uniform logarithmic sobolev inequalities for conservative spin systems with super quadratic single site potential we consider a noninteracting unbounded spin system with conservation of the mean spin we derive a uniform logarithmic sobolev inequality lsi provided the single site potential is a bounded perturbation of a strictly convex function the scaling of the lsi constant is optimal in the system size the argument adapts the two scale approach of grunewald villani westdickenberg and the second author from the quadratic to the general case using an asymmetric brascamp lieb type inequality for covariances we reduce the task of deriving a uniform lsi to the convexification of the coarse grained hamiltonian which follows from a general local cramer theorem

transference principles for log sobolev and spectral gap with applications to conservative spin systems we obtain new principles for transferring log sobolev and spectral gap inequalities from a source metric measure space to a target one when the curvature of the target space is bounded from below as our main application we obtain explicit estimates for the log sobolev and spectral gap constants of various conservative spin system models consisting of non interacting and weakly interacting particles constrained to conserve the mean spin when the self interaction is a perturbation of a strongly convex potential this partially recovers and partially extends previous results of caputo chafai grunewald landim lu menz otto panizo villani westdickenberg and yau when the self interaction is only assumed to be non strongly convex as in the case of the two sided exponential measure we obtain sharp estimates on the system s spectral gap as a function of the mean spin independently of the size of the system

the logarithmic sobolev inequality for discrete spin systems on a lattice for finite range lattice gases with a finite spin space it is shown that the dobrushin shlosman mixing condition is equivalent to the existence of a logarithmic sobolev inequality for the associated unique gibbs state in addition implications of these considerations for the ergodic properties of the corresponding glauber dynamics are examined

from concentration to logarithmic sobolev and poincare inequalities abstract we give a new proof of the fact that gaussian concentration implies the logarithmic sobolev inequality when the curvature is bounded from below and also that exponential concentration implies poincare inequality under null curvature condition our proof holds on non smooth structures such as length spaces and provides a universal control of the constants we also give a new proof of the equivalence between dimension free gaussian concentration and talagrand s transport inequality

synchronization of ts fuzzy complex dynamical networks with time varying impulsive delays and stochastic effects in this paper global exponential synchronization of takagi sugeno ts fuzzy complex dynamical networks with multiple time varying delays and stochastic perturbations is studied via delayed impulsive distributed control both impulsive and continuous parts of the fuzzy model have different multiple time varying delays which make the considered model general and practical a novel lemma on exponential stability of impulsive delayed differential equations was established in which the impulsive functions exhibit multiple time varying delays by utilizing the proposed lemma lyapunov functions the stochastic analysis techniques and the kronecker product general criteria ensuring global exponential synchronization in mean square of the addressed ts fuzzy complex networks are obtained moreover the theory of function minimum value is utilized to reduce the conservativeness of the obtained synchronization criteria which also makes them simple and easy to be verified in practical applications results of this paper improve and extend some existing ones numerical simulations including small world network coupled with time delayed lorenz system are given to show the effectiveness of the theoretical results

quantitative stability of the entropy power inequality we establish quantitative stability results for the entropy power inequality epi specifically we show that if uniformly log concave densities nearly saturate the epi then they must be close to gaussian densities in the quadratic kantorovich wasserstein distance furthermore if one of the densities is gaussian and the other is log concave or more generally has positive spectral gap then the deficit in the epi can be controlled in terms of the l 1 kantorovich wasserstein distance or relative entropy respectively as a counterpoint an example shows that the epi can be unstable with respect to the quadratic kantorovich wasserstein distance when densities are uniformly log concave on sets of measure arbitrarily close to one our stability results can be extended to non log concave densities provided certain regularity conditions are met the proofs are based on mass transportation

isoperimetric and analytic inequalities for log concave probability measures we discuss an approach based on the brunn minkowski inequality to isoperimetric and analytic inequalities for probability measures on euclidean space with logarithmically concave densities in particular we show that such measures have positive isoperimetric constants in the sense of cheeger and thus always share poincare type inequalities we then describe those log concave measures which satisfy isoperimetric inequalities of gaussian type the results are precised in dimension 1

