abstract functional differential equations and reaction diffusion systems functional differential equations and reaction diffusion systems r h martin jr and h l smith abstract several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays suppose q is a bounded domain in rn with aq smooth and a is the laplacian operator on q also let m be a positive integer z a positive number and f fi m a continuous bounded function from 0 xc x q x c z 0 m into rm where c t 0 is the space of continuous functions from z 0 into r the purpose of this paper is to apply abstract results for semilinear functional differential equations in banach spaces to reactiondiffusion systems with time delays having the form a tu x t diau x t i t x ut x t a xeq i 1 m rdd ai x ui x t au i x t 81 x t t a x eaq u x a 0 x x 0 5 t 0 di 0 and ca q 0 o is c and i q x 0 oo r is c2 here an is the outward normal derivative on aq and if di 0 it is assumed that no boundary conditions are specified for this i also tu x t denotes the partial with respect to t whereas ut x denotes the member of c z 0 defined by 0 u x t 0 u x t 0 m our techniques provide basic existence criteria but the main point is that they can also be effectively applied to obtain estimates for solutions especially received by the editors october 7 1987 and in revised form october 7 1988 1980 mathematics subject classification 1985 revision primary 35r10 34k30

spreading speeds and traveling waves for periodic evolution systems abstract the theory of spreading speeds and traveling waves for monotone autonomous semiflows is extended to periodic semiflows in the monostable case then these abstract results are applied to a periodic system modeling man environment man epidemics a periodic time delayed and diffusive equation and a periodic reaction diffusion equation on a cylinder

nonlocal problems involving spatial structure for coupled reaction diffusion systems the purpose of this work is to investigate the uniqueness and existence of solutions for a system of nonlinear parabolic equations weakly coupled with ordinary differential equations in bounded domains subject to nonlocal boundary conditions that involve values of the unknown functions inside of the spatial domain the solutions of such problems allow for considering not only physical chemical or biological properties but also spatial structure of the modelled system the uniqueness of classical solutions of the nonlocal boundary problems for coupled reaction diffusion systems is proved by means of comparison principles for differential inequalities the existence of the unique solution is obtained via a monotone iterative method applications are given to some model problems in epidemiology and ecology with the nonlocal boundary conditions based on the inverse distance weighting interpolation and cokriging

minimal wave speed in a diffusive epidemic model with temporal delay abstract taking incubation period into account we modify capasso et al s epidemic model and consider a reaction diffusion system with time delay by the method of upper and lower solutions to a related second order ordinary differential equation with infinite time delay we establish the existence of the minimal wave speed for the modified epidemic model and show that incubation period reduces the minimal wave speed of epidemic model indeed

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

dynamics of a class of delayed reaction diffusion systems with neumann boundary condition abstract this paper considers a class of delayed reaction diffusion systems under the neumann boundary condition which arise in epidemiology and can describe the temporal and spatial evolutionary phenomena for the bacteria population and the human infective population with the help of the iterative properties of interval mapping and dynamical system approaches some positively invariant sets and attractive basins of the considered systems are analyzed detailedly in addition combining the global attractivity of interval mapping we provide some sufficient conditions to ensure local or global attractivity of steady states of the systems finally we apply these theoretical results to some models with different nonlinearity demonstrating force of infection and then obtain some sufficient conditions about force of infection to describe the survival and extinction of bacteria and infective populations

local spectral radii and collatz wielandt numbers of monic operator polynomials with nonnegative coefficients abstract operator polynomials l li l 1al 1 a1 a0 are considered where a0 al 1 are nonnegative operators in a banach space x with normal cone x for x x we define the local spectral radius rl x and the lower and upper collatz wielandt numbers r l x and r l x respectively of x with respect to l we characterize these quantities with the help of corresponding quantities with respect to the first companion operator belonging to l and the operator function s al 1 1al 2 l 1a0 many properties known in the linear case l 1 have generalizations to the case l 1 e g r l x r l x r l x is true for all x x from these local results we obtain results for the global spectral radius r l which were proved earlier under more restrictive conditions

entire solutions in bistable reaction diffusion equations with nonlocal delayed nonlinearity this paper is concerned with entire solutions for bistable reaction diffusion equations with nonlocal delay in one dimensional spatial domain here the entire solutions are defined in the whole space and for all time t r assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument we prove the existence of entire solutions which behave as two traveling wave solutions coming from both ends of the x axis and annihilating at a finite time furthermore we show that such an entire solution is unique up to space time translations and is liapunov stable a key idea is to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions in order to illustrate our main results two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are considered

