solving large scale linear multicommodity flow problems with an active set strategy and proximal accpm in this paper we propose to solve the linear multicommodity flow problem using a partial lagrangian relaxation the relaxation is restricted to the set of arcs that are likely to be saturated at the optimum this set is itself approximated by an active set strategy the partial lagrangian dual is solved with proximal accpm a variant of the analytic center cutting plane method the new approach makes it possible to solve huge problems when few arcs are saturated at the optimum as appears to be the case in many practical problems

dynamics of ising random bond models neural network and random anisotropy axis model a discrete time retrieval dynamics for a class of random bond models with infinite range interactions is studied in a unified picture the hopfield model of neural networks with the hebb learning rule is considered together with the ising random anisotropy axis model in the strong anisotropy limit the main overlap magnetization the residual overlap and its dispersion as well as the correlation between the gaussian component of the residual overlap and the initial value of the latter obtained in the first step of a recursion relation are used to infer the structure of the recursion for large times a crucial assumption is the strong stationarity of the gaussian component the dynamics are discussed for finite alpha p n the storage ratio in the neural network problem or the ratio of random axis components per site in the limit where both p and n go to infinity the long time behaviour of the theory is shown to yield the equilibrium solution of an earlier work in mean field theory for a tri modal distribution of random axis components explicit results for the basins of attraction of either a ferromagnetic or a spin glass phase are obtained as well as the relaxation time with a square root power law decay near saturation

parallel dynamics of the fully connected blume emery griffiths neural network abstract the parallel dynamics of the fully connected blume emery griffiths neural network model is studied at zero temperature using a probabilistic approach a recursive scheme is found determining the complete time evolution of the order parameters taking into account all feedback correlations it is based upon the evolution of the distribution of the local field the structure of which is determined in detail as an illustrative example explicit analytic formula are given for the first few time steps of the dynamics furthermore equilibrium fixed point equations are derived and compared with the thermodynamic approach the analytic results find excellent confirmation in extensive numerical simulations

persistence and extinction for a class of stochastic sis epidemic models with nonlinear incidence rate abstract in this paper a class of stochastic sis epidemic models with nonlinear incidence rate is investigated it is shown that the extinction and persistence of the disease in probability are determined by a threshold value r 0 that is if r 0 1 and an additional condition holds then disease dies out and if r 0 1 then disease is weak permanent with probability one to obtain the permanence in the mean of the disease a new quantity r 0 is introduced and it is proved that if r 0 1 the disease is permanent in the mean with probability one furthermore the numerical simulations are presented to illustrate some open problems given in remarks 1 3 and 5 of this paper

minimum cost capacity installation for multicommodity network flows consider a directed graphg v a and a set of traffic demands to be shipped between pairs of nodes inv capacity has to be installed on the edges of this graph in integer multiples of a base unit so that traffic can be routed in this paper we consider the problem of minimum cost installation of capacity on the arcs to ensure that the required demands can be shipped simultaneously between node pairs we study two different approaches for solving problems of this type the first one is based on the idea of metric inequalities see onaga and kakusho on feasibility conditions of multicommodity flows in networks ieee transactions on circuit theory ct 18 4 1971 425 429 and uses a formulation with only a variables the second uses an aggregated multicommodity flow formulation and has v a variables we first describe two classes of strong valid inequalities and use them to obtain a complete polyhedral description of the associated polyhedron for the complete graph on three nodes next we explain our solution methods for both of the approaches in detail and present computational results our computational experience shows that the two formulations are comparable and yield effective algorithms for solving real life problems 1998 the mathematical programming society inc published by elsevier science b v

stochastic versions of the lasalle theorem the main aim of this paper is to establish stochastic versions of the well known lasalle stability theorem from these stochastic versions follow many classical results on stochastic stability this shows clearly the power of our new results

