Clay Soil Columns
Directory of Open Access Journals (Sweden)
Muhammad Zaheer
2017-01-01
Full Text Available Solute transport in low-permeability media such as clay has not been studied carefully up to present, and we are often unclear what the proper governing law is for describing the transport process in such media. In this study, we composed and analyzed the breakthrough curve (BTC data and the development of leaching in one-dimensional solute transport experiments in low-permeability homogeneous and saturated media at small scale, to identify key parameters controlling the transport process. Sodium chloride (NaCl was chosen to be the tracer. A number of tracer tests were conducted to inspect the transport process under different conditions. The observed velocity-time behavior for different columns indicated the decline of soil permeability when switching from tracer introducing to tracer flushing. The modeling approaches considered were the Advection-Dispersion Equation (ADE, Two-Region Model (TRM, Continuous Time Random Walk (CTRW, and Fractional Advection-Dispersion Equation (FADE. It was found that all the models can fit the transport process very well; however, ADE and TRM were somewhat unable to characterize the transport behavior in leaching. The CTRW and FADE models were better in capturing the full evaluation of tracer-breakthrough curve and late-time tailing in leaching.
Interrelations between random walks on diagrams (graphs) with and without cycles.
Hill, T L
1988-05-01
Three topics are discussed. A discrete-state, continuous-time random walk with one or more absorption states can be studied by a presumably new method: some mean properties, including the mean time to absorption, can be found from a modified diagram (graph) in which each absorption state is replaced by a one-way cycle back to the starting state. The second problem is a random walk on a diagram (graph) with cycles. The walk terminates on completion of the first cycle. This walk can be replaced by an equivalent walk on a modified diagram with absorption. This absorption diagram can in turn be replaced by another modified diagram with one-way cycles back to the starting state, just as in the first problem. The third problem, important in biophysics, relates to a long-time continuous walk on a diagram with cycles. This diagram can be transformed (in two steps) to a modified, more-detailed, diagram with one-way cycles only. Thus, the one-way cycle fluxes of the original diagram can be found from the state probabilities of the modified diagram. These probabilities can themselves be obtained by simple matrix inversion (the probabilities are determined by linear algebraic steady-state equations). Thus, a simple method is now available to find one-way cycle fluxes exactly (previously Monte Carlo simulation was required to find these fluxes, with attendant fluctuations, for diagrams of any complexity). An incidental benefit of the above procedure is that it provides a simple proof of the one-way cycle flux relation Jn +/- = IIn +/- sigma n/sigma, where n is any cycle of the original diagram.
Effective one-dimensionality of universal ac hopping conduction in the extreme disorder limit
DEFF Research Database (Denmark)
Dyre, Jeppe; Schrøder, Thomas
1996-01-01
A phenomenological picture of ac hopping in the symmetric hopping model (regular lattice, equal site energies, random energy barriers) is proposed according to which conduction in the extreme disorder limit is dominated by essentially one-dimensional "percolation paths." Modeling a percolation path...... as strictly one dimensional with a sharp jump rate cutoff leads to an expression for the universal ac conductivity that fits computer simulations in two and three dimensions better than the effective medium approximation....
Conformal invariance self-avoiding walks in the plane or on a random surface
International Nuclear Information System (INIS)
Duplantier, B.
1988-01-01
The two-dimensional (2D) properties of polymers embedded in a solvent, are studied. They are modeled on a lattice by self-avoiding walks. The polymer properties either in the plane with a fixed metric, or on a random 2D surface, where the metric has critical fluctuations, are considered. In the scope of the work, the following topics are discussed: the watermelon topology; the O(n) model and Coulomb gas technique; the model and critical behaviours of polymers on a two-dimensional random lattice; the conformal invariance in a random surface and higher topologies
International Nuclear Information System (INIS)
Xu Hao; Shi Tianjun
2011-01-01
In this article,the qualities of Wigner function and the corresponding stationary perturbation theory are introduced and applied to one-dimensional infinite potential well and one-dimensional harmonic oscillator, and then the particular Wigner function of one-dimensional infinite potential well is specified and a special constriction effect in its pure state Wigner function is discovered, to which,simultaneously, a detailed and reasonable explanation is elaborated from the perspective of uncertainty principle. Ultimately, the amendment of Wigner function and energy of one-dimensional infinite potential well and one-dimensional harmonic oscillator under perturbation are calculated according to stationary phase space perturbation theory. (authors)
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Moser, Martin
2013-01-01
We investigate the maximum increment of a random walk with heavy-tailed jump size distribution. Here heavy-tailedness is understood as regular variation of the finite-dimensional distributions. The jump sizes constitute a strictly stationary sequence. Using a continuous mapping argument acting...... on the point processes of the normalized jump sizes, we prove that the maximum increment of the random walk converges in distribution to a Fréchet distributed random variable....
Strategies in localization proofs for one-dimensional random ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
tools which are used to analyse these models are generalized spectral .... Thinking of pn rather than Xi as the defining parameters, we therefore have smoothness ...... Anderson model, where dynamical localization away from the critical ...
Continuous-time random walks on networks with vertex- and time-dependent forcing.
Angstmann, C N; Donnelly, I C; Henry, B I; Langlands, T A M
2013-08-01
We have investigated the transport of particles moving as random walks on the vertices of a network, subject to vertex- and time-dependent forcing. We have derived the generalized master equations for this transport using continuous time random walks, characterized by jump and waiting time densities, as the underlying stochastic process. The forcing is incorporated through a vertex- and time-dependent bias in the jump densities governing the random walking particles. As a particular case, we consider particle forcing proportional to the concentration of particles on adjacent vertices, analogous to self-chemotactic attraction in a spatial continuum. Our algebraic and numerical studies of this system reveal an interesting pair-aggregation pattern formation in which the steady state is composed of a high concentration of particles on a small number of isolated pairs of adjacent vertices. The steady states do not exhibit this pair aggregation if the transport is random on the vertices, i.e., without forcing. The manifestation of pair aggregation on a transport network may thus be a signature of self-chemotactic-like forcing.
Schauer, Michael; Mauritz, Karl-Heinz
2003-11-01
To demonstrate the effect of rhythmical auditory stimulation in a musical context for gait therapy in hemiparetic stroke patients, when the stimulation is played back measure by measure initiated by the patient's heel-strikes (musical motor feedback). Does this type of musical feedback improve walking more than a less specific gait therapy? The randomized controlled trial considered 23 registered stroke patients. Two groups were created by randomization: the control group received 15 sessions of conventional gait therapy and the test group received 15 therapy sessions with musical motor feedback. Inpatient rehabilitation hospital. Median post-stroke interval was 44 days and the patients were able to walk without technical aids with a speed of approximately 0.71 m/s. Gait velocity, step duration, gait symmetry, stride length and foot rollover path length (heel-on-toe-off distance). The test group showed more mean improvement than the control group: stride length increased by 18% versus 0%, symmetry deviation decreased by 58% versus 20%, walking speed increased by 27% versus 4% and rollover path length increased by 28% versus 11%. Musical motor feedback improves the stroke patient's walk in selected parameters more than conventional gait therapy. A fixed memory in the patient's mind about the song and its timing may stimulate the improvement of gait even without the presence of an external pacemaker.
International Nuclear Information System (INIS)
Musho, M.K.; Kozak, J.J.
1984-01-01
A method is presented for calculating exactly the relative width (sigma 2 )/sup 1/2// , the skewness γ 1 , and the kurtosis γ 2 characterizing the probability distribution function for three random-walk models of diffusion-controlled processes. For processes in which a diffusing coreactant A reacts irreversibly with a target molecule B situated at a reaction center, three models are considered. The first is the traditional one of an unbiased, nearest-neighbor random walk on a d-dimensional periodic/confining lattice with traps; the second involves the consideration of unbiased, non-nearest-neigh bor (i.e., variable-step length) walks on the same d-dimensional lattice; and, the third deals with the case of a biased, nearest-neighbor walk on a d-dimensional lattice (wherein a walker experiences a potential centered at the deep trap site of the lattice). Our method, which has been described in detail elsewhere [P.A. Politowicz and J. J. Kozak, Phys. Rev. B 28, 5549 (1983)] is based on the use of group theoretic arguments within the framework of the theory of finite Markov processes
Exploring topological phases with quantum walks
International Nuclear Information System (INIS)
Kitagawa, Takuya; Rudner, Mark S.; Berg, Erez; Demler, Eugene
2010-01-01
The quantum walk was originally proposed as a quantum-mechanical analog of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete-time quantum walks provide a versatile platform for studying topological phases, which are currently the subject of intense theoretical and experimental investigations. In particular, we demonstrate that recent experimental realizations of quantum walks with cold atoms, photons, and ions simulate a nontrivial one-dimensional topological phase. With simple modifications, the quantum walk can be engineered to realize all of the topological phases, which have been classified in one and two dimensions. We further discuss the existence of robust edge modes at phase boundaries, which provide experimental signatures for the nontrivial topological character of the system.
A partially reflecting random walk on spheres algorithm for electrical impedance tomography
Energy Technology Data Exchange (ETDEWEB)
Maire, Sylvain, E-mail: maire@univ-tln.fr [Laboratoire LSIS Equipe Signal et Image, Université du Sud Toulon-Var, Av. Georges Pompidou, BP 56, 83162 La Valette du Var Cedex (France); Simon, Martin, E-mail: simon@math.uni-mainz.de [Institute of Mathematics, Johannes Gutenberg University, 55099 Mainz (Germany)
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.
The continuous time random walk, still trendy: fifty-year history, state of art and outlook
Kutner, Ryszard; Masoliver, Jaume
2017-03-01
In this article we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism, the numerous modifications permitted by its flexibility, its various applications, and the promising perspectives in the various fields of knowledge. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We focused on a pivotal role of CTRWs mainly in anomalous stochastic processes discovered in physics and beyond. This article plays the role of an extended announcement of the Eur. Phys. J. B Special Issue [open-calls-for-papers/123-epj-b/1090-ctrw-50-years-on">http://epjb.epj.org/open-calls-for-papers/123-epj-b/1090-ctrw-50-years-on] containing articles which show incredible possibilities of the CTRWs. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Random walk, diffusion and mixing in simulations of scalar transport in fluid flows
International Nuclear Information System (INIS)
Klimenko, A Y
2008-01-01
Physical similarity and mathematical equivalence of continuous diffusion and particle random walk form one of the cornerstones of modern physics and the theory of stochastic processes. In many applied models used in simulation of turbulent transport and turbulent combustion, mixing between particles is used to reflect the influence of the continuous diffusion terms in the transport equations. We show that the continuous scalar transport and diffusion can be accurately specified by means of mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme. This gives an alternative formulation for the stochastic process which is selected to represent the continuous diffusion. This paper focuses on statistical errors and deals with relatively simple cases, where one-particle distributions are sufficient for a complete description of the problem.
Effective degrees of freedom of a random walk on a fractal
Balankin, Alexander S.
2015-12-01
We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.
Stationary Probability and First-Passage Time of Biased Random Walk
International Nuclear Information System (INIS)
Li Jing-Wen; Tang Shen-Li; Xu Xin-Ping
2016-01-01
In this paper, we consider the stationary probability and first-passage time of biased random walk on 1D chain, where at each step the walker moves to the left and right with probabilities p and q respectively (0 ⩽ p, q ⩽ 1, p + q = 1). We derive exact analytical results for the stationary probability and first-passage time as a function of p and q for the first time. Our results suggest that the first-passage time shows a double power-law F ∼ (N − 1) γ , where the exponent γ = 2 for N < |p − q| −1 and γ = 1 for N > |p − q| −1 . Our study sheds useful insights into the biased random-walk process. (paper)
The area distribution of two-dimensional random walks and non-Hermitian Hofstadter quantum mechanics
International Nuclear Information System (INIS)
Matveenko, Sergey; Ouvry, Stéphane
2014-01-01
When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be obtained exactly (Mashkevich and Ouvry 2009 J. Stat. Phys. 137 71). We explicitly map this biased classical random system onto a non-Hermitian Hofstadter-like quantum model where a charged particle on a square lattice coupled to a perpendicular magnetic field hops only to the right. For the commensurate case, when the magnetic flux per unit cell is rational, an exact solution of the quantum model is obtained. The periodicity of the lattice allows one to relate traces of the Nth power of the Hamiltonian to probability distribution generating functions of biased walks of length N. (paper)
Effects of systematic phase errors on optimized quantum random-walk search algorithm
International Nuclear Information System (INIS)
Zhang Yu-Chao; Bao Wan-Su; Wang Xiang; Fu Xiang-Qun
2015-01-01
This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover’s algorithm. (paper)
On properties of continuous-time random walks with non-Poissonian jump-times
International Nuclear Information System (INIS)
Villarroel, Javier; Montero, Miquel
2009-01-01
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary time by recourse to renewal theory. The case of Erlang distributed times is analyzed in detail. Several concrete examples are considered.
Angular Random Walk Estimation of a Time-Domain Switching Micromachined Gyroscope
2016-10-19
angular random walk (ARW), bias instability, and scale factor instability. While there are methods to address issues with bias and scale factor...effects. Thus, it is expected that it will have low bias and scale factor instabilities. Simulated ARW performance of a particular incarnation of the...1 2. PARAMETRIC SYSTEM IDENTIFICATION BASED ON TIME-DOMAIN SWITCHING ........ 2 3. FINITE ELEMENT MODELING OF RESONATOR
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…
Accumulator and random-walk models of psychophysical discrimination: a counter-evaluation.
Vickers, D; Smith, P
1985-01-01
In a recent assessment of models of psychophysical discrimination, Heath criticises the accumulator model for its reliance on computer simulation and qualitative evidence, and contrasts it unfavourably with a modified random-walk model, which yields exact predictions, is susceptible to critical test, and is provided with simple parameter-estimation techniques. A counter-evaluation is presented, in which the approximations employed in the modified random-walk analysis are demonstrated to be seriously inaccurate, the resulting parameter estimates to be artefactually determined, and the proposed test not critical. It is pointed out that Heath's specific application of the model is not legitimate, his data treatment inappropriate, and his hypothesis concerning confidence inconsistent with experimental results. Evidence from adaptive performance changes is presented which shows that the necessary assumptions for quantitative analysis in terms of the modified random-walk model are not satisfied, and that the model can be reconciled with data at the qualitative level only by making it virtually indistinguishable from an accumulator process. A procedure for deriving exact predictions for an accumulator process is outlined.
Distributed clone detection in static wireless sensor networks: random walk with network division.
Khan, Wazir Zada; Aalsalem, Mohammed Y; Saad, N M
2015-01-01
Wireless Sensor Networks (WSNs) are vulnerable to clone attacks or node replication attacks as they are deployed in hostile and unattended environments where they are deprived of physical protection, lacking physical tamper-resistance of sensor nodes. As a result, an adversary can easily capture and compromise sensor nodes and after replicating them, he inserts arbitrary number of clones/replicas into the network. If these clones are not efficiently detected, an adversary can be further capable to mount a wide variety of internal attacks which can emasculate the various protocols and sensor applications. Several solutions have been proposed in the literature to address the crucial problem of clone detection, which are not satisfactory as they suffer from some serious drawbacks. In this paper we propose a novel distributed solution called Random Walk with Network Division (RWND) for the detection of node replication attack in static WSNs which is based on claimer-reporter-witness framework and combines a simple random walk with network division. RWND detects clone(s) by following a claimer-reporter-witness framework and a random walk is employed within each area for the selection of witness nodes. Splitting the network into levels and areas makes clone detection more efficient and the high security of witness nodes is ensured with moderate communication and memory overheads. Our simulation results show that RWND outperforms the existing witness node based strategies with moderate communication and memory overheads.