nonlocal dispersal cooperative systems acceleration propagation among species abstract we focus on the influences of nonlocal dispersal kernels on the spatial propagation in nonlocal dispersal cooperative systems with initial values having nonempty compact supports it is well known that the solution of a monostable nonlocal dispersal scalar equation spreads at a finite speed when the kernel is thin tailed and propagates by accelerating when the kernel has a heavy tail the fat tailed however in such systems we find that one species can propagate by accelerating although its dispersal kernel is thin tailed which is a new and interesting phenomenon more precisely we show that the spatial propagation of every species at large time is mainly determined by the tail of the maximum of their dispersal kernels which further implies that their spatial propagation is accelerated by each other because of the cooperation relation between them this gives us a new understanding of the cooperation relation in the spatial propagation of nonlocal dispersal cooperative systems

particle smoothing for hidden diffusion processes adaptive path integral smoother smoothing methods are used for inference of stochastic processes given noisy observations the estimation of the marginal posterior distribution given all observations is typically a computationally intensive task we propose a novel algorithm based on path integral control theory to efficiently estimate the smoothing distribution of continuous time diffusion processes from partial observations in particular we use an adaptive importance sampling method to improve the effective sampling size of the posterior and the reliability of the estimation of the marginals this is achieved by estimating a feedback controller together with an adaptive initialization and an annealing scheme to sample efficiently from the joint smoothing distribution we compare the results with estimations obtained from the standard forward filter backward simulator ffbsi for two diffusion processes of different complexity we show that the proposed method gives more accurate estimates than the standard ffbsi

travelling fronts and entire solutions of the fisher kpp equation in ℝn this paper is devoted to time global solutions of the fisher kpp equation in n where f is a c 2 concave function on 0 1 such that f 0 f 1 0 and f 0 on 0 1 it is well known that this equation admits a finite dimensional manifold of planar travelling fronts solutions by considering the mixing of any density of travelling fronts we prove the existence of an infinite dimensional manifold of solutions in particular there are infinite dimensional manifolds of nonplanar travelling fronts and radial solutions furthermore up to an additional assumption a given solution u can be represented in terms of such a mixing of travelling fronts

entire solutions in a time delayed and diffusive epidemic model this paper is concerned with entire solutions in the following time delayed and diffusive epidemic model email protected tu 1 x t d email protected u 1 x t a 1 1u 1 x t a 1 2u 2 x t email protected tu 2 x t d email protected u 2 x t a 2 2u 2 x t gu 1x email protected where d i 0 i 1 2 using comparison arguments we establish the existence and its properties of entire solutions for the above system here an entire solution means a classical solution defined for all email protected r

time periodic traveling wave solutions for periodic advection reaction diffusion systems abstract we study the existence uniqueness and asymptotic stability of time periodic traveling wave solutions to a class of periodic advection reaction diffusion systems under certain conditions we prove that there exists a maximal wave speed c such that for each wave speed c c there is a time periodic traveling wave connecting two periodic solutions of the corresponding kinetic system it is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co moving frame coordinate we also show that the traveling wave solutions with wave speed c c are asymptotically stable in certain sense in addition we establish the nonexistence of time periodic traveling waves with speed c c

traveling wave front for a two component lattice dynamical system arising in competition models abstract we study traveling front solutions for a two component system on a one dimensional lattice this system arises in the study of the competition between two species with diffusion or migration if we divide the habitat into discrete regions or niches we consider the case when the nonlinear source terms are of lotka volterra type and of monostable case we first show that there is a positive constant the minimal wave speed such that a traveling front exists if and only if its speed is above this minimal wave speed then we show that any wave profile is strictly monotone moreover under some conditions we show that the wave profile is unique up to translations for a given wave speed finally we characterize the minimal wave speed by the parameters in the system

global asymptotics in some quasimonotone reaction diffusion systems with delays abstract both dichotomy and trichotomy on the global asymptotics of some quasimonotone reaction diffusion systems with delays are established in terms of the principal eigenvalue of linear weakly coupled elliptic systems applications to a class of delayed reaction diffusion models of single species growth and to a reaction diffusion system with delay modelling the spread of bacterial infections are provided

traveling wave solutions of lotka volterra competition systems with nonlocal dispersal in periodic habitats this paper is concerned with space periodic traveling wave solutions of the following lotka volterra competition system with nonlocal dispersal and space periodic dependence partial derivative u 1 partial derivative t integral r n kappa y x u 1 t y dy u 1 t x u 1 a 1 x b 1 x u 1 c 1 x u 1 x is an element of r n partial derivative u 2 partial derivative t integral r n kappa y x u 2 t y dy u 1 t x u 2 a 2 x b 2 x u 2 c 2 x u 2 x is an element of r n under suitable assumptions the system admits two semitrivial space periodic equilibria u 1 x 0 and 0 u 2 x where u 1 x 0 is linearly and globally stable and 0 u 2 x is linearly unstable with respect to space periodic perturbations by sub and supersolution techniques and comparison principals we show that for any given xi is an element of sn 1 there exists a continuous periodic traveling wave solution of the form u 1 t x u 2 t x phi 1 x ct xi ct xi 4 phi 2 x ct xi ct xi connecting u 1 0 and 0 u 2 and propagating in the direction of xi with speed c c xi where c xi is the spreading speed of the system in the direction of moreover for c c xi we also prove the asymptotic stability and uniqueness of traveling wave solution using squeezing techniques c 2016 elsevier inc all rights reserved

