weakly lefschetz symplectic manifolds for a symplectic manifold the harmonic cohomology of symplectic divisors introduced by donaldson 1996 and of the more general symplectic zero loci introduced by auroux 1997 are compared with that of its ambient space we also study symplectic manifolds satisfying a weakly lefschetz property that is the s lefschetz property in particular we consider the symplectic blow ups cp m of the complex projective space cp m along weakly lefschetz symplectic submanifolds m cp m as an application we construct for each even integer s 2 compact symplectic manifolds which are s lefschetz but not s 1 lefschetz

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

lichnerowicz jacobi cohomology in this paper we extend the notion of lichnerowicz poisson cohomology to jacobi manifolds we study the relation of the so called lichnerowicz jacobi cohomology with the basic de rham cohomology and the cohomology of the lie algebra of functions relative to the representation defined by the hamiltonian vector fields a natural pairing with the canonical homology is constructed the relation between the lichnerowicz poisson cohomology of a quantizable poisson manifold and the lichnerowicz jacobi cohomology of the total space of a prequantization bundle is obtained particular cases of cosymplectic contact and locally conformal symplectic manifolds are discussed finally the lichnerowicz jacobi cohomology of a non transitive example is studied

poisson homology in degree 0 for some rings of symplectic invariants abstract let g be a finite dimensional semi simple lie algebra h a cartan subalgebra of g and w its weyl group the group w acts diagonally on v h h as well as on c v the purpose of this article is to study the poisson homology of the algebra of invariants c v w endowed with the standard symplectic bracket to begin with we give general results about the poisson homology space in degree 0 denoted by hp 0 c v w in the case where g is of type b n c n or d n results which support alev s conjecture then we are focusing the interest on the particular cases of ranks 2 and 3 by computing the poisson homology space in degree 0 in the cases where g is of type b 2 so 5 d 2 so 4 then b 3 so 7 and d 3 a 3 so 6 sl 4 in order to do this we make use of a functional equation introduced by y berest p etingof and v ginzburg we recover by a different method the result established by j alev and l foissy according to which the dimension of hp 0 c v w equals 2 for b 2 then we calculate the dimension of this space and we show that it is equal to 1 for d 2 we also calculate it for the rank 3 cases we show that it is equal to 3 for b 3 c 3 and 1 for d 3 a 3

analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations abstract we consider elliptic operators associated with discrete groups of quantized canonical transformations in order to be able to apply results from algebraic index theory we define the localized algebraic index of the complete symbol of an elliptic operator with the help of a calculus of semiclassical quantized canonical transformations a version of egorov s theorem and a theorem on trace asymptotics for semiclassical fourier integral operators we show that the localized analytic index and the localized algebraic index coincide as a corollary we express the fredholm index in terms of the algebraic index for a wide class of groups in particular for finite extensions of abelian groups

long time behavior of a two phase optimal design for the heat equation we consider a two phase isotropic optimal design problem within the context of the transient heat equation the objective is to minimize the average of the dissipated thermal energy during a fixed time interval 0 t the time independent material properties are taken as design variables a full relaxation for this problem was established in a munch p pedregal and f periago j math pures appl 9 89 2008 pp 225 247 by using the homogenization method in this paper we study the asymptotic behavior as t goes to infinity of the solutions of the relaxed problem and prove that they converge to an optimal relaxed design of the corresponding two phase optimization problem for the stationary heat equation next we study necessary optimality conditions for the relaxed optimization problem under the transient heat equation and use those to characterize the microstructure of the optimal designs which appears in the form of a sequential laminate of rank at most n the spatial dimension an asymptotic analysis of the optimality conditions lets us prove that for t large enough the order of lamination is in fact of at most n 1 several numerical experiments in two dimensions complete our study

poisson co homology of polynomial poisson algebras in dimension four sklyanin s case abstract in this paper we compute the poisson co homology of a polynomial poisson structure given by two casimir polynomial functions which define a complete intersection with an isolated singularity

