exponential p convergence analysis for stochastic bam neural networks with time varying and infinite distributed delays we discuss exponential p convergence for stochastic bam neural networks the delays here are multiple time varying and infinite distributed delays we establish a new l operator delay differential integral inequality delay dependent criteria ensuring exponential p convergence are obtained giving the detail estimations of the exponential p convergence ball this paper is concerned with the problem of global exponential p convergence for stochastic bam neural networks with time varying and infinite distributed delays by constructing a new delay differential integral inequality and a novel l operator differential integral inequality and coupling with stochastic analysis techniques some delay dependent sufficient conditions are derived to guarantee exponential p convergence and the state variables of the discussed stochastic bam neural networks are globally exponentially convergent to a ball in the state space with a pre specified convergence rate meanwhile the exponential p convergent balls are also estimated here the existence and the uniqueness of the equilibrium point needs not to be considered finally two examples with numerical simulations are given to illustrate the effectiveness of the theoretical results

representations in l2 spaces on infinite dimensional symmetric cones abstract in this paper we study representations of the automorphism groups of classical infinite dimensional tube domains in particular we construct the l2 realization of all unitary highest weight representations including the vector valued case we also find a projective representation of the full identity component of the affine automorphism group of the hilbert schmidt version of the tube domain with trivial cocycle on the subgroup corresponding to the trace class version but non trivial on the large group finally we show that the operator valued measures corresponding to the vector valued highest weight representations have densities of a rather weak type with respect to wishart distributions which makes it possible to determine their supports

on differentiable vectors for representations of infinite dimensional lie groups in this paper we develop two types of tools to deal with differentiability properties of vectors in continuous representations g gl v of an infinite dimensional lie group g on a locally convex space v the first class of results concerns the space v of smooth vectors if g is a banach lie group we define a topology on the space v of smooth vectors for which the action of g on this space is smooth if v is a banach space then v is a frechet space this applies in particular to c dynamical systems a g where g is a banach lie group for unitary representations we show that a vector v is smooth if the corresponding positive definite function g v v is smooth the second class of results concerns criteria for ck vectors in terms of operators of the derived representation for a banach lie group g acting on a banach space v in particular we provide for each k n examples of continuous unitary representations for which the space of ck 1 vectors is trivial and the space of ck vectors is dense

unitary highest weight modules of inductive limit lie algebras and groups abstract representations of inductive limits of finite dimensional lie groups and algebras am our main objects of study such representations can be constructed by taking inductive limits of the representations of the finite dimensional groups or algebras for finite dimensional lie groups and algebras of hermitian symmetric type enright howe wallach classified those highest weight representations which are unitarizable in this paper we consider the limits of the algebras u p n so 2n and sp n r the limits of the corresponding maximal compact subgroup and the limits of the corresponding generalized verma modules we give necessary and sufficient conditions for the inductive limit representation to be unitarizable in all three cases we show that a necessary condition for unitarizability is that the highest weight is eventually constant we also give sufficient conditions depending on the constant which will ensure that the limit is unitarizable

arimoto renyi conditional entropy and bayesian m ary hypothesis testing this paper gives upper and lower bounds on the minimum error probability of bayesian m ary hypothesis testing in terms of the arimoto renyi conditional entropy of an arbitrary order alpha the improved tightness of these bounds over their specialized versions with the shannon conditional entropy alpha 1 is demonstrated in particular in the case where m is finite we show how to generalize fano s inequality under both the conventional and list decision settings as a counterpart to the generalized fano s inequality allowing m to be infinite a lower bound on the arimoto renyi conditional entropy is derived as a function of the minimum error probability explicit upper and lower bounds on the minimum error probability are obtained as a function of the arimoto renyi conditional entropy for both positive and negative alpha furthermore we give upper bounds on the minimum error probability as functions of the renyi divergence in the setup of discrete memoryless channels we analyze the exponentially vanishing decay of the arimoto renyi conditional entropy of the transmitted codeword given the channel output when averaged over a random coding ensemble

periodic bi directional cohen grossberg neural networks with distributed delays abstract some sufficient conditions are obtained for the global exponential stability of periodic solutions to periodic bi directional cohen grossberg neural networks involving distributed delays by using the lyapunov functional method and some analytical techniques these results improve and generalize some previous works and are helpful for designing a global exponential stable periodic bi directional cohen grossberg neural networks

