topology identification of weighted complex dynamical networks abstract recently various papers investigated the geometry features synchronization and control of complex network provided with certain topology while the exact topology of a network is sometimes unknown or uncertain using lyapunov theory we propose an adaptive feedback controlling method to identify the exact topology of a rather general weighted complex dynamical network model by receiving the network nodes evolution the topology of such kind of network with identical or different nodes or even with switching topology can be monitored experiments show that the methods presented in this paper are of high accuracy with good performance

a sufficient condition for stability of a polytope of matrices abstract in this paper we study the stability of interval dynamical systems a sufficient condition for the stability of a polytope of matrices which is shown to be necessary and sufficient for a certain class of matrices is obtained the results developed can also be applied to the stability of a positive cone of matrices and sufficient conditions for the stability of interval dynamical systems are obtained a relationship between real parts of eigenvalues and matrix measures is also presented

on ad n x2 k series of universal quantum dimensions we present a universal in vogel s sense expression for the quantum dimension of the cartan product of arbitrary powers of the adjoint and x2 representations of simple lie algebras the same formula mysteriously yields quantum dimensions of some other representations of the same lie algebra for permuted universal parameters provided linear resolvability of singularities is applied we list these representations for the exceptional algebras and their stable versions for the classical algebras when the rank of the classical algebra is sufficiently large with regard to the powers of representations universal formulas may have singularities at the points in vogel s plane corresponding to some simple lie algebras we prove that our formula is linearly resolvable at all those singular points i e yields finite answers when restricted either on the classical or the exceptional lines and make a conjecture that these answers coincide with quantum dimensions of some irreducible representations in a number of cases particularly in the case of so 8 algebra which belongs both to the orthogonal and the exceptional lines it is confirmed that both resolutions yield relevant answers we note that an irreducible representation may have several universal formulas for its quantum dimension and discuss the impact of this phenomenon to the method presented by cohen and de man c r acad sci ser 1 322 5 427 432 1996 for derivation of universal formulas

global convergence rate of recurrently connected neural networks we discuss recurrently connected neural networks investigating their global exponential stability ges some sufficient conditions for a class of recurrent neural networks belonging to ges are given sharp convergence rate is given too

equivariant novikov conjecture for groups acting on euclidean buildings we prove the equivariant novikov conjecture for groups acting on euclidean buildings by using an equivariant f tilsum skandalis methocl we also obtain an equivariant version of the connes gromov moscovic th eorem for almost flat c algebra bundles

operator norm localization for linear groups and its application to k theory abstract we prove the operator norm localization property for linear groups as an application we prove the coarse novikov conjecture for box spaces of a linear group

localizing gauge theories from noncommutative geometry abstract we recall the emergence within noncommutative geometry of a generalized gauge theory from a real spectral triple for a unital c algebra a this includes a gauge group determined by the unitaries in a and gauge fields arising from a so called perturbation semigroup which is associated to a our main new result is the construction of an upper semi continuous c bundle on a hausdorff base space x whose space of continuous sections is isomorphic to a the gauge group acts by vertical automorphisms on this c bundle and can under some conditions be identified with the space of continuous sections of a group bundle on x moreover in some cases the gauge group is found to coincide with the group of inner automorphisms of a we discuss two classes of examples of our construction yang mills theory and toric noncommutative manifolds and we show that they actually give rise to continuous c bundles moreover in these examples the gauge groups coincide with the inner automorphism groups and can be realized as spaces of sections of group bundles that we explicitly determine

the equivariant coarse novikov conjecture and coarse embedding the equivariant coarse novikov conjecture provides an algorithm for determining nonvanishing of equivariant higher index of elliptic differential operators on noncompact manifolds in this article we prove the equivariant coarse novikov conjecture under certain coarse embeddability conditions more precisely if a discrete group gamma acts on a bounded geometric space x properly isometrically and with bounded distortion x gamma and gamma admit coarse embeddings into hilbert space then the gamma equivariant coarse novikov conjecture holds for x here bounded distortion means that for any gamma in gamma sup x in y d gamma x x infty where y is a fundamental domain of the gamma action on x