the number of synaptic inputs and the synchrony of large sparse neuronal networks the prevalence of coherent oscillations in various frequency ranges in the central nervous system raises the question of the mechanisms that synchronize large populations of neurons we study synchronization in models of large networks of spiking neurons with random sparse connectivity synchrony occurs only when the average number of synapses m that a cell receives is larger than a critical value mc below mc the system is in an asynchronous state in the limit of weak coupling assuming identical neurons we reduce the model to a system of phase oscillators that are coupled via an effective interaction in this framework we develop an approximate theory for sparse networks of identical neurons to estimate mc analytically from the fourier coefficients of our approach relies on the assumption that the dynamics of a neuron depend mainly on the number of cells that are presynaptic to it we apply this theory to compute mc for a model of inhibitory networks of integrate and fire i f neurons as a function of the intrinsic neuronal properties e g the refractory period tr the synaptic time constants and the strength of the external stimulus iext the number mc is found to be nonmonotonous with the strength of iext for tr 0 we estimate the minimum value of mc over all the parameters of the model to be 363 8 above mc the neurons tend to fire in smeared one cluster states at high firing rates and smeared two or more cluster states at low firing rates refractoriness decreases mc at intermediate and high firing rates these results are compared to numerical simulations we show numerically that systems with different sizes n behave in the same way provided the connectivity m is such that 1 meff 1 m 1 n remains constant when n varies this allows extrapolating the large n behavior of a network from numerical simulations of networks of relatively small sizes n 800 in our case we find that our theory predicts with remarkable accuracy the value of mc and the patterns of synchrony above mc provided the synaptic coupling is not too large we also study the strong coupling regime of inhibitory sparse networks all of our simulations demonstrate that increasing the coupling strength reduces the level of synchrony of the neuronal activity above a critical coupling strength the network activity is asynchronous we point out a fundamental limitation for the mechanisms of synchrony relying on inhibition alone if heterogeneities in the intrinsic properties of the neurons and spatial fluctuations in the external input are also taken into account

gerstenhaber algebras and bv algebras in poisson geometry the purpose of this paper is to establish an explicit correspondence between various geometric structures on a vector bundle with some well known algebraic structures such as gerstenhaber algebras and bv algebras some applications are discussed in particular we find an explicit connection between the koszul brylinski operator and the modular class of a poisson manifold as a consequence we prove that poisson homology is isomorphic to poisson cohomology for unimodular poisson structures

equivariant lefschetz number of differential operators let g be a compact lie group acting on a compact complex manifold m by holomorphic transformations we prove a trace density formula for the g lefschetz number of a holomorphic differential operator on m we generalize the recent results of engeli and the first author to orbifolds

cross correlations in high conductance states of a model cortical network neuronal firing correlations are studied using simulations of a simple network model for a cortical column in a high conductance state with dynamically balanced excitation and inhibition although correlations between individual pairs of neurons exhibit considerable heterogeneity population averages show systematic behavior when the network is in a stationary state the average correlations are generically small correlation coefficients are of order 1 n where n is the number of neurons in the network however when the input to the network varies strongly in time much larger values are found in this situation the network is out of balance and the synaptic conductance is low at times when the strongest firing occurs however examination of the correlation functions of synaptic currents reveals that after these bursts balance is restored within a few milliseconds by a rapid increase in inhibitory synaptic conductance these findings suggest an extension of the notion of the balanced state to include balanced fluctuations of synaptic currents with a characteristic timescale of a few milliseconds

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

generalized double affine hecke algebras of rank 1 and quantized del pezzo surfaces abstract let d be a simply laced dynkin diagram of rank r whose affinization has the shape of a star i e d 4 e 6 e 7 e 8 to such a diagram one can attach a group g whose generators correspond to the legs of the affinization have orders equal to the leg lengths plus 1 and the product of the generators is 1 the group g is then a 2 dimensional crystallographic group g z l z 2 where l is 2 3 4 and 6 respectively in this paper we define a flat deformation h t q of the group algebra c g of this group by replacing the relations saying that the generators have prescribed orders by their deformations saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots which are deformation parameters the algebra h t q for d 4 is the cherednik algebra of type c c 1 which was studied by noumi sahi and stokman and controls askey wilson polynomials we prove that h t q is the universal deformation of the twisted group algebra of g and that this deformation is compatible with certain filtrations on c g we also show that if q is a root of unity then for generic t the algebra h t q is an azumaya algebra and its center is the function algebra on an affine del pezzo surface for generic q the spherical subalgebra e h t q e provides a quantization of such surfaces we also discuss connections of h t q with preprojective algebras and painleve vi