Empirical scaling of the length of the longest increasing subsequences of random walks
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.
Distributed clone detection in static wireless sensor networks: random walk with network division.
Directory of Open Access Journals (Sweden)
Wazir Zada Khan
Full Text Available Wireless Sensor Networks (WSNs are vulnerable to clone attacks or node replication attacks as they are deployed in hostile and unattended environments where they are deprived of physical protection, lacking physical tamper-resistance of sensor nodes. As a result, an adversary can easily capture and compromise sensor nodes and after replicating them, he inserts arbitrary number of clones/replicas into the network. If these clones are not efficiently detected, an adversary can be further capable to mount a wide variety of internal attacks which can emasculate the various protocols and sensor applications. Several solutions have been proposed in the literature to address the crucial problem of clone detection, which are not satisfactory as they suffer from some serious drawbacks. In this paper we propose a novel distributed solution called Random Walk with Network Division (RWND for the detection of node replication attack in static WSNs which is based on claimer-reporter-witness framework and combines a simple random walk with network division. RWND detects clone(s by following a claimer-reporter-witness framework and a random walk is employed within each area for the selection of witness nodes. Splitting the network into levels and areas makes clone detection more efficient and the high security of witness nodes is ensured with moderate communication and memory overheads. Our simulation results show that RWND outperforms the existing witness node based strategies with moderate communication and memory overheads.
Bridging Weighted Rules and Graph Random Walks for Statistical Relational Models
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Seyed Mehran Kazemi
2018-02-01
Full Text Available The aim of statistical relational learning is to learn statistical models from relational or graph-structured data. Three main statistical relational learning paradigms include weighted rule learning, random walks on graphs, and tensor factorization. These paradigms have been mostly developed and studied in isolation for many years, with few works attempting at understanding the relationship among them or combining them. In this article, we study the relationship between the path ranking algorithm (PRA, one of the most well-known relational learning methods in the graph random walk paradigm, and relational logistic regression (RLR, one of the recent developments in weighted rule learning. We provide a simple way to normalize relations and prove that relational logistic regression using normalized relations generalizes the path ranking algorithm. This result provides a better understanding of relational learning, especially for the weighted rule learning and graph random walk paradigms. It opens up the possibility of using the more flexible RLR rules within PRA models and even generalizing both by including normalized and unnormalized relations in the same model.
Mannerkorpi, Kaisa; Nordeman, Lena; Cider, ?sa; Jonsson, Gunilla
2010-01-01
Introduction The objective of this study was to investigate the effects of moderate-to-high intensity Nordic walking (NW) on functional capacity and pain in fibromyalgia (FM). Methods A total of 67 women with FM were recruited to the study and randomized either to moderate-to-high intensity Nordic Walking (n = 34, age 48 ? 7.8 years) or to a control group engaging in supervised low-intensity walking (LIW, n = 33, age 50 ? 7.6 years). Primary outcomes were the six-minute walk test (6MWT) and t...
Random walks in nanotube composites: Improved algorithms and the role of thermal boundary resistance
International Nuclear Information System (INIS)
Duong, Hai M.; Papavassiliou, Dimitrios V.; Lee, Lloyd L.; Mullen, Kieran J.
2005-01-01
Random walk simulations of thermal walkers are used to study the effect of interfacial resistance on heat flow in randomly dispersed carbon nanotube composites. The adopted algorithm effectively makes the thermal conductivity of the nanotubes themselves infinite. The probability that a walker colliding with a matrix-nanotube interface reflects back into the matrix phase or crosses into the carbon nanotube phase is determined by the thermal boundary (Kapitza) resistance. The use of 'cold' and 'hot' walkers produces a steady state temperature profile that allows accurate determination of the thermal conductivity. The effects of the carbon nanotube orientation, aspect ratio, volume fraction, and Kapitza resistance on the composite effective conductivity are quantified
Random Walk Model for Cell-To-Cell Misalignments in Accelerator Structures
International Nuclear Information System (INIS)
Stupakov, Gennady
2000-01-01
Due to manufacturing and construction errors, cells in accelerator structures can be misaligned relative to each other. As a consequence, the beam generates a transverse wakefield even when it passes through the structure on axis. The most important effect is the long-range transverse wakefield that deflects the bunches and causes growth of the bunch train projected emittance. In this paper, the effect of the cell-to-cell misalignments is evaluated using a random walk model that assumes that each cell is shifted by a random step relative to the previous one. The model is compared with measurements of a few accelerator structures
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
Vamos, C; Vereecken, H
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
International Nuclear Information System (INIS)
Vamos, Calin; Suciu, Nicolae; Vereecken, Harry
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested
Random-walk approach to the d -dimensional disordered Lorentz gas
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.
Distribution of sizes of erased loops for loop-erased random walks
Dhar, Deepak; Dhar, Abhishek
1997-01-01
We study the distribution of sizes of erased loops for loop-erased random walks on regular and fractal lattices. We show that for arbitrary graphs the probability $P(l)$ of generating a loop of perimeter $l$ is expressible in terms of the probability $P_{st}(l)$ of forming a loop of perimeter $l$ when a bond is added to a random spanning tree on the same graph by the simple relation $P(l)=P_{st}(l)/l$. On $d$-dimensional hypercubical lattices, $P(l)$ varies as $l^{-\\sigma}$ for large $l$, whe...
GLOBAL RANDOM WALK SIMULATIONS FOR SENSITIVITY AND UNCERTAINTY ANALYSIS OF PASSIVE TRANSPORT MODELS
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Nicolae Suciu
2011-07-01
Full Text Available The Global Random Walk algorithm (GRW performs a simultaneoustracking on a fixed grid of huge numbers of particles at costscomparable to those of a single-trajectory simulation by the traditional Particle Tracking (PT approach. Statistical ensembles of GRW simulations of a typical advection-dispersion process in groundwater systems with randomly distributed spatial parameters are used to obtain reliable estimations of the input parameters for the upscaled transport model and of their correlations, input-output correlations, as well as full probability distributions of the input and output parameters.
Combs-Miller, Stephanie A; Kalpathi Parameswaran, Anu; Colburn, Dawn; Ertel, Tara; Harmeyer, Amanda; Tucker, Lindsay; Schmid, Arlene A
2014-09-01
To compare the effects of body weight-supported treadmill training and overground walking training when matched for task and dose (duration/frequency/intensity) on improving walking function, activity, and participation after stroke. Single-blind, pilot randomized controlled trial with three-month follow-up. University and community settings. A convenience sample of participants (N = 20) at least six months post-stroke and able to walk independently were recruited. Thirty-minute walking interventions (body weight-supported treadmill training or overground walking training) were administered five times a week for two weeks. Intensity was monitored with the Borg Rating of Perceived Exertion Scale at five-minute increments to maintain a moderate training intensity. Walking speed (comfortable/fast 10-meter walk), walking endurance (6-minute walk), spatiotemporal symmetry, and the ICF Measure of Participation and ACTivity were assessed before, immediately after, and three months following the intervention. The overground walking training group demonstrated significantly greater improvements in comfortable walking speed compared with the body weight-supported treadmill training group immediately (change of 0.11 m/s vs. 0.06 m/s, respectively; p = 0.047) and three months (change of 0.14 m/s vs. 0.08 m/s, respectively; p = 0.029) after training. Only the overground walking training group significantly improved comfortable walking speed (p = 0.001), aspects of gait symmetry (p = 0.032), and activity (p = 0.003) immediately after training. Gains were maintained at the three-month follow-up (p training was more beneficial than body weight-supported treadmill training at improving self-selected walking speed for the participants in this study. © The Author(s) 2014.
A novel Random Walk algorithm with Compulsive Evolution for heat exchanger network synthesis
International Nuclear Information System (INIS)
Xiao, Yuan; Cui, Guomin
2017-01-01
Highlights: • A novel Random Walk Algorithm with Compulsive Evolution is proposed for HENS. • A simple and feasible evolution strategy is presented in RWCE algorithm. • The integer and continuous variables of HEN are optimized simultaneously in RWCE. • RWCE is demonstrated a relatively strong global search ability in HEN optimization. - Abstract: The heat exchanger network (HEN) synthesis can be characterized as highly combinatorial, nonlinear and nonconvex, contributing to unmanageable computational time and a challenge in identifying the global optimal network design. Stochastic methods are robust and show a powerful global optimizing ability. Based on the common characteristic of different stochastic methods, namely randomness, a novel Random Walk algorithm with Compulsive Evolution (RWCE) is proposed to achieve the best possible total annual cost of heat exchanger network with the relatively simple and feasible evolution strategy. A population of heat exchanger networks is first randomly initialized. Next, the heat load of heat exchanger for each individual is randomly expanded or contracted in order to optimize both the integer and continuous variables simultaneously and to obtain the lowest total annual cost. Besides, when individuals approach to local optima, there is a certain probability for them to compulsively accept the imperfect networks in order to keep the population diversity and ability of global optimization. The presented method is then applied to heat exchanger network synthesis cases from the literature to compare the best results published. RWCE consistently has a lower computed total annual cost compared to previously published results.
A correlated Walks' theory for DNA denaturation
International Nuclear Information System (INIS)
Mejdani, R.
1994-08-01
We have shown that by using a correlated Walks' theory for the lattice gas model on a one-dimensional lattice, we can study, beside the saturation curves obtained before for the enzyme kinetics, also the DNA denaturation process. In the limit of no interactions between sites the equation for melting curves of DNA reduces to the random model equation. Thus our leads naturally to this classical equation in the limiting case. (author). 22 refs, 3 figs
Study of one dimensional magnetic system via field theory
International Nuclear Information System (INIS)
Talim, S.L.
1988-04-01
We present a study of one-dimensional magnetic system using field theory methods. We studied the discreteness effects in a classical anisotropic one dimensional antiferromagnet in an external magnetic field. It is shown that for TMMC, at the temperatures and magnetic fields where most experiments have been done, the corrections are small and can be neglected. (author)
Merom, Dafna; Grunseit, Anne; Eramudugolla, Ranmalee; Jefferis, Barbara; Mcneill, Jade; Anstey, Kaarin J
2016-01-01
A physically active lifestyle has the potential to prevent cognitive decline and dementia, yet the optimal type of physical activity/exercise remains unclear. Dance is of special interest as it complex sensorimotor rhythmic activity with additional cognitive, social, and affective dimensions. To determine whether dance benefits executive function more than walking, an activity that is simple and functional. Two-arm randomized controlled trial among community-dwelling older adults. The intervention group received 1 h of ballroom dancing twice weekly over 8 months (~69 sessions) in local community dance studios. The control group received a combination of a home walking program with a pedometer and optional biweekly group-based walking in local community park to facilitate socialization. Executive function tests: processing speed and task shift by the Trail Making Tests, response inhibition by the Stroop Color-Word Test, working memory by the Digit Span Backwards test, immediate and delayed verbal recall by the Rey Auditory Verbal Learning Test, and visuospatial recall by the Brief Visuospatial Memory Test (BVST). One hundred and fifteen adults (mean 69.5 years, SD 6.4) completed baseline and delayed baseline (3 weeks apart) before being randomized to either dance (n = 60) or walking (n = 55). Of those randomized, 79 (68%) completed the follow-up measurements (32 weeks from baseline). In the dance group only, "non-completers" had significantly lower baseline scores on all executive function tests than those who completed the full program. Intention-to-treat analyses showed no group effect. In a random effects model including participants who completed all measurements, adjusted for baseline score and covariates (age, education, estimated verbal intelligence, and community), a between-group effect in favor of dance was noted only for BVST total learning (Cohen's D Effect size 0.29, p = 0.07) and delayed recall (Cohen's D Effect size = 0
Banck-Petersen, Anna; Olsen, Cecilie K; Djurhuus, Sissal S; Herrstedt, Anita; Thorsen-Streit, Sarah; Ried-Larsen, Mathias; Østerlind, Kell; Osterkamp, Jens; Krarup, Peter-Martin; Vistisen, Kirsten; Mosgaard, Camilla S; Pedersen, Bente K; Højman, Pernille; Christensen, Jesper F
2018-03-01
Low physical activity level is associated with poor prognosis in patients with colorectal cancer (CRC). To increase physical activity, technology-based platforms are emerging and provide intriguing opportunities to prescribe and monitor active lifestyle interventions. The "Interval Walking in Colorectal Cancer"(I-WALK-CRC) study explores the feasibility and efficacy a home-based interval-walking intervention delivered by a smart-phone application in order to improve cardio-metabolic health profile among CRC survivors. The aim of the present report is to describe the design, methods and recruitment results of the I-WALK-CRC study.Methods/Results: The I-WALK-CRC study is a randomized controlled trial designed to evaluate the feasibility and efficacy of a home-based interval walking intervention compared to a waiting-list control group for physiological and patient-reported outcomes. Patients who had completed surgery for local stage disease and patients who had completed surgery and any adjuvant chemotherapy for locally advanced stage disease were eligible for inclusion. Between October 1st , 2015, and February 1st , 2017, 136 inquiries were recorded; 83 patients were eligible for enrollment, and 42 patients accepted participation. Age and employment status were associated with participation, as participants were significantly younger (60.5 vs 70.8 years, P CRC survivors was feasible but we aim to better the recruitment rate in future studies. Further, the study clearly favored younger participants. The I-WALK-CRC study will provide important information regarding feasibility and efficacy of a home-based walking exercise program in CRC survivors.
A random walk model for evaluating clinical trials involving serial observations.
Hopper, J L; Young, G P
1988-05-01
For clinical trials where the variable of interest is ordered and categorical (for example, disease severity, symptom scale), and where measurements are taken at intervals, it might be possible to achieve a greater discrimination between the efficacy of treatments by modelling each patient's progress as a stochastic process. The random walk is a simple, easily interpreted model that can be fitted by maximum likelihood using a maximization routine with inference based on standard likelihood theory. In general the model can allow for randomly censored data, incorporates measured prognostic factors, and inference is conditional on the (possibly non-random) allocation of patients. Tests of fit and of model assumptions are proposed, and application to two therapeutic trials of gastroenterological disorders are presented. The model gave measures of the rate of, and variability in, improvement for patients under different treatments. A small simulation study suggested that the model is more powerful than considering the difference between initial and final scores, even when applied to data generated by a mechanism other than the random walk model assumed in the analysis. It thus provides a useful additional statistical method for evaluating clinical trials.
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.
Ma, Tianren; Xia, Zhengyou
2017-05-01
Currently, with the rapid development of information technology, the electronic media for social communication is becoming more and more popular. Discovery of communities is a very effective way to understand the properties of complex networks. However, traditional community detection algorithms consider the structural characteristics of a social organization only, with more information about nodes and edges wasted. In the meanwhile, these algorithms do not consider each node on its merits. Label propagation algorithm (LPA) is a near linear time algorithm which aims to find the community in the network. It attracts many scholars owing to its high efficiency. In recent years, there are more improved algorithms that were put forward based on LPA. In this paper, an improved LPA based on random walk and node importance (NILPA) is proposed. Firstly, a list of node importance is obtained through calculation. The nodes in the network are sorted in descending order of importance. On the basis of random walk, a matrix is constructed to measure the similarity of nodes and it avoids the random choice in the LPA. Secondly, a new metric IAS (importance and similarity) is calculated by node importance and similarity matrix, which we can use to avoid the random selection in the original LPA and improve the algorithm stability. Finally, a test in real-world and synthetic networks is given. The result shows that this algorithm has better performance than existing methods in finding community structure.