property γ factors and the hochschild cohomology problem the main result of this article is that the kth continuous hochschild cohomology groups hk and hk b h of a von neumann factor b h of type ii1 with property are 0 for all positive integers k the method of proof involves the construction of hyperfinite subfactors with special properties and a new inequality of grothendieck type for multilinear maps we prove joint continuity in the 2 norm of separately ultraweakly continuous multilinear maps and combine these results to reduce to the case of completely bounded cohomology which is already solved

analysis of a reaction diffusion system modeling man environment man epidemics in this paper an old model for the temporal and spatial evolution of orofecal transmitted disease is reexamined it consists of a system of two coupled reaction diffusion equations for the concentration of bacteria and infective humans under the assumptions that the total population of humans is unaffected by the disease and only a small proportion of the population is affected at any one time the force of infection on healthy humans is assumed to be a sigmoidal function of bacterial concentration tending to some finite limit and with zero gradient at zero this last feature models an immune response to low concentrations of the infectious agent in practice the diffusion coefficient for infective humans ismuch smaller than that of bacteria and is therefore set to zero a detailed analysis of the steady state bifurcation pattern is then performed for the case of homogeneous dirichlet boundary conditions applied at the endpoints of a one dimensional interval particular attention is paid to the limiti

global attractivity spreading speeds and traveling waves of delayed nonlocal reaction diffusion systems abstract the purpose of this work is to study the spatial dynamics of some delayed nonlocal reaction diffusion systems in whole space we first establish a series of comparison theorems to investigate the global attractivity of the equilibria for a delayed nonlocal reaction diffusion system with and without quasi monotonicity then we show that the spreading speed of a general system without quasi monotone conditions is coincident with the minimal wave speed applying a fluctuation method we further provide some sufficient conditions to ensure the upward convergence of the spreading speed and traveling wave solutions finally we point out the effects of the delay and nonlocality on the spreading speed of the non quasi monotone systems

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

saddle point behavior for monotone semiflows and reaction diffusion models the saddle point behavior is established for monotone semiflows with weak bistability structure and then these results are applied to three reaction diffusion systems modeling man environment man epidemics single loop positive feedback and two species competition respectively

enhanced targeted sampling of high dimensional free energy landscapes using variationally enhanced sampling with an application to chignolin the capabilities of molecular simulations have been greatly extended by a number of widely used enhanced sampling methods that facilitate escaping from metastable states and crossing large barriers despite these developments there are still many problems which remain out of reach for these methods which has led to a vigorous effort in this area one of the most important problems that remains unsolved is sampling high dimensional free energy landscapes and systems that are not easily described by a small number of collective variables in this work we demonstrate a new way to compute free energy landscapes of high dimensionality based on the previously introduced variationally enhanced sampling and we apply it to the miniprotein chignolin

traveling wave solutions in partially degenerate cooperative reaction diffusion systems abstract we study the existence of traveling wave solutions for partially degenerate cooperative reaction diffusion systems that can have three or more equilibria we show via integral systems that there exist traveling wave solutions in a partially degenerate reaction diffusion system with speeds above two well defined extended real numbers we prove that the two numbers are the same and may be characterized as the spreading speed as well as the slowest speed of a class of traveling wave solutions provided that the linear determinacy conditions are satisfied we demonstrate our theoretical results by examining a partially degenerate lotka volterra competition model with advection terms

traveling waves for epidemic models with nonlocal dispersal in time and space periodic habitats abstract this paper deals with the spatial spreading speed and traveling wave solutions of a general epidemic model with nonlocal dispersal in time and space periodic habitats it should be mentioned that the existence of spreading speed and traveling wave solutions of nonlocal dispersal cooperative system in space time periodic habitats have been established previously in this paper we further show that the epidemic system has a spreading speed c and for any c c there exist a unique continuous space time periodic traveling wave solution 1 x c t t c t 2 x c t t c t of epidemic model in the direction of with speed c and there is no such solution for c c

