application of the karhunen loeve procedure for the characterization of human faces the use of natural symmetries mirror images in a well defined family of patterns human faces is discussed within the framework of the karhunen loeve expansion this results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix without increasing the complexity of the calculation the resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average

exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

lyapunov functionals for delay differential equations model of viral infections we study global properties of a class of delay differential equations model for virus infections with nonlinear transmissions compared with the typical virus infection dynamical model this model has two important and novel features to give a more complex and general infection process a general nonlinear contact rate between target cells and viruses and the removal rate of infected cells are considered and two constant delays are incorporated into the model which describe i the time needed for a newly infected cell to start producing viruses and ii the time needed for a newly produced virus to become infectious mature respectively by the lyapunov direct method and using the technology of constructing lyapunov functionals we establish global asymptotic stability of the infection free equilibrium and the infected equilibrium we also discuss the effects of two delays on global dynamical properties by comparing the results with the stability conditions for the model without delays further we

shift equivalence of measures and the intrinsic structure of shocks in the asymmetric simple exclusion process we investigate the properties of non translation invariant measures describing particle systems on mathbb z which are asymptotic to different translation invariant measures on the left and on the right often the structure of the transition region can only be observed from a point of view which is random in particular configuration dependent two such measures will be called shift equivalent if they differ only by the choice of such a viewpoint we introduce certain quantities called translation sums which under some auxiliary conditions characterize the equivalence classes our prime example is the asymmetric simple exclusion process for which the measures in question describe the microscopic structure of shocks in this case we compute explicitly the translation sums and find that shocks generated in different ways in particular via initial conditions in an infinite system or by boundary conditions in a finite system are described by shift equivalent measures we show also that when the shock in the infinite system is observed from the location of a second class particle treating this particle either as a first class particle or as an empty site leads to shift equivalent shock measures

a stochastic model for internal hiv dynamics in this paper we analyse a stochastic model representing hiv internal virus dynamics the stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling we show that the model established in this paper possesses non negative solutions as this is essential in any population dynamics model we also carry out analysis on the asymptotic behaviour of the model we approximate one of the variables by a mean reverting process and find out the mean and variance of this process numerical simulations conclude the paper

a differential equation model of hiv infection of cd4 t cells with cure rate abstract a differential equation model of hiv infection of cd4 t cells with cure rate is studied we prove that if the basic reproduction number r 0 1 the hiv infection is cleared from the t cell population and the disease dies out if r 0 1 the hiv infection persists in the host we find that the chronic disease steady state is globally asymptotically stable if r 0 1 furthermore we also obtain the conditions for which the system exists an orbitally asymptotically stable periodic solution numerical simulations are presented to illustrate the results

threshold dynamics of a delayed nonlocal reaction diffusion hiv infection model with both cell free and cell to cell transmissions abstract in this paper we derive and analyze an hiv infection model containing a fixed latent period and both cell free and cell to cell transmissions the model is described by a spatially non local reaction diffusion system with the zero flux condition on the boundary we first show that the model admits global solutions and possesses a global attractor following the definition of the next infection operator we obtain the expression of the basic reproduction number 0 which is shown as a threshold parameter for the model dynamics our results indicate that the clearance persistence of hiv is governed by the sign of 0 1 in particular an explicit formula of 0 is given in the homogeneous case

asymptotic behaviors of a cell to cell hiv 1 infection model perturbed by white noise abstract in this paper we analyze a mathematical model of cell to cell hiv 1 infection to c d 4 t cells perturbed by stochastic perturbations first of all we investigate that there exists a unique global positive solution of the system for any positive initial value then by using lyapunov analysis methods we study the asymptotic property of this solution moreover we discuss whether there is a stationary distribution for this system and if it owns the ergodic property numerical simulations are presented to illustrate the theoretical results

