a graph theory approach to identify resonant and non resonant transmission paths in statistical modal energy distribution analysis statistical modal energy distribution analysis smeda extends classical statistical energy analysis sea to the mid frequency range by establishing power balance equations between modes in different subsystems this circumvents the sea requirement of modal energy equipartition and enables applying smeda to the cases of low modal overlap locally excited subsystems and to deal with complex heterogeneous subsystems as well yet widening the range of application of sea is done at a price with large models because the number of modes per subsystem can become considerable when the frequency increases therefore it would be worthwhile to have at one s disposal tools for a quick identification and ranking of the resonant and non resonant paths involved in modal energy transmission between subsystems it will be shown that previously developed graph theory algorithms for transmission path analysis tpa in sea can be adapted to smeda and prove useful for that purpose the case of airborne transmission between two cavities separated apart by homogeneous and ribbed plates will be first addressed to illustrate the potential of the graph approach a more complex case representing transmission between non contiguous cavities in a shipbuilding structure will be also presented

the parisi formula has a unique minimizer in 1979 parisi phys rev lett 43 1754 1756 1979 predicted a variational formula for the thermodynamic limit of the free energy in the sherrington kirkpatrick model and described the role played by its minimizer this formula was verified in the seminal work of talagrand ann math 163 1 221 263 2006 and later generalized to the mixed p spin models by panchenko ann probab 42 3 946 958 2014 in this paper we prove that the minimizer in parisi s formula is unique at any temperature and external field by establishing the strict convexity of the parisi functional

stochastic volterra equations in banach spaces and stochastic partial differential equation abstract in this paper we study the existence uniqueness and large deviation estimate for stochastic volterra integral equations with singular kernels in 2 smooth banach spaces then we apply them to a large class of semilinear stochastic partial differential equations spde and obtain the existence of unique maximal strong solutions in the sense of sde and pde under local lipschitz conditions moreover stochastic navier stokes equations are also investigated

theoretical issues on lti systems that preserve signal richness in this paper theoretical issues about linear time invariant lti systems that preserve signal richness are explored this paper considers two particular definitions of signal richness and finds the necessary and sufficient conditions under which an lti system preserves the richness property several examples are presented to clarify the issues involved in the problem paraunitary pu and unimodular matrices can be shown not to preserve richness unless they are constant matrices or a delayed version in the pu case some richness preserving properties of cascaded systems are also investigated a structured proof of the necessary and sufficient conditions is presented the relationship between persistent excitation pe and the proposed definitions of richness is also described

variational approximation for fokker planck equation on riemannian manifold under the bounded geometry assumption on riemannian manifold m a variational approximation for fokker planck equation on m is constructed by the scheme of jordan et al in siam j math anal 29 1 1 17 1998 moreover the uniqueness and global l p estimate of the solution for 1 p dim m dim m 1 are obtained for a broad class of potential

freidlin wentzell s large deviations for stochastic evolution equations abstract we prove a freidlin wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises in particular our general result can be used to deal with a large class of quasi linear stochastic partial differential equations such as stochastic porous medium equations and stochastic reaction diffusion equations with polynomial growth zero order term and p laplacian second order term

clark ocone formula and variational representation for poisson functionals in this paper we first prove a clark ocone formula for any bounded measurable functional on poisson space then using this formula under some conditions on the intensity measure of poisson random measure we prove a variational representation formula for the laplace transform of bounded poisson functionals which has been conjectured by dupuis and ellis a weak convergence approach to the theory of large deviations 1997 wiley p 122

on the existence of smooth densities for jump processes we consider a levy process x t and the solution y t of a stochastic differential equation driven by x t we suppose that x t has infinitely many small jumps but its levy measure may be very singular for instance it may have a countable support we obtain sufficient conditions ensuring the existence of a smooth density for y t these conditions are similar to those of the classical malliavin calculus for continuous diffusions more generally we study the smoothness of the law of variables f defined on a poisson probability space the basic tool is a duality formula from which we estimate the characteristic function of f

the borell ehrhard game a precise description of the convexity of gaussian measures is provided by sharp brunn minkowski type inequalities due to ehrhard and borell we show that these are manifestations of a game theoretic mechanism a minimax variational principle for brownian motion as an application we obtain a gaussian improvement of barthe s reverse brascamp lieb inequality

quantitative differentiation a general formulation let dx denote lebesgue measure on with respect to the measure on the collection of balls the subcollection of balls has infinite measure let have bounded gradient for any there is a natural scale invariant quantity that measures the deviation of from being an affine linear function the most basic case of quantitative differentiation due to peter jones asserts that for all the measure of the collection of balls on which the deviation from linearity is is finite and controlled by independent of the particular function the purpose of this paper is to explain the sense in which this model case is actually a particular instance of a general phenomenon that is present in many different geometric analytic contexts essentially in each case that fits the framework to prove the relevant quantitative differentiation theorem it suffices to verify that the family of relative defects is monotone and coercive we indicate one recent application to theoretical computer science and others to partial regularity theory in geometric analysis and nonlinear pdes 2012 wiley periodicals inc