Testing self-regulation interventions to increase walking using factorial randomized N-of-1 trials.
Sniehotta, Falko F; Presseau, Justin; Hobbs, Nicola; Araújo-Soares, Vera
2012-11-01
To investigate the suitability of N-of-1 randomized controlled trials (RCTs) as a means of testing the effectiveness of behavior change techniques based on self-regulation theory (goal setting and self-monitoring) for promoting walking in healthy adult volunteers. A series of N-of-1 RCTs in 10 normal and overweight adults ages 19-67 (M = 36.9 years). We randomly allocated 60 days within each individual to text message-prompted daily goal-setting and/or self-monitoring interventions in accordance with a 2 (step-count goal prompt vs. alternative goal prompt) × 2 (self-monitoring: open vs. blinded Omron-HJ-113-E pedometer) factorial design. Aggregated data were analyzed using random intercept multilevel models. Single cases were analyzed individually. The primary outcome was daily pedometer step counts over 60 days. Single-case analyses showed that 4 participants significantly increased walking: 2 on self-monitoring days and 2 on goal-setting days, compared with control days. Six participants did not benefit from the interventions. In aggregated analyses, mean step counts were higher on goal-setting days (8,499.9 vs. 7,956.3) and on self-monitoring days (8,630.3 vs. 7,825.9). Multilevel analyses showed a significant effect of the self-monitoring condition (p = .01), the goal-setting condition approached significance (p = .08), and there was a small linear increase in walking over time (p = .03). N-of-1 randomized trials are a suitable means to test behavioral interventions in individual participants.
Randomized controlled trial of physical activity, cognition, and walking in multiple sclerosis.
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.
Magnetic ordering in arrays of one-dimensional nanoparticle chains
International Nuclear Information System (INIS)
Serantes, D; Baldomir, D; Pereiro, M; Hernando, B; Prida, V M; Sanchez Llamazares, J L; Zhukov, A; Ilyn, M; Gonzalez, J
2009-01-01
The magnetic order in parallel-aligned one-dimensional (1D) chains of magnetic nanoparticles is studied using a Monte Carlo technique. If the easy anisotropy axes are collinear along the chains a macroscopic mean-field approach indicates antiferromagnetic (AFM) order even when no interparticle interactions are taken into account, which evidences that a mean-field treatment is inadequate for the study of the magnetic order in these highly anisotropic systems. From the direct microscopic analysis of the evolution of the magnetic moments, we observe spontaneous intra-chain ferromagnetic (FM)-type and inter-chain AFM-type ordering at low temperatures (although not completely regular) for the easy-axes collinear case, whereas a random distribution of the anisotropy axes leads to a sort of intra-chain AFM arrangement with no inter-chain regular order. When the magnetic anisotropy is neglected a perfectly regular intra-chain FM-like order is attained. Therefore it is shown that the magnetic anisotropy, and particularly the spatial distribution of the easy axes, is a key parameter governing the magnetic ordering type of 1D-nanoparticle chains.
Quantitative characterisation of an engineering write-up using random walk analysis
Directory of Open Access Journals (Sweden)
Sunday A. Oke
2008-02-01
Full Text Available This contribution reports on the investigation of correlation properties in an English scientific text (engineering write-up by means of a random walk. Though the idea to use a random walk to characterise correlations is not new (it was used e.g. in the genome analysis and in the analysis of texts, a random walk approach to the analysis of an English scientific text is still far from being exploited in its full strength as demonstrated in this paper. A method of high-dimensional embedding is proposed. Case examples were drawn arbitrarily from four engineering write-ups (Ph.D. synopsis of three engineering departments in the Faculty of Technology, University of Ibadan, Nigeria. Thirteen additional analyses of non-engineering English texts were made and the results compared to the engineering English texts. Thus, a total of seventeen write-ups of eight Faculties and sixteen Departments of the University of Ibadan were considered. The characterising exponents which relate the average distance of random walkers away from a known starting position to the elapsed time steps were estimated for the seventeen cases according to the power law and in three different dimensional spaces. The average characteristic exponent obtained for the seventeen cases and over three different dimensional spaces studied was 1.42 to 2-decimal with a minimum and a maximum coefficient of determination (R2 of 0.9495 and 0.9994 respectively. This is found to be 284% of the average characterising exponent value (0.5, as supported by the literature for random walkers based on the pseudo-random number generator. The average characteristic exponent obtained for the four cases that were engineering-based and over the three different dimensional studied spaces was 1.41 to 2-decimal (closer by 99.3% to 1.42 with a minimum and a maximum coefficient of determination (R2 of 0.9507 and 0.9974 respectively. This is found to be 282% of the average characterising exponent value (0.5, as
Intra-fraction motion of the prostate is a random walk
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 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 isocenter during a fraction, and
Intra-fraction motion of the prostate is a random walk
International Nuclear Information System (INIS)
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 (r 2 = 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
Taniguchi, Chie; Sato, Chifumi
2016-10-01
We examined the effects of home-based walking on sedentary Japanese women's pregnancy outcomes and mood. A randomized controlled trial was conducted, involving 118 women aged 22-36 years. Participants were randomly assigned to walking intervention (n = 60) or control (n = 58) groups. The walking group was instructed to walk briskly for 30 min, three times weekly from 30 weeks' gestation until delivery. Both groups counted their daily steps using pedometers. Pregnancy and delivery outcomes were assessed, participants completed the Profile of Mood States, and we used the intention-to-treat principle. Groups showed no differences regarding pregnancy or delivery outcomes. The walking group exhibited decreased scores on the depression-dejection and confusion subscales of the Profile of Mood States. Five of the 54 women in the intervention group who remained in the study (9.2%) completed 100% of the prescribed walking program; 32 (59.3%) women completed 80% or more. Unsupervised walking improves sedentary pregnant women's mood, indicating that regular walking during pregnancy should be promoted in this group. © 2016 John Wiley & Sons Australia, Ltd.
RETRAN-02 one-dimensional kinetics model: a review
International Nuclear Information System (INIS)
Gose, G.C.; McClure, J.A.
1986-01-01
RETRAN-02 is a modular code system that has been designed for one-dimensional, transient thermal-hydraulics analysis. In RETRAN-02, core power behavior may be treated using a one-dimensional reactor kinetics model. This model allows the user to investigate the interaction of time- and space-dependent effects in the reactor core on overall system behavior for specific LWR operational transients. The purpose of this paper is to review the recent analysis and development activities related to the one dimensional kinetics model in RETRAN-02
Plasma properties of quasi-one-dimensional ring
Shmelev, G M
2001-01-01
The plasma properties of the quasi-one-dimensional ring in the threshold cases of low and high frequencies, corresponding to the plasma oscillations and dielectric relaxation are studied within the frames of the classical approach. The plasma oscillations spectrum and the electron dielectric relaxation frequency in the quasi-one-dimensional ring are calculated. The plasmons spectrum equidistance is identified. It is shown , that in contrast to the three-dimensional case there takes place the dielectric relaxation dispersion, wherefrom there follows the possibility of studying the carriers distribution in the quasi-one-dimensional rings through the method of the dielectric relaxation spectroscopy
Geometrically biased random walks in bacteria-driven micro-shuttles
International Nuclear Information System (INIS)
Angelani, Luca; Di Leonardo, Roberto
2010-01-01
Micron-sized objects having asymmetric boundaries can rectify the chaotic motions of an active bacterial suspension and perform geometrically biased random walks. Using numerical simulations in a planar geometry, we show that arrow-shaped micro-shuttles, constrained to move in one dimension (1D) in a bath of self-propelled micro-organisms, spontaneously perform unidirectional translational motions with a strongly shape-dependent speed. Relaxing the 1D constraint, a random motion in the whole plane sets in at long times, due to random changes in shuttle orientation caused by bacterial collisions. The complex dynamics arising from the mechanical interactions between bacteria and the object boundaries can be described by a Gaussian stochastic force with a shape-dependent mean and a self-correlation decaying exponentially on the timescale of seconds.
Fractal spectra in generalized Fibonacci one-dimensional magnonic quasicrystals
Energy Technology Data Exchange (ETDEWEB)
Costa, C.H.O. [Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio grande do Norte, 59072-970 Natal-RN (Brazil); Vasconcelos, M.S., E-mail: manoelvasconcelos@yahoo.com.br [Escola de Ciencias e Tecnologia, Universidade Federal do Rio grande do Norte, 59072-970 Natal-RN (Brazil); Barbosa, P.H.R.; Barbosa Filho, F.F. [Departamento de Fisica, Universidade Federal do Piaui, 64049-550 Teresina-Pi (Brazil)
2012-07-15
In this work we carry out a theoretical analysis of the spectra of magnons in quasiperiodic magnonic crystals arranged in accordance with generalized Fibonacci sequences in the exchange regime, by using a model based on a transfer-matrix method together random-phase approximation (RPA). The generalized Fibonacci sequences are characterized by an irrational parameter {sigma}(p,q), which rules the physical properties of the system. We discussed the magnonic fractal spectra for first three generalizations, i.e., silver, bronze and nickel mean. By varying the generation number, we have found that the fragmentation process of allowed bands makes possible the emergence of new allowed magnonic bulk bands in spectra regions that were magnonic band gaps before, such as which occurs in doped semiconductor devices. This interesting property arises in one-dimensional magnonic quasicrystals fabricated in accordance to quasiperiodic sequences, without the need to introduce some deferent atomic layer or defect in the system. We also make a qualitative and quantitative investigations on these magnonic spectra by analyzing the distribution and magnitude of allowed bulk bands in function of the generalized Fibonacci number F{sub n} and as well as how they scale as a function of the number of generations of the sequences, respectively. - Highlights: Black-Right-Pointing-Pointer Quasiperiodic magnonic crystals are arranged in accordance with the generalized Fibonacci sequence. Black-Right-Pointing-Pointer Heisenberg model in exchange regime is applied. Black-Right-Pointing-Pointer We use a theoretical model based on a transfer-matrix method together random-phase approximation. Black-Right-Pointing-Pointer Fractal spectra are characterized. Black-Right-Pointing-Pointer We analyze the distribution of allowed bulk bands in function of the generalized Fibonacci number.
Applications of a general random-walk theory for confined diffusion.
Calvo-Muñoz, Elisa M; Selvan, Myvizhi Esai; Xiong, Ruichang; Ojha, Madhusudan; Keffer, David J; Nicholson, Donald M; Egami, Takeshi
2011-01-01
A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.
Random-walk simulation of diffusion-controlled processes among static traps
International Nuclear Information System (INIS)
Lee, S.B.; Kim, I.C.; Miller, C.A.; Torquato, S.; Department of Mechanical and Aerospace Engineering and Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910)
1989-01-01
We present computer-simulation results for the trapping rate (rate constant) k associated with diffusion-controlled reactions among identical, static spherical traps distributed with an arbitrary degree of impenetrability using a Pearson random-walk algorithm. We specifically consider the penetrable-concentric-shell model in which each trap of diameter σ is composed of a mutually impenetrable core of diameter λσ, encompassed by a perfectly penetrable shell of thickness (1-λ)σ/2: λ=0 corresponding to randomly centered or ''fully penetrable'' traps and λ=1 corresponding to totally impenetrable traps. Trapping rates are calculated accurately from the random-walk algorithm at the extreme limits of λ (λ=0 and 1) and at an intermediate value (λ=0.8), for a wide range of trap densities. Our simulation procedure has a relatively fast execution time. It is found that k increases with increasing impenetrability at fixed trap concentration. These ''exact'' data are compared with previous theories for the trapping rate. Although a good approximate theory exists for the fully-penetrable-trap case, there are no currently available theories that can provide good estimates of the trapping rate for a moderate to high density of traps with nonzero hard cores (λ>0)
Tan, Zhi-Jie; Zou, Xian-Wu; Huang, Sheng-You; Zhang, Wei; Jin, Zhun-Zhi
2002-07-01
We investigate the pattern of particle distribution and its evolution with time in multiparticle systems using the model of random walks with memory enhancement and decay. This model describes some biological intelligent walks. With decrease in the memory decay exponent α, the distribution of particles changes from a random dispersive pattern to a locally dense one, and then returns to the random one. Correspondingly, the fractal dimension Df,p characterizing the distribution of particle positions increases from a low value to a maximum and then decreases to the low one again. This is determined by the degree of overlap of regions consisting of sites with remanent information. The second moment of the density ρ(2) was introduced to investigate the inhomogeneity of the particle distribution. The dependence of ρ(2) on α is similar to that of Df,p on α. ρ(2) increases with time as a power law in the process of adjusting the particle distribution, and then ρ(2) tends to a stable equilibrium value.
Directory of Open Access Journals (Sweden)
Marcelo Cardoso de Souza
Full Text Available ABSTRACT Objective: The purpose was to evaluate the effectiveness of a progressive muscle strengthening program using a Swiss ball for AS patients. Methods: Sixty patients with AS were randomized into the intervention group (IG or the control group (CG. Eight exercises were performed by the IG patients with free weights on a Swiss ball two times per week for 16 weeks. The evaluations were performed by a blinded evaluator at baseline and after 4, 8, 12 and 16 weeks using the following instruments: the one-repetition maximum test (1 RM, BASMI, BASFI, HAQ-S, SF-36, 6-minute walk test, time up and go test, BASDAI, ASDAS, ESR and CRP dosage and Likert scale. Results: There was a statistical difference between groups for: strength (1 RM capacity in the following exercises: abdominal, rowing, squat, triceps and reverse fly (p < 0.005; 6-minute walk test (p < 0.001; timed up and go test (p = 0.025 and Likert scale (p < 0.001, all of them with better results for the IG. No differences were observed between the groups with respect to the functional capacity evaluation using the BASFI, HAQ-S, BASMI, SF-36, TUG, ASDAS, ESR and CPR dosage. Conclusions: Progressive muscle strengthening using a Swiss ball is effective for improving muscle strength and walking performance in patients with AS.
Rote, Aubrianne E; Klos, Lori A; Brondino, Michael J; Harley, Amy E; Swartz, Ann M
2015-06-16
Facebook may be a useful tool to provide a social support group to encourage increases in physical activity. This study examines the efficacy of a Facebook social support group to increase steps/day in young women. Female college freshmen (N = 63) were randomized to one of two 8-week interventions: a Facebook Social Support Group (n = 32) or a Standard Walking Intervention (n = 31). Participants in both groups received weekly step goals and tracked steps/day with a pedometer. Women in the Facebook Social Support Group were also enrolled in a Facebook group and asked to post information about their steps/day and provide feedback to one another. Women in both intervention arms significantly increased steps/day pre- to postintervention (F(8,425) = 94.43, P Facebook Social Support Group increased steps/day significantly more (F(1,138) = 11.34, P Facebook to offer a social support group to increase physical activity in young women. Women in the Facebook Social Support Group increased walking by approximately 1.5 miles/day more than women in the Standard Walking Intervention which, if maintained, could have a profound impact on their future health.
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-01-01
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested
Negative differential resistance in a one-dimensional molecular wire ...