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

generalization of gartner ellis theorem a generalization of the gartner ellis theorem for arbitrary random sequences is established it is shown that the conventional formula of the large deviation rate function based on the moment generating function techniques fails to describe the general possibly nonconvex large deviation rate for an arbitrary random sequence an nonconvex extension formula obtained by twisting the conventional large deviation rate function around a continuous functional is therefore proposed as a result a new gartner ellis upper bound is proved it is demonstrated by an example that a tight upper bound on the large deviation rate of an arbitrary random sequence can be obtained by choosing the right continuous functional even if the true large deviation rate is not convex also proved is a parallel extension of the gartner ellis lower bound with the introduction of a new notion of gartner ellis set within which the upper bound coincides with the lower bound for countably many points

channel coding rate in the finite blocklength regime this paper investigates the maximal channel coding rate achievable at a given blocklength and error probability for general classes of channels new achievability and converse bounds are given which are tighter than existing bounds for wide ranges of parameters of interest and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100 it is also shown analytically that the maximal rate achievable with error probability isclosely approximated by c v n q 1 where c is the capacity v is a characteristic of the channel referred to as channel dispersion and q is the complementary gaussian cumulative distribution function

the classification of locally finite split simple lie algebras one of the great early achievements in lie theory is the classification of the finite dimensional simple complex lie algebras by w killing and e cartan more than 50 years later new aspects were added to this classification by the theory of coxeter groups and the visualization of the classification in terms of dynkin diagrams furthermore serre s description of the simple lie algebras by generators and relations provided a direct way to construct the lie algebras from the cartan matrix corresponding to the choice of a root base i e a system of simple roots

convergence behavior of delayed bidirectional associative memory cellular neural networks with asymptotically periodic coefficients this paper considers the convergence behavior of delayed bam cellular neural networks with asymptotically periodic coefficients by applying mathematical analysis techniques some new sufficient conditions are obtained to ensure that solutions of the networks converge to a periodic function

on improved delay dependent criterion for global stability of bidirectional associative memory neural networks with time varying delays in the paper the global robust asymptotic stability of bidirectional associative memory bam neural networks with time varying delays and uncertainties is investigated a novel stability criterion is presented based on the lyapunov method the criterion is represented in terms of linear matrix inequality lmi which can be solved easily by various optimization algorithms a numerical example is illustrated to show the effectiveness of our new result

existence and global exponential stability of periodic solution for discrete time bam neural networks the discrete time analogues of bidirectional associative memory neural networks with periodic coefficients and distributed delays are formulated and studied and by using the continuation theorem of coincidence degree theory we derive the existence of periodic solution for the discrete time bam neural networks and by constructing a appropriate lyapunov type sequence we prove the global exponential stability of the periodic solution for the model it is shown that the discrete time analogues inherit the existence and global exponential stability of periodic solution for the continuous time bam neural networks an example is given to illustrate the effectiveness of the obtained results

on zero rate error exponents of finite state channels with input dependent states we derive a single letter formula for the zero rate reliability error exponent of a finite state channel whose state variable depends deterministically and recursively on past channel inputs where the code complies with a given channel input constraint special attention is then devoted to the important special case of the gaussian channel with intersymbol interference where more explicit results are obtained

a note on the poor verdu upper bound for the channel reliability function in an earlier work poor and verdu 1995 established an upper bound for the reliability function of arbitrary single user discrete time channels with memory they also conjectured that their bound is tight for all coding rates we demonstrate via a counterexample involving memoryless binary erasure channels becs that the poor verdu upper bound is not tight at low rates we conclude by examining possible improvements to this bound

iwasawa decompositions of some infinite dimensional lie groups we set up an abstract framework that allows the investigation of iwasawa decompositions for involutive infinite dimensional lie groups modeled on banach spaces this provides a method to construct iwasawa decompositions for classical real or complex banach lie groups associated with the schatten ideals o p h on a complex separable hilbert space h if 1 p

global stability of periodic solution for bidirectional associative memory neural networks with varying time delay this paper investigates the global stability of periodic solution for bidirectional associative memory neural networks by using linear matrix inequality and presents new sufficient conditions on the existence uniqueness global exponential stability and asymptotic stability of periodic solution for bidirectional associative memory neural networks with varying time delays in addition exponential convergence rate is estimated by the equation in the paper furthermore the results in this paper are generalized and the ones reported in the existing literatures are improved numerical simulations are given to verify the effectiveness of our main results

a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

existence and stability of periodic solution for bam neural networks with distributed delays we use the continuation theorem of coincidence degree theory and liapunov functions to study the existence and stability of positive periodic solutions for a class of two layer heteroassociative networks called bidirectional associative memory networksdx idt a i t x i t j 1 mp j i t f j y j t t j i t y j t i i t i 1 2 n dy jdt b j t y j t i 1 nq i j t f i x i t s i j t x i t j j t j 1 2 manddx idt a i t x i t j 1 mp j i t f j 0 h j i s y j t s ds i i t i 1 2 n dy jdt b j t y j t i 1 nq i j t f i 0 k i j s x i t s ds j j t j 1 2 m