control design for fuzzy systems based on relaxed nonquadratic stability and h_ infty performance conditions in this paper new approaches to hinfin controller design for a class of discrete time nonlinear fuzzy systems are proposed based on a relaxed approach in which basis dependent lyapunov functions are used first two relaxed conditions of nonquadratic stability with h infin norm bound are presented for this class of systems the two relaxed conditions are shown to be useful in designing fuzzy control systems by introducing some additional instrumental matrix variables the two relaxed conditions are used to develop hinfin controllers in the control design the first relaxed condition has fewer inequality constraints but only admits a common additional matrix variable while the second one can admit multiple additional matrix variables finally two examples are given to demonstrate the applicability of the proposed approach

synchronization of chaotic systems from a fuzzy regulation approach in this paper some results on fuzzy regulation and fuzzy modeling are presented for synchronization of chaotic systems described by takagi sugeno ts fuzzy models using linear local controllers it is shown that the synchronization error is bounded if the local controller can be appropriately designed and that such an error is independent of initial conditions this feature allows synchronizing not only similar chaotic systems but under certain conditions different chaotic systems can be synchronized as well in other words this approach can be used to obtain either complete or generalized synchronization several simulations are carried out to illustrate how the problem can be solved in a practical way by using the linear matrix inequalities lmi technique

lsi for kawasaki dynamics with weak interaction we consider a large lattice system of unbounded continuous spins that are governed by a ginzburg landau type potential and a weak quadratic interaction we derive the logarithmic sobolev inequality lsi for kawasaki dynamics uniform in the boundary data the scaling of the lsi constant is optimal in the system size and our argument is independent of the geometric structure of the system the proof consists of an application of the two scale approach of grunewald otto westdickenberg villani several ideas are needed to solve new technical difficulties due to the interaction let us mention the application of a new covariance estimate a conditioning technique and a generalization of the local cramer theorem

second order poincare inequalities and clts on wiener space we prove infinite dimensional second order poincare inequalities on wiener space thus closing a circle of ideas linking limit theorems for functionals of gaussian fields stein s method and malliavin calculus we provide two applications i to a new second order characterization of clts on a fixed wiener chaos and ii to linear functionals of gaussian subordinated fields

fuzzy shortest path problems incorporating interactivity among paths abstract this paper deals with a shortest path problem on a network in which a fuzzy number instead of a real number is assigned to each arc length such a problem is ill posed because each arc cannot be identified as being either on the shortest path or not therefore based on the possibility theory we introduce the concept of degree of possibility that an arc is on the shortest path every pair of distinct paths from the source node to any other node is implicitly assumed to be noninteractive in the conventional approaches this assumption is unrealistic and involve inconsistencies to overcome this drawback we define a new comparison index between the sum of fuzzy numbers by considering interactivity among fuzzy numbers an algorithm is presented to determine the degree of possibility for each arc on a network finally this algorithm is evaluated by means of large scale numerical examples consequently we can find this approach is efficient even for real world practical networks

the fuzzy discrete time robust regulation problem an lmi approach this paper is concerned with the design of a robust regulator capable of achieving trajectory tracking for discrete time nonlinear systems under parameter uncertainty by assuming that the behavior of the nonlinear system is described at least locally by a takagi sugeno dynamic fuzzy model an approach based in the combination of this fuzzy modeling and the regulator theory is presented conditions for the existence of a robust regulator under this approach are then derived and extended to include the use of the linear matrix inequality lmi technique

the shortest path problem with discrete fuzzy arc lengths in the past the fuzzy shortest path problem in a network has attracted attention from many researchers for its importance to various applications in this paper we propose a new algorithm to deal with the fuzzy shortest path problem it is composed of fuzzy shortest path length procedure and similarity measure the former is presented to determine the fuzzy shortest path length from source node to the destination node in the network and the latter is used to measure the similarity degree between fuzzy length sets this algorithm not only can yield shortest length but also can offer the actual shortest path to decision makers an illustrative example is also included to demonstrate our proposed algorithm