Indian Academy of Sciences (India)
voltage characteristics of a one-dimensional molecular wire with odd number of ... lem, although interesting both from a fundamental point of view and in terms of ..... SKP acknowledges the DST, Government of India, for financial support.
The one-dimensional extended Bose–Hubbard model
Indian Academy of Sciences (India)
Unknown
method to obtain the zero-temperature phase diagram of the one-dimensional, extended ... Progress in this field has been driven by an interplay between ... superconductor-insulator transition in thin films of superconducting materials like bis-.
Scaling Law for Photon Transmission through Optically Turbid Slabs Based on Random Walk Theory
Directory of Open Access Journals (Sweden)
Xuesong Li
2012-03-01
Full Text Available Past work has demonstrated the value of a random walk theory (RWT to solve multiple-scattering problems arising in numerous contexts. This paper’s goal is to investigate the application range of the RWT using Monte Carlo simulations and extending it to anisotropic media using scaling laws. Meanwhile, this paper also reiterates rules for converting RWT formulas to real physical dimensions, and corrects some errors which appear in an earlier publication. The RWT theory, validated by the Monte Carlo simulations and combined with the scaling law, is expected to be useful to study multiple scattering and to greatly reduce the computation cost.
Random walk in degree space and the time-dependent Watts-Strogatz model
Grande, H. L. Casa; Cotacallapa, M.; Hase, M. O.
2016-01-01
In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erd\\"os-R\\'enyi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical for...
Random walk in degree space and the time-dependent Watts-Strogatz model
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.
A stylistic classification of Russian-language texts based on the random walk model
Kramarenko, A. A.; Nekrasov, K. A.; Filimonov, V. V.; Zhivoderov, A. A.; Amieva, A. A.
2017-09-01
A formal approach to text analysis is suggested that is based on the random walk model. The frequencies and reciprocal positions of the vowel letters are matched up by a process of quasi-particle migration. Statistically significant difference in the migration parameters for the texts of different functional styles is found. Thus, a possibility of classification of texts using the suggested method is demonstrated. Five groups of the texts are singled out that can be distinguished from one another by the parameters of the quasi-particle migration process.
Czech Academy of Sciences Publication Activity Database
Papáček, Š.; Matonoha, Ctirad; Štumbauer, V.; Štys, D.
2012-01-01
Roč. 82, č. 10 (2012), s. 2022-2032 ISSN 0378-4754. [Modelling 2009. IMACS Conference on Mathematical Modelling and Computational Methods in Applied Sciences and Engineering /4./. Rožnov pod Radhoštěm, 22.06.2009-26.06.2009] Grant - others:CENAKVA(CZ) CZ.1.05/2.1.00/01.0024; GA JU(CZ) 152//2010/Z Institutional research plan: CEZ:AV0Z10300504 Keywords : multiscale modelling * distributed parameter system * boundary value problem * random walk * photosynthetic factory Subject RIV: EI - Biotechnology ; Bionics Impact factor: 0.836, year: 2012
DEFF Research Database (Denmark)
Visser, Andre
1997-01-01
Random walk simulation has the potential to be an extremely powerful tool in the investigation of turbulence in environmental processes. However, care must be taken in applying such simulations to the motion of particles in turbulent marine systems where turbulent diffusivity is commonly spatially...... are incorrect, and a simple technique that can properly simulate turbulent diffusion in the marine environment is discussed...... non-uniform. The problems associated with this nonuniformity are far from negligible and have been recognised for quite some time. However, incorrect implementations continue to appear in the Literature. In this note computer simulations are presented to illustrate how and why these implementations...
Elliptic random-walk equation for suspension and tracer transport in porous media
DEFF Research Database (Denmark)
Shapiro, Alexander; Bedrikovetsky, P. G.
2008-01-01
. The new theory predicts delay of the maximum of the tracer, compared to the velocity of the flow, while its forward "tail" contains much more particles than in the solution of the classical parabolic (advection-dispersion) equation. This is in agreement with the experimental observations and predictions......We propose a new approach to transport of the suspensions and tracers in porous media. The approach is based on a modified version of the continuous time random walk (CTRW) theory. In the framework of this theory we derive an elliptic transport equation. The new equation contains the time...... of the CTRW theory. (C) 2008 Elsevier B.V. All rights reserved....
The Effects of One-Dimensional Glide on the Reaction Kinetics of Interstitial Clusters
International Nuclear Information System (INIS)
Heinisch, Howard L.; Singh, B N.; Golubov, S I.
2000-01-01
Collision cascades in metals produce small interstitial clusters and perfect dislocation loops that glide in thermally activated one-dimensional (1D) random walks. These gliding defects can change their Burgers vectors by thermal activation or by interactions with other defects. Their migration is therefore''mixed 1D/3D migration'' along a 3D path consisting of 1D segments. The defect reaction kinetics under mixed 1D/3D diffusion are different from pure 1D diffusion and pure 3D diffusion, both of which can be formulated within analytical rate theory models of microstructure evolution under irradiation. Atomic-scale kinetic Monte Carlo (kMC) defect migration simulations are used to investigate the effects of mixed 1D/3D migration on defect reaction kinetics as a guide for implementing mixed 1D/3D migration into the analytical rate theory. The functional dependence of the sink strength on the sixe and concentration of sinks under mixed 1D/3D migration is shown to lie between that for pure 1D and pure 3D migration and varies with L, the average distance between direction changes of the gliding defects. It is shown that the sink strength in simulations for spherical sinks of radius R under mixed 1D/3D migration for values of L greater than R can be approximated by an expression that varies directly as R2. For small L, the form of the transition from mixed 1D/3D to pure 3D diffusion as L decreases is demonstrated in the simulations, the results of which can be used in the future development of an analytical expression describing this transition region
One-dimensional reactor kinetics model for RETRAN
International Nuclear Information System (INIS)
Gose, G.C.; Peterson, C.E.; Ellis, N.L.; McClure, J.A.
1981-01-01
This paper describes a one-dimensional spatial neutron kinetics model that was developed for the RETRAN code. The RETRAN -01 code has a point kinetics model to describe the reactor core behavior during thermal-hydraulic transients. A one-dimensional neutronics model has been developed for RETRAN-02. The ability to account for flux shape changes will permit an improved representation of the thermal and hydraulic feedback effects for many operational transients. 19 refs
One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
Cazalilla, M. A.; Citro, R.; Giamarchi, T.; Orignac, E.; Rigol, M.
2011-01-01
The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with results from exactly solvable models and computational approaches, the concept of bosonic Tomonaga-Luttinger liquids relevant for one-dimensional Bose fluids is introduced, and compared with Bose-Einstein condensates existing in dimensions higher than one. The effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium ...
One dimensional models of excitons in carbon nanotubes
DEFF Research Database (Denmark)
Cornean, Horia Decebal; Duclos, P.; Pedersen, Thomas Garm
Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable.......Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable....
Directory of Open Access Journals (Sweden)
Dafna eMerom
2016-02-01
Full Text Available Background: A physically active lifestyle has the potential to prevent cognitive decline and dementia, yet the optimal type of physical activity/exercise remains unclear. Dance is of special interest as it complex sensorimotor rhythmic activity with additional cognitive, social and affective dimensions. Objectives: to determine whether dance benefits executive function more than walking, an activity that is simple and functional. Methods: Two-arm randomised controlled trial among community-dwelling older adults. The intervention group received 1 hour of ballroom dancing twice weekly over 8 months (~69sessions in local community dance studios. The control group received a combination of a home walking program with a pedometer and optional biweekly group-based walking in local community park to facilitate socialisation. Main outcomes: Main outcomes: executive function tests: processing speed and task shift by the Trail Making Tests (TMT, response inhibition by the Stroop Colour-Word Test (SCWT, working memory by the Digit Span Backwards (DSB test, immediate and delayed verbal recall by the Rey Auditory Verbal Learning Test (RAVLT and visuospatial recall by the Brief Visuospatial Memory Test (BVST. Results: One hundred and fifteen adults (69.5 years, SD6.4 completed baseline and delayed baseline (3 weeks apart before being randomised to either dance (n=60 or walking (n=55. Of those randomized, 79 (68% completed the follow-up measurements (32 weeks from baseline. In the dance group only, ‘non-completers’ had significant lower baseline scores on all executive function tests than those completed the full program. Intention-to-treat analyses showed no group effect. In a random effects model including participants who completed all measurements, adjusted for baseline score and covariates (age, education, estimated verbal intelligence, community, a between group effect in favour of dance was noted only for BVST total learning (Cohen’s D Effect size
Energy Technology Data Exchange (ETDEWEB)
Wollschlaeger, A.
1996-12-31
The presented particle tracking model is for the numerical calculation of heavy metal transport in natural waters. The Navier-Stokes-Equations are solved with the Finite-Element-Method. The advective movement of the particles is interpolated from the velocities on the discrete mesh. The influence of turbulence is simulated with a Random-Walk-Model where particles are distributed due to a given probability function. Both parts are added and lead to the new particle position. The characteristics of the heavy metals are assigned to the particules as their attributes. Dissolved heavy metals are transported only by the flow. Heavy metals which are bound to particulate matter have an additional settling velocity. The sorption and the remobilization processes are approximated through a probability law which maintains the proportionality ratio between dissolved heavy metals and those which are bound to particulate matter. At the bed heavy metals bound to particulate matter are subjected to deposition and erosion processes. The model treats these processes by considering the absorption intensity of the heavy metals to the bottom sediments. Calculations of the Weser estuary show that the particle tracking model allows the simulation of the heavy metal behaviour even under complex flow conditions. (orig.) [Deutsch] Das vorgestellte Partikelmodell dient zur numerischen Berechnung des Schwermetalltransports in natuerlichen Gewaessern. Die Navier-Stokes-Gleichungen werden mit der Methode der Finiten Elemente geloest. Die advektive Bewegung der Teilchen ergibt sich aus der Interpolation der Geschwindigkeiten auf dem diskreten Netz. Der Einfluss der Turbulenz wird mit einem Random-Walk-Modell simuliert, bei dem sich die Partikel anhand einer vorgegebenen Wahrscheinlichkeitsfunktion verteilen. Beide Bewegungsanteile werden zusammengefasst und ergeben die neue Partikelposition. Die Eigenschaften der Schwermetalle werden den Partikeln als Attribute zugeordnet. Geloeste Schwermetalle
Simulation of a directed random-walk model: the effect of pseudo-random-number correlations
Shchur, L. N.; Heringa, J. R.; Blöte, H. W. J.
1996-01-01
We investigate the mechanism that leads to systematic deviations in cluster Monte Carlo simulations when correlated pseudo-random numbers are used. We present a simple model, which enables an analysis of the effects due to correlations in several types of pseudo-random-number sequences. This model provides qualitative understanding of the bias mechanism in a class of cluster Monte Carlo algorithms.
On the effect of memory in one-dimensional K=4 automata on networks
Alonso-Sanz, Ramón; Cárdenas, Juan Pablo
2008-12-01
The effect of implementing memory in cells of one-dimensional CA, and on nodes of various types of automata on networks with increasing degrees of random rewiring is studied in this article, paying particular attention to the case of four inputs. As a rule, memory induces a moderation in the rate of changing nodes and in the damage spreading, albeit in the latter case memory turns out to be ineffective in the control of the damage as the wiring network moves away from the ordered structure that features proper one-dimensional CA. This article complements the previous work done in the two-dimensional context.
A continuous-time random-walk approach to the Cole-Davidson dielectric response of dipolar liquids
DEFF Research Database (Denmark)
Szabat, B.; Langner, K. M.; Klösgen-Buchkremer, Beate Maria
2004-01-01
We show how the Cole-Davidson relaxation response, characteristic of alcoholic systems, can be derived within the framework of the continuous-time random walk (CTRW). Using the random-variable formalism, we indicate that the high-frequency power law of dielectric spectra is determined by the heavy...
A continuous-time random-walk approach to the Cole-Davidson dielectric response of dipolar liquids
DEFF Research Database (Denmark)
Szabat, Bozena; Langner, Karol M.; Klösgen, Beate Maria
2005-01-01
We show how the Cole-Davidson relaxation response, characteristic of alcoholic systems, can be derived within the framework of the continuous-time random walk 4CTRW). Using the random-variable formalism, we indicate that the high-frequency power law of dielectric spectra is determined by the heav...
Walking Away from Type 2 diabetes: a cluster randomized controlled trial.
Yates, T; Edwardson, C L; Henson, J; Gray, L J; Ashra, N B; Troughton, J; Khunti, K; Davies, M J
2017-05-01
This study aimed to investigate whether an established behavioural intervention, Walking Away from Type 2 Diabetes, is effective at promoting and sustaining increased walking activity when delivered within primary care. Cluster randomized controlled trial involving 10 general practices recruited from Leicestershire, UK, in 2009-2010. Eight hundred and eight (36% female) individuals with a high risk of Type 2 diabetes mellitus, identified through a validated risk score, were included. Participants in five practices were randomized to Walking Away from Type 2 Diabetes, a pragmatic 3-h group-based structured education programme incorporating pedometer use with annual follow-on refresher sessions. The primary outcome was accelerometer assessed ambulatory activity (steps/day) at 12 months. Longer term maintenance was assessed at 24 and 36 months. Results were analysed using generalized estimating equation models, accounting for clustering. Complete accelerometer data for the primary outcome were available for 571 (71%) participants. Increases in ambulatory activity of 411 steps/day [95% confidence interval (CI): 117, 704] and self-reported vigorous-intensity physical activity of 218 metabolic equivalent min/week (95% CI: 6, 425) at 12 months were observed in the intervention group compared with control; differences between groups were not sustained at 36 months. No differences between groups were observed for markers of cardiometabolic health. Replacing missing data with multiple imputation did not affect the results. A pragmatic low-resource group-based structured education programme with pedometer use resulted in modest increases in ambulatory activity compared with control conditions after 12 months when implemented within a primary care setting to those at high risk of Type 2 diabetes mellitus; however, the results were not maintained over 36 months. © 2016 Diabetes UK.
Personalized PageRank Clustering: A graph clustering algorithm based on random walks
A. Tabrizi, Shayan; Shakery, Azadeh; Asadpour, Masoud; Abbasi, Maziar; Tavallaie, Mohammad Ali
2013-11-01
Graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications. In addition, exponential growth of real-world graphs such as social networks, biological networks and electrical circuits demands clustering algorithms with nearly-linear time and space complexity. In this paper we propose Personalized PageRank Clustering (PPC) that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph. We combine random walks and modularity to precisely and efficiently reveal the clusters of a graph. PPC is a top-down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly-linear approaches that are mainly bottom-up. It also gives a hierarchy of clusters that is useful in many applications. PPC has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets. Furthermore, its top-down approach makes it a flexible solution for clustering problems with different requirements.
Two-state random walk model of lattice diffusion - 1. Self-correlation function
International Nuclear Information System (INIS)
Balakrishnan, V.; Venkataraman, G.
1981-01-01
Diffusion with interruptions (arising from localized oscillations, or traps, or mixing between jump diffusion and fluid-like diffusion, etc.) is a very general phenomenon. Its manifestations range from superionic conductance to the behaviour of hydrogen in metals. Based on a continuous-time random walk approach, we present a comprehensive two-state random walk model for the diffusion of a particle on a lattice, incorporating arbitrary holding-time distributions for both localized residence at the sites and inter-site flights, and also the correct first-waiting-time distributions. A synthesis is thus achieved of the two extremes of jump diffusion (zero flight time) and fluid-like diffusion (zero residence time). Various earlier models emerge as special cases of our theory. Among the noteworthy results obtained are: closed-form solutions (in d dimensions, and with arbitrary directional bias) for temporarily uncorrelated jump diffusion and for the fluid diffusion counterpart; a compact, general formula for the mean square displacement; the effects of a continuous spectrum of time scales in the holding-time distributions, etc. The dynamic mobility and the structure factor for 'oscillatory diffusion' are taken up in part 2. (author)
Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?