quantization on the grassmann manifold the problem of quantization in an euclidean space with unitary constraints can be formulated as an unconstrained problem on a grassmann manifold such constraints arise in areas such as wireless communication with multiple antennas at the transmitter and at the receiver due to the constraints the distortion rate analysis developed for euclidean spaces cannot be applied directly this paper extends gersho s asymptotic large rate small distortion distortion bounds to the case when the source is distributed on the complex grassmann manifold the special structure of the grassmann manifold and the distortion measures defined on it differentiate this problem from the traditional vector quantization in euclidean spaces

global stability for a virus dynamics model with nonlinear incidence of infection and removal global dynamics of a compartmental model which describes virus propagation in vivo is studied using the direct lyapunov method where the incidence rate of the infection and the removal rate of the virus are assumed to be nonlinear in the case where the functional quotient between the force of infection and the removal rate of the virus is a nonincreasing function of the virus concentration the existence of a threshold parameter i e the basic reproduction number or basic reproductive ratio is established and the global stability of the equilibria is discussed moreover in the absence of the above mentioned monotonicity property estimations for the sizes of the domains of attraction are given biological significance of the results and possible extensions of the model are also discussed

multiple shocks in a driven diffusive system with two species of particles abstract a one dimensional driven diffusive system with two types of particles and nearest neighbors interactions has been considered on a finite lattice with open boundaries the particles can enter and leave the system from both ends of the lattice and there is also a probability for converting the particle type at the boundaries we will show that on a special manifold in the parameters space multiple shocks evolve in the system for both species of particles which perform continuous time random walks on the lattice

shock fluctuations in asymmetric simple exclusion the one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the burgers equation we study the process with rates of jumpsp q to the right and left respectively and with initial product measure with densities to the left and right of the origin respectively with shock initial conditions we prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times if this particle is added at another site then it describes the behavior of a characteristic of the burgers equation for vanishing left density 0 we prove in the scale t1 2 that the position of the shock at timet depends only on the initial configuration in a region depending ont the proofs are based on laws of large numbers for the second class particle

one dimensional partially asymmetric simple exclusion process with open boundaries orthogonal polynomials approach the stationary state of the partially asymmetric simple exclusion process with open boundaries is reconsidered the so called matrix product ansatz is employed this enables us to construct the stationary state in the form of the product of the matrices d and e noticing the fact that the matrix c d e for the model is related to certain q orthogonal polynomials the model is analysed for a wide range of parameters the current and the correlation length are evaluated in the thermodynamic limit it turns out that the phase diagram for the correlation length is richer than that for the totally asymmetric case

shocks in the asymmetric exclusion process with internal degree of freedom we determine all families of markovian three state lattice gases with pair interaction and a single local conservation law one such family of models is an asymmetric exclusion process where particles exist in two different nonconserved states we derive conditions on the transition rates between the two states such that the shock has a particularly simple structure with minimal intrinsic shock width and random walk dynamics we calculate the drift velocity and diffusion coefficient of the shock

asymptotic properties of a hiv 1 infection model with time delay based on some important biological meanings a class of more general hiv 1 infection models with time delay is proposed in the paper in the hiv 1 infection model time delay is used to describe the time between infection of uninfected target cells and the emission of viral particles on a cellular level as proposed by herz et al a v m herz s bonhoeffer r m anderson r m may m a nowak viral dynamics in vivo limitations on estimates of intracellular delay and virus decay proc natl acad sci usa 93 1996 7247 7251 then the effect of time delay on stability of the equilibria of the hiv 1 infection model has been studied and sufficient criteria for local asymptotic stability of the infected equilibrium and global asymptotic stability of the viral free equilibrium are given

global properties for virus dynamics model with mitotic transmission and intracellular delay abstract in this paper we study the basic model of viral infections with mitotic transmission and intracellular delay discrete the delay corresponds to the time between infection of uninfected cells and the emission of virus on a cellular level by means of volterra type lyapunov functionals we provide the global stability for this model let be the number of virus produced per infected cell if crit the critical number satisfies crit then the virus free steady state is globally asymptotically stable on the contrary if crit then the infected steady state is globally asymptotically stable if a sufficient condition is satisfied