a less conservative stability test for second order linear time varying vector differential equations system stability and stability bounds play an essential role in control theory this note is concerned with the exponential stability of a class of second order linear time varying vector differential equations with real piecewise continuous coefficient matrices a less conservative explicit condition for stability of such a system is derived using the matrix measure theory and a more accurate upper bound for the decay exponent of its stable solution is established examples are included for illustration

robust μ stability for uncertain stochastic neural networks with unbounded time varying delays in this paper we investigate the global robust stability for uncertain stochastic neural networks with unbounded time varying delays and norm bounded parameter uncertainties a new concept of global robust stability in the mean square for neural networks is given first then by means of the linear matrix inequality lmi approach stability criteria are presented several corollaries are also derived a simple example is presented to demonstrate the effectiveness of the main result

global asymptotic stability for a linear system in a saturated mode we study an ordinary differential equation which models the behaviour of a class of neural networks which are similar to the hopfield networks and which can give convergence in finite time for application to optimisation problems and other applications we are concerned with global asymptotic stability this paper gives new results on this topic

the c algebra of a vector bundle and fields of cuntz algebras abstract we study the cuntz pimsner algebra associated with the module of continuous sections of a hilbert bundle and prove that it is a continuous bundle of cuntz algebras furthermore we assign to bundles of cuntz algebras carrying a global circle action a class in the representable kk group of the zero grade bundle we explicitly compute such class for the cuntz pimsner algebra of a vector bundle

higher index theory for certain expanders and gromov monster groups ii abstract in this paper the first of a series of two we continue the study of higher index theory for expanders we prove that if a sequence of graphs is an expander and the girth of the graphs tends to infinity then the coarse baum connes assembly map is injective but not surjective for the associated metric space x expanders with this girth property are a necessary ingredient in the construction of the so called gromov monster groups that coarsely contain expanders in their cayley graphs we use this connection to show that the baum connes assembly map with certain coefficients is injective but not surjective for these groups using the results of the second paper in this series we also show that the maximal baum connes assembly map with these coefficients is an isomorphism

un renforcement de la propriete t nous proposons un renforcement de la propriete t de kazhdan en remplacant les representations unitaires par les representations dans des espaces de hilbert qui ne sont pas necessairement unitaires mais a croissance exponentielle suffisamment petite on sait qu un groupe localement compact a la propriete t si et seulement si il existe un idempotent p dans c max g tel que pour toute representation unitaire continue h de g p est le projecteur orthogonal sur le sous espace ferme de h forme des vecteurs ginvariants pour la propriete t renforcee nous posons une definition dans ce style on appelle longueur sur un groupe localement compact g une fonction continue g r verifiant g 1 g et g1g2 g1 g2 pour g g1 g2 g dans la suite pour tout groupe localement compact g on supposera choisie une mesure de haar a gauche qui munit cc g d une structure d algebre par convolution

the maximal coarse baum connes conjecture for spaces which admit a fibred coarse embedding into hilbert space abstract we introduce a notion of fibred coarse embedding into hilbert space for metric spaces which is a generalization of gromov s notion of coarse embedding into hilbert space it turns out that a large class of expander graphs admit such an embedding we show that the maximal coarse baum connes conjecture holds for metric spaces with bounded geometry which admit a fibred coarse embedding into hilbert space

new conditions on global stability of cohen grossberg neural networks in this letter we discuss the dynamics of the cohen grossberg neural networks we provide a new and relaxed set of sufficient conditions for the cohen grossberg networks to be absolutely stable and exponentially stable globally we also provide an estimate of the rate of convergence

nonlinear measures a new approach to exponential stability analysis for hopfield type neural networks in this paper a new concept called nonlinear measure is introduced to quantify stability of nonlinear systems in the way similar to the matrix measure for stability of linear systems based on the new concept a novel approach for stability analysis of neural networks is developed with this approach a series of new sufficient conditions for global and local exponential stability of hopfield type neural networks is presented which generalizes those existing results by means of the introduced nonlinear measure the exponential convergence rate of the neural networks to stable equilibrium point is estimated and for local stability the attraction region of the stable equilibrium point is characterized the developed approach can be generalized to stability analysis of other general nonlinear systems