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
Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?
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.
A lattice-model representation of continuous-time random walks
International Nuclear Information System (INIS)
Campos, Daniel; Mendez, Vicenc
2008-01-01
We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied
A lattice-model representation of continuous-time random walks
Energy Technology Data Exchange (ETDEWEB)
Campos, Daniel [School of Mathematics, Department of Applied Mathematics, University of Manchester, Manchester M60 1QD (United Kingdom); Mendez, Vicenc [Grup de Fisica Estadistica, Departament de Fisica, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain)], E-mail: daniel.campos@uab.es, E-mail: vicenc.mendez@uab.es
2008-02-29
We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied.
Anomalous diffusion and Levy random walk of magnetic field lines in three dimensional turbulence
International Nuclear Information System (INIS)
Zimbardo, G.; Veltri, P.; Basile, G.; Principato, S.
1995-01-01
The transport of magnetic field lines is studied numerically where three dimensional (3-D) magnetic fluctuations, with a power law spectrum, and periodic over the simulation box are superimposed on an average uniform magnetic field. The weak and the strong turbulence regime, δB∼B 0 , are investigated. In the weak turbulence case, magnetic flux tubes are separated from each other by percolating layers in which field lines undergo a chaotic motion. In this regime the field lines may exhibit Levy, rather than Gaussian, random walk, changing from Levy flights to trapped motion. The anomalous diffusion laws left-angle Δx 2 i right-angle ∝s α with α>1 and α<1, are obtained for a number of cases, and the non-Gaussian character of the field line random walk is pointed out by computing the kurtosis. Increasing the fluctuation level, and, therefore stochasticity, normal diffusion (α congruent 1) is recovered and the kurtoses reach their Gaussian value. However, the numerical results show that neither the quasi-linear theory nor the two dimensional percolation theory can be safely extrapolated to the considered 3-D strong turbulence regime. copyright 1995 American Institute of Physics
Mean first passage time for random walk on dual structure of dendrimer
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.
Wei, Kun; Zhong, Suchuan
2017-08-01
Phenomenologically inspired by dolphins' unihemispheric sleep, we introduce a minimal model for random walks with physiological memory. The physiological memory consists of long-term memory which includes unconscious implicit memory and conscious explicit memory, and working memory which serves as a multi-component system for integrating, manipulating and managing short-term storage. The model assumes that the sleeping state allows retrievals of episodic objects merely from the episodic buffer where these memory objects are invoked corresponding to the ambient objects and are thus object-oriented, together with intermittent but increasing use of implicit memory in which decisions are unconsciously picked up from historical time series. The process of memory decay and forgetting is constructed in the episodic buffer. The walker's risk attitude, as a product of physiological heuristics according to the performance of objected-oriented decisions, is imposed on implicit memory. The analytical results of unihemispheric random walks with the mixture of object-oriented and time-oriented memory, as well as the long-time behavior which tends to the use of implicit memory, are provided, indicating the common sense that a conservative risk attitude is inclinable to slow movement.
Modeling spreading of oil slicks based on random walk methods and Voronoi diagrams
International Nuclear Information System (INIS)
Durgut, İsmail; Reed, Mark
2017-01-01
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. - Highlights: • A methodology for representation of a surface oil slick using a Voronoi diagram • An algorithm simulating the spreading of oil slick with the Voronoi diagram representation • The algorithm employs the Gaussian random walk method through individual particle stepping. • The diffusive spreading is based on a theoretical model of the spreading process. • Algorithm is computationally robust and successfully reproduces analytical solutions to the spreading process.
Navigational efficiency in a biased and correlated random walk model of individual animal movement.
Bailey, Joseph D; Wallis, Jamie; Codling, Edward A
2018-01-01
Understanding how an individual animal is able to navigate through its environment is a key question in movement ecology that can give insight into observed movement patterns and the mechanisms behind them. Efficiency of navigation is important for behavioral processes at a range of different spatio-temporal scales, including foraging and migration. Random walk models provide a standard framework for modeling individual animal movement and navigation. Here we consider a vector-weighted biased and correlated random walk (BCRW) model for directed movement (taxis), where external navigation cues are balanced with forward persistence. We derive a mathematical approximation of the expected navigational efficiency for any BCRW of this form and confirm the model predictions using simulations. We demonstrate how the navigational efficiency is related to the weighting given to forward persistence and external navigation cues, and highlight the counter-intuitive result that for low (but realistic) levels of error on forward persistence, a higher navigational efficiency is achieved by giving more weighting to this indirect navigation cue rather than direct navigational cues. We discuss and interpret the relevance of these results for understanding animal movement and navigation strategies. © 2017 by the Ecological Society of America.
Asymptotic results for the semi-Markovian random walk with delay
International Nuclear Information System (INIS)
Khaniyev, T.A.; Aliyev, R.T.
2006-12-01
In this study, the semi-Markovian random walk with a discrete interference of chance (X(t) ) is considered and under some weak assumptions the ergodicity of this process is discussed. Characteristic function of the ergodic distribution of X(t) is expressed by means of the probability characteristics of the boundary functionals (N,S N ). Some exact formulas for first and second moments of ergodic distribution of the process X(t) are obtained when the random variable ζ 1 - s, which is describing a discrete interference of chance, has Gamma distribution on the interval [0, ∞) with parameter (α,λ) . Based on these results, the asymptotic expansions with three terms for the first two moments of the ergodic distribution of the process X(t) are obtained, as λ → 0. (author)
Random walk analysis of grain motion during superplastic deformation of TZP
International Nuclear Information System (INIS)
Okamoto, T; Yasuda, K; Shiota, T
2009-01-01
This study focuses on grain motion in TZP (Tetragonal Zirconia Polycrystal) ceramics during superplastic deformation. The specimen was 16 times elongated repeatedly at 1400 0 C in air. The increment of true plastic strain was set to be 2%, and the specimen was deformed up to 30.3% true plastic strain finally. After each deformation, displacement vectors of specified 748 grains were measured from their position vectors determined by FE-SEM micrographs. As a result, the grains move to the tensile loading direction in zigzag way. And also, the zigzag motion changes with plastic strain: The grains move randomly (random walk motion) by the first 15% true plastic strain, and then grain motion becomes spatially uniform gradually. It is related to changes of constraint of surrounding matrix.
Some application of the model of partition points on a one-dimensional lattice
International Nuclear Information System (INIS)
Mejdani, R.
1991-07-01
We have shown that by using a model of the gas of partition points on one-dimensional lattice, we can find some results about the enzyme kinetics or the average domain-size, which we have obtained before by using a correlated Walks' theory or a probabilistic (combinatoric) way. We have discussed also the problem related with the spread of an infection of disease and the stochastic model of partition points. We think that this model, as a very simple model and mathematically transparent, can be advantageous for other theoretical investigations in chemistry or modern biology. (author). 14 refs, 6 figs, 1 tab
A review on one dimensional perovskite nanocrystals for piezoelectric applications
Directory of Open Access Journals (Sweden)
Li-Qian Cheng
2016-03-01
Full Text Available In recent years, one-dimensional piezoelectric nanomaterials have become a research topic of interest because of their special morphology and excellent piezoelectric properties. This article presents a short review on one dimensional perovskite piezoelectric materials in different systems including Pb(Zr,TiO3, BaTiO3 and (K,NaNbO3 (KNN. We emphasize KNN as a promising lead-free piezoelectric compound with a high Curie temperature and high piezoelectric properties and describe its synthesis and characterization. In particular, details are presented for nanoscale piezoelectricity characterization of a single KNN nanocrystal by piezoresponse force microscopy. Finally, this review describes recent progress in applications based on one dimensional piezoelectric nanostructures with a focus on energy harvesting composite materials.
Strong chaos in one-dimensional quantum system
International Nuclear Information System (INIS)
Yang, C.-D.; Wei, C.-H.
2008-01-01
According to the Poincare-Bendixson theorem, a minimum of three autonomous equations is required to exhibit deterministic chaos. Because a one-dimensional quantum system is described by only two autonomous equations using de Broglie-Bohm's trajectory interpretation, chaos in one-dimensional quantum systems has long been considered impossible. We will prove in this paper that chaos phenomenon does exist in one-dimensional quantum systems, if the domain of quantum motions is extended to complex space by noting that the quantum world is actually characterized by a four-dimensional complex spacetime according to the E (∞) theory. Furthermore, we point out that the interaction between the real and imaginary parts of complex trajectories produces a new chaos phenomenon unique to quantum systems, called strong chaos, which describes the situation that quantum trajectories may emerge and diverge spontaneously without any perturbation in the initial position
Müller, Christian L.; Sbalzarini, Ivo F.; van Gunsteren, Wilfred F.; Žagrović, Bojan; Hünenberger, Philippe H.
2009-06-01
The concept of high-resolution shapes (also referred to as folds or states, depending on the context) of a polymer chain plays a central role in polymer science, structural biology, bioinformatics, and biopolymer dynamics. However, although the idea of shape is intuitively very useful, there is no unambiguous mathematical definition for this concept. In the present work, the distributions of high-resolution shapes within the ideal random-walk ensembles with N =3,…,6 beads (or up to N =10 for some properties) are investigated using a systematic (grid-based) approach based on a simple working definition of shapes relying on the root-mean-square atomic positional deviation as a metric (i.e., to define the distance between pairs of structures) and a single cutoff criterion for the shape assignment. Although the random-walk ensemble appears to represent the paramount of homogeneity and randomness, this analysis reveals that the distribution of shapes within this ensemble, i.e., in the total absence of interatomic interactions characteristic of a specific polymer (beyond the generic connectivity constraint), is significantly inhomogeneous. In particular, a specific (densest) shape occurs with a local probability that is 1.28, 1.79, 2.94, and 10.05 times (N =3,…,6) higher than the corresponding average over all possible shapes (these results can tentatively be extrapolated to a factor as large as about 1028 for N =100). The qualitative results of this analysis lead to a few rather counterintuitive suggestions, namely, that, e.g., (i) a fold classification analysis applied to the random-walk ensemble would lead to the identification of random-walk "folds;" (ii) a clustering analysis applied to the random-walk ensemble would also lead to the identification random-walk "states" and associated relative free energies; and (iii) a random-walk ensemble of polymer chains could lead to well-defined diffraction patterns in hypothetical fiber or crystal diffraction experiments
Absorption in one-dimensional metallic-dielectric photonic crystals
International Nuclear Information System (INIS)
Yu Junfei; Shen Yifeng; Liu Xiaohan; Fu Rongtang; Zi Jian; Zhu Zhiqiang
2004-01-01
We show theoretically that the absorption of one-dimensional metallic-dielectric photonic crystals can be enhanced considerably over the corresponding constituent metal. By properly choosing the structural and material parameters, the absorption of one-dimensional metallic-dielectric photonic crystals can be enhanced by one order of magnitude in the visible and in the near infrared regions. It is found that the absorptance of such photonic crystals increases with increasing number of periods. Rules on how to obtain a absorption enhancement in a certain frequency range are discussed. (letter to the editor)
One-dimensional models of excitons in carbon nanotubes
DEFF Research Database (Denmark)
Cornean, Horia Decebal; Duclos, Pierre; Pedersen, Thomas Garm
2004-01-01
Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one-dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable.......Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one-dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable....
Effects of exercise on brain activity during walking in older adults: a randomized controlled trial.
Shimada, Hiroyuki; Ishii, Kenji; Makizako, Hyuma; Ishiwata, Kiichi; Oda, Keiichi; Suzukawa, Megumi
2017-05-30
Physical activity may preserve neuronal plasticity, increase synapse formation, and cause the release of hormonal factors that promote neurogenesis and neuronal function. Previous studies have reported enhanced neurocognitive function following exercise training. However, the specific cortical regions activated during exercise training remain largely undefined. In this study, we quantitatively and objectively evaluated the effects of exercise on brain activity during walking in healthy older adults. A total of 24 elderly women (75-83 years old) were randomly allocated to either an intervention group or a control group. Those in the intervention group attended 3 months of biweekly 90-min sessions focused on aerobic exercise, strength training, and physical therapy. We monitored changes in regional cerebral glucose metabolism during walking in both groups using positron emission tomography (PET) and [ 18 F]fluorodeoxyglucose (FDG). All subjects completed the 3-month experiment and the adherence to the exercise program was 100%. Compared with the control group, the intervention group showed a significantly greater step length in the right foot after 3 months of physical activity. The FDG-PET assessment revealed a significant post-intervention increase in regional glucose metabolism in the left posterior entorhinal cortex, left superior temporal gyrus, and right superior temporopolar area in the intervention group. Interestingly, the control group showed a relative increase in regional glucose metabolism in the left premotor and supplemental motor areas, left and right somatosensory association cortex, and right primary visual cortex after the 3-month period. We found no significant differences in FDG uptake between the intervention and control groups before vs. after the intervention. Exercise training increased activity in specific brain regions, such as the precuneus and entorhinal cortices, which play an important role in episodic and spatial memory. Further
Høyer, Ellen; Jahnsen, Reidun; Stanghelle, Johan Kvalvik; Strand, Liv Inger
2012-01-01
Treadmill training with body weight support (TTBWS) for relearning walking ability after brain damage is an approach under current investigation. Efficiency of this method beyond traditional training is lacking evidence, especially in patients needing walking assistance after stroke. The objective of this study was to investigate change in walking and transfer abilities, comparing TTBWS with traditional walking training. A single-blinded, randomized controlled trial was conducted. Sixty patients referred for multi-disciplinary primary rehabilitation were assigned into one of two intervention groups, one received 30 sessions of TTBWS plus traditional training, the other traditional training alone. Daily training was 1 hr. Outcome measures were Functional Ambulation Categories (FAC), Walking, Functional Independence Measure (FIM); shorter transfer and stairs, 10 m and 6-min walk tests. Substantial improvements in walking and transfer were shown within both groups after 5 and 11 weeks of intervention. Overall no statistical significant differences were found between the groups, but 12 of 17 physical measures tended to show improvements in favour of the treadmill approach. Both training strategies provided significant improvements in the tested activities, suggesting that similar outcomes can be obtained in the two modalities by systematic, intensive and goal directed training.
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Rackauskas, Alfredas
2010-01-01
In this paper, we deal with the asymptotic distribution of the maximum increment of a random walk with a regularly varying jump size distribution. This problem is motivated by a long-standing problem on change point detection for epidemic alternatives. It turns out that the limit distribution...... of the maximum increment of the random walk is one of the classical extreme value distributions, the Fréchet distribution. We prove the results in the general framework of point processes and for jump sizes taking values in a separable Banach space...
Generalized Pareto for Pattern-Oriented Random Walk Modelling of Organisms' Movements.
Directory of Open Access Journals (Sweden)
Sophie Bertrand
Full Text Available How organisms move and disperse is crucial to understand how population dynamics relates to the spatial heterogeneity of the environment. Random walk (RW models are typical tools to describe movement patterns. Whether Lévy or alternative RW better describes forager movements is keenly debated. We get around this issue using the Generalized Pareto Distribution (GPD. GPD includes as specific cases Normal, exponential and power law distributions, which underlie Brownian, Poisson-like and Lévy walks respectively. Whereas previous studies typically confronted a limited set of candidate models, GPD lets the most likely RW model emerge from the data. We illustrate the wide applicability of the method using GPS-tracked seabird foraging movements and fishing vessel movements tracked by Vessel Monitoring System (VMS, both collected in the Peruvian pelagic ecosystem. The two parameters from the fitted GPD, a scale and a shape parameter, provide a synoptic characterization of the observed movement in terms of characteristic scale and diffusive property. They reveal and quantify the variability, among species and individuals, of the spatial strategies selected by predators foraging on a common prey field. The GPD parameters constitute relevant metrics for (1 providing a synthetic and pattern-oriented description of movement, (2 using top predators as ecosystem indicators and (3 studying the variability of spatial behaviour among species or among individuals with different personalities.
Bantoft, Christina; Summers, Mathew J; Tranent, Peter J; Palmer, Matthew A; Cooley, P Dean; Pedersen, Scott J
2016-02-01
In the present study, we examined the effect of working while seated, while standing, or while walking on measures of short-term memory, working memory, selective and sustained attention, and information-processing speed. The advent of computer-based technology has revolutionized the adult workplace, such that average adult full-time employees spend the majority of their working day seated. Prolonged sitting is associated with increasing obesity and chronic health conditions in children and adults. One possible intervention to reduce the negative health impacts of the modern office environment involves modifying the workplace to increase incidental activity and exercise during the workday. Although modifications, such as sit-stand desks, have been shown to improve physiological function, there is mixed information regarding the impact of such office modification on individual cognitive performance and thereby the efficiency of the work environment. In a fully counterbalanced randomized control trial, we assessed the cognitive performance of 45 undergraduate students for up to a 1-hr period in each condition. The results indicate that there is no significant change in the measures used to assess cognitive performance associated with working while seated, while standing, or while walking at low intensity. These results indicate that cognitive performance is not degraded with short-term use of alternate workstations. © 2015, Human Factors and Ergonomics Society.
Generalized Pareto for Pattern-Oriented Random Walk Modelling of Organisms' Movements.
Bertrand, Sophie; Joo, Rocío; Fablet, Ronan
2015-01-01
How organisms move and disperse is crucial to understand how population dynamics relates to the spatial heterogeneity of the environment. Random walk (RW) models are typical tools to describe movement patterns. Whether Lévy or alternative RW better describes forager movements is keenly debated. We get around this issue using the Generalized Pareto Distribution (GPD). GPD includes as specific cases Normal, exponential and power law distributions, which underlie Brownian, Poisson-like and Lévy walks respectively. Whereas previous studies typically confronted a limited set of candidate models, GPD lets the most likely RW model emerge from the data. We illustrate the wide applicability of the method using GPS-tracked seabird foraging movements and fishing vessel movements tracked by Vessel Monitoring System (VMS), both collected in the Peruvian pelagic ecosystem. The two parameters from the fitted GPD, a scale and a shape parameter, provide a synoptic characterization of the observed movement in terms of characteristic scale and diffusive property. They reveal and quantify the variability, among species and individuals, of the spatial strategies selected by predators foraging on a common prey field. The GPD parameters constitute relevant metrics for (1) providing a synthetic and pattern-oriented description of movement, (2) using top predators as ecosystem indicators and (3) studying the variability of spatial behaviour among species or among individuals with different personalities.
Approximate characteristics for one-dimensional two-phase flows
International Nuclear Information System (INIS)
Sarayloo, A.; Peddleson, J.
1985-01-01
An approximate method for determining the characteristics associated with one-dimensional particulate two-phase flow models is presented. The method is based on iteration and is valid for small particulate volume fractions. The method is applied to several special cases involving incompressible particles suspended in a gas. The influences of certain changes in the physical model are investigated
Correlation Functions of the One-Dimensional Attractive Bose Gas
International Nuclear Information System (INIS)
Calabrese, Pasquale; Caux, Jean-Sebastien
2007-01-01
The zero-temperature correlation functions of the one-dimensional attractive Bose gas with a delta-function interaction are calculated analytically for any value of the interaction parameter and number of particles, directly from the integrability of the model. We point out a number of interesting features, including zero recoil energy for a large number of particles, analogous to the Moessbauer effect
Analytical solutions of one-dimensional advection–diffusion
Indian Academy of Sciences (India)
Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal ﬁnite initially solute free domain,for two dispersion problems.In the ﬁrst one,temporally dependent solute dispersion along uniform ﬂow in homogeneous domain is studied.In the second problem the ...
Underwater striling engine design with modified one-dimensional model
Directory of Open Access Journals (Sweden)
Daijin Li
2015-05-01
Full Text Available Stirling engines are regarded as an efficient and promising power system for underwater devices. Currently, many researches on one-dimensional model is used to evaluate thermodynamic performance of Stirling engine, but in which there are still some aspects which cannot be modeled with proper mathematical models such as mechanical loss or auxiliary power. In this paper, a four-cylinder double-acting Stirling engine for Unmanned Underwater Vehicles (UUVs is discussed. And a one-dimensional model incorporated with empirical equations of mechanical loss and auxiliary power obtained from experiments is derived while referring to the Stirling engine computer model of National Aeronautics and Space Administration (NASA. The P-40 Stirling engine with sufficient testing results from NASA is utilized to validate the accuracy of this one-dimensional model. It shows that the maximum error of output power of theoretical analysis results is less than 18% over testing results, and the maximum error of input power is no more than 9%. Finally, a Stirling engine for UUVs is designed with Schmidt analysis method and the modified one-dimensional model, and the results indicate this designed engine is capable of showing desired output power.
Quantitative hyperbolicity estimates in one-dimensional dynamics
International Nuclear Information System (INIS)
Day, S; Kokubu, H; Pilarczyk, P; Luzzatto, S; Mischaikow, K; Oka, H
2008-01-01
We develop a rigorous computational method for estimating the Lyapunov exponents in uniformly expanding regions of the phase space for one-dimensional maps. Our method uses rigorous numerics and graph algorithms to provide results that are mathematically meaningful and can be achieved in an efficient way
Quasi-one-dimensional scattering in a discrete model
DEFF Research Database (Denmark)
Valiente, Manuel; Mølmer, Klaus
2011-01-01
We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero...
Structure Variation from One-Dimensional Chain to Three ...
Indian Academy of Sciences (India)
WEN-XUAN LI, XIAO-MIN GU, WEN-LI ZHANG and LIANG NI. School of Chemistry ... Compound 1 possesses one-dimensional chain structure, and expands into ..... sis of fine chemicals and pharmaceuticals.30 The results were summarized ...
Current-Voltage Characteristics of Quasi-One-Dimensional Superconductors
DEFF Research Database (Denmark)
Vodolazov, D.Y.; Peeters, F.M.; Piraux, L.
2003-01-01
The current-voltage (I-V) characteristics of quasi-one-dimensional superconductors were discussed. The I-V characteristics exhibited an unusual S behavior. The dynamics of superconducting condensate and the existence of two different critical currents resulted in such an unusual behavior....
Appropriateness of one-dimensional calculations for repository analysis
International Nuclear Information System (INIS)
Eaton, R.R.
1994-01-01
This paper brings into focus the results of numerous studies that have addressed issues associated with the validity of assumptions which are used to justify reducing the dimensionality of numerical calculations of water flow through Yucca Mountain, NV. It is shown that in many cases, one-dimensional modeling is more rigorous than previously assumed
One-dimensional position readout from microchannel plates
International Nuclear Information System (INIS)
Connell, K.A.; Przybylski, M.M.
1982-01-01
The development of a one-dimensional position readout system with microchannel plates, is described, for heavy ion detectors for use in a particle time-of-flight telescope and as a position sensitive device in front of an ionisation counter at the Nuclear Structure Facility. (U.K.)
Lekhnitskii's formalism of one-dimensional quasicrystals and its ...
Indian Academy of Sciences (India)
To illustrate its utility, the generalized Lekhnitskii's formal- ism is used to analyse the coupled phonon and phason fields in an infinite quasicrystal medium con- taining an elliptic rigid inclusion. Keywords. Generalized Lekhnitskii's formalism; one-dimensional quasicrystals; plane problems; elliptic inclusion. PACS Nos 61.44.
Backward scattering in the one-dimensional Fermi gas
International Nuclear Information System (INIS)
Apostol, M.
1980-05-01
The Ward identity is derived for non-relativistic fermions with two-body spin-independent interaction. Using this identity for the one-dimensional Fermi gas with backward scattering the equations of the perturbation theory are solved for the effective interaction and the collective excitations of the particle density fluctuations are obtained. (author)
Simulation of the diffraction pattern of one dimensional quasicrystal ...
African Journals Online (AJOL)
The effects of the variation of atomic spacing ratio of a one dimensional quasicrystal material are investigated. The work involves the use of the solid state simulation code, Laue written by Silsbee and Drager. We are able to observe the general features of the diffraction pattern by a quasicrystal. In addition, it has been found ...
Monte Carlo investigation of the one-dimensional Potts model
International Nuclear Information System (INIS)
Karma, A.S.; Nolan, M.J.
1983-01-01
Monte Carlo results are presented for a variety of one-dimensional dynamical q-state Potts models. Our calculations confirm the expected universal value z = 2 for the dynamic scaling exponent. Our results also indicate that an increase in q at fixed correlation length drives the dynamics into the scaling regime
State reconstruction of one-dimensional wave packets
Krähmer, D. S.; Leonhardt, U.
1997-12-01
We review and analyze the method [U. Leonhardt, M.G. Raymer: Phys. Rev. Lett. 76, 1985 (1996)] for quantum-state reconstruction of one-dimensional non-relativistic wave packets from position observations. We illuminate the theoretical background of the technique and show how to extend the procedure to the continuous part of the spectrum.
One-dimensional autonomous systems and dissipative systems
International Nuclear Information System (INIS)
Lopez, G.
1996-01-01
The Lagrangian and the Generalized Linear Momentum are given in terms of a constant of motion for a one-dimensional autonomous system. The possibility of having an explicit Hamiltonian expression is also analyzed. The approach is applied to some dissipative systems. Copyright copyright 1996 Academic Press, Inc
Quantum transport in strongly interacting one-dimensional nanostructures
Agundez, R.R.
2015-01-01
In this thesis we study quantum transport in several one-dimensional systems with strong electronic interactions. The first chapter contains an introduction to the concepts treated throughout this thesis, such as the Aharonov-Bohm effect, the Kondo effect, the Fano effect and quantum state transfer.
Statistics of resonances in one-dimensional continuous systems
Indian Academy of Sciences (India)
Vol. 73, No. 3. — journal of. September 2009 physics pp. 565–572. Statistics of resonances in one-dimensional continuous systems. JOSHUA FEINBERG. Physics Department, University of Haifa at Oranim, Tivon 36006, Israel ..... relativistic quantum mechanics (Israel Program for Scientific Translations, Jerusalem,. 1969).
Statistical mechanics of quantum one-dimensional damped harmonic oscillator
International Nuclear Information System (INIS)
Borges, E.N.M.; Borges, O.N.; Ribeiro, L.A.A.
1985-01-01
We calculate the thermal correlation functions of the one-dimensional damped harmonic oscillator in contact with a reservoir, in an exact form by applying Green's function method. In this way the thermal fluctuations are incorporated in the Caldirola-Kanai Hamiltonian
Anomalous heat conduction in a one-dimensional ideal gas.
Casati, Giulio; Prosen, Tomaz
2003-01-01
We provide firm convincing evidence that the energy transport in a one-dimensional gas of elastically colliding free particles of unequal masses is anomalous, i.e., the Fourier law does not hold. Our conclusions are confirmed by a theoretical and numerical analysis based on a Green-Kubo-type approach specialized to momentum-conserving lattices.
Relativistic band gaps in one-dimensional disordered systems
International Nuclear Information System (INIS)
Clerk, G.J.; McKellar, B.H.J.
1992-01-01
Conditions for the existence of band gaps in a one-dimensional disordered array of δ-function potentials possessing short range order are developed in a relativistic framework. Both Lorentz vector and scalar type potentials are treated. The relationship between the energy gaps and the transmission properties of the array are also discussed. 20 refs., 2 figs
The electromagnetic Brillouin precursor in one-dimensional photonic crystals
Uitham, R.; Hoenders, B. J.
2008-01-01
We have calculated the electromagnetic Brillouin precursor that arises in a one-dimensional photonic crystal that consists of two homogeneous slabs which each have a single electron resonance. This forerunner is compared with the Brillouin precursor that arises in a homogeneous double-electron
On the quantisation of one-dimensional bags
International Nuclear Information System (INIS)
Fairley, G.T.; Squires, E.J.
1976-01-01
The quantisation of one-dimensional MIT bags by expanding the fields as a sum of classical modes and truncating the series after the first term is discussed. The lowest states of a bag in a world containing two scalar quark fields are obtained. Problems associated with the zero-point oscillations of the field are discussed. (Auth.)
The appropriateness of one-dimensional Yucca Mountain hydrologic calculations
International Nuclear Information System (INIS)
Eaton, R.R.
1993-07-01
This report brings into focus the results of numerous studies that have addressed issues associated with the validity of assumptions which are used to justify reducing the dimensionality of numerical calculations of water flow through Yucca Mountain, NV. it is shown that, in many cases, one-dimensional modeling is more rigorous than previously assumed
Light propagation in one-dimensional porous silicon complex systems
Oton, C.J.; Dal Negro, L.; Gaburro, Z.; Pavesi, L.; Johnson, P.J.; Lagendijk, Aart; Wiersma, D.S.
2003-01-01
We discuss the optical properties of one-dimensional complex dielectric systems, in particular the time-resolved transmission through thick porous silicon quasiperiodic multi-layers. Both in numerical calculations and experiments we find dramatic distortion effects, i.e. pulse stretching and
Analytical approach for collective diffusion: one-dimensional heterogeneous lattice
Czech Academy of Sciences Publication Activity Database
Tarasenko, Alexander
2016-01-01
Roč. 144, č. 14 (2016), 1-11, č. článku 144105. ISSN 0021-9606 Institutional support: RVO:68378271 Keywords : diffusion * Monte Carlo simulations * one-dimensional heterogeneous lattice Subject RIV: BE - Theoretical Physics Impact factor: 2.965, year: 2016
Approximate Approaches to the One-Dimensional Finite Potential Well
Singh, Shilpi; Pathak, Praveen; Singh, Vijay A.
2011-01-01
The one-dimensional finite well is a textbook problem. We propose approximate approaches to obtain the energy levels of the well. The finite well is also encountered in semiconductor heterostructures where the carrier mass inside the well (m[subscript i]) is taken to be distinct from mass outside (m[subscript o]). A relevant parameter is the mass…
Toward precise solution of one-dimensional velocity inverse problems
International Nuclear Information System (INIS)
Gray, S.; Hagin, F.