rare event simulation of small noise diffusions an important sampling method for certain rare event problems involving small noise diffusions is proposed standard monte carlo schemes for these problems behave exponentially poorly in the small noise limit previous work in rare event simulation has focused on developing estimators with optimal exponential variance decay rates this criterion still allows for exponential growth of the statistical relative error we show that an estimator related to a deterministic control problem not only has an optimal variance decay rate but can have vanishingly small relative statistical error in the small noise limit the sampling method based on this estimator can be seen as the limit of the zero variance importance sampling scheme which uses the solution of the second order partial differential equation pde associated with the diffusion in the scheme proposed here this pde is replaced by a hamilton jacobi equation whose solution is computed pointwise on the fly from its variational formulation an operation that remains practical even in high dimensional problems we test the scheme on several simple illustrative examples as well as a stochastic pde the noisy allen cahn equation 2012 wiley periodicals inc

antipodal paraunitary matrices and their application to ofdm systems paraunitary pu matrices and filterbanks have played an important role in many applications this paper studies a special class of pu matrices called antipodal paraunitary apu matrices apu matrices are pu matrices whose coefficient matrices consist of spl plusmn 1 only several new methods will be introduced for the construction of apu matrices in particular a new method based on the butterfly structure that has a low cost implementation is proposed moreover one application of apu matrices in precoded orthogonal frequency division multiplexing ofdm systems will be considered by using an apu precoding matrix the complexity will be very low and experiments show that the use of apu matrices can greatly enhance the performance

large deviation properties of weakly interacting processes via weak convergence methods we study large deviation properties of systems of weakly interacting particles modeled by ito stochastic differential equations sdes it is known under certain conditions that the corresponding sequence of empirical measures converges as the number of particles tends to infinity to the weak solution of an associated mckean vlasov equation we derive a large deviation principle via the weak convergence approach the proof which avoids discretization arguments is based on a representation theorem weak convergence and ideas from stochastic optimal control the method works under rather mild assumptions and also for models described by sdes not of diffusion type to illustrate this we treat the case of sdes with delay

optimal control of partially observable stochastic systems with an exponential of integral performance index the stochastic control problem with linear stochastic differential equations driven by brownian motion processes and as cost functional the exponential of a quadratic form is considered the soluti

on the optimal control of stochastic systems with an exponential of integral performance index abstract in this paper a theory of optimal control is developed for stochastic systems whose performance is measured by the exponential of an integral form such a formulation of the cost function is shown to be not only general and useful but also analytically tractable starting with very general classes of stochastic systems optimality conditions are obtained which exploit the multiplicative decomposability of the exponential of integral form specializing to partially observed systems of stochastic differential equations with brownian motion disturbances optimality conditions are obtained which parallel those for systems with integral costs also treated are the special cases of linear systems with exponential of quadratic costs for which explicit optimal controls are obtainable in addition several general results of independent interest are obtained which concern optimality of stochastic systems

persistence of excitation conditions and the convergence of adaptive schemes in the study of the behavior of adaptive filtering algorithms persistence of excitation of the input process arises as a sufficient condition for convergence and perhaps more importantly for convergence rate of the parameter estimates in this paper the underlying nature of the persistence requirement is presented and discussed relating its normal specification in terms of moment conditions with covariance decays etc to sample path properties deterministic and stochastic persistence conditions and persistence measures are treated as well as persistence conditions for output error equation error and adaptive control schemes

applying a fuzzy set based method for robust estimation of coupling loss factors finite element models have been used by many authors to provide accurate estimations of coupling loss factors although much progress has been achieved in this area little attention has been paid to the influence of uncertain parameters in the finite element model used to estimate these factors it is well known that in the mid frequency range uncertainty is a major issue in this context a spectral element method combined with a special implementation of a fuzzy set based method which is called the transformation method is proposed as an alternative to compute coupling loss factors the proposed technique is applied to a frame type junction which can consist of two beams connected at an arbitrary angle in this context two problems are investigated in the first one the influence of the confidence intervals of the coupling loss factors on the estimated energy envelopes assuming a unit power input is considered in the other problem the influence of the envelope of the input power obtained considering the confidence intervals of the coupling loss factors is also taken into account the estimates of the intervals are obtained by using the spectral element method combined with a fuzzy set based method results using a monte carlo analysis for the estimation of the coupling loss factors under the influence of uncertain parameters are shown for comparison and verification of the fuzzy method

statistical energy analysis with fuzzy parameters to handle populations of structures statistical modal energy distribution analysis smeda approach was developed to enlarge the application field of statistical energy analysis sea when equipartition of modal energies is not achieved smeda gives more precise results than standard sea when compared to exact energy response of a deterministic system in the case of low modal overlap heterogeneous systems or point excitation the present paper was initiated by this question when considering a population of similar structures each of them being described by smeda do the ensemble averaged energies of subsystem and injected power tend to satisfy sea equations in other terms despite the non equipartition of energy observed on each element of the population of structures does the ensemble averaging leads to sea equation where equipartition of energy is assumed the response to that question that rises from this paper is yes if the terms of the sea equation are fuzzy numbers it results that the energy response given by the model can be interpreted using fuzzy numbers theory