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

on banach spaces with kasparov and yu s property h abstract a new geometric property of banach spaces recently introduced by g kasparov and g yu called property h has important applications to the strong novikov conjecture and the coarse novikov conjecture yet is far from being well understood in this paper we investigate various uniformly continuous maps on unit spheres of banach spaces and prove that all separable banach lattices with nontrivial cotype have property h

stability analysis of neural net controllers using fuzzy neural networks neural networks can only be trained with a crisp and finite data set therefore the approximation quality of a trained network is hard to verify so a common way in proving stability of a trained neural net controller is to demonstrate the existence of a lyapunov function in this article we propose a new method how stability of a neural net controller used as a closed loop feedback controller can be proven instead of finding a lyapunov function conditions for a fuzzy training set are developed if a fuzzy neural net is trained using this training set special properties of fuzzy neural nets can be used for estimating the generalization error after defuzzification of the fuzzy net finite stability of the process can be concluded

on equilibria stability and instability of hopfield neural networks existence and uniqueness of equilibrium as well as its stability and instability of a continuous time hopfield neural network are studied a set of new and simple sufficient conditions are derived

stability of a complex dynamical network model abstract in this paper firstly we propose a complex dynamical network model which is always uniformly asymptotically stable about its equilibrium then we give theoretical analysis of its uniform asymptotical stability by using lyapunov stability theory finally we show a numerical example to verify our theoretical result

the coarse novikov conjecture and banach spaces with property h in this paper we prove the coarse novikov conjecture for metric spaces with bounded geometry which are coarsely embeddable into banach spaces with a geometric condition called property h introduced by g kasparov and g yu

k theory for the maximal roe algebra of certain expanders abstract we study in this paper the maximal version of the coarse baum connes assembly map for families of expanding graphs arising from residually finite groups unlike for the usual roe algebra we show that this assembly map is closely related to the maximal baum connes assembly map for the group and is an isomorphism for a class of expanders we also introduce a quantitative baum connes assembly map and discuss its connections to k theory of maximal roe algebras

casimir eigenvalues for universal lie algebra for two different natural definitions of casimir operators for simple lie algebras we show that their eigenvalues in the adjoint representation can be expressed polynomially in the universal vogel s parameters and give explicit formulae for the generating functions of these eigenvalues

the sextonions and e712 we fill in the hole in the exceptional series of lie algebras that was observed by cvitanovic deligne cohen and deman more precisely we show that the intermediate lie algebra between e7 and e8 satisfies some of the decomposition and dimension formulas of the exceptional simple lie algebras a key role is played by the sextonions a six dimensional algebra between the quaternions and octonions using the sextonions we show similar results hold for the rows of an expanded freudenthal magic chart we also obtain new interpretations of the adjoint variety of the exceptional group g2

ein neuer zusammenhang zwischen einfachen gruppen und einfachen singularitaten we describe a new construction to obtain a simple hypersurface singularity from the corresponding simple complex lie groupg letx be the closed orbit in the projective space attached to the lie algebra mathfrak g ofg consider a regular nilpotent element y 0 in mathfrak g and denote byh y 0 the hyperplane orthogonal toy 0 with respect to the killing form then the hyperplane sectionx h y 0 has exactly one singularity which is simple of desired type by variation of the pointy 0 we obtain a versal deformation the construction generalizes with minor modifications to any characteristicp of the basefield even in bad characteristic we recover at least the positive part of the semiuniversal deformation we prove that forp 2 a simple quasihomogeneous singularity of type a7 resp d8 is adjacent to e7 resp e8 provided its dimension is even furthermore a8 is adjacent to e8 forp 3

stability analysis of dynamical neural networks in this paper we use the matrix measure technique to study the stability of dynamical neural networks testable conditions for global exponential stability of nonlinear dynamical systems and dynamical neural networks are given it shows how a few well known results can be unified and generalized in a straightforward way local exponential stability of a class of dynamical neural networks is also studied we point out that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point from this some well known and new sufficient conditions for local exponential stability of neural networks are obtained

