distribution free consistent independence tests via center outward ranks and signs this article investigates the problem of testing independence of two random vectors of general dimensions for this we give for the first time a distribution free consistent test our approach com

computational aspects of cui freeden statistics for equidistribution on the sphere abstract in this paper we derive the asymptotic statistical properties of a class of generalized discrepancies introduced by cui and freeden siam j sci comput 1997 to test equidistribution on the sphere we show that they have highly desirable properties and encompass several statistics already proposed in the literature in particular it turns out that the limiting distribution is an infinite weighted sum of chi squared random variables issues concerning the approximation of this distribution are considered in detail and explicit bounds for the approximation error are given the statistics are then applied to assess the equidistribution of hammersley low discrepancy sequences on the sphere and the uniformity of a dataset concerning magnetic orientations

paper error propagation properties of recursive least squares adaptation algorithms the numerical properties of implementations of the recursive least squares identification algorithm are of great importance for their continuous use in various adaptive schemes here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates it is shown that conventional ls algorithms including bierman s ud factorization algorithm are exponentially stable with respect to such errors i e the effect of the error decays exponentially the base of the decay is equal to the forgetting factor the same is true for fast lattice algorithms the fast least squares algorithm sometimes known as the fast kalman algorithm is however shown to be unstable with respect to such errors

long range order in the scaling behaviour of hyperbolic dynamical systems abstract detailed statistical analyses of chaotic signals have been so far limited to 2 d maps with one expanding and one contracting direction here by studying filtered signals we provide evidence that the existence of a further stable direction can transform self similarity into self affinity and generate phase transitions according to the thermodynamic formalism of dynamical systems in a hyperbolic case the dimension spectrum is computed exactly as a function of the filter cut off frequency moreover the validity of the kaplan yorke formula and of its generalization are rigorously proven finally the scaling function is shown to satisfy a stochastic recursive relation whose lyapunov exponent allows to control the extension of the range of interactions in the associated hamiltonian

proof of the outage probability conjecture for miso channels it is conjectured that the covariance matrices minimizing the outage probability under a power constraint for multiple input multiple output channels with gaussian fading are diagonal with either zeros or constant values on the diagonal in the multiple input single output miso setting this is equivalent to conjecture that the gaussian quadratic forms having largest tail probability correspond to such diagonal matrices this paper provides a proof of the conjecture in this miso setting

poisson law for the number of lattice points in a random strip with finite area let a smooth curve be given by a functionr f in polar coordinate system in the plane and letr be a uniformly distributed random variable on the interval a 1 l a 2 l with somea 2 a 1 0 and a largel 0 ya g sinai has conjectured that given some real numbersc 2 c 1 the number of lattice points in the domain between the curves left r frac c 1 r right and left r frac c 2 r right is asymptotically poisson distributed for good functionsf we cannot prove this conjecture but we show that if a probability measure with some nice properties is given on the space of smooth functions then almost all functions with respect to this measure satisfy sinai s conjecture this is an improvement of an earlier result of sinai 9 and actually the proof also contains many ideas of that paper

the realized empirical distribution function of stochastic variance with application to goodness of fit testing abstract we propose a nonparametric estimator of the empirical distribution function edf of the latent spot variance of the log price of a financial asset we show that over a fixed time span our realized edf or redf inferred from noisy high frequency data is consistent as the mesh of the observation grid goes to zero in a double asymptotic framework with time also increasing to infinity the redf converges to the cumulative distribution function of volatility if it exists we exploit these results to construct some new goodness of fit tests for stochastic volatility models in a monte carlo study the redf is found to be accurate over the entire support of volatility this leads to goodness of fit tests that are both correctly sized and relatively powerful against common alternatives in an empirical application we recover the redf from stock market high frequency data we inspect the goodness of fit of several two parameter marginal distributions that are inherent in standard stochastic volatility models the inverse gaussian offers the best overall description of random equity variation but the fit is less than perfect this suggests an extra parameter as available in e g the generalized inverse gaussian is required to model stochastic variance

expansions for von mises functionals berry esseen results and expansions are derived for the distribution function of von mises functionals of order r under moment conditions and conditions on the smoothness of the limit distribution

detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble a method to characterize dynamical interdependence among nonlinear systems is derived based on mutual nonlinear prediction systems with nonlinear correlation will show mutual nonlinear prediction when standard analysis with linear cross correlation might fail mutual nonlinear prediction also provides information on the directionality of the coupling between systems furthermore the existence of bidirectional mutual nonlinear prediction in unidirectionally coupled systems implies generalized synchrony numerical examples studied include three classes of unidirectionally coupled systems systems with identical parameters nonidentical parameters and stochastic driving of a nonlinear system this technique is then applied to the activity of motoneurons within a spinal cord motoneuron pool the interrelationships examined include single neuron unit firing the total number of neurons discharging at one time as measured by the integrated monosynaptic reflex and intracellular measurements of integrated excitatory postsynaptic potentials epsp s dynamical interdependence perhaps generalized synchrony was identified in this neuronal network between simultaneous single unit firings between units and the population and between units and intracellular epsp s

optimality functions in stochastic programming optimality functions define stationarity in nonlinear programming semi infinite optimization and optimal control in some sense in this paper we consider optimality functions for stochastic programs with nonlinear possibly nonconvex expected value objective and constraint functions we show that an optimality function directly relates to the difference in function values at a candidate point and a local minimizer we construct confidence intervals for the value of the optimality function at a candidate point and hence provide a quantitative measure of solution quality based on sample average approximations we develop an algorithm for classes of stochastic programs that include cvar problems and utilize optimality functions to select sample sizes

decoupling inequalities for the tail probabilities of multivariate u statistics in this paper we present a decoupling inequality that shows that multivariate u statistics can be studied as sums of conditionally independent random variables this result has important implications in several areas of probability and statistics including the study of random graphs and multiple stochastic integration more precisely we get the following result let x j be a sequence of independent random variables on a measurable space mathscr j s and let x j i j 1 ldots k be k independent copies of x i let f i 1i 2 ldots i k be families of functions of k variables taking s times cdots times s into a banach space b cdots then for all n geq k geq 2 t 0 there exist numerical constants c k depending on k only so that p bigg big sum 1 leq i 1 neq i 2 neq cdots neq i k leq n f i 1 cdots i k x 1 i 1 x 1 i 2 ldots x 1 i k big geq t bigg leq c kp bigg c k big sum 1 leq i 1 neq i 2 neq cdots neq i k leq n f i 1 cdots i k x 1 i 1 x 2 i 2 ldots x k i k big geq t bigg the reverse bound holds if in addition the following symmetry condition holds almost surely f i 1i 2 cdots i k x i 1 x i 2 ldots x i k f i pi 1 i pi 2 cdots i pi k x i pi 1 x i pi 2 ldots x i pi k for all permutations pi of 1 ldots k

measuring and testing dependence by correlation of distances distance correlation is a new measure of dependence between random vectors distance covariance and distance correlation are analogous to product moment covariance and correlation but unlike the classical definition of correlation distance correlation is zero only if the random vectors are independent the empirical distance dependence measures are based on certain euclidean distances between sample elements rather than sample moments yet have a compact representation analogous to the classical covariance and correlation asymptotic properties and applications in testing independence are discussed implementation of the test and monte carlo results are also presented

a generalized discrepancy and quadrature error bound an error bound for multidimensional quadrature is derived that includes the koksma hlawka inequality as a special case this error bound takes the form of a product of two terms one term which depends only on the integrand is defined as a generalized variation the other term which depends only on the quadrature rule is defined as a generalized discrepancy the generalized discrepancy is a figure of merit for quadrature rules and includes as special cases the l p star discrepancy and p that arises in the study of lattice rules

finite deformation post buckling analysis involving inelasticity and contact constraints this paper is concerned with the numerical solution of large deflection structural problems involving finite strains subject to contact constraints and unilateral boundary conditions and exhibiting inelastic constitutive response first a three dimensional finite strain beam model is summarized and its numerical implementation in the two dimensional case is discussed next a penalty formulation for the solution of contact problems is presented and the correct expression for consistent tangent matrix is developed finally basic strategies for tracing limit points are reviewed and a modification of the arc length method is proposed the good performance of the procedures discussed is illustrated by means of numerical examples

interaction of a non self adjoint one dimensional continuum and moving multi degree of freedom oscillator abstract a method for computing the dynamic responses due to the interaction of two non self adjoint systems a linear one dimensional 1d continuum and a linear multi degree of freedom mdof oscillator travelling over the continuum is presented the solution method is applicable to a broad class of 1d continua whose dynamics may be governed by various linear operators and subjected to different boundary conditions the problem is reduced to the integration of a system of linear differential equations with time dependent coefficients these coefficients are found to depend on eigenvalues as well as eigenfunctions and eigenvectors of the continuum and the oscillator two examples are included representing bridge and railway track vibrations to demonstrate the application of the method and discuss its convergence