an isoperimetric inequality for uniformly log concave measures and uniformly convex bodies abstract we prove an isoperimetric inequality for the uniform measure on a uniformly convex body and for a class of uniformly log concave measures that we introduce these inequalities imply up to universal constants the log sobolev inequalities proved by bobkov ledoux s g bobkov m ledoux from brunn minkowski to brascamp lieb and to logarithmic sobolev inequalities geom funct anal 10 5 2000 1028 1052 and the isoperimetric inequalities due to bakry ledoux d bakry m ledoux levy gromov s isoperimetric inequality for an infinite dimensional diffusion generator invent math 123 2 1996 259 281 and bobkov zegarlinski s g bobkov b zegarlinski entropy bounds and isoperimetry mem amer math soc 176 829 2005 x 69 we also recover a concentration inequality for uniformly convex bodies similar to that proved by gromov milman m gromov v d milman generalization of the spherical isoperimetric inequality to uniformly convex banach spaces compos math 62 3 1987 263 282

isoperimetric constants for product probability measures a dimension free lower bound is found for isoperimetric constants of product probability measures from this some analytic inequalities are derived

fuzzy optimal search methods abstract this paper gives analytical approaches and algorithms for decision tree search techniques the decision trees are assumed to have a fixed number of stages and predefined possible states at every stage the costs of traversing the tree are characterized as approximate and defined as fuzzy numbers two search methods each drawing from an existing non fuzzy search algorithm are described the first method is a dynamic programming search where the principle of optimality with fuzzy costs is addressed the second method is an a search for which the notion of a lower bound estimate of costs is utilized to increase the efficiency of the search algorithms for each method are included theorems and proofs which complete the analytical development of these techniques are also included finally a numerical example illustrating the procedure is given

the behavior of the specific entropy in the hydrodynamic scaling limit the paper studies the behavior of the specific entropyfor onedimensional simple exclusion processes under the hydrodynamic scaling of time and space it is shown that if the initial configurations possess a macroscopic profile then for each positive macroscopic time the specific microscopic entropyconverges to the macroscopic entropy the latter is defined in terms of the solution of the corresponding hydrodynamic equation 1 introduction the paper concerns simple exclusion models on the periodic integer lattice the symmetric simple exclusion process is reversible and we studyit under diffusive parabolic scaling of time and space the corresponding hydrodynamic equation describing the behavior of the limiting macroscopic densityis the heat equation it has smooth solutions uniquely defined bythe initial data asy mmetric simple exclusion models are nonreversible and require euler hyperbolic scaling which leads to inviscid burgers type equations solutions of such equations are not unique and may develop shocks relevant solutions are known to be the entropic solutions of these equations we studythe behavior of the microscopic entropyrelative to uniform measures and to local gibbs measures in words a version of the main result can be stated as follows let the initial configurations be deterministic and possess a macroscopic profile then under the appropriate scaling of time and space for anypositive macroscopic time the specific microscopic entropyconverges to the macroscopic entropycalculated from the relevant solution of the hydrodynamic equation the main emphasis is placed on the asymmetric case when the solution of the hydrodynamic equation develops shocks and the macroscopic entropy is lost at each shock our results show that in the scaling limit the particle system closely follows the hydrodynamic equation and loses the same amount of the specific entropyat the same macroscopic time the keyidea of this paper is presented in lemma a 1 it is a rather general statement which could be adopted for applications to other models one of the important ingredients of the proof of lemma a 1 is the logarithmic sobolev inequality theorem a 1 let us stress that we do not need an estimate on the constant in the logarithmic sobolev inequality the main difficulty in apply ing

fuzzy intersection graphs abstract this paper extends the use of graphs to the modelling of systems under unceertainty when random assumptions do not adequately hold the paper includes the theoretical and computational aspects which are derived from the matrix representation of fuzzy intersection graphs their ability for applications is also discussed

entropy jumps in the presence of a spectral gap it is shown that if x is a random variable whose density satisfies a poincare inequality and y is an independent copy of x then the entropy of x y p 2 is greater than that of x by a fixed fraction of the entropy gap between x and the gaussian of the same variance the argument uses a new formula for the fisher information of a marginal which can be viewed as a local reverse form of the brunn minkowski inequality in its functional form due to prekopa and leindler