a concentration theorem of expanders on hadamard manifolds in this note we prove a concentration theorem of expanders as a simple corollary one can prove that expanding sequences of graphs do not admit coarse embeddings into hadamard manifolds with bounded sectional curvatures published by elsevier inc

triality exceptional lie algebras and deligne dimension formulas abstract we give a computer free proof of the deligne cohen and de man formulas for the dimensions of the irreducible g modules appearing in g k k 4 where g ranges over the exceptional complex simple lie algebras we give additional dimension formulas for the exceptional series as well as uniform dimension formulas for other representations distinguished by freudenthal along the rows of his magic chart our proofs use the triality model of the magic square which we review and present a simplified proof of its validity we conclude with some general remarks about obtaining series of lie algebras in the spirit of deligne and vogel

groupoids and an index theorem for conical pseudo manifolds we define an analytical index map and a topological index map for conical pseudomanifolds these constructions generalize the analogous constructions used by atiyah and singer in the proof of their topological index theorem for a smooth compact manifold m a main ingredient is a non commutative algebra that plays in our setting the role of c 0 t m we prove a thom isomorphism between non commutative algebras which gives a new example of wrong way functoriality in k theory we then give a new proof of the atiyah singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds we thus prove a topological index theorem for conical pseudomanifolds

the c0 x algebra of a net and index theory abstract given a connected and locally compact hausdorff space x with a good base k we assign in a functorial way a c 0 x algebra to any precosheaf of c algebras a defined over k afterwards we consider the representation theory and the kasparov k homology of a and interpret them in terms respectively of the representation theory and the k homology of the associated c 0 x algebra when a is an observable net over the spacetime x in the sense of algebraic quantum field theory this yields a geometric description of the recently discovered representations affected by the topology of x

global exponential stability of high order hopfield type neural networks this paper studies the problem of global exponential stability for a class of high order hopfield type neural networks by utilizing lyapunov functions several sufficient conditions for the global exponential stability of equilibrium point are obtained the exponential convergence rate of the equilibrium point is also estimated as a special case several new criteria on global exponential stability for the corresponding first order hopfield neural networks are obtained those criteria generalize some of the recent results reported in the literature

on hypersphericity of manifolds with finite asymptotic dimension we prove the following embedding theorems in the coarse geometry theorem a every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into the product of n 1 locally finite trees corollary every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into a non positively curved manifold of dimension 2n 2 the corollary is used in the proof of the following theorem b for every uniformly contractible manifold x whose asymptotic dimension is finite the product x x r is integrally hyperspherical for some n theorem b together with a theorem of gromov lawson implies the result previously proven by g yu 1998 which states that an aspherical manifold whose fundamental group has a finite asymptotic dimension cannot carry a metric of positive scalar curvature we also prove that if a uniformly contractible manifold x of bounded geometry is large scale uniformly embeddable into a hilbert space then x is stably integrally hyperspherical

the coarse geometric novikov conjecture for subspaces of non positively curved manifolds abstract in this paper we prove the coarse geometric novikov conjecture for metric spaces with bounded geometry which admit a coarse embedding into a simply connected complete riemannian manifold of non positive sectional curvature

mathcal c _ 0 x algebras stability and strongly self absorbing mathcal c algebras we study permanence properties of the classes of stable and so called mathcal d stable mathcal c algebras respectively more precisely we show that a mathcal c 0 x algebra a is stable if all its fibres are provided that the underlying compact metrizable space x has finite covering dimension or that the cuntz semigroup of a is almost unperforated a condition which is automatically satisfied for mathcal c algebras absorbing the jiang su algebra mathcal z tensorially furthermore we prove that if mathcal d is a k 1 injective strongly self absorbing mathcal c algebra then a absorbs mathcal d tensorially if and only if all its fibres do again provided that x is finite dimensional this latter statement generalizes results of blanchard and kirchberg we also show that the condition on the dimension of x cannot be dropped along the way we obtain a useful characterization of when a mathcal c algebra with weakly unperforated cuntz semigroup is stable which allows us to show that stability passes to extensions of mathcal z absorbing mathcal c algebras

