retrieval properties of a hopfield model with random asymmetric interactions the process of pattern retrieval in a hopfield model in which a random antisymmetric component is added to the otherwise symmetric synaptic matrix is studied by computer simulations the introduction of the antisymmetric component is found to increase the fraction of random inputs that converge to the memory states however the size of the basin of attraction of a memory state does not show any significant change when asymmetry is introduced in the synaptic matrix we show that this is due to the fact that the spurious fixed points which are destabilized by the introduction of asymmetry have very small basins of attraction the convergence time to spurious fixed point attractors increases faster than that for the memory states as the asymmetry parameter is increased the possibility of convergence to spurious fixed points is greatly reduced if a suitable upper limit is set for the convergence time this prescription works better if the synaptic matrix has an antisymmetric component

structure of metastable states in the hopfield model an upper bound for the number of metastable states in the hopfield model is calculated as a function of the hamming fraction from an input pattern for all finite values of alpha the ratio of number of patterns to nodes the hamming fraction from the input pattern to the nearest metastable state is infinite when alpha 0 113 the bound also implies that there is a gap between a set of states close to the input pattern and another set centred around the hamming fraction 0 5 from it

restriction to compact subgroups in the cyclic homology of reductive p adic groups restriction of functions from a reductive p adic group g to its compact subgroups defines an operator on the hochschild and cyclic homology of the hecke algebra of g we study the commutation relations between this operator and others coming from representation theory jacquet functors idempotents in the bernstein centre and characters of admissible representations

controllability of nonlinear evolution delay integrodifferential systems in this paper the approximate controllability of nonlinear delay integrodifferential evolution systems with preassigned responses is studied these controllability results are for nonlinear systems that are not associated with linear systems and no compactness assumption is imposed

metastable states of neural networks incorporating the physiological dale hypothesis physiologically it is likely that excitatory and inhibitory neurons are rather clearly distinguished or in other words each neuron has in most cases a unique excitatory or inhibitory property the dale hypothesis to study the consequence of the physiological constraint the author proposes a learning rule for neural networks which incorporates the constraint then the distribution of the metastable states is calculated and it is found that the retrieval states form a much larger group in the proposed model than in the hopfield model the author also studies the process of retrieval by considering the statistical dynamics of the overlaps the result suggests that excitatory neurons and inhibitory neurons are preferably balanced in number if the attraction basins of the stored patterns are to be sufficiently large

the periodic cyclic homology of crossed products of finite type algebras we study the periodic cyclic homology groups of the cross product of a finite type algebra a by a discrete group in case a is commutative and the group is finite our results are complete and given in terms of the singular cohomology of the sets of fixed points these groups identify our cyclic homology groups with the orbifold cohomology of the underlying algebraic orbifold the proof is based on a careful study of localization at fixed points and of the resulting koszul complexes this is achieved by extending to our class of noncommutative algebras the concept of an infinitesimal neighborhood that plays such an important role in commutative algebra we provide examples of azumaya algebras for which this identification is however no longer valid as an example we discuss some affine weyl groups

stochastic analyses of the dynamics of generalized little hopfield hemmen type neural networks stochastic analyses are conducted of model neural networks of the generalized little hopfield hemmen type in which the synaptic connections with linearly embeddedp sets of patterns are free of symmetric ones and a glauber dynamics of a markovian type is assumed two kinds of approaches are taken to study the stochastic dynamical behavior of the network system first by developing the method of the nonlinear master equation in the thermodynamic limitn an exact self consistent equation is derived for the time evolultion of the pattern overlaps which play the role of the order parameters of the system the self consistent equation is shown to describe almost completely the macroscopic dynamical behavior of the network system second conducting the system size expansion of the master equation for then body probability distribution of the glauber dynamics makes it possible to analyze the fluctuations in the course of the analysis the self consistent equation for the pattern overlaps is derived again the main result of the rigorous fluctuation analysis is that as far as the fluctuations are concerned the time course of the pattern overlap fluctuations behaves independently of the fluctuations in the remaining modes of the system s macrovariables in accordance with the self determining property of the macroscopic motion of the pattern overlaps for neural networks with linear synaptic couplings

hochschild homology of affine hecke algebras abstract let h h r q be an affine hecke algebra with complex possibly unequal parameters q which are not roots of unity we compute the hochschild and the cyclic homology of h it turns out that these are independent of q and that they admit an easy description in terms of the extended quotient of a torus by a weyl group both of which are canonically associated to the root datum r for positive q we also prove that the representations of the family of algebras h r q c come in families which depend analytically on analogous results are obtained for graded hecke algebras and for schwartz completions of affine hecke algebras

approximate controllability of semilinear functional equations in hilbert spaces in this paper approximate and complete controllability for semilinear functional differential systems is studied in hilbert spaces sufficient conditions are established for each of these types of controllability the results address the limitation that linear systems in infinite dimensional spaces with compact semigroup cannot be completely controllable the conditions are obtained by using the schauder fixed point theorem when the semigroup is compact and the banach fixed point theorem when the semigroup is not compact

controllability of neutral functional integrodifferential systems in banach spaces abstract sufficient conditions for controllability of neutral functional integrodifferential systems in a banach space are established the results are obtained by using the schaefer fixed point theorem an example is provided to illustrate the theory

a note on approximate controllability of semilinear systems abstract for the following distributed parameter semilinear system x ax f x bu naito 5 showed that under suitable hypotheses approximate contrallability is attainable if f x m 1 x for some m 0 and some 0 1 in this paper this condition is simplified to requiring only that lim x f x x 0 in addition a uniform lipschitz continuity assumption on f is replaced by requiring f being locally lipschitz continuous

controllability of functional semilinear integrodifferential systems in banach spaces sufficient conditions for controllability of functional semilinear integrodifferential systems in a banach space are established the results are obtained by using the schaefer fixed point theorem

the number of metastable states in the projection rule neural network we calculate the direct average n of the number of metastable states in the projection rule neural network by means of the saddle point method n is obtained as a function of the hamming distance g to a given pattern stability gamma and energy e the critical storage capacity of the model is calculated the examination of the energy dependence of n leads to lower bounds for the energies of the spin glass states

controllability properties of linear and semilinear abstract control systems we consider control systems described by a semilinear abstract equation y ay f y u bu in hilbert space general conditions for exact reachability and approximate controllability are given which are related with two families of associated quadratic optimal control problems the minimum norm optimal control and the construction of the reachable set of the corresponding linear system y ay bu are characterized respectively exact reachability for a class of semilinear control systems is obtained under some assumptions on the range of a nonlinear operator mathcal f t 0 t see definition in 4 generated by the nonlinear function f

approximate controllability for a class of semilinear abstract equations in this paper a class of control systems governed by the semilinear abstract equation dot y ay f y bv is considered a sufficient condition for the approximate controllability is obtained which improves j henry s results on a nonlinear parabolic control systems with some more serious restrictions it is suitable not only to the infinite dimensional case but also to the finite dimensional case two examples are given to explain the applications of the theory

orbital integrals on p adic groups a proof of the howe conjecture let g be a connected reductive group over a p adic field f of characteristic 0 let g g f let o be a compact subset of g og the invariant subset gxg1 g e g x e co of g we say that a closed invariant subset of g q is compact modulo conjugation if q c wg for some compact co it is equivalent to assume that the traces of q on all cartan subgroups of g are compact the purpose of this article is to prove the following theorem concerning invariant distributions on g which had been conjectured by howe 10 let of q denote the set of invariant distributions supported in u if k is a compact open subgroup of g let xk be the hecke algebra of compactly supported functions on g with complex values invariant on the left and right by k

controllability of integrodifferential systems in banach spaces sufficient conditions for controllability of integrodifferential systems in a banach space are established the results are obtained by using the schaefer fixed point theorem an example is provided to illustrate the theory

cyclic homology of totally disconnected groups acting on buildings abstract we prove a homological counterpart of a conjecture of p baum and a connes concerning k theory for convolution c algebras of p adic groups by calculating the periodic cyclic homology for the convolution algebra of a totally disconnected group acting properly on a building

local controllability of quasilinear integrodifferential evolution systems in banach spaces sufficient conditions for local controllability of quasilinear integrodifferential systems in banach spaces are established the results are obtained by using the analytic semigroup theory and the schauder fixed point theorem an example is provided to illustrate the theory

on the k0 of a p adic group this article deals with various topics related with grothendieck groups invariant distributions parabolic and compact inductions for a p adic group g the main result is a description of the k0 of the hecke algebra of g in terms of discrete series of levi subgroups which has an interesting behavior with regard to parabolic restriction and induction a similar description but no more compatible with these parabolic functors is obtained for overline mathcal h and the hattori rank map gets an easy description in this dictionary we follow a beautiful idea of j bernstein consisting in comparing two natural filtrations on these objects one of combinatorial nature and one of topological nature the combinatorial filtrations are related to the structure of levi subgroupsin g and have counterparts concerning many classical objects of interest as the grothendieck group of finite length g modules r g the set sr of regular semi simple conjugacy classes and the variety g of infinitesimal characters these filtrations will turn out to be compatible in a sense to be specified with regard to all the classical operations or morphisms between these objects

controllability of semilinear control systems dominated by the linear part while various equivalent conditions for controllability have been obtained in the case of linear control systems controllability problems of semilinear control systems usually require some complicated and limited assumptions in this paper we show the approximate controllability of an abstract semilinear control system under the assumption which has a simple form and can be easily checked in many examples

cyclic homology and the selberg principle abstract an abstract selberg principle is proved for a smooth compactly supported function f on a connected reductive p adic group which is the trace of some idempotent n n matrix this selberg principle states that the orbital integral of f relative to a non compact element vanishes this generalizes the work of julg and valette who treated the rank one case versions of the abstract selberg principle are proved also for finite groups and for discrete groups computations of the hochschild and cyclic homology of the convolution algebra of compactly supported functions are given

approximate controllability of semilinear neutral evolution systems with delay this paper considers the approximate controllability for a class of neutral control systems governed by semilinear neutral delayed equations sufficient conditions for approximate controllability are established by constructing fundamental solutions and using resolvent condition banach contraction mapping principle and techniques on fractional power operators the obtained results improve some existing analogous ones on this topic to some extent an example is presented finally to illustrate the applications of the obtained results

low firing rates an effective hamiltonian for excitatory neurons the authors analyse the behaviour of an attractor neural network which exhibits low mean temporal activity levels despite the fact that the intrinsic neuronal cycle time is very short 2 3 ms information and computation are represented on the excitatory neurons only the influence of inhibitory neurons which are assumed to react on a shorter timescale than the excitatory ones is expressed as an effective interaction of the excitatory neurons this leads to an effective model which describes the interplay of excitation and inhibition acting on excitatory neurons in terms of the excitatory neural variables alone the network operates in the presence of fast noise which is large relative to the frozen randomness induced by the stored patterns the overall fraction of active neurons is controlled by a single free parameter which expresses the relative strength of the effective inhibition associative retrieval is identified as usual with the breakdown of ergodicity in the dynamics of the network in particular with the presence of dynamical attractors corresponding to the retrieval of a given pattern in such an attractor the activity of neurons corresponding to active sites in the stored patterns increases at the expense of other neurons yet only a small fraction of the neurons active in the pattern are in the active state in each elementary time cycle and they vary from cycle to cycle in an uncorrelated fashion due to the noise hence the observed mean activity rate of any individual neuron is kept low this scenario is demonstrated by an analytical study based on the replica method and the results are tested by numerical simulations