reflection positivity and conformal symmetry abstract a reflection positive hilbert space is a triple e e where e is a hilbert space a unitary involution and e a closed subspace on which the hermitian form v w v w is positive semidefinite for a triple g s where g is a lie group an involutive automorphism of g and s a subsemigroup invariant under the involution s s s 1 a unitary representation of g on e e is called reflection positive if g g and s e e this is the first in a series of papers in which we develop a new and systematic approach to reflection positive representations based on reflection positive distributions and reflection positive distribution vectors this approach is most natural to obtain classification results in particular in the abelian case among the tools we develop is a generalization of the bochner schwartz theorem to positive definite distributions on open convex cones we further illustrate our techniques with a non abelian example by constructing reflection positive distribution vectors for complementary series representations of the conformal group o 1 n 1 r of the sphere s n

saddle point in the minimax converse for channel coding a minimax metaconverse has recently been proposed as a simultaneous generalization of a number of classical results and a tool for the nonasymptotic analysis in this paper it is shown that the order of optimizing the input and output distributions can be interchanged without affecting the bound in the course of the proof a number of auxiliary results of separate interest are obtained in particular it is shown that the optimization problem is convex and can be solved in many cases by the symmetry considerations as a consequence it is demonstrated that in the latter cases the multiletter input distribution in information spectrum verdu han converse bound can be taken to be a memoryless product of single letter ones a tight converse for the binary erasure channel is rederived by computing the optimal nonproduct output distribution for discrete memoryless channels a conjecture of poor and verdu regarding the tightness of the information spectrum bound on the error exponents is resolved in the negative concept of the channel symmetry group is established and relations with the definitions of symmetry by gallager and dobrushin are investigated

a new stability criterion for bidirectional associative memory neural networks of neutral type in the paper the global asymptotic stability of equilibrium is considered for continuous bidirectional associative memory bam neural networks of neutral type by using the lyapunov method a new stability criterion is derived in terms of linear matrix inequality lmi to ascertain the global asymptotic stability of the bam the lmi can be solved easily by various convex optimization algorithms a numerical example is illustrated to verify our result

generalizing the fano inequality the fano inequality gives a lower bound on the mutual information between two random variables that take values on an m element set provided at least one of the random variables is equiprobable the authors show several simple lower bounds on mutual information which do not assume such a restriction in particular this ran be accomplished by replacing log m with the infinite order renyi entropy in the fano inequality applications to hypothesis testing are exhibited along with bounds on mutual information in terms of the a priori and a posteriori error probabilities

unitary highest weight representations in hilbert spaces of holomorphic functions on infinite dimensional domains abstract automorphism groups of symmetric domains in hilbert spaces form a natural class of infinite dimensional lie algebras and corresponding banach lie groups we give a classification of the algebraic category of unitary highest weight modules for such lie algebras and show that infinite dimensional versions of the lie algebras s o 2 n have no unitary highest weight representations and thus do not meet the physical requirement of having positive energy highest weight modules correspond to unitary representations of global banach lie groups realized in hilbert spaces of vector valued holomorphic functions on the relevant domains in hilbert spaces the construction of such holomorphic representations of certain banach lie groups followed by the application of the general framework of harish chandra type groups in an appropriate banach setting leads to the integration of the lie algebra representation to a group representation the extension of this theory to infinite dimensional settings is explored

a lower bound on the probability of error in multihypothesis testing consider two random variables x and y where x is finitely or countably infinitely valued and where y is arbitrary let spl epsiv denote the minimum probability of error incurred in estimating x from y it is shown that spl epsiv spl ges sub 0 spl les spl alpha spl les 1 sup sup 1 spl alpha p spl pi x y spl les spl alpha where spl pi x y denotes the posterior probability of x given y this bound finds information theoretic applications in the proof of converse channel coding theorems it generalizes and strengthens previous lower bounds due to shannon and to verdu and han 1994

global stability and asymptotically periodic solution for nonautonomous cooperative lotka volterra diffusion system two asymptotically cooperative lotka volterra populations in the two patch system with diffusion were considered in this paper each population could diffuse independently and discretely between its intrapatch and interpatch by means of constructing a suitable liapunov function we obtained that the systems had a unique asymptotically periodic solution which was globally asymptotically stable