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

on the parallel dynamics for the little hopfield model we propose a method algorithm for calculation of the explicit formulas for evolution of the main and the residual overlaps it allows us to confirm the gardner derrida mottishaw second step formula for the main overlap and to go beyond to the next steps we discuss the dynamical status of the amit gutfreund sompolinsky formula for the main overlap and some computersimulation results

a partitioning algorithm for the network loading problem this paper proposes a benders like partitioning algorithm to solve the network loading problem the approach is an iterative method in which the integer programming solver is not used to produce the best integer point in the polyhedral relaxation of the set of feasible capacities rather it selects an integer solution that is closest to the best known integer solution contrary to previous approaches the method does not exploit the original mixed integer programming formulation of the problem the effort of computing integer solutions is entirely left to a pure integer programming solver while valid inequalities are generated by solving standard nonlinear multicommodity flow problems the method is compared to alternative approaches proposed in the literature and appears to be efficient for computing good upper bounds

global stability for non monotone delay equations with application to a model of blood cell production abstract a set of sufficient conditions for the global stability of the positive equilibrium is established for a large class of non monotone time delayed differential equations by the method of fluctuations and the exponential ordering approach then these analytic results are applied to a mathematical model of white blood cell production numerical simulations are also presented to illustrate the global stability regions of parameters and the long term behavior of solutions

retrieval and chaos in layered q ising neural networks using a probabilistic approach we study the parallel dynamics of theq ising layered networks for arbitraryq by introducing auxiliary thermal fields we express the stochastic dynamics within the gain function formulation of the deterministic dynamics evolution equations are derived for arbitraryq at both zero and finite temperatures an explicit analysis of the fixed point equations is carried out for bothq 3 andq the retrieval properties are discussed in terms of the gain parameter the storage capacity and the temperature using the time evolution of the distance between two network configurations we investigate the possibility of microscopic chaos chaotic behavior is always present for arbitrary finiteq however in the limitq the existence of chaos depends on the parameters of the system

dynamical behavior of an epidemic model with a nonlinear incidence rate abstract in this paper we study the global dynamics of an epidemic model with vital dynamics and nonlinear incidence rate of saturated mass action by carrying out global qualitative and bifurcation analyses it is shown that either the number of infective individuals tends to zero as time evolves or there is a region such that the disease will be persistent if the initial position lies in the region and the disease will disappear if the initial position lies outside this region when such a region exists it is shown that the model undergoes a bogdanov takens bifurcation i e it exhibits a saddle node bifurcation hopf bifurcations and a homoclinic bifurcation existence of none one or two limit cycles is also discussed

dynamics of a neural network model with finite connectivity and cycle stored patterns the spatiotemporal evolution and memory retrieval properties of a hopfield like neural network with cycle stored patterns and finite connectivity are studied the analytical studies on a mean field version show that given the number of stored patterns p there is a critical connectivity kc such that the retrieval states are stable fixed points if and only if k kc the dependence of kc on the number of stored patterns is also present the numerical simulations are applied to the short ranged model with local interaction it is revealed that given p the memory retrieval function is kept if the connectivity is high enough while the dynamics of the system is in the frozen phase however when the connectivity k is less than a critical value kc the system is in the chaotic phase and loses its memory retrieval ability the critical points of both the dynamical phase transition and memory loss phase transition are obtained by simulation data

on the parallel dynamics of the q state potts and q ising neural networks using a probabilistic approach the parallel dynamics of theq state potts andq ising neural networks are studied at zero and at nonzero temperatures evolution equations are derived for the first time step and arbitraryq these formulas constitute recursion relations for the exact parallel dynamics of the extremely diluted asymmetric versions of these networks an explicit analysis including dynamical capacity temperature diagrams and the temperature dependence of the overlap is carried out forq 3 both types of models are compared

optimal harvesting of a stochastic mutualism model with levy jumps in this letter a stochastic mutualism model with levy jumps and harvesting is considered under some simple assumptions sufficient and necessary criteria for the existence of optimal harvesting policy are established the optimal harvesting effort and the maximum of sustainable yield are also obtained the effects of random noises on the optimal harvesting of the model are discussed and some numerical simulations are introduced to illustrate the main results

