on tests for normality the problem of deciding whether a sample of a random field was generated by a gaussian distribution is considered based on extensions of large deviation estimates due to m d donsker and s r s varadhan 1985 a test that is optimal in a generalized neyman pearson sense is proposed this test turns out to depend on properties of the entropy of gaussian processes and does not depend on cumulant computations

state estimation of t s fuzzy delayed neural networks with markovian jumping parameters using sampled data control abstract in this paper we are concerned with the problem of state estimation of takagi sugeno t s fuzzy delayed neural networks with markovian jumping parameters via sampled data control based on the fuzzy model based control approach and linear matrix inequality lmi technique several novel conditions are derived to guarantee the stability of the suggested system a new class of lyapunov functional which contains integral terms is constructed to derive delay dependent stability criteria some characteristics of the sampling input delay are proposed based on the input delay approach numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results

a general central limit theorem for fkg systems a central limit theorem is given which is applicable to not necessarily monotonic functions of random variables satisfying the fkg inequalities one consequence is convergence of the block spin scaling limit for the magnetization and energy densities jointly to the infinite temperature fixed point of independent gaussian blocks for a large class of ising ferromagnets whenever the susceptibility is finite another consequence is a central limit theorem for the density of thesurface of the infinite cluster in percolation models

a variational formula for the free energy of an interacting many particle system we consider n bosons in a box in r d with volume n rho under the influence of a mutually repellent pair potential the particle density p is an element of 0 infinity is kept fixed our main result is the identification of the limiting free energy f beta p at positive temperature 1 beta in terms of an explicit variational formula for any fixed rho if beta is sufficiently small and for any fixed beta if rho is sufficiently small the thermodynamic equilibrium is described by the symmetrized trace of e beta h n where h n denotes the corresponding hamilton operator the well known feynman kac formula reformulates this trace in terms of n interacting brownian bridges due to the symmetrization the bridges are organized in an ensemble of cycles of various lengths the novelty of our approach is a description in terms of a marked poisson point process whose marks are the cycles this allows for an asymptotic analysis of the system via a large deviations analysis of the stationary empirical field the resulting variational formula ranges over random shift invariant marked point fields and optimizes the sum of the interaction and the relative entropy with respect to the reference process in our proof of the lower bound for the free energy we drop all interaction involving infinitely long cycles and their possible presence is signalled by a loss of mass of the finitely long cycles in the variational formula in the proof of the upper bound we only keep the mass on the finitely long cycles we expect that the precise relationship between these two bounds lies at the heart of bose einstein condensation and intend to analyze it further in future

exponential synchronization of chaotic neural networks with time varying delay via intermittent output feedback approach abstract this paper is dealt with the problem of exponential synchronization for chaotic neural networks with time varying delay by using intermittent output feedback control based on the lyapunov krasovskii functional method and the lower bound lemma for reciprocally convex technique a novel criterion for existence of the controller is first established to ensure synchronization between the master and slave systems moreover from the delay point of view the derived criterion is extended to the relaxed case because of introducing an adjustable parameter in the lyapunov krasovskii functional finally a numerical simulation is carried out to demonstrate the effectiveness of the proposed synchronization law

the equivalence of ensembles for classical systems of particles for systems of particles in classical phase space with standard hamiltonian we consider spatially averaged microcanonical gibbs distributions in finite boxes we show that infinite volume limits along suitable subsequences exist and are grand canonical gibbs measures on the way we establish a variational formula for the thermodynamic entropy density as well as a variational characterization of grand canonical gibbs measures

global asymptotic stability of recurrent neural networks with multiple time varying delays in this paper several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time varying delays the lyapunov krasovskii stability theory for functional differential equations and the linear matrix inequality lmi approach are employed in our investigation the results are shown to be generalizations of some previously published results and are less conservative than existing results the present results are also applied to recurrent neural networks with constant time delays

quenched asymptotics of the ground state energy of random schrodinger operators with scaled gibbsian potentials this article describes the almost sure infinite volume asymptotics of the ground state energy of random schrodinger operators with scaled gibbsian potentials the random potential is obtained by distributing soft obstacles according to an infinite volume grand canonical tempered gibbs measure with a superstable pair interaction there is no restriction on the strength of the pair interaction it may be taken e g at a critical point the potential is scaled with the box size in a critical way i e the scale is determined by the typical size of large deviations in the gibbsian cloud the almost sure infinite volume asymptotics of the ground state energy is described in terms of two equivalent deterministic variational principles involving only thermodynamic quantities the qualitative behaviour of the ground state energy asymptotics is analysed depending on the dimension and on the holder exponents of the free energy density it is identified which cases lead to a phase transition of the asymptotic behaviour of the ground state energy

existence of gibbsian point processes with geometry dependent interactions we establish the existence of stationary gibbsian point processes for interactions that act on hyperedges between the points for example such interactions can depend on delaunay edges or triangles cliques of voronoi cells or clusters of k nearest neighbors the classical case of pair interactions is also included the basic tools are an entropy bound and stationarity