a master equation formalism for macroscopic modeling of asynchronous irregular activity states many efforts have been devoted to modeling asynchronous irregular ai activity states which resemble the complex activity states seen in the cerebral cortex of awake animals most of models have considered balanced networks of excitatory and inhibitory spiking neurons in which ai states are sustained through recurrent sparse connectivity with or without external input in this letter we propose a mesoscopic description of such ai states using master equation formalism we derive a second order mean field set of ordinary differential equations describing the temporal evolution of randomly connected balanced networks this formalism takes into account finite size effects and is applicable to any neuron model as long as its transfer function can be characterized we compare the predictions of this approach with numerical simulations for different network configurations and parameter spaces considering the randomly connected network as a unit this approach could be used to build large scale networks of such connected units with an aim to model activity states constrained by macroscopic measurements such as voltage sensitive dye imaging

estimation of sparse nonnegative sources from noisy overcomplete mixtures using map in this letter we propose a new algorithm for estimating sparse nonnegative sources from a set of noisy linear mixtures in particular we consider difficult situations with high noise levels and more sources than sensors underdetermined case we show that when sources are very sparse in time and overlapped at some locations they can be recovered even with very low signal to noise ratio and by using many fewer sensors than sources a theoretical analysis based on bayesian estimation tools is included showing strong connections with algorithms in related areas of research such as ica nmf focuss and sparse representation of data with overcomplete dictionaries our algorithm uses a bayesian approach by modeling sparse signals through mixed state random variables this new model for priors imposes l0 norm based sparsity we start our analysis for the case of nonoverlapped sources 1 sparse which allows us to simplify the search of the posterior maximum avoiding a combinatorial search general algorithms for overlapped cases such as 2 sparse and k sparse sources are derived by using the algorithm for 1 sparse signals recursively additionally a combination of our map algorithm with the nn ksvd algorithm is proposed for estimating the mixing matrix and the sources simultaneously in a real blind fashion a complete set of simulation results is included showing the performance of our algorithm

hard lefschetz theorem for sasakian manifolds we prove that on a compact sasakian manifold m g of dimension 2n 1 for any 0 p n the wedge product with d defines an isomorphism between the spaces of harmonic forms n p m and n p 1 m therefore it induces an isomorphism between the de rham cohomology spaces h m and h m such isomorphism is proven to be independent of the choice of a compatible sasakian metric on a given contact manifold as a consequence an obstruction for a contact manifold to admit sasakian structures is found

quasiconvexification in 3 d for a variational reformulation of an optimal design problem in conductivity abstract we analyze a typical 3 d conductivity problem which consists in seeking the optimal layout of two materials in a given design domain r 3 by minimizing the l 2 norm of the electric field under a constraint on the amount on each material that we can use we utilize a characterization of the 3 d divergence free vector fields which is especially appropriate for a variational reformulation by using gradient young measures as a main tool we can give an explicit form of the constrained quasiconvexification of the cost density this result is similar to the one in the 2 d situation however the characterization of the divergence free vector fields introduces a certain nonlinearity in the problem that needs to be addressed properly

an algebraic index theorem for orbifolds abstract using the concept of a twisted trace density on a cyclic groupoid a trace is constructed on a formal deformation quantization of a symplectic orbifold an algebraic index theorem for orbifolds follows as a consequence of a local riemann roch theorem for such densities in the case of a reduced orbifold this proves a conjecture by fedosov schulze and tarkhanov finally it is shown how the kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem

optimal design in conductivity under locally constrained heat flux this paper addresses the relaxation of an optimal design problem in conductivity under a point wise constraint on the heat flux by using a variational approach developed by the authors in a previous work we obtained a complete relaxation involving the explicit computation of constrained quasiconvex envelopes this relaxed formulation turns out to be very simple in the remarkable compliance case for which numerical simulations are performed those simulations show that our approach and results are interesting from a theoretical point of view as well as from a practical perspective the emphasis of our work is placed on the local constraint on the heat flux which seems to be a new ingredient for this kind of optimal design problems

uniqueness of multiplicative determinants on elliptic pseudodifferential operators we describe all multiplicative determinants on the pathwise connected component of identity in the group of invertible classical pseudodifferential operators on a closed manifold that are continuous along continuous paths and the restriction to zero order operators of which is of class c1 this boils down to a description of all traces on zero order classical pseudodifferential operators which turn out to be linear combinations of the wodzicki residue w and leading symbol traces introduced in pr1 both of which are continuous consequently multiplicative determinants are parametrized by the residue determinant w87 sc and a new leading symbol determinant both of which are expressed in terms of a homogeneous component of the symbol of the logarithm of the operator

optimal design via variational principles the three dimensional case the analysis of some three dimensional optimal design problems leads us to study variational principles under curl free and divergence free constraints simultaneously we explicitly exploit the relationship between curl free and div free restrictions in order to take advantage of the accumulated experience in the classical curl case by the introduction of potentials our discussion takes place in the three dimensional situation this is a first contribution in the sense that we only deal with the most basic issues

homology of algebras of families of pseudodifferential operators abstract we compute the hochschild cyclic and periodic cyclic homology groups of algebras of families of laurent complete symbols on manifolds with corners we show in particular that the spectral sequence associated with hochschild homology degenerates at e 2 and converges to hochschild homology as a byproduct we identify the space of residue traces on fibrations by manifolds with corners in the process we prove some structural results about algebras of complete symbols on manifolds with corners

space time topology optimization for one dimensional wave propagation abstract a space time extension of the topology optimization method is presented the formulation with design variables in both the spatial and temporal domains is used to create structures with an optimized distribution of material properties that can vary in time the method is outlined for one dimensional transient wave propagation in an elastic rod with time dependent young s modulus by two simulation examples it is demonstrated how dynamic structures can display rich dynamic behavior such as wavenumber frequency shifts and lack of energy conservation the optimization method s potential for creating structures with novel dynamic behavior is illustrated by a simple example it is shown that an elastic rod in which the optimized stiffness distribution is allowed to vary in time can be much more efficient in prohibiting wave propagation compared to a static bandgap structure optimized designs in form of spatio temporal laminates and checkerboards are generated and discussed the example lays the foundation for creating designs with more advanced functionalities in future work

hochschild lefschetz class for mathcal d modules we introduce a notion of hochschild lefschetz class for a good coherent mathcal d module on a compact complex manifold and prove that this class is compatible with the direct image functor we prove an orbifold riemann roch formula for a mathcal d module on a compact complex orbifold

the effects of pair wise and higher order correlations on the firing rate of a postsynaptic neuron coincident firing of neurons projecting to a common target cell is likely to raise the probability of firing of this postsynaptic cell therefore synchronized firing constitutes a significant event for postsynaptic neurons and is likely to play a role in neuronal information processing physiological data on synchronized firing in cortical networks are based primarily on paired recordings and cross correlation analysis however pair wise correlations among all inputs onto a postsynaptic neuron do not uniquely determine the distribution of simultaneous postsynaptic events we develop a framework in order to calculate the amount of synchronous firing that based on maximum entropy should exist in a homogeneous neural network in which the neurons have known pair wise correlations and higher order structure is absent according to the distribution of maximal entropy synchronous events in which a large proportion of the neurons participates should exist even in the case of weak pair wise correlations network simulations also exhibit these highly synchronous events in the case of weak pair wise correlations if such a group of neurons provides input to a common postsynaptic target these network bursts may enhance the impact of this input especially in the case of a high postsynaptic threshold the proportion of neurons participating in synchronous bursts can be approximated by our method under restricted conditions when these conditions are not fulfilled the spike trains have less than maximal entropy which is indicative of the presence of higher order structure in this situation the degree of synchronicity cannot be derived from the pair wise correlations

homologie des invariants d une algebre de weyl sous l action d un groupe fini resume soit g un sous groupe fini de sp 2 n c operant par automorphismes dans l algebre de weyl a n c nous calculons les groupes d homologie et de cohomologie de hochschild de l algebre d invariants a n c g let g be a finite subgroup of sp 2 n c acting by automorphisms in the weyl algebra a n c we compute the hochschild homology and cohomology groups of the invariant algebra a n c g

higher order statistics of input ensembles and the response of simple model neurons pairwise correlations among spike trains recorded in vivo have been frequently reported it has been argued that correlated activity could play an important role in the brain because it efficiently modulates the response of a postsynaptic neuron we show here that a neuron s output firing rate critically depends on the higher order statistics of the input ensemble we constructed two statistical models of populations of spiking neurons that fired with the same rates and had identical pairwise correlations but differed with regard to the higher order interactions within the population the first ensemble was characterized by clusters of spikes synchronized over the whole population in the second ensemble the size of spike clusters was on average proportional to the pairwise correlation for both input models we assessed the role of the size of the population the firing rate and the pairwise correlation on the output rate of two simple model neurons a continuous firing rate model and a conductance based leaky integrate and fire neuron an approximation to the mean output rate of the firing rate neuron could be derived analytically with the help of shot noise theory interestingly the essential features of the mean response of the two neuron models were similar for both neuron models the three input parameters played radically different roles with respect to the postsynaptic firing rate depending on the interaction structure of the input for instance in the case of an ensemble with small and distributed spike clusters the output firing rate was efficiently controlled by the size of the input population in addition to the interaction structure the ratio of inhibition to excitation was found to strongly modulate the effect of correlation on the postsynaptic firing rate

a spatio temporal design problem for a damped wave equation we analyze in this work a spatio temporal optimal design problem governed by a linear damped one dimensional wave equation the problem consists of simultaneously seeking the spatio temporal layout of two isotropic materials and the static position of the damping set in order to minimize a functional depending quadratically on the gradient of the state the lack of classical solutions for this kind of nonlinear problem is well known we examine a well posed relaxation by using the representation of a two dimensional divergence free vector as a rotated gradient we transform the original optimal design problem into a nonconvex vector variational problem by means of gradient young measures we compute an explicit form of the constrained quasi convexification of the cost density moreover this quasi convexification is recovered by first order laminates which give the optimal distribution of materials and damping set at every point finally we analyze the relaxed problem and some numerical experiments ar

optimal shape and position of the actuators for the stabilization of a string abstract the energy in a string subject to constant viscous damping k on a subset of length l 0 decays exponentially in time we consider the problem of optimizing the decay rate for the which are the unions of at most n intervals this rate is given by the spectral abscissa of the linear operator associated to the wave equation we are interested in small values of k therefore we consider the derivative of the spectral abscissa at k 0 we prove that except for the case l 1 2 when the number of intervals is not fixed a priori an optimal domain does not exist we study numerically the case of one or two intervals using a genetic algorithm these numerical results are not intuitive in particular the optimal position of one interval is never at the middle of the string

on the topological derivative in shape optimization in this paper the topological derivative for an arbitrary shape functional is defined examples are provided for elliptic equations and the elasticity system in the plane the topological derivative can be used for solving shape optimization problems in structural mechanics

examples of non kahler hamiltonian circle manifolds with the strong lefschetz property abstract in this paper we construct six dimensional compact non kahler hamiltonian circle manifolds which satisfy the strong lefschetz property themselves but nevertheless have a non lefschetz symplectic quotient this provides the first known counterexamples to the question whether the strong lefschetz property descends to the symplectic quotient we also give examples of hamiltonian strong lefschetz circle manifolds which have a non lefschetz fixed point submanifold in addition we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong lefschetz manifold we then use it to show the existence of lefschetz four manifolds with non lefschetz finite covering spaces

explicit computation of the relaxed density coming from a three dimensional optimal design problem we analyze the relaxation of a typical three dimensional optimal design problem in conductivity consisting of minimizing the square of the l2 norm of the underlying electric potential under a volume constraint via a variational reformulation of the problem our main achievement is the explicit characterization of the constrained quasiconvexification of the cost density

cyclic cocycles on deformation quantizations and higher index theorems abstract we construct a nontrivial cyclic cocycle on the weyl algebra of a symplectic vector space using this cyclic cocycle we construct an explicit local quasi isomorphism from the complex of differential forms on a symplectic manifold to the complex of cyclic cochains of any formal deformation quantization thereof we give a new proof of nest tsygan s algebraic higher index theorem by computing the pairing between such cyclic cocycles and the k theory of the formal deformation quantization furthermore we extend this approach to derive an algebraic higher index theorem on a symplectic orbifold as an application we obtain the analytic higher index theorem of connes moscovici and its extension to orbifolds

lyapunov optimization of a damped system our aim is to optimize the damping of a linear vibrating system the penalty function is the average total energy which is equal to the trace of the corresponding lyapunov solution we prove the existence and the uniqueness of the global minimum if the damping varies over the set of all possible positive definite matrices the minimum is shown to be taken on the so called modal critical damping thus confirming a long existing conjecture we also give some preliminary results concerning dampings which depend linearly on the viscosity parameters whereas the damper positions are kept fixed we produce physical examples on which the minimum is taken on a negative viscosity or which have several local minima both phenomena seem to be a consequence of a bad choice of the damper positions

algebraic index theorem we prove the atiyah singer index theorem where the algebra of pseudodifferential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold

chaotic balanced state in a model of cortical circuits the nature and origin of the temporal irregularity in the electrical activity of cortical neurons in vivo are not well understood we consider the hypothesis that this irregularity is due to a balance of excitatory and inhibitory currents into the cortical cells we study a network model with excitatory and inhibitory populations of simple binary units the internal feedback is mediated by relatively large synaptic strengths so that the magnitude of the total excitatory and inhibitory feedback is much larger than the neuronal threshold the connectivity is random and sparse the mean number of connections per unit is large though small compared to the total number of cells in the network the network also receives a large temporally regular input from external sources we present an analytical solution of the mean field theory of this model which is exact in the limit of large network size this theory reveals a new cooperative stationary state of large networks which we term a balanced state in thi