stability of asymmetric hopfield networks in this paper we discuss dynamical behaviors of recurrently asymmetrically connected neural networks in detail we propose an effective approach to study global and local stability of the networks many of well known existing results are unified in our framework which gives much better test conditions for global and local stability sufficient conditions for the uniqueness of the equilibrium point and its stability conditions are given too

an input output based robust stabilization criterion for neural network control of nonlinear systems a stabilization method based on the input output conicity criterion is presented conventional learning algorithms are applied to adjust the controller dynamics and robust stability of the closed loop system is guaranteed by modifying the training patterns which yield unstable behavior the methodology developed expands the class of nonlinear systems to be controlled using neural control schemes so that the stabilization of a broad class of neural network based control systems even with unknown dynamics is assured straightforwardness in the application of this method is evident in contrast to the lyapunov function approach

metric sparsification and operator norm localization abstract we study an operator norm localization property and its applications to the coarse novikov conjecture in operator k theory in particular we introduce a sufficient geometric condition called metric sparsification for the operator norm localization property this is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property we also show that a sequence of expanding graphs does not possess the operator norm localization property

some remarks on kasparov theory on considere une autre preuve de l invariance d homotopie du bifoncteur ext on etudie l associativite du produit de kasparov a travers la motion de connextion

exponential stability preservation in discrete time analogues of artificial neural networks with distributed delays this paper demonstrates that there is a discrete time analogue which does not require any restriction on the size of the time step in order to preserve the exponential stability of an artificial neural network with distributed delays the analysis exploits an appropriate lyapunov sequence and a discrete time system of halanay inequalities and also either a young inequality or a geometric arithmetic mean inequality to derive several sufficient conditions on the network parameters for the exponential stability of the analogue the sufficiency conditions are independent of the time step and they correspond to those that establish the exponential stability of the continuous time network

the generator problem for z stable c algebras the generator problem was posed by kadison in 1967 and it remains open until today we provide a solution for the class of c algebras absorbing the jiang su algebra z tensorially more precisely we show that every unital separable z stable c algebra a is singly generated which means that there exists an element x a that is not contained in any proper sub c algebra of a to give applications of our result we observe that z can be embedded into the reduced group c algebra of a discrete group that contains a non cyclic free subgroup it follows that certain tensor products with reduced group c algebras are singly generated in particular c r f c r f is singly generated

the coarse geometric novikov conjecture and uniform convexity abstract the coarse geometric novikov conjecture provides an algorithm to determine when the higher index of an elliptic operator on a noncompact space is nonzero the purpose of this paper is to prove the coarse geometric novikov conjecture for spaces which admit a coarse uniform embedding into a uniformly convex banach space

smooth dense subalgebras of reduced group c algebras schwartz cohomology of groups and cyclic cohomology abstract we introduce the notion of schwartz co homology of a discrete group with a length function which is the natural generalization of the bounded cohomology of a discrete group we prove that if the length function is chosen to be a word length on a group of polynomial growth then its schwartz cohomology is canonically isomorphic to the usual group cohomology with complex coefficients using this result we will show that the group cohomology of a discrete group of polynomial growth is of polynomial growth in the sense of connes and moscovici and that there are no nontrivial idempotents in the group c algebra of a torsion free group of polynomial growth by the method of cyclic cohomology of connes

k theoretic amenability for sl2 qp and the action on the associated tree abstract it is proved that if a locally compact group g acts simplicially on a tree in such a way that the stabilizers of the vertices are amenable then g is k amenable in particular the canonical map from the full c algebra onto the reduced c algebra of g induces isomorphisms in k theory the main corollary of our result is that sl 2 q p and some other groups over local fields are k amenable