schilder theorem for the brownian motion on the diffeomorphism group of the circle abstract we prove a large deviation principle for flows associated to stochastic differential equations with non lipschitz coefficients as an application we establish a schilder theorem for the brownian motion on the group of diffeomorphisms of the circle

explicit stochastic analysis of brownian motion and point measures on riemannian manifolds abstract the gradient and divergence operators of stochastic analysis on riemannian manifolds are expressed using the gradient and divergence of the flat brownian motion by this method we obtain the almost sure version of several useful identities that are usually stated under expectations the manifold valued brownian motion and random point measures on manifolds are treated successively in the same framework and stochastic analysis of the brownian motion on a riemannian manifold turns out to be closely related to classical stochastic calculus for jump processes in the setting of point measures we introduce a damped gradient that was lacking in the multidimensional case

parameter drift in lms adaptive filters we examine general conditions under which the lms adaptive filter generates unbounded parameter estimates when driven by bounded sequences this unexpected parameter divergence or drift is related to the inadequacy of excitation in the input sequence and is characterized by slow i e nonexponential escape of the parameter estimate vector to infinity in spite of all other signals inputs outputs prediction errors remaining bounded or even decaying to zero the analysis proceeds by showing that in a general adaptive filtering setting the sequence of regressors information vectors provides a natural decomposition of the parameter estimate space into subspaces each corresponding to a characteristic class of filter excitation this subspace decomposition is applied to the lms adaptive filter yielding direct links between filter behavior and modes of excitation in particular stability and instability of the parameter estimates in the presence of bounded disturbances and prediction errors is obtained for various classes of excitation this behavior is examined in detail for the first and second order cases and is sufficient to characterize the behavior of higher order adaptive filters the instability drift results are due to modes of decaying excitation and bounds on the rates of drift are derived this drift mechanism is inherent in the algorithm and is not due to numerical implementation problems or violation of small step size conditions examples are presented where drift may occur in restricted complexity filtering and in the related stochastic gradient algorithm an analysis of leakage in terms of input excitation reveals a tradeoff in performance between parameter and prediction errors a modified form of leakage using the subspace decomposition is suggested to remove this difficulty

generalized signal richness preservation problem and vandermonde form preserving matrices in this paper a theoretical problem arising in digital communications namely the generalized signal richness preservation problem is addressed and studied in order to solve the problem a special class of square matrices namely the vandermonde form preserving vfp matrices is introduced and found to be highly relevant to the problem several properties of vfp matrices are studied in detail the necessary and sufficient conditions of the problem have been found and a systematic proof is also presented

estimation of sea coupling loss factors using a dual formulation and fem modal information part ii numerical applications numerical applications of the approach presented in the first of these two companion papers is proposed in the cases of coupled beams and coupled plates results are compared with other calculations clf calculation for coupled beams is achieved with analytical modal description the influence of thickness ratio and damping about the quality of the prediction are presented and discussed clf determination with fem modal description are then applied to the case of two thin plates coupled in an l shape this case permit to achieve comparison with other calculation and will be representative of the applicability of the method to more complex structures as industrial ones a very good agreement is noticed that validate the calculation of clf with the present method

large deviations for small noise diffusions with discontinuous statistics this paper proves the large deviation principle for a class of non degenerate small noise diffusions with discontinuous drift and with state dependent diffusion matrix the proof is based on a variational representation for functionals of strong solutions of stochastic differential equations and on weak convergence methods

extension of the statistical modal energy distribution analysis for estimating energy density in coupled subsystems abstract the present article deals with an extension of the statistical modal energy distribution analysis smeda method to estimate kinetic and potential energy density in coupled subsystems the smeda method uses the modal bases of uncoupled subsystems and focuses on the modal energies rather than the global energies of subsystems such as sea statistical energy analysis this method permits extending sea to subsystems with low modal overlap or to localized excitations as it does not assume the existence of modal energy equipartition we demonstrate that by using the modal energies of subsystems computed by smeda it is possible to estimate energy distribution in subsystems this approach has the same advantages of standard sea as it uses very short calculations to analyze damping effects the estimation of energy distribution from smeda is applied to an academic case and an industrial example

a variational representation for certain functionals of brownian motion in this paper we show that the variational representation log ee f w inf v e 1 2 int 0 1 parallel v s parallel 2 ds f w int 0 cdot v s ds holds where w is a standard d dimensional brownian motion f is any bounded measurable function that maps c 0 1 mathbb r d into mathbb r and the infimum is over all processes v that are progressively measurable with respect to the augmentation of the filtration generated by w an application is made to a problem concerned with large deviations and an extension to unbounded functions is given