critical exponents from power spectra we have simulated the two and three dimensional ising models at their respective critical points with a conventional monte carlo algorithm from the power spectrum of the magnetization autocorrelations we have determined the dynamic critical exponents and obtained the valuesz 2 16 2 19 andz 2 05 in agreement with the results quoted in the literature we have also studied the power spectrum for the kardar parisi zhang and sun guo grant equations describing interface dynamics arguments similar to what was recently used to conclude thatz 4 for model b in critical dynamics were applied to the sun guo grant growth model and the known exact values for the roughening and dynamic exponents were obtained from an analysis of the corresponding power spectrum in self organized critical sand models one obtains a recently proposed hyperscaling relation

spectral method determination of dynamic exponents for ising models abstract we have carried out extensive monte carlo simulations of the ferromagnetic ising model on square and cubic lattices by analysing the power spectrum of the magnetization autocorrelation function we have values of the dynamic exponents for the two models our results are z 2 13 0 02 in two dimensions and z 2 04 0 03 in three dimensions

computationally feasible bounds for partially observed markov decision processes a partially observed markov decision process pomdp is a sequential decision problem where information concerning parameters of interest is incomplete and possible actions include sampling surveying or otherwise collecting additional information such problems can theoretically be solved as dynamic programs but the relevant state space is infinite which inhibits algorithmic solution this paper explains how to approximate the state space by a finite grid of points and use that grid to construct upper and lower value function bounds generate approximate nonstationary and stationary policies and bound the value loss relative to optimal for using these policies in the decision problem a numerical example illustrates the methodology

boundedness and exponential stability for nonautonomous rcnns with distributed delays some sufficient conditions for the ultimate boundedness and global exponential stability of a class of nonautonomous reaction diffusion cellular neural networks rcnns with distributed delays are obtained by means of the lyapunov functional method without assuming that the activation functions f i j l are bounded the results extend and improve the earlier publications

impulsive delay differential inequality and stability of neural networks in this article a generalized model of neural networks involving time varying delays and impulses is considered by establishing the delay differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive delay model are obtained the results extend and improve the earlier publications an example is given to illustrate the theory

global stability analysis in delayed cellular neural networks in this paper the author analyzes further problems of global stability for a class of cellular neural networks with delays by means of the lyapunov functional method inequalities a 2 b 2 g 2ab and a 3 b 3 c 3 g 3abc a b cg 0 analysis technique some stability criteria are obtained under more general conditions these criteria can be applied to design globally stable networks and thus have important significance in both theory and applications

the three dimensional ising model revisited numerically several basic universal amplitude ratios are studied afresh for three dimensional nearest neighbor ising models in revising earlier work modern estimates of the critical temperature and exponents are used in conjunction with biased inhomogeneous differential approximants to extrapolate the longest available series expansions to find the critical amplitudes c for the susceptibility 1 for the correlation length 1 a for the specific heat c t and b for the spontaneous magnetization m0 we find c c 4 95 0 15 1 1 1 960 0 01 a a 0 523 0 009 a c b 0 0581 0 0010 while a 1 3 verifies hyperuniversality to within 0 8 a method for calculating amplitude ratios which allows for corrections to scaling yields estimates for c c and 1 1 in excellent agreement with those derived from the individual amplitudes finally explicit formulae are given for the numerical evaluation of t 1 t c t and m0 t over the full temperature range from criticality to t 0 and corresponding plots and convenient near critical representations are also presented

an optimal one way multigrid algorithm for discrete time stochastic control the numerical solution of discrete time stationary infinite horizon discounted stochastic control problems is considered for the case where the state space is continuous and the problem is to be solved approximately within a desired accuracy after a discussion of problem discretization the authors introduce a multigrid version of the successive approximation algorithm that proceeds one way from coarse to fine grids and analyze its computational requirements as a function of the desired accuracy and of the discount factor they also study the effects of a certain mixing ergodicity condition on the algorithm s performance it is shown that the one way multigrid algorithm improves upon the complexity of its single grid variant and is in a certain sense optimal

solving continuous state pomdps via density projection research on numerical solution methods for partially observable markov decision processes pomdps has primarily focused on finite state models and these algorithms do not generally extend to continuous state pomdps due to the infinite dimensionality of the belief space in this paper we develop a computationally viable and theoretically sound method for solving continuous state pomdps by effectively reducing the dimensionality of the belief space via density projection the density projection technique is also incorporated into particle filtering to provide a filtering scheme for online decision making we provide an error bound between the value function induced by the policy obtained by our method and the true value function of the pomdp and also an error bound between projection particle filtering and exact filtering finally we illustrate the effectiveness of our method through an inventory control problem

robust stability analysis for interval cohen grossberg neural networks with unknown time varying delays in this paper robust stability problems for interval cohen grossberg neural networks with unknown time varying delays are investigated using linear matrix inequality m matrix theory and halanay inequality techniques new sufficient conditions independent of time varying delays are derived to guarantee the uniqueness and the global robust stability of the equilibrium point of interval cohen grossberg neural networks with time varying delays all these results have no restriction on the rate of change of the time varying delays compared to some existing results these new criteria are less conservative and are more convenient to check two numerical examples are used to show the effectiveness of the present results

improved stability criteria for a class of neural networks with variable delays and impulsive perturbations this paper further investigates the problem of stability analysis for a kind of neural networks with variable delays and nonlinear impulses with the help of m matrix the homeomorphism theory some effective inequalities and analysis techniques certain novel criteria on the existence uniqueness and exponential stability of the equilibrium point have been established moreover these criteria possess adjustable real parameters which extend and improve many existing results in the literature in the end two numerical examples are provided to illustrate the validation of the theoretical results

critical slowing down in ising model for creutz algorithm abstract dynamical critical exponents for the two dimensional ising model are computed on a cellular automaton from the relaxations of the time displaced correlation and auto correlation functions for the order parameter and the internal energy at the critical temperatures and from the nonlinear relaxation time for the order parameter near the critical temperature the analysis of the data within the frame of the dynamical finite size scaling hypothesis gives z m z e 2 20 and z a m 1 91 and z a e 0 19 for the linear dynamical exponents corresponding respectively to the relaxations of the correlation and the autocorrelation functions for the order parameter and the internal energy and nl m 2 07 for the nonlinear dynamical exponent for the order parameter these values verify the scaling relations between the dynamical exponents

global exponential stability for shunting inhibitory cnns with delays in this paper the global exponential stability for shunting inhibitory cellular neural networks sicnns with delays is studied by constructing suitable lyapunov functionals and applying some critical analysis techniques the sufficient conditions guaranteeing the network s global exponential stability are obtained our results impose less restrictive conditions than those in the references moreover an example is given to illustrate the feasibility of the conditions in our results

on the dynamic exponent of the two dimensional ising model the authors use the method of damage spreading to measure the time taken for the equilibrium damage the magnetization to disappear in finite systems 10 or 2 27

mixing times of critical two dimensional potts models we study dynamical aspects of the q state potts model on an n n box at its critical c q heat bath glauber dynamics and cluster dynamics such as swendsen wang that circumvent low temperature bottlenecks are all expected to undergo critical slowdowns in the presence of periodic boundary conditions the inverse spectral gap which in the subcritical regime is o 1 should at criticality be polynomial in n for 1 4 in accordance with the predicted discontinuous phase transition this was confirmed for q 2 the ising model by the second author and sly and for sufficiently large q by borgs et al here we show that the following holds for the critical potts model on the torus for q 3 the inverse gap of glauber dynamics is no 1 for q 4 it is at most no log n and for every q 4 in the phase coexistence regime the inverse gaps of both glauber dynamics and swendsen wang dynamics are exponential in n for free or monochromatic boundary conditions and large q we show that the dynamics at criticality is faster than on the torus unlike the ising model where free periodic boundary conditions induce similar dynamical behavior at all temperatures the inverse gap of swendsen wang dynamics is exp no 1 2017 wiley periodicals inc