extending the scope of empirical likelihood this article extends the scope of empirical likelihood methodology ill three directions to allow for plug in estimates of nuisance parameters in estimating equations slower than root n rates of convergence and settings in which there are a relatively large number of estimating equations compared to the sample size calibrating empirical likelihood confidence regions with plug in is sometimes intractable due to the complexity of the asymptotics so we introduce a bootstrap approximation that call be used in such situations we provide a range of examples from survival analysis and nonparametric statistics to illustrate the main results

equidistribution on the sphere a concept of generalized discrepancy which involves pseudodifferential operators to give a criterion of equidistributed pointsets is developed on the sphere a simply structured formula in terms of elementary functions is established for the computation of the generalized discrepancy with the help of this formula five kinds of point systems on the sphere namely lattices in polar coordinates transformed two dimensional sequences rotations on the sphere triangulations and sum of three squares sequence are investigated quantitative tests are done and the results are compared with one another our calculations exhibit different orders of convergence of the generalized discrepancy for different types of point systems

uniform rates of convergence in the clt for quadratic forms in multidimensional spaces let x x 1 x 2 be a sequence of i i d random vectors taking values in a d dimensional real linear space d assume that e x 0 and that x is not concentrated in a proper subspace of d let g denote a mean zero gaussian random vector with the same covariance operator as that of x we investigate the distributions of non degenerate quadratic forms s n of the normalized sums s n n 1 2 x 1 x n and show that provided that d 9 and the fourth moment of x exists the bound n 1 is optimal and improves e g the well known bound n d d 1 due to esseen 1945 the result extends to the case of random vectors taking values in a hilbert space furthermore we provide explicit bounds for n and for the concentration function of the random variable s n

nonlinear response of shear deformable beams on tensionless nonlinear viscoelastic foundation under moving loads abstract in this paper a boundary element method is developed for the geometrically nonlinear response of shear deformable beams of simply or multiply connected constant cross section traversed by moving loads resting on tensionless nonlinear three parameter viscoelastic foundation undergoing moderate large deflections under general boundary conditions the beam is subjected to the combined action of arbitrarily distributed or concentrated transverse moving loading as well as to axial loading to account for shear deformations the concept of shear deformation coefficients is used three boundary value problems are formulated with respect to the transverse displacement to the axial displacement and to a stress functions and solved using the analog equation method a boundary element based method application of the boundary element technique yields a system of nonlinear differential algebraic equations which is solved using an efficient time discretization scheme from which the transverse and axial displacements are computed the evaluation of the shear deformation coefficient is accomplished from the aforementioned stress function using only boundary integration analyses are performed to illustrate wherever possible the accuracy of the developed method to investigate the effects of various parameters such as the load velocity load frequency shear deformation foundation nonlinearity damping on the beam displacements and stress resultants and to examine how the consideration of shear and axial compression affects the response of the system

intermittency transitions to strange nonchaotic attractors in a quasiperiodically driven duffing oscillator different mechanisms for the creation of strange nonchaotic attractors snas are studied in a two frequency parametrically driven duffing oscillator we focus on intermittency transitions in particular and show that snas in this system are created through quasiperiodic saddle node bifurcations type i intermittency as well as through a quasiperiodic subharmonic bifurcation type iii intermittency the intermittent attractors are characterized via a number of lyapunov measures including the behavior of the largest nontrivial lyapunov exponent and its variance as well as through distributions of finite time lyapunov exponents these attractors are ubiquitous in quasiperiodically driven systems the regions of occurrence of various snas are identified in a phase diagram of the duffing system

asymptotics for minimal discrete energy on the sphere we investigate the energy of arrangements of n points on the surface of the unit sphere sd in rd 1 that interact through a power law potential v 1 rs where s 0 and r is euclidean distance with ed s n denoting the minimal energy for such n point arrangements we obtain bounds valid for all n for ed s n in the cases when 0 s d and 2 d s for s d we determine the precise asymptotic behavior of ed d n as n as a corollary lower bounds are given for the separation of any pair of points in an n point minimal energy configuration when s d 2 for the unit sphere in r3 d 2 we present two conjectures concerning the asymptotic expansion of e2 s n that relate to the zeta function l s for a hexagonal lattice in the plane we prove an asymptotic upper bound that supports the first of these conjectures of related interest we derive an asymptotic formula for the partial sums of l s when 0 s 2 the divergent case

a colonel blotto gladiator game we consider a stochastic version of the well known blotto game called the gladiator game in this zero sum allocation game two teams of gladiators engage in a sequence of one on one fights in which the probability of winning is a function of the gladiators strengths each team s strategy is the allocation of its total strength among its gladiators we find the nash equilibria and the value of this class of games and show how they depend on the total strength of teams and the number of gladiators in each team to do this we study interesting majorization type probability inequalities concerning linear combinations of gamma random variables similar inequalities have been used in models of telecommunications and research and development