the theory of large deviations from boltzmann s 1877 calculation to equilibrium macrostates in 2d turbulence abstract after presenting some basic ideas in the theory of large deviations this paper applies the theory to a number of problems in statistical mechanics these include deriving the form of the gibbs state for a discrete ideal gas describing probabilistically the phase transition in the curie weiss model of a ferromagnet and deriving variational formulas that describe the equilibrium macrostates in models of two dimensional turbulence a general approach to the large deviation analysis of models in statistical mechanics is also formulated

normality of nilpotent varieties in e6 abstract we determine which nilpotent orbits in e6 have closures which are normal varieties and which do not at the same time we are able to verify a conjecture in e sommers comm math univ sancti pauli 49 1 2000 101 104 concerning functions on non special nilpotent orbits for e6

delay dependent global exponential stability for delayed recurrent neural networks this paper deals with the global exponential stability for delayed recurrent neural networks drnns by constructing an augmented lyapunov krasovskii functional and adopting the reciprocally convex combination approach and wirtinger based integral inequality delay dependent global exponential stability criteria are derived in terms of linear matrix inequalities meanwhile a general and effective method on global exponential stability analysis for drnns is given through a lemma where the exponential convergence rate can be estimated with this lemma some global asymptotic stability criteria of drnns acquired in previous studies can be generalized to global exponential stability ones finally a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results

hydrodynamical limit for a hamiltonian system with weak noise starting from a general hamiltonian system with superstable pairwise potential we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles we prolve that in the scaling limit the time conserved quantities energy momenta and density satisfy the euler equation of conservation laws up to a fixed timet provided that the euler equation has a smooth solution with a given initial data up to timet the strength of the noise term is chosen to be very small but nonvanishing so that it disappears in the scaling limit

r local delaunay inhibition model unlike in the classical framework of gibbs point processes usually acting on the complete graph in the context of nearest neighbour gibbs point processes the nonnegativeness of the interaction functions do not ensure the local stability property this paper introduces domain wise but not pointwise inhibition stationary gibbs models based on some tailor made delaunay subgraphs all of them are subgraphs of the r local delaunay graph defined as the delaunay subgraph specifically not containing the edges of delaunay triangles with circumscribed circles of radii greater than some large positive real value r the usual relative compactness criterion for point processes needed for the existence result is directly derived from the ruelle bound of the correlation functions furthermore assuming only the nonnegativeness of the energy function we have managed to prove the existence of the existence of r local delaunay stationary gibbs states based on nonnegative interaction functions thanks to the use of the compactness of sublevel sets of the relative entropy

entropy for translation invariant random cluster measures we study translation invariant random cluster measures with techniques from large deviation theory and convex analysis in particular we prove a large deviation principle with rate function given by a specific entropy and a dobrushinlanfordruelle variational principle that characterizes translation invariant random cluster measures as the solutions of the variational equation for free energy consequences of these theorems include inequalities for edge and cluster densities of translationinvariant random cluster measures 1 introduction the random cluster model was introduced around 1972 by fortuin and kasteleyn 18 as a family of models that contains the bernoulli bond percolation model the ising model and the q state potts models as special cases it has developed into an important and very successful tool for studying the ising and potts models our paper focuses on the properties of the random cluster measures themselves our starting point is grimmett s 23 development of elements of a thermodynamic formalism for this model beginning with a definition of infinite volume random cluster measures in terms of a dlr dobrushinlanfordruelle equation just as for gibbsian systems natural next questions concern the validity of large deviation principles and variational characterizations of infinite volume measures these questions we answer in the present paper and derive some consequences here is a brief overview of the dlr approach of 23 the random cluster measures of interest live on the graph formed by putting edges between nearest neighbor vertices of the d dimensional hypercubic lattice d the edge that connects two vertices x and y that are l 1 distance one apart is

exponential synchronization of a class of neural networks with sampled data control abstract this paper investigates the problem of the master slave synchronization for a class of neural networks with discrete and distributed delays under sampled data control by introducing some new terms a novel piecewise time dependent lyapunov krasovskii functional lkf is constructed to fully capture the available characteristics of real sampling information and nonlinear function vector of the system based on the lkf and wirtinger based inequality less conservative synchronization criteria are obtained to guarantee the exponential stability of the error system and then the slave system is synchronized with the master system the designed sampled data controller can be obtained by solving a set of linear matrix inequalities lmis which depend on the maximum sampling period and the decay rate the criteria are less conservative than the ones obtained in the existing works a numerical example is presented to illustrate the effectiveness and merits of the proposed method

large deviations for the empirical field of a gibbs measure on applique le principe de contraction pour obtenir un principe de grande deviation pour la distribution des distributions empiriques on donne une description detaillee de la fonction de taux resultante

on entropy minimization and convergence we examine the minimization of information entropy for measures on the phase space of bounded domains subject to constraints that are averages of grand canonical distributions we describe the set of all such constraints and show that it equals the set of averages of all probability measures absolutely continuous with respect to the standard measure on the phase space with the exception of the measure concentrated on the empty configuration we also investigate how the set of constrains relates to the domain of the microcanonical thermodynamic limit entropy we then show that for fixed constraints the parameters of the corresponding grand canonical distribution converge as volume increases to the corresponding parameters derivatives when they exist of the thermodynamic limit entropy the results hold when the energy is the sum of any stable tempered interaction potential that satisfies the gibbs variational principle e g lennard jones and the kinetic energy the same tools and the strict convexity of the thermodynamic limit pressure for continuous systems valid whenever the gibbs variational principle holds give solid foundation to the folklore local homeomorphism between thermodynamic and macroscopic quantities

complete equivalence of the gibbs ensembles for one dimensional markov systems we show the equivalence of the gibbs ensembles at the level of measures for one dimensional markov systems with arbitrary boundary conditions that is the limit of the microcanonical gibbs ensemble is a gibbs measure with an interaction depending on the microcanonical constraint in fact the usual microcanonical condition is replaced by the sharper constraint that all type frequencies of neighboring spins including the boundary spins are fixed when conditioning on a set of different frequencies of neighboring spins compatible with physical quantities like energy density we get the usual microcanonical ensemble we show that the limit is a gibbs measure for a nearest neighbor potential depending on the pair measure which maximizes the entropy on the given set of pair measures for this we show the large deviation property of the pair empirical measure for arbitrary boundary conditions we establish analogous results for finite range potentials

new exponential stability results for delayed neural networks with time varying delays abstract this paper presents new sufficient conditions for the uniqueness and exponential stability of the equilibrium point for delayed neural networks with time varying delays by employing a more general type of lyapunov krasovskii functional and using lmi linear matrix inequality we derive new results for exponential stability of the equilibrium point for delayed neural networks the results establish a relation between the delay time and the parameters of the network the results are compared with the previous results derived in the literature

galton watson trees with vanishing martingale limit we show that an infinite galton watson tree conditioned on its martingale limit being smaller than varepsilon agrees up to generation k with a regular mu ary tree where mu is the essential minimum of the offspring distribution and the random variable k is strongly concentrated near an explicit deterministic function growing like a multiple of log 1 varepsilon more precisely we show that if mu ge 2 then with high probability as varepsilon downarrow 0 k takes exactly one or two values this shows in particular that the conditioned trees converge to the regular mu ary tree providing an example of entropic repulsion where the limit has vanishing entropy our proofs are based on recent results on the left tail behaviour of the martingale limit obtained by fleischmann and wachtel 11

nilpotent orbits normality and hamiltonian group actions the theory of coadjoint orbits of lie groups is central to a number of areas in mathematics a list of such areas would include 1 group representation theory 2 symmetry related hamiltonian mechanics and attendant physical theories 3 symplectic geometry 4 moment maps and 5 geometric quantization from many points of view the most interesting cases arise when the group g in question is semisimple for semisimple g the most familiar of the orbits are orbits of semisimple elements in that case the associated representation theory is pretty much understood the borel weil bott theorem and noncompact analogs e g zuckerman functors the isotropy subgroups are reductive and the orbits are in one form or another related to flag manifolds and their natural generalizations a totally different experience is encountered with nilpotent orbits of semisimple groups here the associated representation theory unipotent representations is poorly understood and there is a loss of reductivity of isotropy subgroups to make matters worse or really more interesting orbits are no longer closed and there can be a failure of normality for orbit closures in addition simple connectivity is generally gone but more seriously there may exist no invariant polarizations the interest in nilpotent orbits of semisimple lie groups has increased sharply over the last two decades this perhaps may be attributed to the recurring experience that sophisticated aspects of semisimple group theory often lead one to these orbits e g the springer correspondence with representations of the weyl group this paper presents new results concerning the symplectic and algebraic geometry of the nilpotent orbits 0 and the symmetry groups of that geometry the starting point is the recognition made also by others that the ring r of regular functions on any g homogeneous cover m of 0 is not only a poisson algebra the case for any coadjoint orbit but that r is also naturally graded the key theme is that the same nilpotent orbit may be shared by more than one simple group the key result is the determination of all pairs of simple lie groups having a shared nilpotent orbit furthermore there is then a unique maximal such group and this group is encoded in the symplectic and algebraic

admissible delay upper bounds for global asymptotic stability of neural networks with time varying delays this paper is concerned with global asymptotic stability of a neural network with a time varying delay where the delay function is differentiable uniformly bounded with delay derivative bounded from above first a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions this inequality provides a tighter bound in the form of a convex combination than some existing ones second by constructing proper lyapunov krasovskii functional global asymptotic stability of the neural network is analyzed for two types of the time varying delays depending on whether or not the lower bound of the delay derivative is known third noticing that sufficient conditions on stability from estimation on the derivative of some lyapunov krasovskii functional are affine both on the delay function and its derivative allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study finally two numerical examples are given to substantiate the effectiveness of the proposed method

improved results on robust exponential stability criteria for neutral type delayed neural networks abstract in this paper we investigate the problem of robust global exponential stability analysis for a class of neutral type neural networks the interval time varying delays allow for both slow and fast time varying delays the values of the time varying uncertain parameters are assumed to be bounded within given compact sets improved global exponential stability condition is derived by employing new lyapunov krasovskii functional and the integral inequality the developed nominal and robust stability criteria is delay dependent and characterized by linear matrix inequalities lmis the developed results are less conservative than previous published ones in the literature which are illustrated by representative numerical examples

large deviations and the maximum entropy principle for marked point random fields we establish large deviation principles for the stationary and the individual empirical fields of poisson and certain interacting random fields of marked point particles in d the underlying topologies are induced by a class of not necessarily bounded local functions and thus finer than the usual weak topologies our methods yield further that the limiting behaviour of conditional poisson distributions as well as certain distributions of gibbsian type is governed by the maximum entropy principle we also discuss various applications and examples

large deviations for gibbs random fields a large deviation principle for gibbs random fields on zd is proven and a corresponding large deviations proof of the gibbs variational formula is given a generalization of the lanford theory of large deviations is also obtained

self similarity of brownian motion and a large deviation principle for random fields on a binary tree using self similarity of brownian motion and its representation as a product measure on a binary tree we construct a random sequence of probability measures which converges to the distribution of the brownian bridge we establish a large deviation principle for random fields on a binary tree this leads to a class of probability measures with a certain self similarity property the same construction can be carried out forc 0 1 valued processes and we can describe for instance ac 0 1 valued ornstein uhlenbeck process as a large deviation of brownian sheet

entropy limit theorems and variational principles for disordered lattice systems we study infinite volume limits and gibbs states of disordered lattice systems with bounded and continuous potentials our main tools are a generalization of relative entropy for random reference measures and a large deviation theory for nonstationary independent processes we find that many familiar results of invariant potentials such as large deviation theorems variational principles and equivalence of ensembles continue to hold for disordered models with suitably modified statements

large deviations and the equivalence of ensembles for gibbsian particle systems with superstable interaction for gibbsian systems of particles inr d we investigate large deviations of the translation invariant empirical fields in increasing boxes the particle interaction is given by a superstable regular pair potential the large deviation principle is established for systems with free or periodic boundary conditions and under a stronger stability hypothesis on the potential for systems with tempered boundary conditions and for tempered infinite volume gibbs measures as a by product we obtain the gibbs variational formula for the pressure we also prove the asymptotic equivalence of microcanonical and grand canonical gibbs distributions and establish a variational expression for the thermodynamic entropy density

complete delay decomposing approach to asymptotic stability for neural networks with time varying delays this paper is concerned with the problem of stability of neural networks with time varying delays a novel lyapunov krasovskii functional decomposing the delays in all integral terms is proposed by exploiting all possible information and considering independent upper bounds of the delay derivative in various delay intervals some new generalized delay dependent stability criteria are established which are different from the existing ones and improve upon previous results numerical examples are finally given to demonstrate the effectiveness and the merits of the proposed method

positivity of the self diffusion matrix of interacting brownian particles with hard core we prove the positivity of the self diffusion matrix of interacting brownian particles with hard core when the dimension of the space is greater than or equal to 2 here the self diffusion matrix is a coefficient matrix of the diffusive limit of a tagged particle we will do this for all activities z 0 of gibbs measures in particular for large z the case of high density particles a typical example of such a particle system is an infinite amount of hard core brownian balls

some novel approaches on state estimation of delayed neural networks this paper studies the issue of state estimation for a class of neural networks nns with time varying delay a novel lyapunov krasovskii functional lkf is constructed where triple integral terms are used and a secondary delay partition approach sdpa is employed compared with the existing delay partition approaches the proposed approach can exploit more information on the time delay intervals by taking full advantage of a modified wirtinger s integral inequality mwii improved delay dependent stability criteria are derived which guarantee the existence of desired state estimator for delayed neural networks dnns a better estimator gain matrix is obtained in terms of the solution of linear matrix inequalities lmis in addition a new activation function dividing method is developed by bringing in some adjustable parameters three numerical examples with simulations are presented to demonstrate the effectiveness and merits of the proposed methods

stability criteria for recurrent neural networks with time varying delay based on secondary delay partitioning method a secondary delay partitioning method is proposed to study the stability problem for a class of recurrent neural networks rnns with time varying delay the total interval of the time varying delay is first divided into two parts and then each part is further divided into several subintervals to deal with the state variables associated with these subintervals an extended reciprocal convex combination approach and a double integral term with variable upper and lower limits of integral as a lyapunov functional are proposed which help to obtain the stability criterion the main feature of the proposed result is more effective for the rnns with fast time varying delay a numerical example is used to show the effectiveness of the proposed stability result

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

phase transitions for dilute particle systems with lennard jones potential we consider a classical dilute particle system in a large box with pair interaction given by a lennard jones type potential the inverse temperature is picked proportionally to the logarithm of the particle density we identify the free energy per particle in terms of a variational formula and show that this formula exhibits a cascade of phase transitions as the temperature parameter ranges from zero to infinity loosely speaking the particle system separates into spatially distant components in such a way that within each phase all components are of the same size which is the larger the lower the temperature the main tool in our proof is a new large deviation principle for sparse point configurations

large deviations for many brownian bridges with symmetrised initial terminal condition consider a large system of n brownian motions in mathbb r d with some non degenerate initial measure on some fixed time interval 0 with symmetrised initial terminal condition that is for any i the terminal location of the i th motion is affixed to the initial point of the i th motion where is a uniformly distributed random permutation of 1 n such systems play an important role in quantum physics in the description of boson systems at positive temperature 1 in this paper we describe the large n behaviour of the empirical path measure the mean of the dirac measures in the n paths and of the mean of the normalised occupation measures of the n motions in terms of large deviations principles the rate functions are given as variational formulas involving certain entropies and fenchel legendre transforms consequences are drawn for asymptotic independence statements and laws of large numbers in the special case related to quantum physics our rate function for the occupation measures turns out to be equal to the well known donsker varadhan rate function for the occupation measures of one motion in the limit of diverging time this enables us to prove a simple formula for the large n asymptotic of the symmetrised trace of rm e beta mathcal h n where mathcal h n is an n particle hamilton operator in a trap

strict convexity of the free energy of the canonical ensemble under decay of correlations we consider a one dimensional lattice system of unbounded real valued spins we allow arbitrary strong attractive nearest neighbor interaction we show that the free energy of the canonical ensemble ce converges uniformly in c 2 to the free energy of the grand ce gce the error estimates are quantitative a direct consequence is that the free energy of the ce is uniformly strictly convex for large systems another consequence is a quantitative local cramer theorem which yields the strict convexity of the coarse grained hamiltonian with small adaptations the argument could be generalized to systems with finite range interaction on a graph as long as the degree of the graph is uniformly bounded and the associated gce has uniform decay of correlations

existence of delaunay pairwise gibbs point process with superstable component the present stuffy deals with the existence of delaunay pairwise gibbs point process with superstable component by using the well known preston theorem in particular we prove the stability the lower regularity and the quasilocality properties of the delaunay model

new delay dependent stability results for neural networks with time varying delay this paper studies the problem of stability analysis for neural networks nns with a time varying delay unlike the previous works the activation functions are assumed to be neither monotonic nor differentiable nor bounded by defining a more general type of lyapunov functionals some new less conservative delay dependent stability criteria are established in terms of linear matrix inequalities lmis meanwhile the computational complexity of the newly obtained stability conditions is reduced because less variables are involved numerical examples are given to illustrate the effectiveness and the benefits of the proposed method

lmi conditions for global stability of fractional order neural networks fractional order neural networks play a vital role in modeling the information processing of neuronal interactions it is still an open and necessary topic for fractional order neural networks to investigate their global stability this paper proposes some simplified linear matrix inequality lmi stability conditions for fractional order linear and nonlinear systems then the global stability analysis of fractional order neural networks employs the results from the obtained lmi conditions in the lmi form the obtained results include the existence and uniqueness of equilibrium point and its global stability which simplify and extend some previous work on the stability analysis of the fractional order neural networks moreover a generalized projective synchronization method between such neural systems is given along with its corresponding lmi condition finally two numerical examples are provided to illustrate the effectiveness of the established lmi conditions

relaxed stability criteria for neural networks with time varying delay using extended secondary delay partitioning and equivalent reciprocal convex combination techniques this article investigates global asymptotic stability for neural networks nns with time varying delay which is differentiable and uniformly bounded and the delay derivative exists and is upper bounded first we propose the extended secondary delay partitioning technique to construct the novel lyapunov krasovskii functional where both single integral and double integral state variables are considered while the single integral ones are only solved by the traditional secondary delay partitioning second a novel free weight matrix equality fwme is presented to resolve the reciprocal convex combination problem equivalently and directly without schur complement which eliminates the need of positive definite matrices and is less conservative and restrictive compared with various improved reciprocal convex inequalities furthermore by the present extended secondary delay partitioning equivalent reciprocal convex combination technique and bessel legendre inequality two different relaxed sufficient conditions ensuring global asymptotic stability for nns are obtained for time varying delays respectively with unknown and known lower bounds of the delay derivative finally two examples are given to illustrate the superiority and effectiveness of the presented method

on the structure of homogeneous symplectic varieties of complete intersection a normal complex algebraic variety x is called a symplectic variety if its regular locus xreg admits a holomorphic symplectic 2 form such that it extends to a holomorphic 2 form on a resolution f x x affine symplectic varieties are constructed in various ways such as nilpotent orbit closures of a semisimple complex lie algebra cf cm slodowy slices to nilpotent orbits cf sl or symplectic reductions of holomorphic symplectic manifolds with hamiltonian actions usually these examples come up with c actions in this article we shall study a 2n dimensional affine symplectic variety x c defined as a complete intersection of r homogeneous polynomials fi z1 z2n r 1 i r here we assume that weights of all coordinates are 1 wt z1 wt z2n r 1 the c action on c induces a c action on x we also assume that the symplectic form is homogeneous with respect to thisc action namely for some integer l we have t t where t c the integer l is called the weight of and is denoted by wt a main result theorem 2 is that such an x is isomorphic as a cvariety to a nilpotent orbit closure of a semisimple complex lie algebra and corresponds to the kostant kirillov form on o a nilpotent orbit closure does not generally have complete intersection singularities and the orbit that appears in theorem 2 should be very restricted one we conjecture that such a nilpotent orbit closure would be the nilpotent variety of a semisimple complex lie algebra as a particular case we consider a symplectic hypersurface i e r 1 as is studied in lnsv we have very few examples of quasihomogeneous symplectic hypersurfaces in our homogeneous case it exists only when n 1 and x must be isomorphic to an a1 surface singularity theorem 3

global asymptotic stability of delayed cellular neural networks a new criterion for the global asymptotic stability of the equilibrium point of cellular neural networks with multiple time delays is presented the obtained result possesses the structure of a linear matrix inequality and can be solved efficiently using the recently developed interior point algorithm a numerical example is used to show the effectiveness of the obtained result

large deviations and maximum entropy principle for interacting random fields on mathbb z d we present a new approach to the principle of large deviations for the empirical field of a gibbsian random field on the integer lattice zd this approach has two main features first we can replace the traditional weak topology by the finer topology of convergence of cylinder probabilities and thus obtain estimates which are finer and more widely applicable second we obtain as an immediate consequence a limit theorem for conditional distributions under conditions on the empirical field the limits being those predicted by the maximum entropy principle this result implies a general version of the equivalence of gibbs ensembles stating that every microcanonical limiting state is a grand canonical equilibrium state we also prove a converse to the last statement and discuss some applications 0 introduction as is well known the study of the asymptotic probabilities of large fluctuations of time averages or space averages away from the mean is based on two fundamental principles the principle of large deviations and the maximum entropy principle the former provides the exact rate of exponential decay of the fluctuation probabilities whereas the latter predicts the limiting conditional distribution under the condition that the fluctuations are large it is obvious that these principles are intimately related in this paper we investigate these principles in the case of interacting random fields on the integer lattice 7zd the setup is the following first we let e 4 be any measurable space we shall assume throughout that e a is standard borel but we shall avoid making any explicit topological assumptions on e so we do not assume that e is polish next we let s zd be the d dimensional integer lattice and q f e gas the associated product space in lattice models of statistical mechanics e is called the state space or single spin space and q f the configuration space we let j s f denote the set of all probability

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

new results on stability analysis for delayed markovian generalized neural networks with partly unknown transition rates the stability of delayed markovian generalized neural networks is studied where the transition rates of the modes are partly unknown the partly unknown transition rates generalize the traditional works that are with all known transition rates then a lyapunov krasovskii functional lkf with a delay product type dpt term is constructed the dpt term is not only simple but also fully utilizes the information of time delay based on the new dpt lkf stability criteria are presented which are with lower computational complexity and less conservative in the end the validity and superiorities of the analytical results are verified by several examples

microcanonical distributions for lattice gases in this article a large deviation principle cf theorem 1 3 for the empirical distribution functional is applied to prove a rather general version of boltzmann s principle cf theorem 3 5 for models with shift invariant finite range potentials the final section contains an application of these considerations to the two dimensional ising model at sub critical temperature

stability analysis based on partition trajectory approach for switched neural networks with fractional brown noise disturbance abstractin this brief the stability problem based on feedback control for two types of stochastic neural networks driven by fractional brown noise is considered one class is the switched neural networks without time delays and the other one is with time delays a novel analysis method very different to the usual approach based on the ito formula and infinitesimal operator is proposed in this paper by the idea of splitting time of trajectory and associating with holder inequality some criteria are obtained to guarantee the switched neural networks with two types to be stable in the end two numerical examples and auxiliary figures are presented to show the feasibility and effectiveness for the proposed results

n v limit for stochastic dynamics in continuous particle systems we provide an n v limit for the infinite particle infinite volume stochastic dynamics associated with gibbs states in continuous particle systems on d d 1 starting point is an n particle stochastic dynamic with singular interaction and reflecting boundary condition in a subset d with finite volume lebesgue measure v the aim is to approximate the infinite particle infinite volume stochastic dynamic by the above n particle dynamic in as n and v such that n v where is the particle density first we derive an improved ruelle bound for the canonical correlation functions under an appropriate relation between n and v then tightness is shown by using the lyons zheng decomposition the equilibrium measures of the accumulation points are identified as infinite volume canonical gibbs measures by an integration by parts formula and the accumulation points themselves are identified as infinite particle infinite volume stochastic dynamics via the associated martingale problem assuming a property closely related to markov uniqueness and weaker than essential self adjointness via mosco convergence techniques we can identify the accumulation points as markov processes and show uniqueness i e all accumulation corresponding to one invariant canonical gibbs measure coincide the proofs work for general repulsive interaction potentials of ruelle type and all temperatures densities and dimensions d 1 respectively may have a nontrivial negative part and infinite range as e g the lennard jones potential additionally our result provides as a by product an approximation of grand canonical gibbs measures by finite volume canonical gibbs measures with empty boundary condition

phase transition in the nearest neighbor continuum potts model in the present study we establish a phase transition in the nearest neighbor continuum potts model the repulsion between particles of different type acts only on a nearest neighbor graph more precisely a subgraph of the delaunay graph this work is an adaptation of the lebowitz and lieb soft core continuum potts model

conditional limit theorems under markov conditioning let x 1 x 2 cdots be independent identically distributed random variables taking values in a finite set x and consider the conditional joint distribution of the first m elements of the sample x 1 cdots x n on the condition that x 1 x 1 and the sliding block sample average of a function h cdot cdot defined on x 2 exceeds a threshold alpha eh x 1 x 2 for m fixed and n rightarrow infty this conditional joint distribution is shown to converge m the m step joint distribution of a markov chain started in x 1 which is closest to x l x 2 cdots in kullback leibler information divergence among all markov chains whose two dimensional stationary distribution p cdot cdot satisfies sum p x y h x y geq alpha provided some distribution p on x 2 having equal marginals does satisfy this constraint with strict inequality similar conditional limit theorems are obtained when x 1 x 2 cdots is an arbitrary finite order markov chain and more general conditioning is allowed

new delay dependent stability criteria for neural networks with time varying delay using delay decomposition approach this brief is concerned with the problem of asymptotic stability of neural networks with time varying delays the activation functions are monotone nondecreasing with known lower and upper bounds novel stability criteria are derived by employing new lyapunov krasovskii functional and the integral inequality the developed stability criteria have delay dependencies and the results are characterized by linear matrix inequalities new and less conservative solutions to the global stability problem are provided in terms of feasibility testing numerical examples are finally given to demonstrate the effectiveness of the proposed method

stability analysis for delayed neural networks with an improved general free matrix based integral inequality this paper revisits the problem of stability analysis for neural networks with a time varying delay an improved general free matrix based fmb integral inequality is proposed with an undetermined number m compared with the conventional fmb ones the improved inequality involves a much smaller number of free matrix variables in particular the improved fmb integral inequality is expressed in a concrete form for any value of m by employing the new inequality with a properly constructed lyapunov krasovskii functional a new stability condition is derived for neural networks with a time varying delay two commonly used numerical examples are given to show strong competitiveness of the proposed approach in both the conservatism and computation burdens

new lyapunov krasovskii functionals for global asymptotic stability of delayed neural networks this brief deals with the problem of global asymptotic stability for a class of delayed neural networks some new lyapunov krasovskii functionals are constructed by nonuniformly dividing the delay interval into multiple segments and choosing proper functionals with different weighting matrices corresponding to different segments in the lyapunov krasovskii functionals then using these new lyapunov krasovskii functionals some new delay dependent criteria for global asymptotic stability are derived for delayed neural networks where both constant time delays and time varying delays are treated these criteria are much less conservative than some existing results which is shown through a numerical example

consistency of likelihood estimation for gibbs point processes strong consistency of the maximum likelihood estimator mle for parametric gibbs point process models is established the setting is very general it includes pairwise pair potentials finite and infinite multibody interactions and geometrical interactions where the range can be finite or infinite the gibbs interaction may depend linearly or non linearly on the parameters a particular case being hardcore parameters and interaction range parameters as important examples we deduce the consistency of the mle for all parameters of the strauss model the hardcore strauss model the lennard jones model and the area interaction model

discrete lattice systems and the equivalence of microcanonical canonical and grand canonical gibbs states it is proven that a microcanonical gibbs measure on a classical discrete lattice system is a mixture of canonical gibbs measures provided the potential is approximately periodic has finite range and possesses a commensurability property no periodicity is imposed on the measure when the potential is not approximately periodic or does not have the commensurability property the inclusion does not hold

a new criterion of delay dependent asymptotic stability for hopfield neural networks with time delay in this brief the problem of global asymptotic stability for delayed hopfield neural networks hnns is investigated a new criterion of asymptotic stability is derived by introducing a new kind of lyapunov krasovskii functional and is formulated in terms of a linear matrix inequality lmi which can be readily solved via standard software this new criterion based on a delay fractioning approach proves to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning an example is provided to show the effectiveness and the advantage of the proposed result

entropic repulsion of the lattice free field consider the massless free field on thed dimensional lattice d d 3 that is the centered gaussian field on open image in new window with covariances given by the green function of the simple random walk on d we show that the probability that all the spins are positive in a box of volumen d decays exponentially at a rate of ordernd 2 logn and compute explicitly the corresponding constant in terms of the capacity of the unit cube the result is extended to a class of transient random walks with transition functions in the domain of the normal and stable law

large deviation principles for euclidean functionals and other nearly additive processes we prove a large deviation principle for a process indexed by cubes of the multidimensional integer lattice or euclidean space under approximate additivity and regularity hypotheses the rate function is the convex dual of the limiting logarithmic moment generating function in some applications the rate function can be expressed in terms of relative entropy the general result applies to processes in euclidean combinatorial optimization statistical mechanics and computational geometry examples include the length of the minimal tour the traveling salesman problem the length of the minimal matching graph the length of the minimal spanning tree the length of the k nearest neighbors graph and the free energy of a short range spin glass model

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

comparison of finite volume canonical and grand canonical gibbs measures the continuous case we consider a continuous gas with finite range positive pair potential and we assume that the cluster expansion convergence condition holds we prove a sharp bound on the difference between the finite volume grand canonical and canonical expectation of local observable the bound is given in terms of the support of the observable of its grand canonical variance and of the volume on which the system is confined

phase transition in continuum potts models we establish phase transitions for a class of continuum multi type particle systems with finite range repulsive pair interaction between particles of different type this proves an old conjecture of lebowitz and lieb a phase transition still occurs when we allow a background pair interaction between all particles which is superstable and has sufficiently short range of repulsion our approach involves a random cluster representation analogous to the fortuin kasteleyn representation of the potts model in the course of our argument we establish the existence of a percolation transition for gibbsian particle systems with random edges between the particles and also give an alternative proof for the existence of gibbs measures with supperstable interaction

a note on the uniqueness result for the inverse henderson problem the inverse henderson problem of statistical mechanics is the theoretical foundation for many bottom up coarse graining techniques for the numerical simulation of complex soft matter physics this inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles roughly stated it asks for the interaction potential given the equilibrium pair correlation function of the system in 1974 henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system here we provide a rigorous proof of a slightly more general version of the latter statement using georgii s variant of the gibbs variational principle the inverse henderson problem of statistical mechanics is the theoretical foundation for many bottom up coarse graining techniques for the numerical simulation of complex soft matter physics this inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles roughly stated it asks for the interaction potential given the equilibrium pair correlation function of the system in 1974 henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system here we provide a rigorous proof of a slightly more general version of the latter statement using georgii s variant of the gibbs variational principle

stability analysis of lur e systems with additive delay components via a relaxed matrix inequality abstract this paper is concerned with the stability analysis of lur e systems with sector bounded nonlinearity and two additive time varying delay components in order to accurately understand the effect of time delays on the system stability the extended matrix inequality for estimating the derivative of the lyapunov krasovskii functionals lkfs is employed to achieve the conservatism reduction of stability criteria it reduces estimation gap of the popular reciprocally convex combination lemma rccl combining the extended matrix inequality and two types of lkfs lead to several stability criteria which are less conservative than the rccl based criteria under the same lkfs finally the advantages of the proposed criteria are demonstrated through two examples

a characterization of nilpotent orbit closures among symplectic singularities we prove that a conical symplectic variety with maximal weight 1 is isomorphic to i an affine space with the standard symplectic form or ii a normal nilpotent orbit closure of a complex semisimple lie algebra

improved delay dependent stability criteria for generalized neural networks with time varying delays abstract this paper is concerned with the problem of stability analysis for generalized neural networks with time varying delays a novel integral inequality which includes several existing inequalities as special cases is presented by employing a suitable lyapunov krasovskii functional lkf and using the proposed integral inequality to estimate the derivative of the lkf improved delay dependent stability criteria expressed in terms of linear matrix inequalities are derived finally four numerical examples are provided to demonstrate the effectiveness and the improvement of the proposed method

producing stable periodic solutions of switched impulsive delayed neural networks using a matrix based cubic convex combination approach this article is dedicated to designing a novel periodic impulsive control strategy for producing globally exponentially stable periodic solutions for switched neural networks with discrete and finite distributed time varying delays first tunable parameters and cubic convex combination approach are proposed to study the globally exponential convergence of switched neural networks second a sufficient criterion for the existence uniqueness and globally exponential stability of a periodic solution is demonstrated by using contraction mapping theorem and the impulse delay dependent lyapunov krasovskii functional method it is worth emphasizing that the addressed lyapunov krasovskii functional covers both triple integral terms and novel quadruple integral terms which makes the conservatism of the above criteria decrease even if the original neural network models are unstable or the impulsive effects are strong the addressed neural network model can produce a globally exponentially stable periodic solution these results here which include boundedness globally uniformly exponential convergence and globally exponentially stability of the periodic solution generalize and improve the earlier publications finally two numerical examples and their computer simulations are given to show the effectiveness of theoretical results