a new approach for estimating the attraction domain for hopfield type neural networks in this letter using methods proposed by e kaslik st balint and their colleagues we develop a new method expansion approach for estimating the attraction domain of asymptotically stable equilibrium points of hopfield type neural networks we prove theoretically and demonstrate numerically that the proposed approach is feasible and efficient the numerical results that obtained in the application examples including the network system considered by e kaslik l br escu and st balint indicate that the proposed approach is able to achieve better attraction domain estimation

the yang mills flow and the atiyah bott formula on compact kahler manifolds we study the yang mills flow on a holomorphic vector bundle e over a compact k ahler manifold x along a solution of the flow we show that the curvature endomorphism i lambda f a t approaches in l 2 an endomorphism with constant eigenvalues given by the slopes of the quotients from the harder narasimhan filtration of e this proves a sharp lower bound for the hermitian yang mills functional and thus the yang mills functional generalizing to arbitrary dimension a formula of atiyah and bott first proven on riemann surfaces furthermore we show any reflexive extension to all of x of the limiting bundle e infty is isomorphic to rm gr rm hns e verifying a conjecture of bando and siu

connections with l p bounds on curvature we show by means of the implicit function theorem that coulomb gauges exist for fields over a ball inr n when the integrall n 2 field norm is sufficiently small we then are able to prove a weak compactness theorem for fields on compact manifolds withl p integral norms bounded p n 2

the limit of the hermitian yang mills flow on reflexive sheaves abstract in this paper we study the asymptotic behavior of the hermitian yang mills flow on a reflexive sheaf we prove that the limiting reflexive sheaf is isomorphic to the double dual of the graded sheaf associated to the harder narasimhan seshadri filtration this answers a question by bando and siu

analytic cycles bott chern forms and singular sets for the yang mills flow on kahler manifolds abstract it is shown that the singular set for the yang mills flow on unstable holomorphic vector bundles over compact kahler manifolds is completely determined by the harder narasimhan seshadri filtration of the initial holomorphic bundle we assign a multiplicity to irreducible top dimensional components of the singular set of a holomorphic bundle with a filtration by saturated subsheaves we derive a singular bott chern formula relating the second chern form of a smooth metric on the bundle to the chern current of an admissible metric on the associated graded sheaf this is used to show that the multiplicities of the top dimensional bubbling locus defined via the yang mills density agree with the corresponding multiplicities for the harder narasimhan seshadri filtration the set theoretic equality of singular sets is a consequence

singularities of hermitian yang mills connections and harder narasimhan seshadri filtrations this is the first of a series of papers where we relate tangent cones of hermitian yang mills connections at a singularity to the complex algebraic geometry of the underlying reflexive sheaf in this paper we work on the case when the sheaf is locally modeled on the pullback of a holomorphic vector bundle from the projective space and we shall impose an extra assumption that the graded sheaf determined by the harder narasimhan seshadri filtrations of the vector bundle is reflexive in general we conjecture that the tangent cone is uniquely determined by the double dual of the associated graded object of a harder narasimhan seshadri filtration of an algebraic tangent cone which is a certain torsion free sheaf on the projective space in this paper we also prove this conjecture when there is an algebraic tangent cone which is locally free and stable

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

optimal quasi convex combinations for stochastic approximation algorithms with parallel observers abstract motivated by numerous potential applications in decentralized estimation detection and adaptive control monte carlo optimization etc two types of stochastic approximation sa algorithms with parallel observers are developed to find the root of a non linear function with random noise corrupted measurements instead of employing the classical robbins monro rm sa procedures with a single observer a collection of physically separated parallel observers are used to estimate the same parameter a newly formed approximation sequence is obtained by means of an appropriate quasi convex combination of the most current values obtained from all the observers in addition to getting strong consistency and asymptotic normality the optimal convex combination coefficients are derived comparisons of asymptotic performance are made these comparisons indicate that the algorithms suggested here are asymptotically better than the classical approach

asymptotic properties of distributed and communication stochastic approximation algorithms the asymptotic properties of extensions of the type of distributed or decentralized stochastic approximation proposed in 1 are developed such algorithms have numerous potential applications in decentralized estimation detection and adaptive control or in decentralized monte carlo simulation for system optimization where they can exploit the possibilities of parallel processing the structure involves several isolated processors recursive algorithms that communicate to each other asynchronously and at random intervals the asymptotic small gain properties are derived the communication intervals need not be strictly bounded and they and the system noise can depend on the communicating system state state space constraints are also handled in many applications the dynamical terms are merely indicator functions or have other types of discontinuities the typical such case is also treated as is the case where there is noise in the communication the linear stochastic differential equation

on the blow up set of the yang mills flow on kahler surfaces the yang mills flow on a kahler surface with holomorphic initial data converges smoothly away from a singular set determined by the harder narasimhan seshadri filtration of the initial holomorphic bundle

a simple proof of a theorem by uhlenbeck and yau a subbundle of a hermitian holomorphic vector bundle e h can be metrically and differentially defined by the orthogonal projection onto itself a weakly holomorphic subbundle of e h is by definition an orthogonal projection lying in the sobolev space l21 of l2 sections of end e with l2 first order derivatives in the sense of distributions which satisfies furthermore id d 0 a weakly holomorphic subbundle of e h is shown to define a coherent subsheaf of open image in new window e and implicitly a holomorphic subbundle of e in the complement of an analytic subset of codimension 2 this result provided the key technical argument to the proof given by uhlenbeck and yau for the kobayashi hitchin correspondence on compact kahler manifolds we give here a much simpler proof based on current theory the idea is to construct local meromorphic sections of im which locally span the fibers we first make this construction on one dimensional submanifolds of x and subsequently extend it by means of a hartogs type theorem of shiffman s