shock fluctuations in the asymmetric simple exclusion process we consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively q p ferrari et al 1991 have shown that if the initial measure isv a product measure with densities and to the left and right of the origin respectively then there exists a microscopic shock for the system a shock is a random positionx t such that the system as seen from this position at timet has asymptotic product distributions with densities and to the left and right of the origin respectively uniformly int we compute the diffusion coefficient of the shockd lim t t 1 e x t 2 ex t 2 and findd p q 1 1 1 as conjectured by spohn 1991 we show that in the scale sqrt t the position ofx t is determined by the initial distribution of particles in a region of length proportional tot we prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities and this is the so called dynamical phase transition under shock initial conditions we show how the density fluctuation fields depend on the initial configuration

shocks in the asymmetric exclusion process in this paper we consider limit theorems for the asymmetric nearest neighbor exclusion process on the integers the initial distribution is a product measure with asymptotic density at and at earlier results described the limiting behavior in all cases except for 0 1 2 1 here we treat the exceptional case which is more delicate it corresponds to the one in which a shock wave occurs in an associated partial differential equation in the cases treated earlier the limit was an extremal invariant measure by contrast in the present case the limit is a mixture of two invariant measures our theorem resolves a conjecture made by the third author in 1975 7 the convergence proof is based on coupling and symmetry considerations

partially asymmetric exclusion process with open boundaries exclusive diffusion on a one dimensional lattice is studied in the model particles hop stochastically in both directions but with different rates at the ends of the lattice particles are injected and removed the exact stationary probability measure is represented in the form of a matrix product as a generalization of the solution given by derrida et al j phys a 26 1493 1993 for the fully asymmetric process the phase diagram of the current on the infinite lattice is obtained analytic expressions for the current in the different phases are derived the model is equivalent to an xxz heisenberg chain with a certain type of boundary terms the ground state of which corresponds to the stationary solution of the master equation

what is the set of images of an object under all possible illumination conditions the appearance of an object depends on both the viewpoint from which it is observed and the light sources by which it is illuminated if the appearance of two objects is never identical for any pose or lighting conditions then in theory the objects can always be distinguished or recognized the question arises what is the set of images of an object under all lighting conditions and pose in this paper we consider only the set of images of an object under variable illumination including multiple extended light sources and shadows we prove that the set of n pixel images of a convex object with a lambertian reflectance function illuminated by an arbitrary number of point light sources at infinity forms a convex polyhedral cone in r n and that the dimension of this illumination cone equals the number of distinct surface normals furthermore the illumination cone can be constructed from as few as three images in addition the set of n pixel images of an object of any shape and with a more general reflectance function seen under all possible illumination conditions still forms a convex cone in r n extensions of these results to color images are presented these results immediately suggest certain approaches to object recognition throughout we present results demonstrating the illumination cone representation

global stability and hopf bifurcation of an hiv 1 infection model with saturation incidence and delayed ctl immune response abstract in this paper an hiv 1 infection model with saturation incidence and time delay due to the ctl immune response is investigated by analyzing corresponding characteristic equations the local stability of each of feasible equilibria and the existence of hopf bifurcation at the ctl activated infection equilibrium are established respectively by means of lyapunov functionals and lasalle s invariance principle it is shown that the infection free equilibrium is globally asymptotically stable when the basic reproduction ratio is less than unity when the immune response reproductive ratio is less than unity and the basic reproductive ratio is greater than unity the ctl inactivated infection equilibrium of the system is globally asymptotically stable

threshold dynamics of hiv 1 virus model with cell to cell transmission cell mediated immune responses and distributed delay we study the problem of global asymptotic stability for equilibria of a hiv 1 virus model we broaden the construction method into the viral model with infinite distributed delay and cell to cell transmission respectively numerical examples are given to illustrate the effectiveness of the theoretical results for sharp threshold property the goal of this paper is to study the threshold dynamics of an hiv 1 viral infection model with cell mediated immune responses and direct cell to cell transmission mechanism the model demonstrates global threshold dynamics with respect to the reproductive numbers for viral infection 0 and for ctl immune response 1 the proofs of main results come from suitable uses of analyzing the characteristic equation and constructing lyapunov functionals specifically if 0 1 the ctl activated equilibrium e2 is locally and globally asymptotically stable and the infection is chronic with persistent ctls response numerical simulations are performed to support our results

dynamics of a diffusive virus model with general incidence function cell to cell transmission and time delay abstract in this paper we revisit a diffusive virus dynamics model with general incidence function and time delay one novelty of our model is that we introduce cell to cell transmission via formation of virological synapses to reflect the fact that it may play a more important role in virus spreading in addition to virus to cell infection we justify the well posedness of the model and identify the basic reproduction number 0 for the model to be a sharp threshold value the global stability of equilibria is determined by constructing suitable lyapunov functionals in the sense that the infection free equilibrium is globally asymptotically stable if 0 1 and when 0 1 the global asymptotic stability of infection equilibrium implies that the infection will persist a significant impact of the cell to cell transmission is that they increase the basic reproduction number if one neglects either the cell to cell transmission or virus to cell infection the basic reproduction number of the model that is under evaluated last we perform numerical simulation to support our theoretic results we set the domain of the viruses to be a two dimensional square domain with the homogeneous neumann boundary conditions to reflect the spatial spreading

global stability of a diffusive and delayed virus dynamics model with beddington deangelis incidence function and ctl immune response in this paper we study a diffusive and delayed virus dynamics model with beddington deangelis incidence and ctl immune response by constructing lyapunov functionals we show that if the basic reproductive number is less than or equal to one then the infection free equilibrium is globally asymptotically stable if the immune reproductive number is less than or equal to one and the basic reproductive number is greater than one then the immune free equilibrium is globally asymptotically stable if the immune reproductive number is greater than one then the interior equilibrium is globally asymptotically stable

exact solution of the totally asymmetric simple exclusion process shock profiles the microscopic structure of macroscopic shocks in the one dimensional totally asymmetric simple exclusion process is obtained exactly from the complete solution of the stationary state of a model system containing two types of particles first and second class this nonequilibrium steady state factorizes about any second class particle which implies factorization in the one component system about the random shock position it also exhibits several other interesting features including long range correlations in the limit of zero density of the second class particles the solution also shows that a finite number of second class particles in a uniform background of first class particles form a weakly bound state

global stability for a delayed hiv 1 infection model with nonlinear incidence of infection abstract in this paper a delayed hiv 1 infection model with nonlinear incidence of infection is reinvestigated it is shown that if the reproduction number r 1 then the system is permanent and the infective equilibrium of the system is globally asymptotically stable thus the global dynamics of the system is completely determined by the reproduction number r the results obtained enrich and improve the corresponding results given by wang et al x wang y tao x song a delayed hiv 1 infection model with beddington deangelis functional response nonlinear dynamics 62 2010 67 72 the conclusions we established also verify the numerical simulation results on the global asymptotic stability of the infective equilibrium in the paper d li w ma asymptotic properties of an hiv 1 infection model with time delay j math anal appl 335 2007 683 691

on jack hale s problem for impulsive systems abstract an interesting problem of jack hale deals with the existence of a maximal compact invariant set in discrete dynamical systems a solution for this problem is known for locally bounded dynamical systems following this line of research we consider in this paper a class of systems whose continuous dynamics are interrupted by abrupt changes of state and we present sufficient conditions to obtain the existence of a maximal compact invariant set for a system in this class we use the theory of asymptotic compactness to get the results

global dynamics of a diffusive and delayed viral infection model with cellular infection and nonlinear infection rate abstract a diffusive and delayed viral dynamics model which incorporates cell to cell transmission cell mediated immune responses and general nonlinear incidence is investigated by constructing lyapunov functionals it is shown that the global threshold dynamics of the model is fully determined by the basic reproduction numbers of the virus and the immune response r 0 and r 1 the result implies that both the basic reproduction number of the virus and the immune response might be underevaluated without considering either the virus to cell transmission or cell to cell transmission the main results obtained in this paper extend some known results

asymptotic behavior of a stochastic delayed hiv 1 infection model with nonlinear incidence abstract in this paper a stochastic delayed hiv 1 infection model with nonlinear incidence is proposed and investigated first of all we prove that there is a unique global positive solution as desired in any population dynamics then by constructing some suitable lyapunov functions we show that if the basic reproduction number r 0 1 then the solution of the stochastic system oscillates around the infection free equilibrium e 0 while if r 0 1 then the solution of the stochastic system fluctuates around the infective equilibrium e sufficient conditions of these results are established finally we give some examples and a series of numerical simulations to illustrate the analytical results

monte carlo extrinsic estimators of manifold valued parameters monte carlo mc methods have become an important tool for inferences in non gaussian and non euclidean settings we study their use in those signal image processing scenarios where the parameter spaces are certain riemannian manifolds finite dimensional lie groups and their quotient sets we investigate the estimation of means and variances of the manifold valued parameters using two popular sampling methods independent and importance sampling using euclidean embeddings we specify a notion of extrinsic means employ monte carlo methods to estimate these means and utilize large sample asymptotics to approximate the estimator covariances experimental results are presented for target pose estimation orthogonal groups and signal subspace estimation grassmann manifolds asymptotic covariances are utilized to construct confidence regions to compare estimators and to determine the sample size for mc sampling

statistical computations on grassmann and stiefel manifolds for image and video based recognition in this paper we examine image and video based recognition applications where the underlying models have a special structure the linear subspace structure we discuss how commonly used parametric models for videos and image sets can be described using the unified framework of grassmann and stiefel manifolds we first show that the parameters of linear dynamic models are finite dimensional linear subspaces of appropriate dimensions unordered image sets as samples from a finite dimensional linear subspace naturally fall under this framework we show that an inference over subspaces can be naturally cast as an inference problem on the grassmann manifold to perform recognition using subspace based models we need tools from the riemannian geometry of the grassmann manifold this involves a study of the geometric properties of the space appropriate definitions of riemannian metrics and definition of geodesics further we derive statistical modeling of inter and intraclass variations that respect the geometry of the space we apply techniques such as intrinsic and extrinsic statistics to enable maximum likelihood classification we also provide algorithms for unsupervised clustering derived from the geometry of the manifold finally we demonstrate the improved performance of these methods in a wide variety of vision applications such as activity recognition video based face recognition object recognition from image sets and activity based video clustering

global stability and periodic solution of the viral dynamics it is well known that the mathematical models provide very important information for the research of human immunodeficiency virus type 1 and hepatitis c virus hcv however the infection rate of almost all mathematical models is linear the linearity shows the simple interaction between the t cells and the viral particles in this paper we consider the classical mathematical model with saturation response of the infection rate by stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection free steady state we also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution numerical simulations are presented to illustrate the results

a flag representation for finite collections of subspaces of mixed dimensions abstract given a finite set of subspaces of r n perhaps of differing dimensions we describe a flag of vector spaces i e a nested sequence of vector spaces that best represents the collection based on a natural optimization criterion and we present an algorithm for its computation the utility of this flag representation lies in its ability to represent a collection of subspaces of differing dimensions when the set of subspaces all have the same dimension d the flag mean is related to several commonly used subspace representations for instance the d dimensional subspace in the flag corresponds to the extrinsic manifold mean when the set of subspaces is both well clustered and equidimensional of dimension d then the d dimensional component of the flag provides an approximation to the karcher mean an intermediate matrix used to construct the flag can also be used to recover the canonical components at the heart of multiset canonical correlation analysis two examples utilizing the carnegie mellon university pose illumination and expression database cmu pie serve as visual illustrations of the algorithm

stability analysis of a virus dynamics model with general incidence rate and two delays the aim of this work is to study the dynamical behavior of a virus dynamics model with general incidence rate and two delays the first delay represents the time from the virus entry to the production of new viruses and the second delay corresponds to the time necessary for a newly produced virus to become infectious lyapunov functionals are constructed and lasalle invariance principle for delay differential equations is used to establish the global asymptotic stability of the disease free and the chronic infection equilibria the results obtained show that the global dynamics are completely determined by the value of a certain threshold parameter called the basic reproduction number r 0 and under some assumptions on the general incidence function our results extend the known results on delay virus dynamics considered in the other papers and suggest useful methods to control virus infection these results can be applied to a variety of possible incidence functions that could be used in virus dynamics model as well as epidemic models

bethe ansatz solution for a defect particle in the asymmetric exclusion process the asymmetric exclusion process on a ring in one dimension is considered with a single defect particle the steady state has previously been solved by a matrix product method here we use the bethe ansatz to solve exactly for the long time limit behaviour of the generating function of the distance travelled by the defect particle this allows us to recover steady state properties known from the matrix approach such as the velocity and obtain new results such as the diffusion constant of the defect particle in the case where the defect particle is a second class particle we determine the large deviation function and show that in a certain range the distribution of the distance travelled about the mean is gaussian moreover the variance diffusion constant grows as l1 2 where l is the system size this behaviour can be related to the superdiffusive spreading of excess mass fluctuations on an infinite system in the case where the defect particle produces a shock our expressions for the velocity and the diffusion constant coincide with those calculated previously for an infinite system by ferrari and fontes

matrix product states of three families of one dimensional interacting particle systems abstract the steady states of three families of one dimensional non equilibrium models with open boundaries first proposed in n j phys 5 2003 145 1 are studied using a matrix product formalism it is shown that their associated quadratic algebras have two dimensional representations provided that the transition rates lie on specific manifolds of parameters exact expressions for the correlation functions of each model have also been obtained we have also studied the steady state properties of one of these models first introduced in j phys a math gen a 36 2003 74 with more details by introducing a canonical ensemble we calculate the canonical partition function of this model exactly using the yang lee theory of phase transitions we spot a second order phase transition from a power law to a jammed phase the density profile of particles in each phase has also been studied a simple generalization of this model in which both the left and the right boundaries are open has also been introduced it is shown that double shock structures may evolve in the system under certain conditions

global dynamics for a class of age infection hiv models with nonlinear infection rate abstract in this paper we study the global stability of a class of hiv viral infection models with continuous age structure using the direct lyapunov method in each of the cases where the incidence rates are given by nonlinear infection rate f t g v holling type ii functional response and crowley martin functional response we define the basic reproduction number and prove that it is a sharp threshold determining whether the infection dies out or not we give a rigorous mathematical analysis on technical materials and necessary arguments including relative compactness of the orbit and uniform persistence of system by reformulating the system as a system of volterra integral equations we further investigate global behaviors of hiv viral infection models with holling type ii functional response and crowley martin functional response through numerical simulations

stability analysis of a model for hbv infection with cure of infected cells and intracellular delay a viral infection model of hbv infection of hepatocytes with cure of infected cells and intracellular delay is studied the delay corresponds to the time necessary for a newly produced virion to become infectious particles we prove that the stability is completely determined by the basic reproductive number r 0 if r 0 1 the infection free steady state is globally asymptotically stable if r 0 1 then infection free steady state becomes unstable and a unique infected steady state exists and is locally asymptotically stable on the other hand we derive sufficient conditions for the global asymptotic stability of the infected steady state numerical simulations are presented to illustrate the results

an epidemic model of a vector borne disease with direct transmission and time delay abstract this paper considers an epidemic model of a vector borne disease which has direct mode of transmission in addition to the vector mediated transmission the incidence term is assumed to be of the bilinear mass action form we include both a baseline ode version of the model and a differential delay model with a discrete time delay the ode model shows that the dynamics is completely determined by the basic reproduction number r 0 if r 0 1 the disease free equilibrium is globally stable and the disease dies out if r 0 1 a unique endemic equilibrium exists and is locally asymptotically stable in the interior of the feasible region the delay in the differential delay model accounts for the incubation time the vectors need to become infectious we study the effect of that delay on the stability of the equilibria we show that the introduction of a time delay in the host to vector transmission term can destabilize the system and periodic solutions can arise through hopf bifurcation

global dynamics of a viral infection model with a latent period and beddington deangelis response in this paper we study the global dynamics of a viral infection model with a latent period the model has a nonlinear function which denotes the incidence rate of the virus infection in vivo the basic reproduction number of the virus is identified and it is shown that the uninfected equilibrium is globally asymptotically stable if the basic reproduction number is equal to or less than unity moreover the virus and infected cells eventually persist and there exists a unique infected equilibrium which is globally asymptotically stable if the basic reproduction number is greater than unity the basic reproduction number determines the equilibrium that is globally asymptotically stable even if there is a time delay in the infection

consensus optimization on manifolds the present paper considers distributed consensus algorithms that involve n agents evolving on a connected compact homogeneous manifold the agents track no external reference and communicate their relative state according to a communication graph the consensus problem is formulated in terms of the extrema of a cost function this leads to efficient gradient algorithms to synchronize i e maximizing the consensus or balance i e minimizing the consensus the agents a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time varying the cost function is linked to a specific centroid definition on manifolds introduced here as the induced arithmetic mean that is easily computable in closed form and may be of independent interest for a number of manifolds the special orthogonal group so n and the grassmann manifold text it grass p n are treated as original examples a link is also drawn with the many existing results on the circle

global dynamics of a cell mediated immunity in viral infection models with distributed delays abstract in this paper we investigate global dynamics for a system of delay differential equations which describes a virus immune interaction in vivo the model has two distributed time delays describing time needed for infection of cell and virus replication our model admits three possible equilibria an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection r 0 and for ctl response r 1 such that r 1 r 0 it is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of lyapunov functional more specifically the uninfected equilibrium is globally asymptotically stable if r 0 1 an infected equilibrium without immune response is globally asymptotically stable if r 1 1 r 0 and an infected equilibrium with immune response is globally asymptotically stable if r 1 1 the immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if r 1 1

stability and hopf bifurcation in a delayed viral infection model with mitosis transmission in this paper we study a model of hcv with saturation and delay we stablish the local and global stability of system also we stablish the occurrence of a hopf bifurcation we will determine conditions for the permanence of model and the length of delay to preserve stability we present a sensitivity analysis for the basic reproductive number

shock profiles for the asymmetric simple exclusion process in one dimension the asymmetric simple exclusion process asep on a one dimensional lattice is a system of particles which jump at rates p and 1 p here p 1 2 to adjacent empty sites on their right and left respectively the system is described on suitable macroscopic spatial and temporal scales by the inviscid burgers equation the latter has shock solutions with a discontinuous jump from left density rho to right density rho rho sqrt rho 1 rho rho 1 rho for a special value of the asymmetry given by p 1 p rho 1 rho rho 1 rho the measure is bernoulli with density rho on the left and rho on the right in the weakly asymmetric limit 2p 1 to0 the microscopic width of the shock diverges as 2p 1 1 the stationary measure is then essentially a superposition of bernoulli measures corresponding to a convolution of a density profile described by the viscous burgers equation with a well defined distribution for the location of the second class particle