the first variation of the total mass of log concave functions and related inequalities abstract on the class of log concave functions on r n endowed with a suitable algebraic structure we study the first variation of the total mass functional which corresponds to the volume of convex bodies when restricted to the subclass of characteristic functions we prove some integral representation formulae for such a first variation which suggest to define in a natural way the notion of area measure for a log concave function in the same framework we obtain a functional counterpart of minkowski s first inequality for convex bodies as corollaries we derive a functional form of the isoperimetric inequality and a family of logarithmic type sobolev inequalities with respect to log concave probability measures finally we propose a suitable functional version of the classical minkowski s problem for convex bodies and prove some partial results towards its solution

rogers shephard inequality for log concave functions abstract in this paper we prove different functional inequalities extending the classical rogers shephard inequalities for convex bodies the original inequalities provide an optimal relation between the volume of a convex body and the volume of several symmetrizations of the body such as its difference body we characterize the equality cases in all these inequalities our method is based on the extension of the notion of a convolution body of two convex sets to any pair of log concave functions and the study of some geometrical properties of these new sets

extremal properties of half spaces for log concave distributions n w x n where m s m m is the product measure in r d s y1 1 is the n n dimensional cube in r n and the infimum is then over all borel measurable n n sets a r of measure m a g p 0 p 1 h 0 we are searching for necessary and sufficent conditions under which the n 4 infimum in 1 1 is attained at the half spaces a s x g r x f c of 1 measure p for all p and h the half spaces of this form will be called standard in these notes we give such conditions in the case where m is log concave there exists the following probabilistic consequence of the above property if z z are independent random variables on some probability space 1 n v i p with common distribution m consider a family of random variables s t indexed by a set t and formed by linear combinations n s t s a t z i i is1 where the coefficients a are arbitrary functions on t such that i n s s sup a t f 1 1 i t is1 set m s sup s t then the extremal property of the standard half spaces in t

logarithmic sobolev inequalities and exponential integrability we prove the exponential integrability of lipschitz functions in abstract wiener spaces by using logarithmic sobolev inequalities we introduce two notions of lipschitz continuity and apply the method of davis and simon j funct anal 59 1984 335 395 to prove our main theorem moreover we give several conditions under which the function is exponentially integrable

h filtering of discrete time fuzzy systems via basis dependent lyapunov function approach this paper is concerned with the h filtering problem for a class of discrete time fuzzy systems attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the h sense by using basis dependent lyapunov functions sufficient conditions for the solvability of this problem are obtained it has been shown that the h filtering problem can be solved as a linear matrix inequality lmi optimization problem two examples are provided to demonstrate the applicability of the proposed approach

spectral gap and logarithmic sobolev inequality for kawasaki and glauber dynamics we prove that the spectral gap of the kawasaki dynamics shrink at the rate of 1 l2 for cubes of sizel provided that some mixing conditions are satisfied we also prove that the logarithmic sobolev inequality for the glauber dynamics in standard cubes holds uniformly in the size of the cube if the dobrushin shlosman mixing condition holds for standard cubes

bounds on variance for unimodal distributions we show a direct relationship between the variance and the differential entropy for subclasses of symmetric and asymmetric unimodal distributions by providing an upper bound on variance in terms of entropy power combining this bound with the well known entropy power lower bound on variance we prove that the variance of the appropriate subclasses of unimodal distributions can be bounded below and above by the scaled entropy power as the differential entropy decreases the variance is sandwiched between two exponentially decreasing functions in the differential entropy this establishes that for the subclasses of unimodal distributions the differential entropy can be used as a surrogate for concentration of the distribution

fuzzy logic in commercial expert system results and prospects abstract this paper surveys the use of fuzzy methods in commercial applications of the technology of expert systems and in commercial products which aim to support such applications it attempts to evaluate the utility of such an approach to uncertainty management compared to other well known methods of handling uncertainty in expert systems starting from this base it attempts an evaluation of the prospects for fuzzy expert systems in the medium term as a survey it attempts to list applications and commercial products as comprehensively as is practical and includes an extensive bibliography on the topic