stability of artificial neural networks with impulses sufficient conditions are obtained for the existence and asymptotic stability of a unique equilibrium of a hopfield type neural network with lipschitzian activation functions without assuming their boundedness monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time both the continuous time and their corresponding discrete time networks are considered the sufficient conditions of the discrete time network do not restrict the step size appearing in the discretization process and these conditions approach as the step size tends to zero those of the conditions of the continuous time networks the sufficient conditions are in terms of the parameters of the network only and are easy to verify also when the impulsive jumps are absent the results reduce to those of the non impulsive systems

the equivariant coarse baum connes conjecture for spaces which admit an equivariant coarse embedding into hilbert space abstract in this paper we proved that the equivariant coarse baum connes conjecture holds for a metric space with bounded geometry which admits an equivariant coarse embedding into hilbert space

on the k theory of groups with finite asymptotic dimension it is proved that the assembly maps in algebraic kand l theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for e the result also applies to certain groups that admit only a finite dimensional model for e in particular it applies to discrete subgroups of virtually connected lie groups

on the relation between k and l theory of c algebras we prove the existence of a map of spectra tau a ka rightarrow ell a between connective topological k theory and connective algebraic l theory of a complex c algebra a which is natural in a and compatible with multiplicative structures we determine its effect on homotopy groups and as a consequence obtain a natural equivalence ka left tfrac 1 2 right xrightarrow simeq la left tfrac 1 2 right of periodic k and l theory spectra after inverting 2 we show that this equivalence extends to k and l theory of real c algebras using this we give a comparison between the real baum connes conjecture and the l theoretic farrell jones conjecture we conclude that these conjectures are equivalent after inverting 2 if and only if a certain completion conjecture in l theory is true

robust control of dynamical systems using neural networks with input output feedback linearization this paper presents a control algorithm that combines three valuable features in robust and non linear control namely modelling using neural networks input output feedback linearization and lmi based robust controller design in the first step of the algorithm an affine description of a feedforward neural network model is derived by performing an input output feedback iof linearization an uncertainty description of the iof linearized system is derived based on the parametric uncertainties of the affine model then the lmi based robust controller is designed by means of an optimization procedure a key step in this procedure is the derivation of a polytopic boundary for the state space matrices of the iof linearized system based on the estimated parameters of the neural network and their uncertainty bounds

global exponential stability of neural networks with globally lipschitz continuous activations and its application to linear variational inequality problem this paper investigates the existence uniqueness and global exponential stability ges of the equilibrium point for a large class of neural networks with globally lipschitz continuous activations including the widely used sigmoidal activations and the piecewise linear activations the provided sufficient condition for ges is mild and some conditions easily examined in practice are also presented the ges of neural networks in the case of locally lipschitz continuous activations is also obtained under an appropriate condition the analysis results given in the paper extend substantially the existing relevant stability results in the literature and therefore expand significantly the application range of neural networks in solving optimization problems as a demonstration we apply the obtained analysis results to the design of a recurrent neural network rnn for solving the linear variational inequality problem vip defined on any nonempty and closed box set which includes the box constrained quadratic programming and the linear complementarity problem as the special cases it can be inferred that the linear vip has a unique solution for the class of lyapunov diagonally stable matrices and that the synthesized rnn is globally exponentially convergent to the unique solution some illustrative simulation examples are also given

stability analysis of hopfield type neural networks the paper applies several concepts in robust control research such as linear matrix inequalities edge theorem parameter dependent lyapunov function and popov criteria to investigate the stability property of hopfield type neural networks the existence and uniqueness of an equilibrium is formulated as a matrix determinant problem an induction scheme is used to find the equilibrium to verify whether the determinant is nonzero for a class of matrix a numerical range test is proposed several robust control techniques in particular linear matrix inequalities are used to characterize the local stability of the neural networks around the equilibrium the global stability of the hopfield neural networks is then addressed using a parameter dependent lyapunov function technique all these results are shown to generalize existing results in verifying the existence uniqueness of the equilibrium and local global stability of hopfield type neural networks