existence and uniqueness of entire solutions for a reaction diffusion equation abstract we consider entire solutions of u t u xx f u i e solutions that exist for all x t r 2 where f 0 f 1 0 f 0 in particular we are interested in the entire solutions which behave as two opposite wave fronts of positive speed s approaching each other from both sides of the x axis and then annihilating in a finite time in the case f 1 0 we show that such entire solution exists and is unique up to space time translations in the case f 1 0 we derive two families of such entire solutions in the first family one cannot be any space time translation of the other yet all entire solutions in the second family only differ by a space time translation

spreading speeds of a partially degenerate reaction diffusion system in a periodic habitat abstract this paper is devoted to the study of the spreading speeds of a partially degenerate reaction diffusion system with monostable nonlinearity in a periodic habitat we first obtain sufficient conditions for the existence of principal eigenvalues in the case where solution maps of the associated linear systems lack compactness and prove a threshold type result on the global dynamics for the periodic initial value problem then we establish the existence and computational formulae of spreading speeds for the general initial value problem it turns out that the spreading speed is linearly determinate

rare event simulation of small noise diffusions an important sampling method for certain rare event problems involving small noise diffusions is proposed standard monte carlo schemes for these problems behave exponentially poorly in the small noise limit previous work in rare event simulation has focused on developing estimators with optimal exponential variance decay rates this criterion still allows for exponential growth of the statistical relative error we show that an estimator related to a deterministic control problem not only has an optimal variance decay rate but can have vanishingly small relative statistical error in the small noise limit the sampling method based on this estimator can be seen as the limit of the zero variance importance sampling scheme which uses the solution of the second order partial differential equation pde associated with the diffusion in the scheme proposed here this pde is replaced by a hamilton jacobi equation whose solution is computed pointwise on the fly from its variational formulation an operation that remains practical even in high dimensional problems we test the scheme on several simple illustrative examples as well as a stochastic pde the noisy allen cahn equation 2012 wiley periodicals inc

global bifurcation of steady state solutions in this paper we study the bifurcation of steady state solutions of a reaction diffusion equation in one space variable the steady state solutions satisfy the equation a f u 0 on the interval l 0 or 0 for some nonzero function c c a for the neumann problem we use entirely different techniques to prove that s is never critical for any cubic polynomial j this implies at once that the neumann problem can have at most one nonconstant solution having a given number of maxima or minima this solution is necessarily strongly nondegenerate in the sense that zero is not contained in the spectrum of the linearized operator see 2 for the dirichlet problem the situation is far more complicated and the bifurcation diagrams undergo qualitative changes depending on the positions of the roots off for example fig 1 shows the bifurcation diagram for the positive solutions for two different cubic functions of the form f u a u u b u c it is interesting to note however that in every case we study there are at most three solutions to the dirichlet problem for each

hochschild cohomology for von neumann algebras with cartan subalgebras the main result of this paper is that h n m m 0 n 1 for von neumann algebras m with cartan subalgebras and separable preduals

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

asymptotic behavior of traveling fronts and entire solutions for a periodic bistable competition diffusion system abstract this paper is concerned with a time periodic competition diffusion system u t u x x u r 1 t a 1 t u b 1 t v t 0 x r v t d v x x v r 2 t a 2 t u b 2 t v t 0 x r where u t x and v t x denote the densities of two competing species d 0 is some constant r i t a i t and b i t are t periodic continuous functions under suitable conditions it has been confirmed by bao and wang 2013 2 that this system admits periodic traveling fronts connecting two stable semi trivial t periodic solutions p t 0 and 0 q t associated to the corresponding kinetic system in the present work we first investigate the asymptotic behavior of periodic bistable traveling fronts with non zero speeds at infinity by a dynamical approach combined with the two sided laplace transform method with these asymptotic properties we then obtain some key estimates as a result by applying the super and subsolutions techniques as well as the comparison principle we establish the existence and various qualitative properties of the so called entire solutions defined for all time and the whole space which provides some new spreading ways other than periodic traveling waves for two strongly competing species interacting in a heterogeneous environment

existence and nonexistence of traveling waves and reaction diffusion front propagation in periodic media we review the existence results of traveling wave solutions to the reaction diffusion equations with periodic diffusion convection coefficients and combustion bistable nonlinearities we prove that whenever traveling waves exist the solutions of the initial value problem with either frontlike or pulselike data propagate with the constant effective speeds of traveling waves in all suitable directions in the case of bistable nonlinearity and one space dimension we give an example of nonexistence of traveling waves which causes quenching localization of wavefront propagation quenching localization only occurs when the variations of the media from their constant mean values are large enough our related numerical results also provide evidence for this phenomenon in the parameter regimes not covered by the analytical example finally we comment on the role of the effective wave speeds in determining the effective wavefront equation hamilton jacobi equation of the reactiondiffusion equations under the small diffusion fast reaction limit with a formal geometric optics expansion