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

optimal design of the damping set for the stabilization of the wave equation abstract we consider the problem of optimizing the shape and position of the damping set for the internal stabilization of the linear wave equation in r n n 1 2 in a first theoretical part we reformulate the problem into an equivalent non convex vector variational one using a characterization of divergence free vector fields then by means of gradient young measures we obtain a relaxed formulation of the problem in which the original cost density is replaced by its constrained quasi convexification this implies that the new relaxed problem is well posed in the sense that there exists a minimizer and in addition the infimum of the original problem coincides with the minimum of the relaxed one in a second numerical part we address the resolution of the relaxed problem using a first order gradient descent method we present some numerical experiments which highlight the influence of the over damping phenomena and show that for large values of the damping potential the original problem has no minimizer we then propose a penalization technique to recover the minimizing sequences of the original problem from the optimal solution of the relaxed one

the high conductance state of cortical networks we studied the dynamics of large networks of spiking neurons with conductance based nonlinear synapses and compared them to networks with current based linear synapses for systems with sparse and inhibition dominated recurrent connectivity weak external inputs induced asynchronous irregular firing at low rates membrane potentials fluctuated a few millivolts below threshold and membrane conductances were increased by a factor 2 to 5 with respect to the resting state this combination of parameters characterizes the ongoing spiking activity typically recorded in the cortex in vivo many aspects of the asynchronous irregular state in conductance based networks could be sufficiently well characterized with a simple numerical mean field approach in particular it correctly predicted an intriguing property of conductance based networks that does not appear to be shared by current based models they exhibit states of low rate asynchronous irregular activity that persist for some period of time even in the absence of external inputs and without cortical pacemakers simulations of larger networks up to 350 000 neurons demonstrated that the survival time of self sustained activity increases exponentially with network size

nambu jacobi and generalized jacobi manifolds the geometry of nambu jacobi and generalized jacobi manifolds is studied a large collection of examples is given the characteristic distribution generated by the hamiltonian vector fields on a nambu jacobi manifold is proved to be completely integrable and the induced geometrical structure of the leaves of the corresponding generalized foliation is ellucidated

the graded jacobi algebras and co homology jacobi algebroids i e jacobi versions of lie algebroids are studied in the context of graded jacobi brackets on graded commutative algebras this unifies various concepts of graded lie structures in geometry and physics a method of describing such structures by classical lie algebroids via certain gauging in the spirit of e witten s gauging of the exterior derivative is developed one constructs a corresponding cartan differential calculus graded commutative one in a natural manner this in turn gives canonical generating operators for triangular jacobi algebroids one gets in particular the lichnerowicz jacobi homology operators associated with classical jacobi structures courant jacobi brackets are obtained in a similar way and used to define an abstract notion of a courant jacobi algebroid and dirac jacobi structure

optimal design of multiphase composites under elastodynamic loading abstract an algorithm is proposed to optimize the performance of multiphase structures composites under elastodynamic loading conditions the goal is to determine the distribution of material in the structure such that the time averaged total stored energy of structure is minimized a penalization strategy is suggested to avoid the checkerboard instability simultaneously to generate near 0 1 topologies as a result of this strategy the solutions of presented algorithm are sufficiently smooth and possess the regularity of h 1 function space a simple method for the continuum adjoint sensitivity analysis of the corresponding pde constrained optimization problem is presented it is general and can be easily applied to a wide range of alternative problems the success of the introduced algorithm is studied by numerical experiments on two dimensional model problems for different numbers of phases according to numerical results the objective functional is reduced monotonically with iterations moreover the final topologies at the optimal solutions are near 0 1 the dynamic behavior of optimal designs is compared to that of initial ones to show the impact of optimization on the performance of structures

optimal internal stabilization of the linear system of elasticity we address the non linear optimal design problem which consists in finding the best position and shape of a feedback damping mechanism for the stabilization of the linear system of elasticity non existence of classical designs are related to the over damping phenomenon therefore by means of young measures a relaxation of the original problem is proposed due to the vector character of the elasticity system the relaxation is carried out through div curl young measures which let the analysis be direct and the dimension independent finally the relaxed problem is solved numerically and a penalization technique to recover quasi optimal classical designs from the relaxed ones is implemented in several numerical experiments