markov property and ergodicity of the nonlinear filter in this paper we first prove under quite general conditions that the nonlinear filter and the pair signal filter are feller markov processes the state space of the signal is allowed to be nonlocally compact and the observation function h can be unbounded our proofs in contrast to those of kunita j multivariate anal 1 1971 pp 365 393 spatial stochastic processes birkhauser 1991 pp 233 256 and stettner stochastic differential equations springer verlag 1989 pp 279 292 do not depend upon the uniqueness of the solutions to the filtering equations we then obtain conditions for existence and uniqueness of invariant measures for the nonlinear filter and the pair process these results extend those of kunita and stettner which hold for locally compact state space and bounded h to our general framework finally we show that the recent results of ocone and pardoux siam j control optim 34 1996 pp 226 243 on asymptotic stability of the nonlinear filter which use the kunita stettner setup hold for the general situation considered in this paper

global stability analysis of impulsive bam type cohen grossberg neural networks with delays abstract this paper is concerned with a class of the impulsive bidirectional associative memories neural networks that possesses a cohen grossberg dynamics incorporates time delays and variable coefficients the existence of equilibrium point globally exponential stability and globally exponentially robust stability are investigated by lyapunov function and halanay inequality we can see that impulses do contribution to the exponential stability and robust stability an illustrative example is given to demonstrate the effectiveness of the obtained results

the critical dynamics and the real space renormalization group abstract a general approach of the real space renormalization group to critical dynamics is described the formalism is presented and discussed in particular the application of this formalism to the study of the 1d kinetic ising model and to the second order cumulant approximation of the 2d kinetic ising model on a triangular lattice is carried out the question of universality in the framework of the above formalism is studied and the limitations of the method are presented

delay dependent robust dissipativity conditions for delayed neural networks with random uncertainties this paper deals with the problem of the robust dissipativity analysis for delayed neural networks with randomly occurring uncertainties the randomly occurring uncertainties under consideration are assumed to follow certain mutually uncorrelated bernoulli distributed white noise sequences by using reciprocally convex approach combined with an extended wirtinger inequality some delay dependent conditions for the concerned neural networks to be stochastically strictly q s r dissipative are established finally two numerical examples are given to illustrate the reduced conservatism and effectiveness of our proposed approach

stability analysis on delayed cellular neural networks in this paper we study the problem of stability for the delayed cellular neural networks dcnn by making use of the lyapunov functional method the method of variation of constants and combining with the method of inequality analysis some criterions of global exponential stability and global asympototic stability for delayed cellular neural networks are established these criterions can be used to design globally stable networks and thus have important significance in both theory and applications

critical dynamics of the potts model in several dimensionalities abstract we study critical dynamics of general q state potts models on d dimensional hypercubic lattices the master equation is formulated according to a theory recently presented by the author a simple bond moving technique followed by decimation is used to obtain the dynamical exponents although this approximation yields poor results for the static exponents the dynamic behaviour is closer to monte carlo simulations we compare our results with those obtained with a different formulation of dynamics a final discussion is included

critical dynamics of the three dimensional ising model a monte carlo study extensive monte carlo simulations have been performed to analyze the dynamical behavior of the three dimensional ising model with local dynamics we have studied the equilibrium correlation functions and the power spectral densities of odd and even observables the exponential relaxation times have been calculated in the asymptotic one exponential time region we find that the critical exponentz 2 09 0 02 characterizes the algebraic divergence with lattice size for all observables the influence of scaling corrections has been analyzed we have determined integrated relaxation times as well their dynamical exponentzint agrees withz for correlations of the magnetization and its absolute value but it is different for energy correlations we have applied a scaling method to analyze the behavior of the correlation functions this method verifies excellent scaling behavior and yields a dynamical exponentzscal which perfectly agrees withz

on global exponential stability of cellular neural networks with lipschitz continuous activation function and variable delays for a class of cellular neural networks cnns with variable delays this paper presents some new sufficient conditions for guaranteeing the global exponential stability these conditions are derived by using lyapunov functional method and combining with the inequality 3abc 0 technique furthermore these stability conditions depend only on the network s coefficients and are totally independent of the delays the results which do not require the cloning template to be symmetric are easy to use in network design compared with existing results our results are shown to be superior to other ones numerical examples are given to demonstrate the effectiveness of our results

static and dynamic critical phenomena of the two dimensional q state potts model theq state potts model on the square lattice is studied by monte carlo simulation forq 3 4 5 6 very good agreement is obtained with exact results of kiharaet al and baxter for energy and free energy at the critical point critical exponent estimates forq 3 are 0 4 0 1 1 45 in rough agreement with high temperature series extrapolation and real space renormalization group methods the transition forq 5 6 is found to be a very weakly first order transition i e pronounced pseudocritical phenomena occur specific heat susceptibility etc nearly diverge at the first order transition temperature dynamics is associated to the model in the same way as for the kinetic ising model and the nonlinear slowing down of the order parameter and of the energy is studied the dynamic exponent is estimated to be zv 1 9 within our accuracy noq dependence is detected the relaxation is found to be consistent with dynamic scaling predictions and dynamic scaling functions associated with the nonlinear relaxation are estimated

domain growth kinetics and symmetry breaking in a thermally quenched system the authors simulate thermal quenches on a two dimensional hard core model with symmetry breaking phase transition by dividing large configurations into many small sub squares lack of self averaging is avoided and statistics are improved dynamic scaling is observed during more than two decades

convergence of dynamic programming models weak conditions are presented for approximating dynamic programming models for a sequence of these models continuous convergence of the sequence of associated optimal value functions is obtained under the condition that state and action space converge in the sense of kuratowski and that the mappings of admissible actions as well as the transition law the discount factors and the reward functions converge continuously further a relation for the associated sets of optimal actions is given the analysis is based on results about convergence preserving properties of supremum value functions and integrals the approximation results are extended to so called upper semi continuous convergent sequences and are related to discretization procedures by using projections

on the asymptotic optimality of finite approximations to markov decision processes with borel spaces calculating optimal policies is known to be computationally difficult for markov decision processes mdps with borel state and action spaces this paper studies finite state approximations of discrete time markov decision processes with borel state and action spaces for both discounted and average costs criteria the stationary policies thus obtained are shown to approximate the optimal stationary policy with arbitrary precision under quite general conditions for discounted cost and more restrictive conditions for average cost for compact state mdps we obtain explicit rate of convergence bounds quantifying how the approximation improves as the size of the approximating finite state space increases using information theoretic arguments the order optimality of the obtained convergence rates is established for a large class of problems we also show that as a pre processing step the action space can also be finitely approximated with sufficiently large number points thereby well known algorithms su

point based value iteration for continuous pomdps we propose a novel approach to optimize partially observable markov decisions processes pomdps defined on continuous spaces to date most algorithms for model based pomdps are restricted to discrete states actions and observations but many real world problems such as for instance robot navigation are naturally defined on continuous spaces in this work we demonstrate that the value function for continuous pomdps is convex in the beliefs over continuous state spaces and piecewise linear convex for the particular case of discrete observations and actions but still continuous states we also demonstrate that continuous bellman backups are contracting and isotonic ensuring the monotonic convergence of value iteration algorithms relying on those properties we extend the algorithm originally developed for discrete pomdps to work in continuous state spaces by representing the observation transition and reward models using gaussian mixtures and the beliefs using gaussian mixtures or particle sets with these representations the integrals that appear in the bellman backup can be computed in closed form and therefore the algorithm is computationally feasible finally we further extend to deal with continuous action and observation sets by designing effective sampling approaches

optimal quantization for distribution synthesis finite precision approximations of discrete probability distributions are considered applicable for distribution synthesis e g probabilistic shaping two algorithms are presented that find the optimal m type approximation q of a distribution p in terms of the variational distance lvert q p rvert 1 and the informational divergence d q vert p bounds on the approximation errors are derived and shown to be asymptotically tight several examples illustrate that the variational distance optimal approximation can be quite different from the informational divergence optimal approximation

dynamical finite size scaling function of the four dimensional ising model for creutz algorithm abstract dynamical critical exponents for the four dimensional ising model are computed on a cellular automaton from the relaxations of the time displaced correlation for the order parameter and the internal energy at the critical temperatures the analysis of the data within the frame of the dynamical finite size scaling hypothesis gives the linear dynamical critical exponents for the order parameter and the internal energy in our calculation the linear dynamical critical exponents are found z m z h i 2 04 at t c z m 1 99 z h i 2 00 at t c l the values of z m z h i 2 04 obtained for t c verify the dynamical finite size scaling for which it was adopted four dimensional ising model

dynamical behaviors analysis of memristor based fractional order complex valued neural networks with time delay abstract the robust stability for memristor based fractional order complex valued neural networks fcvnns with time delay is investigated here in complex plane by using the lyapunov method and under the sense of filippov solutions the existence of unique equilibrium and globally asymptotic stability for such neural networks nns have been obtained when the nonlinear complex valued activation functions could be split into two real and imaginary parts moreover locally asymptotic stability for such neural nns have been proposed when the nonlinear complex activation functions are bounded lastly three numerical examples are given to confirm the efficiency of theorems

critical dynamics of finite ising model the glauber kinetics of ising spins is considered as a queueing process and simulated event by event as first proposed by bortz kalos and lebowitz the advantage of this algorithm compared to the standard single flip monte carlo method is discussed for the situation of slowing down of dynamics this process is used to generate fluctuations of magnetization and energy in the critical regimet tc of two dimensional ising models the analysis of these fluctuations leads to numerical determination of the critical exponents for dynamics for the size dependence of correlation time attc and for frequency dependence of the power spectrums from the finite size scaling hypothesis scaling relations are settled which are confirmed by this numerical experiment

fuzzy hyperbolic neural network with time varying delays in this paper the formula of fuzzy basis functions with time varying delays dfbf is firstly given based on the dfbf a novel fuzzy hyperbolic neural network with time varying delays dfhnn and its approximation properties are presented respectively by constructing an appropriate lyapunov krasovskii functional the stability of dfhnn is discussed and some new criteria concerning the global exponential stability of dfhnn are proposed finally three numerical examples are given to demonstrate the effectiveness of the obtained results

asymptotic optimality of finite model approximations for partially observed markov decision processes with discounted cost we consider finite model approximations of discrete time partially observed markov decision processes pomdps under the discounted cost criterion after converting the original partially observed stochastic control problem to a fully observed one on the belief space the finite models are obtained through the uniform quantization of the state and action spaces of the belief space markov decision process mdp under mild assumptions on the components of the original model it is established that the policies obtained from these finite models are nearly optimal for the belief space mdp and so for the original partially observed problem the assumptions essentially require that the belief space mdp satisfies a mild weak continuity condition we provide an example and introduce explicit approximation procedures for the quantization of the set of probability measures on the state space of pomdp i e belief space

dynamical properties of the two and three dimensional ising models by damage spreading the method of damage spreading is used to measure the dynamic exponent z for both the two and three dimensional ising models with heat bath dynamics the authors also measure a new exponent alpha describing the rate at which a damage cloud grows they report values of z 2 24 or 0 04 and alpha 0 77 or 0 11 in two dimensions and z 2 202 or 0 03 and alpha 0 92 or 0 10 in three dimensions

non equilibrium relaxation and interface energy of the ising model abstract from the non equilibrium critical relaxation study of the two dimensional ising model the dynamical critical exponent z is estimated to be 2 165 0 010 for this model the relaxation in the ordered phase of this model is consistent with exp t behavior the interface energy of the three dimensional ising model is studied and the critical exponent of the correlation length and the critical amplitude of the surface tension 0 are estimated to be 0 6250 0 0025 and 1 42 0 04 respectively a dynamic monte carlo renormalization group method is successfully applied to the equilibrium properties of the three dimensional ising model

finite memory suboptimal design for partially observed markov decision processes we develop bounds on the value function and a suboptimal design for the partially observed markov decision process these bounds and suboptimal design are based on the m most recent observations and actions an a priori measure of the quality of these bounds is given we show that larger m implies tighter bounds an operations count analysis indicates that a z m 1 s multiplications and additions are required per successive approximations iteration of the suboptimal design algorithm where a z and s are the action observation and state spaces respectively suggesting the algorithm is of potential use for problems with large state spaces a preliminary numerical study indicates that the quality of the suboptimal design can be excellent

globally exponential stability conditions for cellular neural networks with time varying delays in this paper the problems of global exponential stability for cellular neural networks cnn with time varying delays are studied several sufficient conditions guaranteeing the network s global exponential stability are established these results can easily be used to design and verify globally stable networks furthermore the results presented here are independent of the form of specific delays and have important significance in both theory and applications

performance loss bounds for approximate value iteration with state aggregation we consider approximate value iteration with a parameterized approximator in which the state space is partitioned and the optimal cost to go function over each partition is approximated by a constant we establish performance loss bounds for policies derived from approximations associated with fixed points these bounds identify benefits to using invariant distributions of appropriate policies as projection weights such projection weighting relates to what is done by temporal difference learning our analysis also leads to the first performance loss bound for approximate value iteration with an average cost objective

a survey of convergence results on particle filtering methods for practitioners optimal filtering problems are ubiquitous in signal processing and related fields except for a restricted class of models the optimal filter does not admit a closed form expression particle filtering methods are a set of flexible and powerful sequential monte carlo methods designed to solve the optimal filtering problem numerically the posterior distribution of the state is approximated by a large set of dirac delta masses samples particles that evolve randomly in time according to the dynamics of the model and the observations the particles are interacting thus classical limit theorems relying on statistically independent samples do not apply in this paper our aim is to present a survey of convergence results on this class of methods to make them accessible to practitioners

on global exponential stability of delayed cellular neural networks with time varying delays a new sufficient condition has been presented ensuring the global exponential stability of cellular neural networks with time varying delays by using an approach based on delay differential inequality combining with young inequality the results established here extend those earlier given in the literature compared with the method of lyapunov functionals as in most previous studies our method is simpler and more effective for stability analysis

simulation of time exponent in 2d glauber kinetic ising model abstract simulations of the magnetization relaxation of large square lattices at the curie point give a dynamical exponent near 2 2 somewhat higher than expected

exponential stability and periodicity of impulsive cellular neural networks with time delays abstract this paper is concerned with the stability and periodicity for a class of impulsive neural networks with delays by means of the fixed point theory lyapunov functional and analysis technique some sufficient conditions of exponential stability and periodicity are obtained we can see that impulses do contribution to the stability and periodicity an example is given to demonstrate the effectiveness of the obtained results

on near optimality of the set of finite state controllers for average cost pomdp we consider the average cost problem for partially observable markov decision processes pomdp with finite state observation and control spaces we prove that there exists an e optimal finite state controller fsc functionally independent of initial distributions for any e 0 under the assumption that the optimal liminf average cost function of the pomdp is constant as part of our proof we establish that if the optimal liminf average cost function is constant then the optimal limsup average cost function is also constant and the two are equal we also discuss the connection between the existence of nearly optimal finite history controllers and two other important issues for average cost pomdp the existence of an average cost that is independent of the initial state distribution and the existence of a bounded solution to the constant average cost optimality equation

critical ising on the square lattice mixes in polynomial time the ising model is widely regarded as the most studied model of spin systems in statistical physics the focus of this paper is its dynamic stochastic version the glauber dynamics introduced in 1963 and by now the most popular means of sampling the ising measure intensive study throughout the last three decades has yielded a rigorous understanding of the spectral gap of the dynamics on mathbb z 2 everywhere except at criticality while the critical behavior of the ising model has long been the focus for physicists mathematicians have only recently developed an understanding of its critical geometry with the advent of sle cle and new tools to study conformally invariant systems

stability bifurcation and global existence of a hopf bifurcating periodic solution for a class of three neuron delayed network models in this paper a system of three delay differential equations representing a hopfield type general model for three neurons with two way bidirectional time delayed connections between the neurons and time delayed self connection from each neuron to itself is studied delay independent and delay dependent sufficient conditions for linear stability instability and the occurrence of a hopf bifurcation about the trivial equilibrium are addressed the partition of the resulting parametric space into regions of stability instability and hopf bifurcation in the absence of self connection is realized to extend the local hopf branches for large delay values a particular bidirectional delayed tri neuron model without self connection is investigated sufficient conditions for global existence of multiple non constant periodic solutions are obtained for such a model using the global hopf bifurcation theorem for functional differential equations due to j wu and the bendixson criterion for higher dimensional ordinary differential equations due to li and muldowney and following the approach developed by wei and li

simulation of domain wall dynamics in the 2d anisotropic ising model the authors first show that the movement of a domain wall in a highly anisotropic ising model of spins in two dimensions can be mapped to a random walk movement of labelled walkers in one dimension this movement is correlated in the sense that the transition probability of a given walker labelled i depends upon the current positions of its labelled neighbours i 1 and i 1 a monte carlo simulation of the walk for various numbers of walkers up to a maximum of 50 and for quite long times up to a maximum of 25 104 monte carlo steps yields useful and interesting information about the dynamics they verify that i the centre of mass of the walkers executes an unbiased random walk for all times starting from the lowest times and ii the moment of inertia of the walkers asymptotically reaches a constant value which scales with the number of walkers they also discuss the relation of this work to the dynamics in the 2d ising model identifying phi with the dynamical exponent z the random walk equivalence also provides a geometrical interpretation of the known results for the solid on solid model

optimization and convergence of observation channels in stochastic control this paper studies the optimization of observation channels stochastic kernels in partially observed stochastic control problems in particular existence and continuity properties are investigated mostly but not exclusively concentrating on the single stage case continuity properties of the optimal cost in channels are explored under total variation setwise convergence and weak convergence sufficient conditions for compactness of a class of channels under total variation and setwise convergence are presented and applications to quantization are explored

near optimality of quantized policies in stochastic control under weak continuity conditions abstract this paper studies the approximation of optimal control policies by quantized discretized policies for a very general class of markov decision processes mdps the problem is motivated by applications in networked control systems computational methods for mdps and learning algorithms for mdps we consider the finite action approximation of stationary policies for a discrete time markov decision process with discounted and average costs under a weak continuity assumption on the transition probability which is a significant relaxation of conditions required in earlier literature the discretization is constructive and quantized policies are shown to approximate optimal deterministic stationary policies with arbitrary precision the results are applied to the fully observed reduction of a partially observed markov decision process where weak continuity is a much more reasonable assumption than more stringent conditions such as strong continuity or continuity in total variation

finite linear programming approximations of constrained discounted markov decision processes we consider a markov decision process mdp with constraints under the total expected discounted cost optimality criterion we are interested in proposing approximation methods of the optimal value of this constrained mdp to this end starting from the linear programming lp formulation of the constrained mdp on an infinite dimensional space of measures we propose a finite state approximation of this lp problem this is achieved by suitably approximating a probability measure underlying the random transitions of the dynamics of the system explicit convergence orders of the approximations of the optimal constrained cost are obtained by exploiting convexity properties of the class of relaxed controls we reduce the lp formulation of the constrained mdp to a finite dimensional static optimization problem that can be used to obtain explicit numerical approximations of the corresponding optimal constrained cost a numerical application illustrates our theoretical results

critical relaxation of the two dimensional three state potts model with conserved dynamics the dynamical critical exponent z is obtained using the finite size scaling method for the two dimensional three state potts model with conserved dynamics it is observed that there is a change in the dynamical behaviour of the system at the size n 15 for finite lattices of sizes n or 15 the asymptotic behaviour is observed and z is calculated as z 2 78 or 0 20

delay dependent robust h control of uncertain linear systems with time varying delays abstract this paper proposes an optimization based approach to the robust h control problem of uncertain continuous or discrete time linear time invariant systems with different time varying delays in the state vector and control input of the dynamic equation and controlled output sufficient delay dependent conditions are derived for the control stabilization problem where both the size of the time varying delay and the size of its time derivative in the continuous time case play a crucial role for the closed loop stability with a guaranteed h performance index the solutions that are proposed for the h control problem are similar or less conservative when compared to other recent approaches

description of critical dynamics by static geometry of clusters abstract critical slowing down of relaxation exponent z is modelled by clusters which grow and recede at the end of connected sequences of particles consequently the relaxation time of a cluster of size s is proportional to the number of back and forth steps needed to travel its typical connected length ls this and an assumption on mutual screening of ends lead to z 2 5 0 25 where is a static geometric exponent in ls s ising exponents measured elsewhere with the help of simulation give z in addition a flory like approximation is derived here it relates to and analytically giving z in d 2 3 and 4 respectively we findz 2 14 2 05 and 2 275 1 while z 2 17 4 and 2 04 4 both sets of values are in fair agreement with the literature

stability in asymmetric hopfield nets with transmission delays sufficient conditions are derived for the delay independent stability of the equilibria in hopfield s graded response networks of the type dxi t dt bixi t nj 1aijfj jxj t ij fi t i 1 2 n when the external inputs fi are held temporally uniform a generalization to continuously distributed delays is briefly indicated several illustrative examples are numerically simulated and the results of simulations are graphically displayed