some generalized sufficient convergence criteria for nonlinear continuous neural networks a reason for applying the direct method of lyapunov to artificial neural networks anns is to design dynamical neural networks so that they exhibit global asymptotic stability lyapunov functions that frequently appear in the ann literature include the quadratic function the persidskii function and the lure postnikov function this contribution revisits the quadratic function and shows that via krasovskii like stability criteria it is possible to have a very simple and systematic procedure to obtain not only new and generalized results but also well known sufficient conditions for convergence established recently by non lyapunov methods such as the matrix measure and nonlinear measure

a universal dimension formula for complex simple lie algebras we present a universal formula for the dimension of the cartan powers of the adjoint representation of a complex simple lie algebra i e a universal formula for the hilbert functions of homogeneous complex contact manifolds as well as several other universal formulas these formulas generalize formulas of vogel and deligne and are given in terms of rational functions where both the numerator and denominator decompose into products of linear factors with integer coefficients we discuss consequences of the formulas including a relation with scorza varieties

geometrization of the strong novikov conjecture for residually finite groups in this paper we prove that the strong novikov conjecture for a residually finite group is essentially equivalent to the coarse geometric novikov conjecture for a certain metric space associated to the group as an application we obtain the coarse geometric novikov conjecture for a large class of sequences of expanders

galois symmetry induced by hecke relations in rational conformal field theory and associated modular tensor categories hecke operators relate characters of rational conformal field theories rcfts with different central charges and extend the previously studied galois symmetry of modular representations and fusion algebras we show that the conductor n of a rcft and the quadratic residues mod n play an important role in the computation and classification of galois permutations we establish a field correspondence in different theories through the picture of effective central charge which combines galois inner automorphisms and the structure of simple currents we then make a first attempt to extend hecke operators to the full data of modular tensor categories the galois symmetry encountered in the modular data transforms the fusion and the braiding matrices as well and yields isomorphic structures in theories related by hecke operators

on duality and negative dimensions in the theory of lie groups and symmetric spaces we give one more interpretation of the symbolic formulas u n u n and sp 2n so 2n and show that they can be extended to the classical symmetric spaces using macdonald duality for jack and jacobi symmetric functions

exponential stability and oscillation of hopfield graded response neural network both exponential and stochastic stabilities of the hopfield neural network are analyzed the results are especially useful for analyzing the stabilities of asymmetric neural networks a constraint on the connection matrix has been found under which the neural network has a unique and exponentially stable equilibrium given any connection matrix this constraint can be satisfied through the adjustment of the gains of the amplifiers and the resistances in the neural net circuit a one to one and smooth map between input currents and the equilibria of the neural network can be set up the above results can be applied to the master slave net to prove that the master net can find the best connection matrix for the slave net for the neural network disturbed by some noise the stochastic stability of the network is also analyzed a special asymmetric neural network formed by a closed chain of formal neurons is also studied for its stability and oscillation both stable and oscillatory dynamics are obtained in the closed chain network through the adjustment of the gains and resistances of the amplifiers

global exponential stability of competitive neural networks with different time scales the dynamics of cortical cognitive maps developed by self organization must include the aspects of long and short term memory the behavior of such a neural network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system we present a new method of analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance we are able to show the conditions under which the solutions of such a system are bounded being less restrictive than with the k monotone theory singular perturbation theory or those based on supervised synaptic learning we prove the existence and the uniqueness of the equilibrium a strict lyapunov function for the flow of a competitive neural system with different time scales is given and based on it we are able to prove the global exponential stability of the equilibrium point

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

continuous fields of c algebras arising from extensions of tensor c categories abstract the notion of extension of a given c category c by a c algebra a is introduced in the commutative case a c the objects of the extension category are interpreted as fiber bundles over of objects belonging to the initial category it is shown that the doplicher roberts algebra dr algebra in the following associated to an object in the extension of a strict tensor c category is a continuous field of dr algebras coming from the initial one in the case of the category of the hermitian vector bundles over the general result implies that the dr algebra of a vector bundle is a continuous field of cuntz algebras some applications to pimsner c algebras are given