stochastic analysis of a novel nonautonomous periodic siri epidemic system with random disturbances abstract in this paper a new stochastic nonautonomous siri epidemic model is formulated given that the incidence rates of diseases may change with the environment we propose a novel type of transmission function the main aim of this paper is to obtain the thresholds of the stochastic siri epidemic model to this end we investigate the dynamics of the stochastic system and establish the conditions for extinction and persistence in mean of the disease by constructing some suitable lyapunov functions and using stochastic analysis technique furthermore we show that the stochastic system has at least one nontrivial positive periodic solution finally numerical simulations are introduced to illustrate our results

on the parallel dynamics of the diluted clock neural network abstract we present explicit formulae for one step evolution of the overlaps in a clock neural network for the parallel dynamics these formulae constitute recursion relations for the exact dynamics in the case of extreme dilution the fixed point equation for this exactly soluble model is investigated for varying temperature t capacity parameter and the number q of the clock states

parallel dynamics of fully connected q ising neural networks using a probabilistic approach the parallel dynamics of fully connected q ising neural networks is studied for arbitrary q a novel recursive scheme is set up to determine the time evolution of the order parameters through the evolution of the distribution of the local field taking into account all feedback correlations in contrast to extremely diluted and layered network architectures the local field is no longer normally distributed but contains a discrete part as an illustrative example an explicit analysis is carried out for the first four time steps for the case of the q 2 and q 3 model the results are compared with extensive numerical simulations and excellent agreement is found finally equilibrium fixed point equations are derived and compared with the thermodynamic approach based upon the replica symmetric mean field approximation

analysis of a novel stochastic sirs epidemic model with two different saturated incidence rates abstract this paper presents a stochastic sirs epidemic model with two different nonlinear incidence rates and double epidemic asymmetrical hypothesis and we devote to develop a mathematical method to obtain the threshold of the stochastic epidemic model we firstly investigate the boundness and extinction of the stochastic system furthermore we use ito s formula the comparison theorem and some new inequalities techniques of stochastic differential systems to discuss persistence in mean of two diseases on three cases the results indicate that stochastic fluctuations can suppress the disease outbreak finally numerical simulations about different noise disturbance coefficients are carried out to illustrate the obtained theoretical results

a probabilistic approach to parallel dynamics for the little hopfield model presents new results on a probabilistic approach to parallel dynamics of the little hopfield model the authors propose a truncated auxiliary dynamics method to control a feedback noise in this symmetrical neural network with full connection it allows them to propose an ansatz for derivation of the explicit recurrence relations for the main and residual noisy overlap evolution for arbitrary discrete moment t

the signal to noise analysis of the little hopfield model revisited using the generating functional analysis an exact recursion relation is derived for the time evolution of the effective local field of the fully connected little hopfield model it is shown that by leaving out the feedback correlations arising from earlier times in this effective dynamics one precisely finds the recursion relations usually employed in the signal to noise approach the consequences of this approximation as well as the physics behind it are discussed in particular it is pointed out why it is hard to notice the effects especially for model parameters corresponding to retrieval numerical simulations confirm these findings the signal to noise analysis is then extended to include all correlations making it a full theory for dynamics at the level of the generating functional analysis the results are applied to the frequently employed extremely diluted a symmetric architectures and to sequence processing networks

a class of stochastic delayed sir epidemic models with generalized nonlinear incidence rate and temporary immunity abstract a class of sir epidemic model with generalized nonlinear incidence rate is presented in this paper temporary immunity and stochastic perturbation are also considered the existence and uniqueness of the global positive solution is achieved sufficient conditions guaranteeing the extinction and persistence of the epidemic disease are established moreover the threshold behavior is discussed and the threshold value r 0 is obtained we show that if r 0 1 the disease eventually becomes extinct with probability one whereas if r 0 1 then the system remains permanent in the mean