internal null stabilization for some diffusive models of population dynamics we investigate the large time behavior of the solutions to some fisher type models with nonlocal terms describing the dynamics of biological populations with diffusion logistic term and migration two types of logistic terms are taken into account a necessary condition and a sufficient condition for the internal null stabilizability of the solution to a fisher model with nonlocal term are provided in case of null stabilizability with state constraints a feedback stabilizing control of harvesting type is proposed the rate of stabilization corresponding to the feedback stabilizing control is dictated by the principal eigenvalue to a certain linear but not selfadjoint operator a large principal eigenvalue leads to a fast stabilization to zero another goal is to approximate this principal eigenvalue using a method suggested by the theoretical result concerning the large time behavior of the solution to a certain fisher model with a special logistic term an iterative method to improve the position by translations of the support of the feedback stabilizing control in order to get a larger principal eigenvalue and consequently a faster stabilization to zero is derived numerical tests illustrating the effectiveness of the theoretical results are given

a periodic reaction advection diffusion model for a stream population abstract this paper is devoted to the study of spatial dynamics of a periodic reaction advection diffusion model for a stream population in the case of an unbounded domain we establish the existence of the leftward and rightward spreading speeds and their coincidence with the minimal wave speeds for monotone periodic traveling waves respectively in the case of a bounded domain we obtain a threshold result on the global stability of either zero or the positive periodic solution

asymptotic spreading in heterogeneous diffusive excitable media abstract we establish propagation and spreading properties for nonnegative solutions of nonhomogeneous reaction diffusion equations of the type t u a t x u q t x u f t x u with compactly supported initial conditions at t 0 here a q f have a general dependence in t r and x r n we establish properties of families of propagation sets which are defined as families of subsets s t t 0 of r n such that lim inf t inf x s t u t x 0 the aim is to characterize such families as sharply as possible in particular we give some conditions under which 1 a given path t t 0 where t r n forms a family of propagation sets or 2 one can find such a family with s t x r n x r t and lim t r t this second property is called here complete spreading furthermore in the case q 0 and inf t x r r n f u t x 0 0 as well as under some more general assumptions we show that there is a positive spreading speed that is r t can be chosen so that lim inf t r t t 0 in the general case we also show the existence of an explicit upper bound c 0 such that lim sup t r t t c on the other hand we provide explicit examples of reaction diffusion equations such that for an arbitrary e 0 any family of propagation sets s t t 0 has to satisfy s t x r n x e t for large t in connection with spreading properties we derive some new uniqueness results for the entire solutions of this type of equations lastly in the case of space time periodic media we develop a new approach to characterize the largest propagation sets in terms of eigenvalues associated with the linearized equation in the neighborhood of zero

coarse graining from variationally enhanced sampling applied to the ginzburg landau model a powerful way to deal with a complex system is to build a coarse grained model capable of catching its main physical features while being computationally affordable inevitably such coarse grained models introduce a set of phenomenological parameters which are often not easily deducible from the underlying atomistic system we present a unique approach to the calculation of these parameters based on the recently introduced variationally enhanced sampling method it allows us to obtain the parameters from atomistic simulations providing thus a direct connection between the microscopic and the mesoscopic scale the coarse grained model we consider is that of ginzburg landau valid around a second order critical point in particular we use it to describe a lennard jones fluid in the region close to the liquid vapor critical point the procedure is general and can be adapted to other coarse grained models

finite von neumann algebra factors with property γ abstract techniques introduced by g pisier in his proof that finite von neumann factors with property have length at most 5 are modified to prove that the length is 3 it is proved that if such a factor is a complemented subspace of a larger c algebra then there exists a projection of norm one from the larger algebra onto the smaller and a new proof of the fact that the continuous hochschild cohomology group h2c m m vanishes is also included

applications of the cross entropy method to importance sampling and optimal control of diffusions we study the cross entropy method for diffusions one of the results is a versatile cross entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems the approach is based on the minimization of a suitable cross entropy functional with a parametric family of exponentially tilted probability distributions we illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method

adaptive importance sampling for control and inference path integral pi control problems are a restricted class of non linear control problems that can be solved formally as a feynman kac pi and can be estimated using monte carlo sampling in this contribution we review pi control theory in the finite horizon case we subsequently focus on the problem how to compute and represent control solutions we review the most commonly used methods in robotics and control within the pi theory the question of how to compute becomes the question of importance sampling efficient importance samplers are state feedback controllers and the use of these requires an efficient representation learning and representing effective state feedback controllers for non linear stochastic control problems is a very challenging and largely unsolved problem we show how to learn and represent such controllers using ideas from the cross entropy method we derive a gradient descent method that allows to learn feed back controllers using an arbitrary parametrisation we refer to this method as the path integral cross entropy method or pice we illustrate this method for some simple examples the pi control methods can be used to estimate the posterior distribution in latent state models in neuroscience these problems arise when estimating connectivity from neural recording data using em we demonstrate the pi control method as an accurate alternative to particle filtering

entire solutions in nonlocal dispersal equations with bistable nonlinearity abstract we consider entire solutions of nonlocal dispersal equations with bistable nonlinearity in one dimensional spatial domain a two dimensional manifold of entire solutions which behave as two traveling wave solutions coming from both directions is established by an increasing traveling wave front with nonzero wave speed furthermore we show that such an entire solution is unique up to space time translations and liapunov stable a key idea is to characterize the asymptotic behaviors of the solutions as t in terms of appropriate subsolutions and supersolutions we have to emphasize that a lack of regularizing effect occurs

spatial temporal dynamics of a lotka volterra competition model with nonlocal dispersal under shifting environment abstract we consider a competitive system with nonlocal dispersals in a 1 dimensional environment that is worsening with a constant speed reflected by two shifting growth functions by analyzing the spatial temporal dynamics of the model system we are able to identify certain ranges for the worsening speed c respectively for i extinction of both species ii extinction of one species but persistence of the other iii persistence of both species in the case of persistence of a species it is achieved through spreading to the direction of favorable environment with certain speed s and some estimates of these speeds are also obtained we also present some numeric simulation results which confirm our theoretical results and in the mean time motivate some challenging problems for future work

spreading speeds and traveling waves for abstract monostable evolution systems abstract this paper is devoted to the development of the theory of spreading speeds and traveling waves for abstract monostable evolution systems with spatial structure under appropriate assumptions we show that the spreading speeds coincide with the minimal wave speeds for monotone traveling waves in the positive and negative directions then we use this theory to study the spatial dynamics of a parabolic equation in a periodic cylinder with the dirichlet boundary condition a reaction diffusion model with a quiescent stage a porous medium equation in a tube and a lattice system in a periodic habitat

the similarity degree of an operator algebra ii for every integer d ge 1 there is a unital closed subalgebra a d subset b h with similarity degree equal precisely to d in the sense of our previous paper this means that for any unital homomorphism u colon a d to b h we have u cb le k u d with k 0 independent of u and the exponent d in this estimate cannot be improved the proof that the degree is larger than d 1 crucially uses an upper bound for the norms of certain gaussian random matrices due to haagerup and thorbjornsen we also include several complements to our previous publications on the same subject

dynamics of a non local delayed reaction diffusion equation without quasi monotonicity this paper is concerned with the dynamics of a non local delayed reaction diffusion equation without quasi monotonicity on an infinite n dimensional domain which can be derived from the growth of a stage structured single species population we first prove that solutions of the cauchy type problem are positively preserving and bounded if the initial value is non negative and bounded then by establishing a comparison theorem and a series of comparison arguments we prove the global attractivity of the positive equilibrium when there exist no positive equilibria we prove that the zero equilibrium is globally attractive in particular these results are still valid for the non local delayed reaction diffusion equation on a bounded domain with the neumann boundary condition finally we establish the existence of new entire solutions by using the travelling wave solutions of two auxiliary equations and the global attractivity of the positive equilibrium

importance sampling in path space for diffusion processes with slow fast variables importance sampling is a widely used technique to reduce the variance of a monte carlo estimator by an appropriate change of measure in this work we study importance sampling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics for certain exponential type expectation the corresponding control force of the optimal change of measure leads to a zero variance estimator and is related to the solution of a hamilton jacobi bellmann equation we focus on certain diffusions with both slow and fast variables and the main result is that we obtain an upper bound of the relative error for the importance sampling estimators with control obtained from the limiting dynamics we demonstrate our approximation strategy with an illustrative numerical example

local and global bifurcations in an sirs epidemic model this paper studies the existence and stability of the disease free equilibrium and endemic equilibria for the sirs epidemic model with the saturated incidence rate considering the factor of population dynamics such as the disease related the natural mortality and the constant recruitment of population analytical techniques are used to show for some parameter values the periodic solutions can arise through the hopf bifurcation which is important to carry different strategies for the controlling disease then the codimension two bifurcation i e bt bifurcation is investigated by using a global qualitative method and the curves of saddle node bifurcation hopf bifurcation and homoclinic bifurcation are obtained at the degenerate equilibrium moreover several numerical simulations are given to support the theoretical analysis

optimal control of molecular dynamics using markov state models a numerical scheme for solving high dimensional stochastic control problems on an infinite time horizon that appear relevant in the context of molecular dynamics is outlined the scheme rests on the interpretation of the corresponding hamilton jacobi bellman equation as a nonlinear eigenvalue problem that using a logarithmic transformation can be recast as a linear eigenvalue problem for which the principal eigenvalue and its eigenfunction are sought the latter can be computed efficiently by approximating the underlying stochastic process with a coarse grained markov state model for the dominant metastable sets we illustrate our method with two numerical examples one of which involves the task of maximizing the population of helices in an ensemble of small biomolecules alanine dipeptide and discuss the relation to the large deviation principle of donsker and varadhan

fast propagation for reaction diffusion cooperative systems abstract this paper deals with the spatial propagation for reaction diffusion cooperative systems it is well known that the solution of a reaction diffusion equation with monostable nonlinearity spreads at a finite speed when the initial condition decays to zero exponentially or faster and propagates fast when the initial condition decays to zero more slowly than any exponentially decaying function however in reaction diffusion cooperative systems a new possibility happens in which one species propagates fast although its initial condition decays exponentially or faster the fundamental reason is that the growth sources of one species come from the other species simply speaking we find a new interesting phenomenon that the spatial propagation of one species is accelerated by the other species this is a unique phenomenon in reaction diffusion systems we present a framework of fast propagation for reaction diffusion cooperative systems

persistence in dynamical systems soit un espace metrique localement compact de metrique d et soit e un sous ensemble clos de a frontiere e et interieur e on suppose que l on a un flot continu 7b f defini sur e tel que e est invariant par 7b f on considere la notion de persistance et on donne un critere de persistance

spreading speeds and linear determinacy of time dependent diffusive cooperative competitive systems abstract the current paper is devoted to the study of spreading speeds and linear determinacy of diffusive cooperative competitive systems of the form u t t x a u t x f t u t x x h where h r n or z n a is a random or nonlocal dispersal operator in the cases h r n and is a discrete dispersal operator in the case h z n f t u is cooperative or competitive in u and is recurrent in t which includes f t u is periodic and almost periodic in t as special cases first the notion of spreading speed intervals for diffusive cooperative systems is introduced via the natural features of spreading speeds and some basic spreading properties are established next some principal lyapunov exponent and principal floquent bundle theory for linear cooperative systems of ordinary differential equations is developed which plays an important role in the study of spreading speeds of diffusive cooperative competitive systems with time dependence and is also of independent interest in terms of the principal lyapunov exponent and principal floquent bundle theory some upper and lower bounds for the spreading speed intervals for diffusive cooperative systems are then established under certain conditions it is proved that a diffusive cooperative system has a single spreading speed and is linearly determinant finally by transforming a diffusive competitive system to a diffusive cooperative system and applying established results for diffusive cooperative systems upper and lower bounds for the spreading speed intervals for diffusive competitive systems are obtained and linearly determinacy for such systems is discussed

hochschild cohomology of factors with property gamma the main result of this paper is that the k th continuous hochschild cohomology groups h k m m and h k m b h of a von neumann factor m b h o f type ii 1 with property are zero for all positive integers k the method of proof involves the construction of hyperfinite subfactors with special properties and a new inequality of grothendieck type for multilinear maps we prove joint continuity in the 2 norm of separately ultraweakly continuous multilinear maps and combine these results to reduce to the case of completely bounded cohomology which is already solved

existence and uniqueness of traveling waves for non monotone integral equations with application abstract this paper is concerned with the traveling waves in a class of non monotone integral equations first we establish the existence of traveling waves the approach is based on the construction of two associated auxiliary monotone integral equations and a profile set in a suitable banach space then we show that the traveling waves are unique up to translations under some reasonable assumptions the exact asymptotic behavior of the profiles as and the existence of minimal wave speed are also obtained finally we apply our results to an epidemic model with non monotone force of infection

pulsating fronts and front like entire solutions for a reaction advection diffusion competition model in a periodic habitat abstract this paper is devoted to the study of pulsating fronts and pulsating front like entire solutions for a reaction advection diffusion model of two competing species in a periodic habitat under certain assumptions the competition system admits a leftward and a rightward pulsating fronts in the bistable case in this work we construct some other types of entire solutions by interacting the leftward and rightward pulsating fronts some of these entire solutions behave as the two pulsating fronts approaching each other from both sides of the x axis which turn out to be unique and liapunov stable 2 dimensional manifolds of solutions furthermore the leftward and rightward pulsating fronts are on the boundary of these 2 dimensional manifolds the others behave as the two pulsating fronts propagating from one side of the x axis the faster one then invades the slower one as t these kinds of pulsating front like entire solutions then provide some new spreading ways other than pulsating fronts for two strongly competing species interacting in a heterogeneous habitat

equilibrium solutions of a semilinear reaction diffusion system on etudie le systeme u 1 t d 1 u 1 a 11 u 1 a 12 u 2 dans 0 u 2 t a 22 u 2 g u 1 dans 0 avec les conditions aux limites u 1 u 2 0 dans 0 ou est un sous ensemble ouvert borne de r n n 2 et est assez reguliere sous de bonnes hypotheses on peut trouver au moins une deux ou trois solutions d equilibre

entire solutions of the kpp equation this paper deals with the solutions defined for all time of the kpp equation ut uxx f u 0 0 f 0 1 0i n 0 1 and f 0 s f 0 0 in 0 1 this equation admits infinitely many traveling wave type solutions increasing or decreasing in x i t also admits solutions that depend only on t in this paper we build four other manifolds of solutions one is 5 dimensional one is 4 dimensional and two are 3 dimensional some of these new solutions are obtained by considering two traveling waves that come from both sides of the real axis and mix furthermore the traveling wave solutions are on the boundary of these four manifolds c 1999 john wiley sons inc

entire solutions in monostable reaction diffusion equations with delayed nonlinearity abstract entire solutions for monostable reaction diffusion equations with nonlocal delay in one dimensional spatial domain are considered a comparison argument is employed to prove the existence of entire solutions which behave as two traveling wave solutions coming from both directions some new entire solutions are also constructed by mixing traveling wave solutions with heteroclinic orbits of the spatially averaged ordinary differential equations and the existence of such a heteroclinic orbit is established using the monotone dynamical systems theory key techniques include the characterization of the asymptotic behaviors of solutions as t in term of appropriate subsolutions and supersolutions two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are given to illustrate main results

solving the inverse problem of an sis epidemic reaction diffusion model by optimal control methods in this contribution a novel inverse problem on an sis epidemic reaction diffusion model is investigated by employing the optimal control methods by setting a proper regular cost functional and choosing the coefficients to be identified as control variables we embed the original inverse problem which is very difficult to solve into an optimal control problem the existence of the optimal controls and the first order necessary optimality condition satisfied by the optimal controls are established respectively in particular the local uniqueness and stability of the identification of the coefficients are proved by using analytical techniques

existence and stability of time periodic traveling waves for a periodic bistable lotka volterra competition system abstract this paper is concerned with the time periodic lotka volterra competition diffusion system u t d 1 t u x x u r 1 t a 1 t u b 1 t v v t d 2 t v x x v r 2 t a 2 t u b 2 t v x r t 0 where d i t r i t a i t b i t c 2 r are t periodic functions 0 1 i 1 2 under certain conditions the system admits two stable semi trivial periodic solutions p t 0 and 0 q t and a unique coexistence periodic solution u 0 t v 0 t which is unstable and satisfies 0 u 0 t p t and 0 v 0 t q t for t 0 t in this paper we prove that the system admits a time periodic traveling wave solution u x t v x t u x c t t v x c t t connecting two periodic solutions p t 0 and 0 q t as x where c is the wave speed by using a dynamical method we show that the time periodic traveling wave solution u x c t t v x c t t is asymptotically stable and unique modulo translation for front like initial values

remarks on complemented subspaces of von neumann algebras in this note we include two remarks about bounded not necessarily contractive linear projections on a von neumann algebra we show that if m is a von neumann subalgebra of b h which is complemented in b h and isomorphic to m m then m is injective or equivalently m is contractively complemented we do not know how to get rid of the second assumption on m in the second part we show that any complemented reflexive subspace of a c algebra is necessarily linearly isomorphic to a hilbert space

forced waves and their asymptotics in a lotka volterra cooperative model under climate change abstract the existence and asymptotics of forced traveling wave front in a lotka volterra cooperative system under climate change are concerned in this paper by constructing appropriate upper and lower solutions combined with the monotone iteration scheme we show that for any given positive speed of the shifting habitat edge there exists a nondecreasing wave front with the speed consistent with the habitat shifting speed which indicates that no matter how moderate of the habitat shifts two species will still be driven to extinction as the mutualistic effects exist but weak numerical simulations are also given to illustrate our results

on a simple criterion for the existence of a principal eigenfunction of some nonlocal operators abstract in this paper we are interested in the existence of a principal eigenfunction of a nonlocal operator which appears in the description of various phenomena ranging from population dynamics to micro magnetism more precisely we study the following eigenvalue problem j x y g y y g n y d y a x where r n is an open connected set j a non negative kernel and g a positive function first we establish a criterion for the existence of a principal eigenpair p p we also explore the relation between the sign of the largest element of the spectrum with a strong maximum property satisfied by the operator as an application of these results we construct and characterise the solutions of some nonlinear nonlocal reaction diffusion equations