on the ergodic properties of glauber dynamics we show that if there is an infinite volume gibbs measure which satisfies a logarithmic sobolev inequality with local coefficients of moderate growth then the corresponding stochastic dynamics decays to equilibrium exponentially fast in the uniform norm

a way to exploit the fractional stability domain for robust chaos suppression and synchronization via lmis this work is concerned with chaos suppression and synchronization of commensurate fractional systems with order q 0 both certain and uncertain under the riemann liouville definition it is shown that the use of convex structures to exactly rewrite nonlinear expressions allows controller design to systematically exploit the fractional order stability domain via linear matrix inequalities which are efficiently solved via convex optimization techniques exploiting the fractional order domain proves to be advantageous since it is always larger than the integer order counterpart the proposed approach is compared with former results on the subject in order to test its improvements as well as its limitations

job search and employment abstract a multistage search method based on fuzzy preference is used to analyze the processes of job search an employment decision based on fuzzy preference results in an exact choice the incorporation of fuzzy interval preference into employment decision however may lead to multiple choices which provides a theoretical justification for the existence of fuzzy supply of labor thus fuzziness in addition to randomness offers an explanation to wage dispersion

strict convexity of the free energy of the canonical ensemble under decay of correlations we consider a one dimensional lattice system of unbounded real valued spins we allow arbitrary strong attractive nearest neighbor interaction we show that the free energy of the canonical ensemble ce converges uniformly in c 2 to the free energy of the grand ce gce the error estimates are quantitative a direct consequence is that the free energy of the ce is uniformly strictly convex for large systems another consequence is a quantitative local cramer theorem which yields the strict convexity of the coarse grained hamiltonian with small adaptations the argument could be generalized to systems with finite range interaction on a graph as long as the degree of the graph is uniformly bounded and the associated gce has uniform decay of correlations

analytic inequalities isoperimetric inequalities and logarithmic sobolev inequalities abstract there is a simple equivalence between isoperimetric inequalities in riemannian manifolds and certain analytic inequalities on the same manifold more extensive than the familiar equivalence of the classical isoperimetric inequality in euclidean space and the associated sobolev inequality by an isoperimetric inequality in this connection we mean any inequality involving the riemannian volume and riemannian surface measure of a subset and its boundary respectively we exploit the equivalence to give log sobolev inequalities for riemannian manifolds some applications to schrodinger equations are also given

poincare inequality in mean value for gaussian polytopes let k n g 1 g n be the absolute convex hull of n independent standard gaussian random points in mathbb r n with n n we prove that for any 1 lipschitz function f mathbb r n rightarrow mathbb r the polytope k n satisfies the following poincare inequality in mean value mathbb e omega int limits k n omega left f x frac 1 textup vol n left k n omega right int limits k n omega f y dy right 2 dx leq frac c n mathbb e omega int limits k n omega x 2dx where c 0 is an absolute constant this poincare inequality is the one suggested by a conjecture of kannan lovasz and simonovits for general convex bodies moreover we prove in mean value that the volume of the polytope k n is concentrated in a subexponential way within a thin euclidean shell with the optimal dependence of the dimension n an important tool of the proofs is a representation of the law of g 1 g n conditioned by the event that the convex hull of g 1 g n is a n 1 face of k n as an application we also get an estimate of the number of n 1 faces of the polytope k n valid for every n n

comments on exact output regulation for nonlinear systems described by takagi sugeno fuzzy models this letter considers the work entitled exact output regulation for nonlinear systems described by takagi sugeno fuzzy models published previously in the ieee transactions on fuzzy s ystems where the authors try to provide a fuzzy approach to the well known problem of exact output regulation via a dynamic implementation of the nonlinear mapping between the state space and the steady state zero error manifold two problems invalidate this methodology 1 the results do not depend on the fuzzy structure as claimed by the authors and 2 the results have been obtained without properly taking into account the time derivative of the aforementioned nonlinear mapping example b in the above paper is revised and corrected to illustrate these issues

paths of least resistance in possibilistic production systems abstract we introduce the idea of possibilistic production systems we provide a general algorithm for finding a path from an initial node to a goal node we show that the use of a heuristic function can help in the efficient implementation of the search process we see that a significant role in determining potential optimal paths is played by concentrating on the most difficult activity to accomplish

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

nonlinear diffusion limit for a system with nearest neighbor interactions we consider a system of interacting diffusions the variables are to be thought of as charges at sites indexed by a periodic one dimensional lattice the diffusion preserves the total charge and the interaction is of nearest neighbor type with the appropriate scaling of lattice spacing and time a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

logarithmic sobolev inequality for lattice gases with mixing conditions let mu lambda l lambda gc denote the grand canonical gibbs measure of a lattice gas in a cube of sizel with the chemical potential and a fixed boundary condition let mu lambda l n c be the corresponding canonical measure defined by conditioning mu lambda l lambda gc on sigma x in lambda eta x n consider the lattice gas dynamics for which each particle performs random walk with rates depending on near by particles the rates are chosen such that for everyn andl fixed mu lambda l n c is a reversible measure suppose that the dobrushin shlosman mixing conditions holds for mu l lambda gc forall chemical potentials we prove that smallint f log fd mu lambda l n c leqq const l 2 d sqrt f for any probability densityf with respect to mu lambda l n c here the constant is independent ofn orl andd denotes the dirichlet form of the dynamics the dependence onl is optimal

a functional form of the isoperimetric inequality for the gaussian measure abstract letgbe a smooth function on r nwith values in 0 1 using the isoperimetric property of the gaussian measure itis proved that 1 eg e 1 g e g conversely this inequality implies the isoperimetric property of the gaussian measure

exact output regulation for nonlinear systems described by takagi sugeno fuzzy models the exact output regulation for takagi sugeno t s fuzzy models depends on two conditions 1 the local steady state zero error manifolds have to be the same for every local subsystem and 2 the local input matrices have to be the same for every local subsystem included in the t s fuzzy model these conditions are difficult to satisfy in general in this paper those conditions are relaxed by solving the fuzzy regulation problem directly on the overall t s fuzzy model instead of constructing the fuzzy regulator on the basis of linear local controllers by considering the fuzzy model as a special class of linear time varying systems existence conditions are rigorously derived these new conditions which can be solved by means of any mathematical software depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and or the exosystem two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach

a generalized localization theorem and geometric inequalities for convex bodies in this article we generalize a localization theorem of lovasz and simonovits random walks in a convex body and an improved volume algorithm random struct algorithms 4 4 1993 359 412 which is an important tool to prove dimension free functional inequalities for logconcave measures in a previous paper fradelizi and guedon the extreme points of subsets of s concave probabilities and a geometric localization theorem discrete comput geom 31 2004 327 335 we proved that the localization may be deduced from a suitable application of krein milman s theorem to a subset of log concave probabilities satisfying one linear constraint and from the determination of the extreme points of its convex hull here we generalize this result to more constraints give some necessary conditions satisfied by such extreme points and explain how it may be understood as a generalized localization theorem finally using this new localization theorem we solve an open question on the comparison of the volume of sections of non symmetric convex bodies in r n by hyperplanes a surprising feature of the result is

the equivalence of the logarithmic sobolev inequality and the dobrushin shlosman mixing condition given a finite range lattice gas with a compact continuous spin space it is shown cf theorem 1 2 that a uniform logarithmic sobolev inequality cf 1 4 holds if and only if the dobrushin shlosman mixing condition cf 1 5 holds as a consequence of our considerations we also show cf theorems 3 2 and 3 6 that these conditions are equivalent to a statement about the uniform rate at which the associated glauber dynamics tends to equilibrium in this same direction we show cf theorem 3 19 that these ideas lead to a surprisingly strong large deviation principle for the occupation time distribution of the glauber dynamics

robust h control for discrete time fuzzy systems via basis dependent lyapunov functions this paper deals with the robust h control problem for a class of discrete time fuzzy systems with uncertainty the uncertainty is assumed to be of structured linear fractional form by using basis dependent lyapunov function an h control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov and the system matrices which makes the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis it is expected that the basis dependent results are less conservative than the basis independent ones due to the introduction of basis dependent lyapunov function finally numerical examples including the discrete chaotic lorenz system are also given to demonstrate the applicability of the proposed approach

fuzzy optimal flow on imprecise structures abstract the main aim of this paper is to study the maximum flow problem when the underlying associated structure is not well defined and must be modeled as a fuzzy graph however to deal with the problem it is necessary to develop several well known concepts from classical theory in the fuzzy graph context such as flow network and admissible flow the above maximum flow problem is formulated and solved by using algorithms previously developed by the authors

fractional smoothness of images of logarithmically concave measures under polynomials abstract we show that a measure on the real line that is the image of a log concave measure under a polynomial of degree d possesses a density from the nikolskii besov class of fractional order 1 d this result is used to prove an estimate for the total variation distance between such measures in terms of the fortet mourier distance

invariances in variance estimates we provide variants and improvements of the brascamp lieb variance inequality which takes into account the invariance properties of the underlying measure this is applied to spectral gap estimates for log concave measures with many symmetries and to non interacting conservative spin systems

convex bodies and norms associated to convex measures isotropy like properties are considered for finite measures with heavy tails as a basic tool we extend k ball s relationship between convex bodies and finite logarithmically concave measures to a larger class of distributions satisfying convexity conditions of the brunn minkowski type

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

the log sobolev inequality for weakly coupled lattice fields we consider a ferromagnetic spin system with unbounded interactions on the d dimensional integer lattice d 1 under mild assumptions on the one body interactions so that arbitrarily deep double wells are allowed we prove that if the coupling constants are small enough then the finite volume gibbs states satisfy the log sobolev inequality uniformly in the volume and the boundary condition

on the role of convexity in isoperimetry spectral gap and concentration we show that for convex domains in euclidean space cheeger s isoperimetric inequality spectral gap of the neumann laplacian exponential concentration of lipschitz functions and the a priori weakest requirement that lipschitz functions have arbitrarily slow uniform tail decay are all quantitatively equivalent to within universal constants independent of the dimension this substantially extends previous results of maz ya cheeger gromov milman buser and ledoux as an application we conclude a sharp quantitative stability result for the spectral gap of convex domains under convex perturbations which preserve volume up to constants and under maps which are on average lipschitz we also provide a new characterization up to constants of the spectral gap of a convex domain as one over the square of the average distance from the worst subset having half the measure of the domain in addition we easily recover and extend many previously known lower bounds on the spectral gap of convex domains due to payne weinberger li yau kannan lovasz simonovits bobkov and sodin the proof involves estimates on the diffusion semi group following bakry ledoux and a result from riemannian geometry on the concavity of the isoperimetric profile our results extend to the more general setting of riemannian manifolds with density which satisfy the cd 0 curvature dimension condition of bakry emery

log sobolev inequality for the continuum sine gordon model we prove a multiscale generalisation of the bakry emery criterion for a measure to satisfy a log sobolev inequality our criterion relies on the control of an associated pde well known in renormalisation theory the polchinski equation it implies the usual bakry emery criterion but we show that it remains effective for measures which are far from log concave indeed using our criterion we prove that the massive continuum sine gordon model with beta 6 pi satisfies asymptotically optimal log sobolev inequalities for glauber and kawasaki dynamics these dynamics can be seen as singular spdes recently constructed via regularity structures but our results are independent of this theory

a new algorithm for the discrete fuzzy shortest path problem in a network in a network the arc lengths may represent time or cost in practical situations it is reasonable to assume that each arc length is a discrete fuzzy set we called it the discrete fuzzy shortest path problem there were several methods reported to solve this kind of problem in the open literature in these methods they can obtain either the fuzzy shortest length or the shortest path in this paper we propose a new algorithm that can obtain both of them the discrete fuzzy shortest length method is proposed to find the fuzzy shortest length and the fuzzy similarity measure is utilized to get the shortest path an illustrative example is given to demonstrate our proposed algorithm