equivariant comparison of quantum homogeneous spaces we consider the quantum homogeneous spaces of the q deformation of simply connected simple compact lie groups and their poisson lie quantum subgroups we prove the deformation invariance in the equivariant kk theory with respect to the translation action by maximal tori this extends a result of neshveyev and tuset to the equivariant setting as applications we prove the ring isomorphism of the k homology of gq with respect to the coproduct of c gq and an analogue of the borsuk ulam theorem for quantum spheres

equivalence between local exponential stability of the unique equilibrium point and global stability for hopfield type neural networks with two neurons fang and kincaid 1996 proposed an open problem about the relationship between the local stability of the unique equilibrium point and the global stability for a hopfield type neural network with continuously differentiable and monotonically increasing activation functions as a partial answer to the problem in the two neuron case it is proved that for each given specific interconnection weight matrix a hopfield type neural network has a unique equilibrium point which is also locally exponentially stable for any activation functions and for any other network parameters if and only if the network is globally asymptotically stable for any activation functions and for any other network parameters if the derivatives of the activation functions of the network are bounded then the network is globally exponentially stable for any activation functions and for any other network parameters

poincare duality for cuntz pimsner algebras abstract we present a new approach to poincare duality for cuntz pimsner algebras we provide sufficient conditions under which poincare self duality for the coefficient algebra of a hilbert bimodule lifts to poincare self duality for the associated cuntz pimsner algebra with these conditions in hand we can constructively produce fundamental classes in k theory for a wide range of examples we can also produce k homology fundamental classes for the important examples of cuntz krieger algebras following kaminker putnam and crossed products of manifolds by isometries and their non commutative analogues

absolute stability and complete synchronization in a class of neural fields models neural fields are an interesting option for modeling macroscopic parts of the cortex involving several populations of neurons like cortical areas two classes of neural field equations are considered voltage and activity based the spatio temporal behavior of these fields is described by nonlinear integro differential equations the integral term computed over a compact subset of mathbb r q q 1 2 3 involves space and time varying possibly nonsymmetric intracortical connectivity kernels contributions from white matter afferents are represented as external input sigmoidal nonlinearities arise from the relation between average membrane potentials and instantaneous firing rates using methods of functional analysis we characterize the existence and uniqueness of a solution of these equations for general homogeneous i e independent of the spatial variable and spatially locally homogeneous inputs in all cases we give sufficient conditions on the connectivity functions for the solutions to be absolutely stable that is to say asymptotically independent of the initial state of the field these conditions bear on some compact operators defined from the connectivity kernels the maximal slope of the sigmoids and the time constants used in describing the temporal shape of the postsynaptic potentials numerical experiments are presented to illustrate the theory to our knowledge this is the first time that such a complete analysis of the problem of the existence and uniqueness of a solution of these equations has been obtained another important contribution is the analysis of the absolute stability of these solutions more difficult but more general than the linear stability analysis which it implies the reason we have been able to complete this work is our use of the functional analysis framework and the theory of compact operators in a hilbert space which has allowed us to provide simple mathematical answers to some of the questions raised by modelers in neuroscience

identifying assembly maps in k and l theory in this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in k and l theory and c theory

exotic crossed products and the baum connes conjecture we study general properties of exotic crossed product functors and characterise those which extend to functors on equivariant c algebra categories based on correspondences we show that every such functor allows the construction of a descent in kk theory and we use this to show that all crossed products by correspondence functors of k amenable groups are kk equivalent we also show that for second countable groups the minimal exact morita compatible crossed product functor used in the new formulation of the baum connes conjecture by baum guentner and willett 4 extends to correspondences when restricted to separable g c algebras it therefore allows a descent in kk theory for separable systems

fibred coarse embedding into non positively curved manifolds and higher index problem abstract let x n 1 x n be the coarse disjoint union of a sequence of finite metric spaces with uniform bounded geometry in this paper we show that the coarse novikov conjecture holds for x if x admits a fibred coarse embedding into a simply connected complete riemannian manifold of non positive sectional curvature this includes a large class of expander graphs with geometric property t

exponential convergence of delayed dynamical systems we discuss some delayed dynamical systems investigating their stability and convergence we prove that under mild conditions these delayed systems are global exponential convergent

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension