number of distinct sites visited by a random walker trapped by an absorbing boundary the number of distinct sites visited by a lattice random walker is a subject of continuing interest in both mathematics and physics all previous investigations have used the assumption that the lattice is unbounded an assessment of the amount of tissue interrogated by a photon in reflectance measurements for diagnostic purposes suggests analyzing properties of the average number of distinct sites visited by a random walker trapped by an absorbing plane at time t we show that for sufficiently large t this number is the same as the average number of distinct sites visited for this time when the surface is not present a more complete analysis is possible for a random walk on a line terminated by an absorbing point

a second order difference scheme for the time fractional substantial diffusion equation abstract in this work a second order approximation of the fractional substantial derivative is presented by considering a modified shifted substantial grunwald formula and its asymptotic expansion moreover the proposed approximation is applied to a fractional diffusion equation with fractional substantial derivative in time with the use of the fourth order compact scheme in space we give a fully discrete grunwald letnikov formula based compact difference scheme and prove its stability and convergence by the energy method under smooth assumptions in addition the problem with nonsmooth solution is also discussed and an improved algorithm is proposed to deal with the singularity of the fractional substantial derivative numerical examples show the reliability and efficiency of the scheme

mean first passage time of surface mediated diffusion in spherical domains we present an exact calculation of the mean first passage time to a target on the surface of a 2d or 3d spherical domain for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion the presented approach is based on an integral equation which can be solved analytically numerically validated approximation schemes which provide more tractable expressions of the mean first passage time are also proposed in the framework of this minimal model of surface mediated reactions we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface

statistics of persistent events an exactly soluble model it was recently realized that the persistence exponent appearing in the dynamics of nonequilibrium systems is a special member of a continuously varying family of exponents describing generalized persistence properties we propose and solve a simple stochastic spin model where time intervals between spin flips are independent and distributed according to a l evy law both the limit distribution of the mean magnetization and the generalized persistence exponents are obtained exactly we discuss the relevance of this model for phase ordering spin glasses and random walks

residence time distribution for a class of gaussian markov processes we study the distribution of residence time or equivalently that of mean magnetization for a family of gaussian markov processes indexed by a positive parameter alpha the persistence exponent for these processes is simply given by theta alpha but the residence time distribution is nontrivial the shape of this distribution undergoes a qualitative change as theta increases indicating a sharp change in the ergodic properties of the process we develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha for some special values of alpha we obtain closed form expressions of the distribution function s1063 651x 99 03306 1

tabu search directed by direct search methods for nonlinear global optimization abstract in recent years there has been a great deal of interest in metaheuristics in the optimization community tabu search ts represents a popular class of metaheuristics however compared with other metaheuristics like genetic algorithm and simulated annealing contributions of ts that deals with continuous problems are still very limited in this paper we introduce a continuous ts called directed tabu search dts method in the dts method direct search based strategies are used to direct a tabu search these strategies are based on the well known nelder mead method and a new pattern search procedure called adaptive pattern search moreover we introduce a new tabu list conception with anti cycling rules called tabu regions and semi tabu regions in addition diversification and intensification search schemes are employed numerical results show that the proposed method is promising and produces high quality solutions

functionals of brownian motion localization and metric graphs we review several results related to the problem of a quantum particle in a random environment in an introductory part we recall how several functionals of brownian motion arise in the study of electronic transport in weakly disordered metals weak localization two aspects of the physics of the one dimensional strong localization are reviewed some properties of the scattering by a random potential time delay distribution and a study of the spectrum of a random potential on a bounded domain the extreme value statistics of the eigenvalues then we mention several results concerning the diffusion on graphs and more generally the spectral properties of the schrodinger operator on graphs the interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated finally we consider a two dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices we recall the connection between spectral properties of this model and winding functionals of planar brownian motion

on the use of reverse brownian motion to accelerate hybrid simulations multiscale and multiphysics simulations are two rapidly developing fields of scientific computing efficient coupling of continuum deterministic or stochastic constitutive solvers with their discrete stochastic particle based counterparts is a common challenge in both kinds of simulations we focus on interfacial tightly coupled simulations of diffusion that combine continuum and particle based solvers the latter employs the reverse brownian motion rbm a monte carlo approach that allows one to enforce inhomogeneous dirichlet neumann or robin boundary conditions and is trivially parallelizable we discuss numerical approaches for improving the accuracy of rbm in the presence of inhomogeneous neumann boundary conditions and alternative strategies for coupling the rbm solver with its continuum counterpart numerical experiments are used to investigate the convergence stability and computational efficiency of the proposed hybrid algorithm

statistical properties of functionals of the paths of a particle diffusing in a one dimensional random potential we present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one dimensional quenched random potential we demonstrate the implementation of the formalism in two specific examples 1 where the functional corresponds to the local time spent by the particle around the origin and 2 where the functional corresponds to the occupation time spent by the particle on the positive side of the origin within an observation time window of size t we compute the disorder average distributions of the local time the inverse local time the occupation time and the inverse occupation time and show that in many cases disorder modifies the behavior drastically

langevin equations for continuous time levy flights we consider the combined effects of a power law l evy step distribution characterized by the step index f and a power law waiting time distribution characterized by the time index g on the long time behavior of a random walker the main point of our analysis is a formulation in terms of coupled langevin equations which allows in a natural way for the inclusion of external force fields in the anomalous case for f2 and g1 the dynamic exponent z locks onto the ratio f g drawing on recent results on l evy flights in the presence of a random force field we also find that this result is independent of the presence of weak quenched disorder for d below the critical dimension mathit d mathit c 2f 2 the disorder is relevant corresponding to a nontrivial fixed point for the force correlation function

width distribution for random walk interfaces roughening of a one dimensional interface is studied under the assumption that the interface configurations are continuous periodic random walks the distribution of the square of the width of interface mathit w 2 is found to scale as p mathit w 2 mathit w 2 mathrm mathrm ensuremath 1 ensuremath phi mathit w 2 mathit w 2 where mathit w 2 is the average of mathit w 2 we calculate the scaling function ensuremath phi x exactly and compare it both to exact enumerations for a discrete slope surface evolution model and to ensuremath phi s obtained in monte carlo simulations of equilibrium and driven interfaces of chemically reacting systems

correlation based motion vector processing with adaptive interpolation scheme for motion compensated frame interpolation in this paper we address the problems of unreliable motion vectors that cause visual artifacts but cannot be detected by high residual energy or bidirectional prediction difference in motion compensated frame interpolation a correlation based motion vector processing method is proposed to detect and correct those unreliable motion vectors by explicitly considering motion vector correlation in the motion vector reliability classification motion vector correction and frame interpolation stages since our method gradually corrects unreliable motion vectors based on their reliability we can effectively discover the areas where no motion is reliable to be used such as occlusions and deformed structures we also propose an adaptive frame interpolation scheme for the occlusion areas based on the analysis of their surrounding motion distribution as a result the interpolated frames using the proposed scheme have clearer structure edges and ghost artifacts are also greatly reduced experimental results show that our interpolated results have better visual quality than other methods in addition the proposed scheme is robust even for those video sequences that contain multiple and fast motions

cyber swarm algorithms improving particle swarm optimization using adaptive memory strategies particle swarm optimization pso has emerged as an acclaimed approach for solving complex optimization problems the nature metaphors of flocking birds or schooling fish that originally motivated pso have made the algorithm easy to describe but have also occluded the view of valuable strategies based on other foundations from a complementary perspective scatter search ss and path relinking pr provide an optimization framework based on the assumption that useful information about the global solution is typically contained in solutions that lie on paths from good solutions to other good solutions shared and contrasting principles underlying the pso and the ss pr methods provide a fertile basis for combining them drawing especially on the adaptive memory and responsive strategy elements of ss and pr we create a combination to produce a cyber swarm algorithm that proves more effective than the standard pso 2007 recently established as a leading form of pso applied to the challenge of finding global minima for continuous nonlinear functions the cyber swarm algorithm not only is able to obtain better solutions to a well known set of benchmark functions but also proves more robust under a wide range of experimental conditions

a new particle swarm optimization algorithm with an application abstract in this paper for dealing with the portfolio model from stocks market a new particle swarm optimization algorithm npso is presented in which the optimal and sub optimal positions of each particle are considered in the iteration process and the crossover operation is used to avoid premature it is demonstrated from optimization tests that npso outperforms existed pso then npso is used to solve a discontinuous programming model and four different optimal portfolio selections are displayed which are denoted by s 1 s 2 s 3 and s 4 respectively finally actual return rates of these portfolios are obtained and it is analyzed from related graphs that s 2 and s 3 gain better results

fractional time quantum dynamics application of the fractional calculus to quantum processes is presented in particular the quantum dynamics is considered in the framework of the fractional time schr odinger equation se which differs from the standard se by the fractional time derivative ensuremath partial ensuremath partial t ensuremath rightarrow ensuremath partial ensuremath alpha ensuremath partial t ensuremath alpha it is shown that for ensuremath alpha 1 2 the fractional se is isospectral to a comb model an analytical expression for the green s functions of the systems are obtained the semiclassical limit is discussed

asymptotic distributions of continuous time random walks a probabilistic approach we provide a systematic analysis of the possible asymptotic distributions o one dimensional continuous time random walks ctrws by applying the limit theorems of probability theory biased and unbiased walks of coupled and decoupled memory are considered in contrast to previous work concerning decoupled memory and levy walks we deal also with arbitrary coupled memory and with jump densities asymmetric about its mean obtaining asymmetric levy stable limits suprisingly it is found that in most cases coupled memory has no essential influence on the form of the limiting distribution we discuss interesting properties of walks with an infinite mean waiting time between successive jumps

asymptotic behavior of stochastic lattice systems with a caputo fractional time derivative abstract the asymptotic behavior of a stochastic lattice system with a caputo fractional time derivative is investigated in particular the existence of a global forward attracting set in the weak mean square topology is established a general theorem on the existence of solutions for a fractional sde in a hilbert space under the assumption that the nonlinear term is weakly continuous in a given sense is established and applied to the lattice system the existence and uniqueness of solutions for a more general fractional sdes is also obtained under a lipschitz condition

corrections to subspaces indexing model on grassmann manifold for image search in the original paper named above ibid vol 20 no 9 pp 2627 2635 sep 2011 table ii incorrectly appeared as a duplicate of table iii instead table ii should have correctly appeared as shown here

analytical representations of the spread harmonic measure density we study the spread harmonic measure that characterizes the spatial distribution of reaction events on a partially reactive surface for euclidean domains in which brownian motion can be split into independent lateral and transverse displacements we derive analytical formulas for the spread harmonic measure density and analyze its asymptotic behavior this analysis is applicable to slab domains general cylindrical domains and a half space we investigate the spreading effect due to multiple reflections on the surface and the underlying role of finite reactivity we discuss further extensions and applications of analytical results to describe laplacian transfer phenomena such as permeation through semipermeable membranes secondary current distribution on partially blocking electrodes and surface relaxation in nuclear magnetic resonance

effects of an absorbing boundary on the average volume visited by n spherical brownian particles abstract the number of distinct sites visited by a lattice random walk and its continuum analog the volume swept out by a diffusing spherical particle are used to model different phenomena in physics chemistry and biology therefore the problem of finding statistical properties of these random variables is of importance there have been several studies of the more general problem of the volume of the region explored by n random walks or brownian particles in an unbounded space we here study the effects of a planar absorbing boundary on the average of this volume the boundary breaks the translational invariance of the space and introduces an additional spatial parameter the initial distance of the brownian particles from the surface we derive expressions for the average volume visited in three dimensions and the average span in one dimension as functions of the time for given values of the initial distance to the absorbing boundary and n the results can be transformed to those for n lattice random walks by appropriately choosing the radius and diffusion constant of the spheres

residence times and other functionals of reflected brownian motion we study the residence and local times for a brownian particle confined by reflecting boundaries and propose a general solution to the problem of finding the related probability distribution its fourier transform characteristic function and laplace transform survival probability are obtained in a compact matrix form involving the laplace operator eigenbasis explicit combinatorial relations are derived for the moments and the probability distribution is shown to be nearly gaussian when the exploration time is long enough when the eigenbasis or a part of it is known the numerical computation of the residence time distributions is straightforward and accurate the present approach can also be applied to investigate other functionals of reflected brownian motion describing in particular restricted diffusion in an external field or potential e g nuclei diffusing in an inhomogeneous magnetic field theoretical results for the local times are confronted with monte carlo simulations on the unit interval disk and sphere

finding local optima of high dimensional functions using direct search methods this paper focuses on a subclass of box constrained non linear optimization problems we are particularly concerned with settings where gradient information is unreliable or too costly to calculate and the function evaluations themselves are very costly this encourages the use of derivative free optimization methods and especially a subclass of these referred to as direct search methods the thrust of our investigation is twofold first we implement and evaluate a number of traditional direct search methods according to the premise that they should be suitable as local optimizers when used in a metaheuristic framework second we introduce a new direct search method based on scatter search designed to remedy the lack of a good derivative free method for solving problems of high dimensions our new direct search method has convergence properties comparable to those of existing methods in addition to being able to solve larger problems more effectively

number of common sites visited by n random walkers we compute analytically the mean number of common sites w n t visited by n independent random walkers each of length t and all starting at the origin at t 0 in d dimensions we show that in the n d plane there are three distinct regimes for the asymptotic large t growth of w n t these three regimes are separated by two critical lines d 2 and d d c n 2n n 1 in the n d plane for d d c n w n t const as t exactly at the critical dimensions there are logarithmic corrections for d 2 we get w n t t ln t n while for d d c n w n t ln t for large t our analytical predictions are verified in numerical simulations

inter particle communication and search dynamics of lbest particle swarm optimizers an analysis particle swarm optimization pso is arguably one of the most popular nature inspired algorithms for real parameter optimization at present the existing theoretical research on pso focuses on the issues like stability convergence and explosion of the swarm however all of them are based on the gbest global best communication topology which usually is susceptible to false or premature convergence over multi modal fitness landscapes the present standard pso spso 2007 uses an lbest local best topology where a particle is stochastically attracted not towards the best position found in the entire swarm but towards the best position found by any particle in its topological neighborhood this article presents a first step towards a probabilistic analysis of the particle interaction and information exchange in an lbest pso with variable random neighborhood topology as found in spso 2007 it addresses issues like the distribution of particles over neighborhoods the probability distributions of the social and cognitive terms in lbest model and the explorative power of the lbest pso it also presents a state space model of the lbest pso and draws important conclusions regarding the stability and convergence of the particle dynamics in the light of control theory

a novel approach to fruc using discriminant saliency and frame segmentation motion compensated frame interpolation mcfi is a technique used extensively for increasing the temporal frequency of a video sequence in order to obtain a high quality interpolation the motion field between frames must be well estimated however many current techniques for determining the motion are prone to errors in occlusion regions as well as regions with repetitive structure we propose an algorithm for improving both the objective and subjective quality of mcfi by refining the motion vector field we first utilize a discriminant saliency classifier to determine which regions of the motion field are most important to a human observer these regions are refined using a multistage motion vector refinement mvr which promotes motion vector candidates based upon their likelihood given a local neighborhood for regions which fall below the saliency threshold a frame segmentation is used to locate regions of homogeneous color and texture via normalized cuts motion vectors are promoted such that each homogeneous region has a consistent motion experimental results demonstrate an improvement over previous frame rate up conversion fruc methods in both objective and subjective picture quality

first exit times and residence times for discrete random walks on finite lattices in this paper we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice we consider a wide class of random walks and lattices including random walks in a nontrivial potential landscape we also compute quantities of interest for modeling surface reactions and other dynamic processes such as the residence time in a subvolume the joint residence time of several particles and the number of hits on a reflecting surface

collision statistics for random flights with anisotropic scattering and absorption for a broad class of random walks with anisotropic scattering kernels and absorption we derive explicit formulas that allow expressing the moments of the collision number n v performed in a volume v as a function of the particle equilibrium distribution our results apply to arbitrary domains v and boundary conditions and allow assessing the hitting statistics for systems where the typical displacements are comparable to the domain size so that the diffusion limit is possibly not attained an example is discussed for one dimensional random flights with exponential displacements where analytical calculations can be carried out

volume of the domain visited by n spherical brownian particles the average value and variance of the volume of the domain visited in timet byn spherical brownian particles starting initially at the same point are presented as quadratures of the solutions of simple diffusion problems of the survival of a point brownian particle in the presence of one and two spherical traps as an illustration explicit time dependences are obtained for the average volume in one and three dimensions

the existence and asymptotic behavior of solutions to fractional stochastic evolution equations with infinite delay abstract we first prove the existence uniqueness and continuous dependence of mild solutions to stochastic delay evolution equations with a caputo fractional derivative d t c y t a y t f t y t g t y t d w t d t 1 2 1 then we investigate the asymptotic behavior of mild solutions to fractional stochastic delay evolution equations of the form d t c y t a y t i t 1 f t y t i t 1 g t y t d w t d t 0 1 in particular the existence of a global forward attracting set in the mean square topology is established a general theorem on the existence of mild solutions is obtained by using order fractional resolvent operator theory and the schauder fixed point theorem

nonergodicity of a time series obeying levy statistics time averaged autocorrelation functions of a dichotomous random process switching between 1 and 0 and governed by wide power law sojourn time distribution are studied such a process called a levy walk describes dynamical behaviors of many physical systems fluorescence intermittency of semiconductor nanocrystals under continuous laser illumination being one example when the mean sojourn time diverges the process is non ergodic in that case the time average autocorrelation function is not equal to the ensemble averaged autocorrelation function instead it remains random even in the limit of long measurement time several approximations for the distribution of this random autocorrelation function are obtained for different parameter ranges and favorably compared to monte carlo simulations nonergodicity of the power spectrum of the process is briefly discussed and a nonstationary wiener khintchine theorem relating the correlation functions and the power spectrum is presented the considered situation is in full contrast to the usual assumptions of ergodicity and stationarity

a quantum behaved particle swarm optimization with memetic algorithm and memory for continuous non linear large scale problems abstract quantum behaved particle swarm optimization qpso a novel variant of pso inspired by quantum mechanics is a global convergence guaranteed algorithm which outperforms the original pso in search ability and has fewer parameters to control but as many other psos it is easy to fall into local optimum in solving high dimensional complex optimization problems this paper proposes an improved qpso algorithm for continuous non linear large scale problems based on memetic algorithm and memory mechanism the memetic algorithm is used to make all particles each particle corresponding to a memetic gain some experience through a local search before being involved in the evolutionary process and the memory mechanism is used to introduce a so called bird kingdom with memory capacity both of which can improve the global search ability of the algorithm another difference compared to the previous qpsos is that we let each dimension of a particle update with the same random number thus increasing the speed of convergence and enhancing the ability of local search numerical experiments are conducted to compare the proposed algorithm with different variants of pso and other swarm intelligence algorithms the experimental results show the superiority of the proposed approach on benchmark test functions

mathematical basis for a general theory of laplacian transport towards irregular interfaces the theory of laplacian transport towards and across irregular surfaces is reformulated in terms of the dirichlet to neumann operator and its spectral characteristics this permits us to obtain an exact equivalent circuit for the impedance of a working interface of arbitrary shape the important result is that only very few eigenmodes of this operator do govern the entire response of a macroscopic system this property drastically simplifies the understanding of irregular or prefractal interfaces the results can be applied in electrochemistry physiology and chemical engineering fields where exchange processes across surfaces with complex geometry are ubiquitous

a symmetric motion estimation method for motion compensated frame interpolation this paper proposes a new motion compensated frame interpolation mcfi method the proposed method utilizes a symmetric motion estimation sme method which is a new pixel wise motion estimation method for intermediate frame interpolation by using an adaptive search range for the motion estimation the proposed method can obtain a more reliable motion vector for each pixel than previous mcfi methods that use a conventional block matching algorithm bma in addition we propose a combined method of the sme and bma to reduce the computation time of the pixel wise motion estimation method the experimental results show that the proposed method outperforms other mcfi methods in terms of generating objectively and subjectively better interpolated frames

from stochastic dominance to mean risk models semideviations as risk measures abstract two methods are frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches the former is based on an axiomatic model of risk averse preferences but does not provide a convenient computational recipe the latter quantifies the problem in a lucid form of two criteria with possible trade off analysis but cannot model all risk averse preferences in particular if variance is used as a measure of risk the resulting mean variance markowitz model is in general not consistent with stochastic dominance rules this paper shows that the standard semideviation square root of the semivariance as the risk measure makes the mean risk model consistent with the second degree stochastic dominance provided that the trade off coefficient is bounded by a certain constant similar results are obtained for the absolute semideviation and for the absolute and standard deviations in the case of symmetric or bounded distributions in the analysis we use a new tool the outcome risk o r diagram which appears to be particularly useful for comparing uncertain outcomes

statistics of the occupation time of renewal processes we present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time according to the nature of the distribution of time intervals the probability density functions of these random variables have very different scalings in time we analyze successively the cases where this distribution is narrow where it is broad with index 1 and finally where it is broad with index 1 2 the methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes see joint paper by g de smedt c godreche and j m luck 26

langevin formulation of a subdiffusive continuous time random walk in physical time systems living in complex nonequilibrated environments often exhibit subdiffusion characterized by a sublinear power law scaling of the mean square displacement one of the most common models to describe such subdiffusive dynamics is the continuous time random walk ctrw stochastic trajectories of a ctrw can be described in terms of the subordination of a normal diffusive process by an inverse levy stable process here we propose an equivalent langevin formulation of a force free ctrw without subordination by introducing a different type of non gaussian noise we are able to express the ctrw dynamics in terms of a single langevin equation in physical time with additive noise we derive the full multipoint statistics of this noise and compare it with the scaled brownian motion sbm an alternative stochastic model describing subdiffusive dynamics interestingly these two noises are identical up to the second order correlation functions but different in the higher order statistics we extend our formalism to general waiting time distributions and force fields and compare our results with those of the sbm in the presence of external forces our proposed noise generates a different class of stochastic processes resembling a ctrw but with forces acting at all times

wiener sausage volume moments the statistical characteristics of a spatial region visited by a spherical brownian particle during timet wiener sausage are investigated the expectation value and dispersion of this quantity are obtained for a space of arbitrary dimension in the one dimensional case the distribution of probability density and the moments of any order are determined for this quantity

counting statistics a feynman kac perspective by building upon a feynman kac formalism we assess the distribution of the number of collisions in a given region for a broad class of discrete time random walks in absorbing and nonabsorbing media we derive the evolution equation for the generating function of the number of collisions and we complete our analysis by examining the moments of the distribution and their relation to the walker equilibrium density some significant applications are discussed in detail in particular we revisit the gambler s ruin problem and generalize to random walks with absorption the arcsine law for the number of collisions on the half line

descriptive parameter for photon trajectories in a turbid medium in many applications of laser techniques for diagnostic or therapeutic purposes it is necessary to be able to characterize photon trajectories to know which parts of the tissue are being interrogated in this paper we consider the cw reflectance experiment on a semi infinite medium with uniform optical parameters and having a planar interface the analysis is carried out in terms of a continuous time random walk and the relation between the occupancy of a plane parallel to the surface to the maximum depth reached by the random walker is studied the first moment of the ratio of average depth to the average maximum depth yields information about the volume of tissue interrogated as well as giving some indication of the region of tissue that gets the most light we have also calculated the standard deviation of this random variable it is not large enough to qualitatively affect information contained in the first moment

territory covered by n random walkers the problem of evaluating the number of distinct sites s n t covered up to time t by n random walkers is revisited for the nontrivial time regime and for n 1 we show how to get the asymptotic behavior of s n t and we calculate the main and first two corrective terms the mth corrective term decays mildly as 1 ln m n for d dimensional d 1 2 3 simple cubic lattices the main term is the volume of the hypersphere of radius ln n 2 2dt d 1 2 d being the diffusion constant and the corrective terms account for the roughening of the surface of the set of visited sites

a multistage motion vector processing method for motion compensated frame interpolation in this paper a novel low complexity motion vector processing algorithm at the decoder is proposed for motion compensated frame interpolation or frame rate up conversion we address the problems of having broken edges and deformed structures in an interpolated frame by hierarchically refining motion vectors on different block sizes our method explicitly considers the reliability of each received motion vector and has the capability of preserving the structure information this is achieved by analyzing the distribution of residual energies and effectively merging blocks that have unreliable motion vectors the motion vector reliability information is also used as a prior knowledge in motion vector refinement using a constrained vector median filter to avoid choosing identical unreliable one we also propose using chrominance information in our method experimental results show that the proposed scheme has better visual quality and is also robust even in video sequences with complex scenes and fast motion

motion compensated frame interpolation based on multihypothesis motion estimation and texture optimization a novel motion compensated frame interpolation mcfi algorithm to increase video temporal resolutions based on multihypothesis motion estimation and texture optimization is proposed in this paper initially we form multiple motion hypotheses for each pixel by employing different motion estimation parameters i e different block sizes and directions then we determine the best motion hypothesis for each pixel by solving a labeling problem and optimizing the parameters in the labeling problem the cost function is composed of color shape and smoothness terms finally we refine the motion hypothesis field based on the texture optimization technique and blend multiple source pixels to interpolate each pixel in the intermediate frame simulation results demonstrate that the proposed algorithm provides significantly better mcfi performance than conventional algorithms

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

number of distinct sites visited by n random walkers on a euclidean lattice the evaluation of the average number s n t of distinct sites visited up to time t by n independent random walkers all starting from the same origin on an euclidean lattice is addressed we find that for the nontrivial time regime and for large n s n t approx hat s n t 1 delta where hat s n t is the volume of a hypersphere of radius 4dt ln n 1 2 delta 1 2 sum n 1 infty ln n n sum m 0 n s m n ln m ln n d is the dimension of the lattice and the coefficients s m n depend on the dimension and time the first three terms of these series are calculated explicitly and the resulting expressions are compared with other approximations and with simulation results for dimensions 1 2 and 3 some implications of these results on the geometry of the set of visited sites are discussed

weakly non ergodic statistical physics for weakly non ergodic systems the probability density function of a time average observable overline mathcal o is f alpha overline mathcal o 1 over pi lim epsilon to 0 mbox im sum j 1 l p mathrm eq j overline mathcal o mathcal o j i epsilon alpha 1 over sum j 1 l p mathrm eq j overline mathcal o mathcal o j i epsilon alpha where mathcal o j is the value of the observable when the system is in state j 1 l pjeq is the probability that a member of an ensemble of systems occupies state j in equilibrium for a particle undergoing a fractional diffusion process in a binding force field with thermal detailed balance conditions pjeq is boltzmann s canonical probability within the unbiased sub diffusive continuous time random walk model the exponent 0 1 is the anomalous diffusion exponent x2 t found for free boundary conditions when 1 ergodic statistical mechanics is recovered lim alpha to 1 f alpha overline mathcal o delta overline mathcal o langle mathcal o rangle we briefly discuss possible physical applications in single particle experiments

time fractional schrodinger equation the schrodinger equation is considered with the first order time derivative changed to a caputo fractional derivative the time fractional schrodinger equation the resulting hamiltonian is found to be non hermitian and nonlocal in time the resulting wave functions are thus not invariant under time reversal the time fractional schrodinger equation is solved for a free particle and for a potential well probability and the resulting energy levels are found to increase over time to a limiting value depending on the order of the time derivative new identities for the mittag leffler function are also found and presented in an appendix

fractional feynman kac equation for weak ergodicity breaking the continuous time random walk ctrw is a model of anomalous subdiffusion in which particles are immobilized for random times between successive jumps a power law distribution of the waiting times 1 leads to subdiffusion x 2 t for 0 1 in closed systems the long stagnation periods cause time averages to divert from the corresponding ensemble averages which is a manifestation of weak ergodicity breaking the time average of a general observable u t 1 t 0 t u x d is a functional of the path and is described by the well known feynman kac equation if the motion is brownian here we derive forward and backward fractional feynman kac equations for functionals of ctrw in a binding potential we use our equations to study two specific time averages the fraction of time spent by a particle in half box and the time average of the particle s position in a harmonic field in both cases we obtain the probability density function of the time averages for t and the first two moments our results show that both the occupation fraction and the time averaged position are random variables even for long times except for 1 when they are identical to their ensemble averages using our fractional feynman kac equation we also study the dynamics leading to weak ergodicity breaking namely the convergence of the fluctuations to their asymptotic values

optimal temporal interpolation filter for motion compensated frame rate up conversion frame rate up conversion fruc methods that employ motion have been proven to provide better image quality compared to nonmotion based methods while motion based methods improve the quality of interpolation artifacts are introduced in the presence of incorrect motion vectors in this paper we study the design problem of optimal temporal interpolation filter for motion compensated fruc mc fruc the optimal filter is obtained by minimizing the prediction error variance between the original frame and the interpolated frame in fruc applications the original frame that is skipped is not available at the decoder so models for the power spectral density of the original signal and prediction error are used to formulate the problem the closed form solution for the filter is obtained by lagrange multipliers and statistical motion vector error modeling the effect of motion vector errors on resulting optimal filters and prediction error is analyzed the performance of the optimal filter is compared to nonadaptive temporal averaging filters by using two different motion vector reliability measures the results confirm that to improve the quality of temporal interpolation in mc the interpolation filter should be designed based on the reliability of motion vectors and the statistics of the mc prediction error

frame rate up conversion based on variational image fusion this paper presents a new framework for motion compensated frame rate up conversion fruc based on variational image fusion the proposed algorithm consists of two steps 1 generation of multiple intermediate interpolated frames and 2 fusion of those intermediate frames in the first step we determine four different sets of the motion vector field using four neighboring frames we then generate intermediate interpolated frames corresponding to the determined four sets of the motion vector field respectively multiple sets of the motion vector field are used to solve the occlusion problem in motion estimation in the second step the four intermediate interpolated frames are fused into a single frame via a variational image fusion process for effective fusion we determine fusion weights for each intermediate interpolated frame by minimizing the energy which consists of a weighted l1 norm based data energy and gradient driven smoothness energy experimental results demonstrate that the proposed algorithm improves the performance of fruc compared with the existing algorithms

fractional schrodinger equation some properties of the fractional schrodinger equation are studied we prove the hermiticity of the fractional hamilton operator and establish the parity conservation law for fractional quantum mechanics as physical applications of the fractional schrodinger equation we find the energy spectra of a hydrogenlike atom fractional bohr atom and of a fractional oscillator in the semiclassical approximation an equation for the fractional probability current density is developed and discussed we also discuss the relationships between the fractional and standard schrodinger equations

an improved particle swarm optimization algorithm an improved particle swarm optimization ipso is proposed in this paper in the new algorithm a population of points sampled randomly from the feasible space then the population is partitioned into several sub swarms each of which is made to evolve based on particle swarm optimization pso algorithm at periodic stages in the evolution the entire population is shuffled and then points are reassigned to sub swarms to ensure information sharing this method greatly elevates the ability of exploration and exploitation simulations for three benchmark test functions show that ipso possesses better ability to find the global optimum than that of the standard pso algorithm compared with pso ipso is also applied to identify the hydrologic model the results show that ipso remarkably improves the calculation accuracy and is an effective global optimization to calibrate hydrologic model

first passage times for random walks in bounded domains we present a novel computational method of first passage times between a starting site and a target site of regular bounded lattices we derive accurate expressions for all the moments of this first passage time validated by numerical simulations their range of validity is discussed we also consider the case of a starting site and two targets in addition we present the extension to continuous brownian motion these results are of great relevance to any system involving diffusion in confined media

a modified particle swarm optimization algorithm with applications abstract in this paper firstly a modified particle swarm optimization algorithm mpso is developed in which the mean value of past optimal positions for each particle and the mutation operation are considered for avoiding premature in the optimization test mpso performs better than particle swarm optimization algorithm pso then mpso is applied to solve four portfolio optimization models with the real data from the hong kong stock market and optimal values are obtained when the number of swarm n 80 160 respectively finally actual return rates of these models are calculated in numerical experiments and it is illustrated from these graphs of actual return rates that when considering higher return cai s model performs better in short term investment

fractional fokker planck equation solution and application recently metzler et al phys rev lett 82 3563 1999 introduced a fractional fokker planck equation ffpe describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field and a boltzmann thermal heat bath in this paper we present the solution of the ffpe in terms of an integral transformation the transformation maps the solution of ordinary fokker planck equation onto the solution of the ffpe and is based on levy s generalized central limit theorem the meaning of the transformation is explained based on the known asymptotic solution of the continuous time random walk ctrw we investigate in detail i a force free particle ii a particle in a uniform field and iii a particle in a harmonic field we also find an exact solution of the ctrw and compare the ctrw result with the corresponding solution of the ffpe the relation between the fractional first passage time problem in an external nonlinear field and the corresponding integer first passage time is given an example of the one dimensional fractional first passage time in an external linear field is investigated in detail the ffpe is shown to be compatible with the scher montroll approach for dispersive transport and thus is applicable in a large variety of disordered systems the simple ffpe approach can be used as a practical tool for a phenomenological description of certain types of complicated transport phenomena

from continuous time random walks to the fractional fokker planck equation we generalize the continuous time random walk ctrw to include the effect of space dependent jump probabilities when the mean waiting time diverges we derive a fractional fokker planck equation ffpe this equation describes anomalous diffusion in an external force field and close to thermal equilibrium we discuss the domain of validity of the fractional kinetic equation for the force free case we compare between the ctrw solution and that of the ffpe

selective data pruning based compression using high order edge directed interpolation this paper proposes a selective data pruning based compression scheme to improve the rate distortion relation of compressed images and video sequences the original frames are pruned to a smaller size before compression after decoding they are interpolated back to their original size by an edge directed interpolation method the data pruning phase is optimized to obtain the minimal distortion in the interpolation phase furthermore a novel high order interpolation is proposed to adapt the interpolation to several edge directions in the current frame this high order filtering uses more surrounding pixels in the frame than the fourth order edge directed method and it is more robust the algorithm is also considered for multiframe based interpolation by using spatio temporally surrounding pixels coming from the previous frame simulation results are shown for both image interpolation and coding applications to validate the effectiveness of the proposed methods

an evaluating of the sniffer global optimization algorithm using standard test functions abstract the performance of sniffer a new global optimization algorithm is compared with that of simulated annealing using the number of function evaluations as a measure of efficiency the new algorithm is shown to be significantly better at finding the global minimum of seven standard test functions several of the test functions used have many local minima and very steep walls surrounding the global minimum such functions are intended to thwart global minimization algorithms

branching exponential flights travelled lengths and collision statistics the evolution of several physical and biological systems ranging from neutron transport in multiplying media to epidemics or population dynamics can be described in terms of branching exponential flights a stochastic process which couples a galton watson birth death mechanism with random spatial displacements within this context one is often called to assess the length lv that the process travels in a given region v of the phase space or the number of visits nv to this same region in this paper we address this issue by resorting to the feynman kac formalism which allows characterizing the full distribution of lv and nv and in particular deriving explicit moment formulas some other significant physical observables associated to lv and nv such as the survival probability are discussed as well and results are illustrated by revisiting the classical example of the rod model in nuclear reactor physics

a minimax portfolio selection rule with linear programming solution a new principle for choosing portfolios based on historical returns data is introduced the optimal portfolio based on this principle is the solution to a simple linear programming problem this principle uses minimum return rather than variance as a measure of risk in particular the portfolio is chosen that minimizes the maximum loss over all past observation periods for a given level of return this objective function avoids the logical problems of a quadratic nonmonotone utility function implied by mean variance portfolio selection rules the resulting minimax portfolios are diversified for normal returns data the portfolios are nearly equivalent to those chosen by a mean variance rule framing the portfolio selection process as a linear optimization problem also makes it feasible to constrain certain decision variables to be integer or 0 1 valued this feature facilitates the use of more complex decision making models including models with fixed transaction charges and models with boolean type constraints on allocations

numerical schemes of the time tempered fractional feynmankac equation this paper focuses on providing the computation methods for the backward time tempered fractional feynmankac equation being one of the models recently proposed in wu etal 2016 the discretization for the tempered fractional substantial derivative is derived and the corresponding finite difference and finite element schemes are designed with well established stability and convergence the performed numerical experiments show the effectiveness of the presented schemes

generalized fractional schrodinger equation with space time fractional derivatives in this paper the generalized fractional schrodinger equation with space and time fractional derivatives is constructed the equation is solved for free particle and for a square potential well by the method of integral transforms fourier transform and laplace transform and the solution can be expressed in terms of mittag leffler function the green function for free particle is also presented in this paper finally we discuss the relationship between the cases of the generalized fractional schrodinger equation and the ones in standard quantum

fractional feynman kac equation with space dependent anomalous exponent to describe the distribution of functionals for inhomogeneous subdiffusion in space and time dependent force field we derive forward and backward time fractional feynman kac equations with space dependent anomalous exponent based on the space jump random walk model in our examples we get the statistic of occupation fraction and first passage time for anomalous infiltration of free particles in disordered systems by applying the backward version

large deviation functions for nonlinear functionals of a gaussian stationary markov process we introduce a general method based on a mapping onto quantum mechanics for investigating the large t limit of the distribution p r t of the nonlinear functional r v 1 t ensuremath int 0 t mathrm dt ensuremath v x t ensuremath where v x is an arbitrary function of the stationary gaussian markov process x t for stackrel ensuremath rightarrow t ensuremath infty at fixed r we obtain p r t ensuremath sim mathrm exp ensuremath ensuremath theta r t where ensuremath theta r is a large deviation function we present explicit results for a number of special cases including v x xh x where h x is the heaviside function which is related to the cooling and the heating degree days relevant to weather derivatives

particle swarm optimization using dimension selection methods particle swarm optimization pso has undergone many changes since its introduction in 1995 being a stochastic algorithm pso and its randomness present formidable challenge for the theoretical analysis of it and few of the existing pso improvements have make an effort to eliminate the random coefficients in the pso updating formula this paper analyzes the importance of the randomness in the pso and then gives a pso variant without randomness to show that traditional pso cannot work without randomness based on our analysis of the randomness another way of using randomness is proposed in pso with random dimension selection psords algorithm which utilizes random dimension selection instead of stochastic coefficients finally deterministic methods to do the dimension selection are proposed and the resultant pso with distance based dimension selection psodds algorithm is greatly superior to the traditional pso and pso with heuristic dimension selection psohds algorithm is comparable to traditional pso algorithm in addition using our dimension selection method to a newly proposed modified particle swarm optimization mpso algorithm also gets improved results the experiment results demonstrate that our analysis about the randomness is correct and the usage of deterministic dimension selection method is very helpful

continuous time random walks simulation of continuous trajectories continuous time random walks have been developed as a straightforward generalization of classical random walk processes some ten years ago fogedby introduced a continuous representation of these processes by means of a set of langevin equations h c fogedby phys rev e 50 1657 1994 the present work is devoted to a detailed discussion of fogedby s model and presents its application for the robust numerical generation of sample paths of continuous time random walk processes

semi analytical computation of laplacian green functions in three dimensional domains with disconnected spherical boundaries abstract the generalized method of separation of variables gmsv is applied to solve boundary value problems for the laplace operator in three dimensional domains with disconnected spherical boundaries e g an arbitrary configuration of non overlapping partially reactive spherical sinks or obstacles we consider both exterior and interior problems and all most common boundary conditions dirichlet neumann robin and conjugate one using the translational addition theorems for solid harmonics to switch between the local spherical coordinates we obtain a semi analytical expression of the green function as a linear combination of partial solutions whose coefficients are fixed by boundary conditions although the numerical computation of the coefficients involves series truncation and solution of a system of linear algebraic equations the use of the solid harmonics as basis functions naturally adapted to the intrinsic symmetries of the problem makes the gmsv particularly efficient especially for exterior problems the obtained green function is the key ingredient to solve boundary value problems and to determine various characteristics of stationary diffusion such as reaction rate escape probability harmonic measure residence time and mean first passage time to name but a few the relevant aspects of the numerical implementation and potential applications in chemical physics heat transfer electrostatics and hydrodynamics are discussed

subdiffusion in a bounded domain with a partially absorbing reflecting boundary the exit time of a subdiffusive process from a bounded domain with a partially absorbing reflecting boundary is considered the short time and long time behaviors of the exit time probability density are investigated by using a spectral decomposition on the basis of the laplace operator eigenfunctions rotation invariant domains are analyzed in depth in order to illustrate the use of theoretical formulas and to compare them to numerical simulations the asymptotic results obtained are relevant for describing subdiffusion inside a living cell with a semipermeable membrane in a chemical reactor filled with catalytic grains of finite reactivity or in mineral or biological samples which are probed by nuclear magnetic resonance measurements subject to surface relaxation

on distributions of functionals of anomalous diffusion paths functionals of brownian motion have diverse applications in physics mathematics and other fields the probability density function pdf of brownian functionals satisfies the feynman kac formula which is a schrodinger equation in imaginary time in recent years there is a growing interest in particular functionals of non brownian motion or anomalous diffusion but no equation existed for their pdf here we derive a fractional generalization of the feynman kac equation for functionals of anomalous paths based on sub diffusive continuous time random walk we also derive a backward equation and a generalization to levy flights solutions are presented for a wide number of applications including the occupation time in half space and in an interval the first passage time the maximal displacement and the hitting probability we briefly discuss other fractional schrodinger equations that recently appeared in the literature

residence time statistics for normal and fractional diffusion in a force field we investigate statistics of occupation times for an over damped brownian particle in an external force field using a backward fokker planck equation introduced by majumdar and comtet for an arbitrary potential field the distribution of occupation times is expressed in terms of solutions of the corresponding first passage time problem this general relationship between occupation times and first passage times is valid for normal markovian diffusion and for non markovian sub diffusion the latter modeled using the fractional fokker planck equation for binding potential fields we find in the long time limit ergodic behavior for normal diffusion while for the fractional framework weak ergodicity breaking is found in agreement with previous results of bel and barkai on the continuous time random walk on a lattice for non binding cases rich physical behaviors are obtained and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite our work establishes a link between fractional calculus and ergodicity breaking