the threshold of a stochastic delayed sir epidemic model with temporary immunity abstract this paper is concerned with the asymptotic properties of a stochastic delayed sir epidemic model with temporary immunity sufficient conditions for extinction and persistence in the mean of the epidemic are established the threshold between persistence in the mean and extinction of the epidemic is obtained compared with the corresponding deterministic model the threshold affected by the white noise is smaller than the basic reproduction number r 0 of the deterministic system

dynamics of a novel nonlinear stochastic sis epidemic model with double epidemic hypothesis abstract in this paper we propose new mathematical models with nonlinear incidence rate and double epidemic hypothesis then we dedicate to develop a method to obtain the threshold of the stochastic sis epidemic model to this end first we investigate the stability of the equilibria of the deterministic system and obtain the conditions for the extinction and the permanence of two epidemic diseases second we explore and obtain the threshold of a stochastic sis system for the extinction and the permanence in mean of two epidemic diseases the results show that a large stochastic disturbance can cause infectious diseases to go to extinction in other words the persistent infectious disease of a deterministic system can become extinct due to the white noise stochastic disturbance this implies that the stochastic disturbance is conducive to epidemic diseases control to illustrate the performance of the theoretical results we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients

parallel dynamics of extremely diluted symmetric q ising neural networks the parallel dynamics of extremely diluted symmetric q ising neural networks is studied for arbitrary q using a probabilistic approach in spite of the extremely diluted architecture the feedback correlations arising from the symmetry prevent a closed form solution in contrast with the extremely diluted asymmetric model a recursive scheme is found determining the complete time evolution of the order parameters taking into account all feedback it is based upon the evolution of the distribution of the local field as in the fully connected model as an illustrative example an explicit analysis is carried out for the q 2 and q 3 model these results agree with and extend the partial results existing for q 2 for q 2 the analysis is entirely new finally equilibrium fixed point equations are derived and a capacity gain function diagram is obtained

a delayed vaccinated epidemic model with nonlinear incidence rate and levy jumps abstract a stochastic susceptible infectious recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity vaccination and le vy jumps on the transmission of diseases we first determine the existence of a unique global positive solution and a positively invariant set for the stochastic system sufficient conditions for extinction and persistence in the mean of the disease are then achieved by constructing suitable lyapunov functions based on the analysis we conclude that noise intensity and the validity period of vaccination greatly influence the transmission dynamics of the system

layered neural networks exact solutions for the dynamics of layered feedforward neural networks are presented these networks are expected to respond to an input by going through a sequence of preassigned states on the various layers the family of networks considered has a variety of interlayer couplings linear and non linear hebbian hebbian with gaussian synaptic noise and with various kinds of dilution in addition the authors also solve the problem of layered networks with the pseudoinverse projector matrix of couplings in all cases the solutions take the form of layer to layer recursions for the mean overlap with a random key pattern and for the width of the embedding field distribution the dynamics is governed by the fixed points of these recursions for all cases non trivial domains of attraction of the memory states are found and graphically displayed

levy noise impact on a stochastic delayed epidemic model with crowly martin incidence and crowding effect abstract in this paper we consider the dynamical behavior of a delayed stochastic epidemic model sir with levy noise first we prove the existence and the uniqueness of the positive solution then we establish a stochastic threshold as a sufficient condition for the extinction and persistence in mean of the disease finally numerical simulations are presented to support our theoretical results

the stability of stochastic coupled systems with time delays and time varying coupling structure this paper is concerned with the pth moment exponential stability of stochastic coupled systems with time delays and time varying coupling structure sctvcs the coupling structure is time varying first second the method of graph theory has been generalized from a system established on a digraph with constant coupling structure to a digraph with time varying coupling structure successfully combining graph theory with lyapunov method a systematic method is given to construct a lyapunov function for sctvcs several pth moment exponential stability criteria are presented including a lyapunov type theorem and some sufficient criteria in the form of coefficients furthermore the theoretical conclusions are applied to the stochastic coupled oscillators with time varying coupling structure and two stability criteria are obtained finally we give two numerical examples to illustrate the effectiveness of our results