1980-01-01
A family of one-dimensional inverse problems are considered with the goal of reconstructing velocity profiles to reasonably high accuracy. The travel-time variable change is used together with an iteration scheme to produce an effective algorithm for computation. Under modest assumptions the scheme is shown to be convergent
Continuous time random walk: Galilei invariance and relation for the nth moment
International Nuclear Information System (INIS)
Fa, Kwok Sau
2011-01-01
We consider a decoupled continuous time random walk model with a generic waiting time probability density function (PDF). For the force-free case we derive an integro-differential diffusion equation which is related to the Galilei invariance for the probability density. We also derive a general relation which connects the nth moment in the presence of any external force to the second moment without external force, i.e. it is valid for any waiting time PDF. This general relation includes the generalized second Einstein relation, which connects the first moment in the presence of any external force to the second moment without any external force. These expressions for the first two moments are verified by using several kinds of the waiting time PDF. Moreover, we present new anomalous diffusion behaviours for a waiting time PDF given by a product of power-law and exponential function.
Random walk-based similarity measure method for patterns in complex object
Directory of Open Access Journals (Sweden)
Liu Shihu
2017-04-01
Full Text Available This paper discusses the similarity of the patterns in complex objects. The complex object is composed both of the attribute information of patterns and the relational information between patterns. Bearing in mind the specificity of complex object, a random walk-based similarity measurement method for patterns is constructed. In this method, the reachability of any two patterns with respect to the relational information is fully studied, and in the case of similarity of patterns with respect to the relational information can be calculated. On this bases, an integrated similarity measurement method is proposed, and algorithms 1 and 2 show the performed calculation procedure. One can find that this method makes full use of the attribute information and relational information. Finally, a synthetic example shows that our proposed similarity measurement method is validated.
International Nuclear Information System (INIS)
Ni Xiaohui; Jiang Zhiqiang; Zhou Weixing
2009-01-01
The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.
A random walk approach to the diffusion of positrons in gaseous media
International Nuclear Information System (INIS)
Girardi-Schappo, M.; Tenfen, W.; Arretche, F.
2013-01-01
In this work, we present a random walk model to study the positron diffusion in gaseous media. The positron-atom interaction is described through positron-target cross sections. The main idea is to obtain how much energy a positron transfer to the environment atoms, through ionizations and electronic excitations until its annihilation, taking the ratio between each energetically available collision channel to the total one as the probability for each process to occur. As a first application, we studied how the positron diffuse in gases of helium, neon, argon and their mixtures. To characterize the positron dynamics in each system, we calculated the radiation profile generated from the annihilation, their diffusion profiles and the most probable distances for excitation and ionization. (authors)
A random walk evolution model of wireless sensor networks and virus spreading
International Nuclear Information System (INIS)
Wang Ya-Qi; Yang Xiao-Yuan
2013-01-01
In this paper, considering both cluster heads and sensor nodes, we propose a novel evolving a network model based on a random walk to study the fault tolerance decrease of wireless sensor networks (WSNs) due to node failure, and discuss the spreading dynamic behavior of viruses in the evolution model. A theoretical analysis shows that the WSN generated by such an evolution model not only has a strong fault tolerance, but also can dynamically balance the energy loss of the entire network. It is also found that although the increase of the density of cluster heads in the network reduces the network efficiency, it can effectively inhibit the spread of viruses. In addition, the heterogeneity of the network improves the network efficiency and enhances the virus prevalence. We confirm all the theoretical results with sufficient numerical simulations. (general)
Fragmentation of polarized 23Na on 208Pb and the random-walk model
International Nuclear Information System (INIS)
Clarke, N.M.; Karban, O.; Blyth, C.O.; Choi, H.D.; Hall, S.J.; Roman, S.; Tungate, G.; Cole, A.J.; Davis, N.J.; Shotter, A.C.; Connell, K.A.
1993-01-01
Inclusive measurements are presented for the differential cross sections and tensor analyzing powers ( TT 20 and T 20 ) of ions produced by the fragmentation of a beam of polarized 23 Na incident on a 208 Pb target at an energy of 195.5 MeV (8.5 MeV/nucleon). The data are discussed in terms of a simple ''shape-effect'' model, and compared to the predictions of the nuclear random-walk model which has been extended to the calculation of aligned, deformed projectiles. This model reproduces the principal features of the differential cross sections and the trends as a function of mass loss, but gives poorer agreement for the analyzing powers
Cvetkovic, V.; Molin, S.
2012-02-01
We present a methodology that combines numerical simulations of groundwater flow and advective transport in heterogeneous porous media with analytical retention models for computing the infection risk probability from pathogens in aquifers. The methodology is based on the analytical results presented in [1,2] for utilising the colloid filtration theory in a time-domain random walk framework. It is shown that in uniform flow, the results from the numerical simulations of advection yield comparable results as the analytical TDRW model for generating advection segments. It is shown that spatial variability of the attachment rate may be significant, however, it appears to affect risk in a different manner depending on if the flow is uniform or radially converging. In spite of the fact that numerous issues remain open regarding pathogen transport in aquifers on the field scale, the methodology presented here may be useful for screening purposes, and may also serve as a basis for future studies that would include greater complexity.
Microstructure-based characterization of permeability using a random walk model
International Nuclear Information System (INIS)
Chen, F F; Yang, Y S
2012-01-01
Quantitative transport properties of materials are analysed using a random walk model, based on the microscopic compositional distribution of compositions in the materials. A material sample is defined on a simple-cubic lattice, with volume fractions specified for each composition on every volume pixel (voxel). The quantitative relation between bulk permeability and fine-scale anisotropy is investigated by assuming fully anisotropic and fully isotropic voxel morphology. Such a study has prompted an analytic approximate formulation to predict bulk permeability range for a heterogeneous multi-component system that lacks detailed microstructure information. The numerical approach is verified on synthetic structures with known permeability. The analysis technique is applied to a real-world rock sample, as illustrated by a case study detailed in this paper. The investigations show that the bulk permeability is affected significantly by fine length scale anisotropy. (paper)
A random-walk model for pore pressure accumulation in marine soils
DEFF Research Database (Denmark)
Sumer, B. Mutlu; Cheng, Niang-Sheng
1999-01-01
A numerical random-walk model has been developed for the pore-water pressure. The model is based on the analogy between the variation of the pore pressure and the diffusion process of any passive quantity such as concentration. The pore pressure in the former process is analogous...... to the concentration in the latter. In the simulation, particles are released in the soil, and followed as they travel through the statistical field variables. The model has been validated (1) against the Terzaghi consolidation process, and (2) against the process where the pore pressure builds up under progressive...... waves. The model will apparently enable the researcher to handle complex geometries (such as a pipeline buried in a soil) relatively easily. Early results with regard to the latter example, namely the buildup of pore pressure around a buried pipeline subject to a progressive wave, are encouraging....
Penentuan Distribusi Suhu pada Permukaan Geometri Tak Tentu Menggunakan Metode Random Walk
Directory of Open Access Journals (Sweden)
Balduyanus Yosep Godja
2016-05-01
Full Text Available Telah dilakukan penentuan distribusi suhu dalam keadaan tunak pada sebuah plat bergeometri tak tentu menggunakan metode Random Walk yang dilengkapi fungsi green. Setiap sisi plat dikondisikan bervariasi terhadap suhu dalam rentang 10°C sampai 100°C dengan 4 (empat konfigurasi berkeadaan steady. Persamaan Laplace yang mendeskripsikan permasalahan ini dihampiri dengan mensimulasikan sejumlah walker pada setiap titik domain permasalahan untuk kemudian secara acak disebar menuju ke setiap sisi plat. Hasil yang diperoleh untuk setiap kondisi plat menunjukkan kesalahan relatif terhadap solusi numerik metode iterasi jacobi yang telah menghampiri solusi analitik, secara rata-rata adalah 0,85%. Nilai kesalahan tersebut diperoleh dengan menggunakan 5000 walker. Penelitian ini juga mendapatkan bahwa akurasi hampiran ditentukan oleh banyaknya walker yang digunakan. Secara umum, semakin banyak jumlah walker yang digunakan maka akurasi hampiran akan semakin baik.
Magnetic field line random walk in two-dimensional dynamical turbulence
Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.
2017-08-01
The field line random walk (FLRW) of magnetic turbulence is one of the important topics in plasma physics and astrophysics. In this article, by using the field line tracing method, the mean square displacement (MSD) of FLRW is calculated on all possible length scales for pure two-dimensional turbulence with the damping dynamical model. We demonstrate that in order to describe FLRW with the damping dynamical model, a new dimensionless quantity R is needed to be introduced. On different length scales, dimensionless MSD shows different relationships with the dimensionless quantity R. Although the temporal effect affects the MSD of FLRW and even changes regimes of FLRW, it does not affect the relationship between the dimensionless MSD and dimensionless quantity R on all possible length scales.
Estimating filtration coefficients for straining from percolation and random walk theories
DEFF Research Database (Denmark)
Yuan, Hao; Shapiro, Alexander; You, Zhenjiang
2012-01-01
In this paper, laboratory challenge tests are carried out under unfavorable attachment conditions, so that size exclusion or straining is the only particle capture mechanism. The experimental results show that far above the percolation threshold the filtration coefficients are not proportional...... size exclusion theory or the model of parallel tubes with mixing chambers, where the filtration coefficients are proportional to the flux through smaller pores, and the predicted penetration depths are much lower. A special capture mechanism is proposed, which makes it possible to explain...... the experimentally observed power law dependencies of filtration coefficients and large penetration depths of particles. Such a capture mechanism is realized in a 2D pore network model with periodical boundaries with the random walk of particles on the percolation lattice. Geometries of infinite and finite clusters...
SU-F-BRD-09: A Random Walk Model Algorithm for Proton Dose Calculation
International Nuclear Information System (INIS)
Yao, W; Farr, J
2015-01-01
Purpose: To develop a random walk model algorithm for calculating proton dose with balanced computation burden and accuracy. Methods: Random walk (RW) model is sometimes referred to as a density Monte Carlo (MC) simulation. In MC proton dose calculation, the use of Gaussian angular distribution of protons due to multiple Coulomb scatter (MCS) is convenient, but in RW the use of Gaussian angular distribution requires an extremely large computation and memory. Thus, our RW model adopts spatial distribution from the angular one to accelerate the computation and to decrease the memory usage. From the physics and comparison with the MC simulations, we have determined and analytically expressed those critical variables affecting the dose accuracy in our RW model. Results: Besides those variables such as MCS, stopping power, energy spectrum after energy absorption etc., which have been extensively discussed in literature, the following variables were found to be critical in our RW model: (1) inverse squared law that can significantly reduce the computation burden and memory, (2) non-Gaussian spatial distribution after MCS, and (3) the mean direction of scatters at each voxel. In comparison to MC results, taken as reference, for a water phantom irradiated by mono-energetic proton beams from 75 MeV to 221.28 MeV, the gamma test pass rate was 100% for the 2%/2mm/10% criterion. For a highly heterogeneous phantom consisting of water embedded by a 10 cm cortical bone and a 10 cm lung in the Bragg peak region of the proton beam, the gamma test pass rate was greater than 98% for the 3%/3mm/10% criterion. Conclusion: We have determined key variables in our RW model for proton dose calculation. Compared with commercial pencil beam algorithms, our RW model much improves the dose accuracy in heterogeneous regions, and is about 10 times faster than MC simulations
Efficiency analysis of diffusion on T-fractals in the sense of random walks.
Peng, Junhao; Xu, Guoai
2014-04-07
Efficiently controlling the diffusion process is crucial in the study of diffusion problem in complex systems. In the sense of random walks with a single trap, mean trapping time (MTT) and mean diffusing time (MDT) are good measures of trapping efficiency and diffusion efficiency, respectively. They both vary with the location of the node. In this paper, we analyze the effects of node's location on trapping efficiency and diffusion efficiency of T-fractals measured by MTT and MDT. First, we provide methods to calculate the MTT for any target node and the MDT for any source node of T-fractals. The methods can also be used to calculate the mean first-passage time between any pair of nodes. Then, using the MTT and the MDT as the measure of trapping efficiency and diffusion efficiency, respectively, we compare the trapping efficiency and diffusion efficiency among all nodes of T-fractal and find the best (or worst) trapping sites and the best (or worst) diffusing sites. Our results show that the hub node of T-fractal is the best trapping site, but it is also the worst diffusing site; and that the three boundary nodes are the worst trapping sites, but they are also the best diffusing sites. Comparing the maximum of MTT and MDT with their minimums, we find that the maximum of MTT is almost 6 times of the minimum of MTT and the maximum of MDT is almost equal to the minimum for MDT. Thus, the location of target node has large effect on the trapping efficiency, but the location of source node almost has no effect on diffusion efficiency. We also simulate random walks on T-fractals, whose results are consistent with the derived results.
Learning of Multimodal Representations With Random Walks on the Click Graph.
Wu, Fei; Lu, Xinyan; Song, Jun; Yan, Shuicheng; Zhang, Zhongfei Mark; Rui, Yong; Zhuang, Yueting
2016-02-01
In multimedia information retrieval, most classic approaches tend to represent different modalities of media in the same feature space. With the click data collected from the users' searching behavior, existing approaches take either one-to-one paired data (text-image pairs) or ranking examples (text-query-image and/or image-query-text ranking lists) as training examples, which do not make full use of the click data, particularly the implicit connections among the data objects. In this paper, we treat the click data as a large click graph, in which vertices are images/text queries and edges indicate the clicks between an image and a query. We consider learning a multimodal representation from the perspective of encoding the explicit/implicit relevance relationship between the vertices in the click graph. By minimizing both the truncated random walk loss as well as the distance between the learned representation of vertices and their corresponding deep neural network output, the proposed model which is named multimodal random walk neural network (MRW-NN) can be applied to not only learn robust representation of the existing multimodal data in the click graph, but also deal with the unseen queries and images to support cross-modal retrieval. We evaluate the latent representation learned by MRW-NN on a public large-scale click log data set Clickture and further show that MRW-NN achieves much better cross-modal retrieval performance on the unseen queries/images than the other state-of-the-art methods.
Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach
Comolli, Alessandro; Dentz, Marco
2017-09-01
We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy's law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in
Avrachenkov, Konstantin; Borkar, Vivek S; Kadavankandy, Arun; Sreedharan, Jithin K
2018-01-01
In the framework of network sampling, random walk (RW) based estimation techniques provide many pragmatic solutions while uncovering the unknown network as little as possible. Despite several theoretical advances in this area, RW based sampling techniques usually make a strong assumption that the samples are in stationary regime, and hence are impelled to leave out the samples collected during the burn-in period. This work proposes two sampling schemes without burn-in time constraint to estimate the average of an arbitrary function defined on the network nodes, for example, the average age of users in a social network. The central idea of the algorithms lies in exploiting regeneration of RWs at revisits to an aggregated super-node or to a set of nodes, and in strategies to enhance the frequency of such regenerations either by contracting the graph or by making the hitting set larger. Our first algorithm, which is based on reinforcement learning (RL), uses stochastic approximation to derive an estimator. This method can be seen as intermediate between purely stochastic Markov chain Monte Carlo iterations and deterministic relative value iterations. The second algorithm, which we call the Ratio with Tours (RT)-estimator, is a modified form of respondent-driven sampling (RDS) that accommodates the idea of regeneration. We study the methods via simulations on real networks. We observe that the trajectories of RL-estimator are much more stable than those of standard random walk based estimation procedures, and its error performance is comparable to that of respondent-driven sampling (RDS) which has a smaller asymptotic variance than many other estimators. Simulation studies also show that the mean squared error of RT-estimator decays much faster than that of RDS with time. The newly developed RW based estimators (RL- and RT-estimators) allow to avoid burn-in period, provide better control of stability along the sample path, and overall reduce the estimation time. Our
Hurley, Jane C; Hollingshead, Kevin E; Todd, Michael; Jarrett, Catherine L; Tucker, Wesley J; Angadi, Siddhartha S; Adams, Marc A
2015-09-11
Walking is a widely accepted and frequently targeted health promotion approach to increase physical activity (PA). Interventions to increase PA have produced only small improvements. Stronger and more potent behavioral intervention components are needed to increase time spent in PA, improve cardiometabolic risk markers, and optimize health. Our aim is to present the rationale and methods from the WalkIT Trial, a 4-month factorial randomized controlled trial (RCT) in inactive, overweight/obese adults. The main purpose of the study was to evaluate whether intensive adaptive components result in greater improvements to adults' PA compared to the static intervention components. Participants enrolled in a 2x2 factorial RCT and were assigned to one of four semi-automated, text message-based walking interventions. Experimental components included adaptive versus static steps/day goals, and immediate versus delayed reinforcement. Principles of percentile shaping and behavioral economics were used to operationalize experimental components. A Fitbit Zip measured the main outcome: participants' daily physical activity (steps and cadence) over the 4-month duration of the study. Secondary outcomes included self-reported PA, psychosocial outcomes, aerobic fitness, and cardiorespiratory risk factors assessed pre/post in a laboratory setting. Participants were recruited through email listservs and websites affiliated with the university campus, community businesses and local government, social groups, and social media advertising. This study has completed data collection as of December 2014, but data cleaning and preliminary analyses are still in progress. We expect to complete analysis of the main outcomes in late 2015 to early 2016. The Walking Interventions through Texting (WalkIT) Trial will further the understanding of theory-based intervention components to increase the PA of men and women who are healthy, insufficiently active and are overweight or obese. WalkIT is one of
B. Chen (Bohan); J. Blanchet; C.H. Rhee (Chang-Han); A.P. Zwart (Bert)
2017-01-01
textabstractWe propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based on an importance sampling strategy that hinges
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…
Schippers, P.; Verboom, J.; Knaapen, J.P.; Apeldoorn, van R.
1996-01-01
A grid-based random walk model has been developed to simulate animal dispersal, taking landscape heterogeneity and linear barriers such as roads and rivers into account. The model can be used to estimate connectivity and has been parameterized for thebadger in the central part of the Netherlands.
Scholtes, V.A.; Becher, J.G.; Janssen-Potten, Y.J.; Dekkers, H.; Smallenbroek, L.; Dallmeijer, A.J.
2012-01-01
The objective of the study was to evaluate the effectiveness of functional progressive resistance exercise (PRE) training on walking ability in children with cerebral palsy (CP).Fifty-one ambulant children with spastic CP (mean age 10 years 5 months, 29 boys) were randomized to an intervention (n=
Beijeren, H. van; Spohn, H.
1983-01-01
Point scatterers are placed on the real line such that the distances between scatterers are independent identically distributed random variables (stationary renewal process). For a fixed configuration of scatterers a particle performs the following random walk: The particle starts at the pointx with
International Nuclear Information System (INIS)
Reynolds, A M
2009-01-01
The movement patterns of a diverse range of animals have scale-free characteristics. These characteristics provide necessary but not sufficient conditions for the presence of movement patterns that can be approximated by Levy walks. Nevertheless, it has been widely assumed that the occurrence of scale-free animal movements can indeed be attributed to the presence of Levy walks. This is, in part, because it is known that the super-diffusive properties of Levy walks can be advantageous in random search scenarios when searchers have little or no prior knowledge of target locations. However, fractional Brownian motions (fBms) and fractional Levy motions (fLms) are both scale-free and super-diffusive, and so it is possible that these motions rather than Levy walks underlie some or all occurrences of scale-free animal movement patterns. Here this possibility is examined in numerical simulations through a determination of the searching efficiencies of fBm and fLm searches. It is shown that these searches are less efficient than Levy walk searches. This finding does not rule out the possibility that some animals with scale-free movement patterns are executing fBm and fLm searches, but it does make Levy walk searches the more likely possibility.
Bound states of Dipolar Bosons in One-dimensional Systems
DEFF Research Database (Denmark)
G. Volosniev, A.; R. Armstrong, J.; V. Fedorov, D.
2013-01-01
that in the weakly-coupled limit the inter-tube interaction is similar to a zero-range term with a suitable rescaled strength. This allows us to address the corresponding many-body physics of the system by constructing a model where bound chains with one molecule in each tube are the effective degrees of freedom......We consider one-dimensional tubes containing bosonic polar molecules. The long-range dipole-dipole interactions act both within a single tube and between different tubes. We consider arbitrary values of the externally aligned dipole moments with respect to the symmetry axis of the tubes. The few....... This model can be mapped onto one-dimensional Hamiltonians for which exact solutions are known....
Quasi-One-Dimensional Intermittent Flux Behavior in Superconducting Films
Directory of Open Access Journals (Sweden)
A. J. Qviller
2012-01-01
Full Text Available Intermittent filamentary dynamics of the vortex matter in superconductors is found in films of YBa_{2}Cu_{3}O_{7-δ} deposited on tilted substrates. Deposition of this material on such substrates creates parallel channels of easy flux penetration when a magnetic field is applied perpendicular to the film. As the applied field is gradually increased, magneto-optical imaging reveals that flux penetrates via numerous quasi-one-dimensional jumps. The distribution of flux avalanche sizes follows a power law, and data collapse is obtained by finite-size scaling, with the depth of the flux front used as crossover length. The intermittent behavior shows no threshold value in the applied field, in contrast to conventional flux jumping. The results strongly suggest that the quasi-one-dimensional flux jumps are of a different nature than the thermomagnetic dendritic (branching avalanches that are commonly found in superconducting films.
Versatile hydrothermal synthesis of one-dimensional composite structures
Luo, Yonglan
2008-12-01
In this paper we report on a versatile hydrothermal approach developed to fabricate one-dimensional (1D) composite structures. Sulfur and selenium formed liquid and adsorbed onto microrods as droplets and subsequently reacted with metallic ion in solution to produce nanoparticles-decorated composite microrods. 1D composites including ZnO/CdS, ZnO/MnS, ZnO/CuS, ZnO/CdSe, and FeOOH/CdS were successfully made using this hydrothermal strategy and the growth mechanism was also discussed. This hydrothermal strategy is simple and green, and can be extended to the synthesis of various 1D composite structures. Moreover, the interaction between the shell nanoparticles and the one-dimensional nanomaterials were confirmed by photoluminescence investigation of ZnO/CdS.
Solitons in one-dimensional charge density wave systems
International Nuclear Information System (INIS)
Su, W.P.
1981-01-01
Theoretical research on one dimensional charge density wave systems is outlined. A simple coupled electron-photon Hamiltonian is studied including a Green's function approach, molecular dynamics, and Monte Carlo path integral method. As in superconductivity, the nonperturbative nature of the system makes the physical ground states and low energy excitations drastically different from the bare electrons and phonons. Solitons carry quantum numbers which are entirely different from those of the bare electrons and holes. The fractional charge character of the solitons is an example of this fact. Solitons are conveniently generated by doping material with donors or acceptors or by photon absorption. Most predictions of the theory are in qualitative agreement with experiments. The one dimensional charge density wave system has potential technological importance and a possible role in uncovering phenomena which might have implications in relativistic field theory and elementary particle physics
Applications of one-dimensional models in simplified inelastic analyses
International Nuclear Information System (INIS)
Kamal, S.A.; Chern, J.M.; Pai, D.H.
1980-01-01
This paper presents an approximate inelastic analysis based on geometric simplification with emphasis on its applicability, modeling, and the method of defining the loading conditions. Two problems are investigated: a one-dimensional axisymmetric model of generalized plane strain thick-walled cylinder is applied to the primary sodium inlet nozzle of the Clinch River Breeder Reactor Intermediate Heat Exchanger (CRBRP-IHX), and a finite cylindrical shell is used to simulate the branch shell forging (Y) junction. The results are then compared with the available detailed inelastic analyses under cyclic loading conditions in terms of creep and fatigue damages and inelastic ratchetting strains per the ASME Code Case N-47 requirements. In both problems, the one-dimensional simulation is able to trace the detailed stress-strain response. The quantitative comparison is good for the nozzle, but less satisfactory for the Y junction. Refinements are suggested to further improve the simulation
Thermal conductivity in one-dimensional nonlinear systems
Politi, Antonio; Giardinà, Cristian; Livi, Roberto; Vassalli, Massimo
2000-03-01
Thermal conducitivity of one-dimensional nonlinear systems typically diverges in the thermodynamic limit, whenever the momentum is conserved (i.e. in the absence of interactions with an external substrate). Evidence comes from detailed studies of Fermi-Pasta-Ulam and diatomic Toda chains. Here, we discuss the first example of a one-dimensional system obeying Fourier law : a chain of coupled rotators. Numerical estimates of the thermal conductivity obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of the rotator model.
Thermoelectric properties of one-dimensional graphene antidot arrays
International Nuclear Information System (INIS)
Yan, Yonghong; Liang, Qi-Feng; Zhao, Hui; Wu, Chang-Qin; Li, Baowen
2012-01-01
We investigate the thermoelectric properties of one-dimensional (1D) graphene antidot arrays by nonequilibrium Green's function method. We show that by introducing antidots to the pristine graphene nanoribbon the thermal conductance can be reduced greatly while keeping the power factor still high, thus leading to an enhanced thermoelectric figure of merit (ZT). Our numerical results indicate that ZT values of 1D antidot graphene arrays can be up to unity, which means the 1D graphene antidot arrays may be promising for thermoelectric applications. -- Highlights: ► We study thermoelectric properties of one-dimensional (1D) graphene antidot arrays. ► Thermoelectric figure of merit (ZT) of 1D antidot arrays can exceed unity. ► ZT of 1D antidot arrays is larger than that of two-dimensional arrays.
Scattering theory for one-dimensional step potentials
International Nuclear Information System (INIS)
Ruijsenaars, S.N.M.; Bongaarts, P.J.M.
1977-01-01
The scattering theory is treated for the one-dimensional Dirac equation with potentials that are bounded, measurable, real-valued functions on the real line, having constant values, not necessarily the same, on the left and on the right side of a compact interval. Such potentials appear in the Klein paradox. It is shown that appropriately modified wave operators exist and that the corresponding S-operator is unitary. The connection between time-dependent scattering theory and time-independent scattering theory in terms of incoming and outgoing plane wave solutions is established and some further properties are proved. All results and their proofs have a straightforward translation to the one-dimensional Schroedinger equation with the same class of step potentials
Resonance Raman spectroscopy in one-dimensional carbon materials
Directory of Open Access Journals (Sweden)
Dresselhaus Mildred S.
2006-01-01
Full Text Available Brazil has played an important role in the development and use of resonance Raman spectroscopy as a powerful characterization tool for materials science. Here we present a short history of Raman scattering research in Brazil, highlighting the important contributions to the field coming from Brazilian researchers in the past. Next we discuss recent and important contributions where Brazil has become a worldwide leader, that is on the physics of quasi-one dimensional carbon nanotubes. We conclude this article by presenting results from a very recent resonance Raman study of exciting new materials, that are strictly one-dimensional carbon chains formed by the heat treatment of very pure double-wall carbon nanotube samples.
Directory of Open Access Journals (Sweden)
G. Morone
2012-01-01
Full Text Available Foot drop is a quite common problem in nervous system disorders. Neuromuscular electrical stimulation (NMES has showed to be an alternative approach to correct foot drop improving walking ability in patients with stroke. In this study, twenty patients with stroke in subacute phase were enrolled and randomly divided in two groups: one group performing the NMES (i.e. Walkaide Group, WG and the Control Group (CG performing conventional neuromotor rehabilitation. Both groups underwent the same amount of treatment time. Significant improvements of walking speed were recorded for WG (% than for CG (%, as well as in terms of locomotion (Functional Ambulation Classification score: . In terms of mobility and force, ameliorations were recorded, even if not significant (Rivermead Mobility Index: ; Manual Muscle Test: . Similar changes between groups were observed for independence in activities of daily living, neurological assessments, and spasticity reduction. These results highlight the potential efficacy for patients affected by a droop foot of a walking training performed with a neurostimulator in subacute phase.
Kalron, Alon; Rosenblum, Uri; Frid, Lior; Achiron, Anat
2017-03-01
Evaluate the effects of a Pilates exercise programme on walking and balance in people with multiple sclerosis and compare this exercise approach to conventional physical therapy sessions. Randomized controlled trial. Multiple Sclerosis Center, Sheba Medical Center, Tel-Hashomer, Israel. Forty-five people with multiple sclerosis, 29 females, mean age (SD) was 43.2 (11.6) years; mean Expanded Disability Status Scale (S.D) was 4.3 (1.3). Participants received 12 weekly training sessions of either Pilates ( n=22) or standardized physical therapy ( n=23) in an outpatient basis. Spatio-temporal parameters of walking and posturography parameters during static stance. Functional tests included the Time Up and Go Test, 2 and 6-minute walk test, Functional Reach Test, Berg Balance Scale and the Four Square Step Test. In addition, the following self-report forms included the Multiple Sclerosis Walking Scale and Modified Fatigue Impact Scale. At the termination, both groups had significantly increased their walking speed ( P=0.021) and mean step length ( P=0.023). According to the 2-minute and 6-minute walking tests, both groups at the end of the intervention program had increased their walking speed. Mean (SD) increase in the Pilates and physical therapy groups were 39.1 (78.3) and 25.3 (67.2) meters, respectively. There was no effect of group X time in all instrumented and clinical balance and gait measures. Pilates is a possible treatment option for people with multiple sclerosis in order to improve their walking and balance capabilities. However, this approach does not have any significant advantage over standardized physical therapy.
Impurity modes in the one-dimensional XXZ Heisenberg model
International Nuclear Information System (INIS)
Sousa, J.M.; Leite, R.V.; Landim, R.R.; Costa Filho, R.N.
2014-01-01
A Green's function formalism is used to calculate the energy of impurity modes associated with one and/or two magnetic impurities in the one-dimensional Heisenberg XXZ magnetic chain. The system can be tuned from the Heisenberg to the Ising model varying a parameter λ. A numerical study is performed showing two types of localized modes (s and p). The modes depend on λ and the degeneracy of the acoustic modes is broken.
UNICIN - an one-dimensional computer code for reactor kinetics
International Nuclear Information System (INIS)
Rosa, M.A.P.; Alcantara, H.G. de; Nair, R.P.K.
1984-01-01
A program for the solution of the time- and space-dependent multigroup diffusion equations and the delayed-neutron precursors concentration equations in one dimensional geometries by the weighted residual method is described. The discretized equations are solved through an iterative procedure with convergence accelerated by the over-relaxation method. The system is perturbed through the variation of the nuclide concentrations in specified regions. Two feedback effects are included, namely, the temperature and the burnup. (Author) [pt
Nonlinear acoustic wave propagating in one-dimensional layered system
International Nuclear Information System (INIS)
Yun, Y.; Miao, G.Q.; Zhang, P.; Huang, K.; Wei, R.J.
2005-01-01
The propagation of finite-amplitude plane sound in one-dimensional layered media is studied by the extended method of transfer matrix formalism. For the periodic layered system consisting of two alternate types of liquid, the energy distribution and the phase vectors of the interface vibration are computed and analyzed. It is found that in the pass-band, the second harmonic of sound wave can propagate with the characteristic modulation