numerical methods for analysis of plates on tensionless elastic foundations abstract a numerical methodology for analysis of plates resting on tensionless elastic foundations described either by the winkler model or as an elastic half space is presented in this paper the contact surface is assumed unbonded and frictionless the finite element method is used to discretize the plate and foundation to overcome the difficulties in solving the plate foundation equilibrium equations together with the inequality constraints due to the frictionless unilateral contact condition a variational formulation equivalent to these equations is presented from which three alternative linear complementary problems lcp are derived and solved by lemke s complementary pivoting algorithm in the first formulation the lcp variables are the plate displacements and the elastic foundation reaction in the second the lcp is derived in terms of the elastic foundation reaction and in the third formulation the variables are the elastic foundation displacements and the gap between the bodies once the lcp is solved the no contact regions where the plate lifts up away from the foundation and the sub grade reaction as well as the plate displacements and stresses can be easily obtained the methodology is illustrated by three examples and the results are compared with existing analytical and numerical results found in the literature

nonlinear analysis of structural elements under unilateral contact constraints by a ritz type approach a nonlinear modal solution methodology capable of solving equilibrium and stability problems of uni dimensional structural elements beams columns and arches with unilateral contact constraints is presented in this work the contact constraints are imposed by an elastic foundation of the winkler type where special attention is given to the case in which the foundation reacts in compression only characterizing the contact as unilateral a ritz type approach with moveable boundaries where the coordinates defining the limits of the contact regions are considered as additional variables of the problem is proposed to solve this class of unilateral contact problems the methodology is illustrated by particular problems involving beams beam columns and arches and the results are compared with available results obtained by finite element and mathematical programming techniques it is concluded that the ritz type approach proposed is particularly suited for the analysis of structural problems where the number but not the length of the contact regions between the bodies are known a priori therefore it can substitute in these cases finite element applications and be used as a benchmark for more general and complex formulations as well

optimal rates of convergence in the clt for quadratic forms we prove optimal convergence rates in the central limit theorem for sums in r k assuming a fourth moment we obtain a berry esseen type bound of o n 1 for the probability of hitting a ball provided that k 5 the proof still requires a technical assumption related to the independence of coordinates of sums

equivalence of kernel machine regression and kernel distance covariance for multidimensional phenotype association studies summary associating genetic markers with a multidimensional phenotype is an important yet challenging problem in this work we establish the equivalence between two popular methods kernel machine regression kmr and kernel distance covariance kdc kmr is a semiparametric regression framework that models covariate effects parametrically and genetic markers non parametrically while kdc represents a class of methods that include distance covariance dc and hilbert schmidt independence criterion hsic which are nonparametric tests of independence we show that the equivalence between the score test of kmr and the kdc statistic under certain conditions can lead to a novel generalization of the kdc test that incorporates covariates our contributions are 3 fold 1 establishing the equivalence between kmr and kdc 2 showing that the principles of kmr can be applied to the interpretation of kdc 3 the development of a broader class of kdc statistics where the class members are statistics corresponding to different kernel combinations finally we perform simulation studies and an analysis of real data from the alzheimer s disease neuroimaging initiative adni study the adni study suggest that snps of flj16124 exhibit pairwise interaction effects that are strongly correlated to the changes of brain region volumes

optimal bounds in non gaussian limit theorems for u statistics let x x 1 x be i i d random variables taking values in a measurable space x let x y and 1 x denote measurable functions of the arguments x y x assuming that the kernel is symmetric and that e x x 0 for all x and e 1 x 0 we consider u statistics of type t n 1 x j x k n 1 2 1 x j 1 j k n 1 j n it is known that the conditions e 2 x x 1 and e 2 1 x imply that the distribution function of t say f has a limit say f 0 which can be described in terms of the eigenvalues of the hilbert schmidt operator associated with the kernel x y under optimal moment conditions we prove that n sup f x f 0 x f 1 x o n 1 provided that at least nine eigenvalues of the operator do not vanish here f 1 denotes an edgeworth type correction we provide explicit bounds for n and for the concentration functions of statistics of type t

dynamic responses of reissner mindlin plates with free edges resting on tensionless elastic foundations abstract dynamic response analysis is presented for a reissner mindlin plate with four free edges resting on a tensionless elastic foundation of the winkler type and pasternak type the mechanical loads consist of transverse partially distributed impulsive loads and in plane static edge loads while the temperature field is assumed to exhibit a linear variation through the thickness of the plate the material properties are assumed to be independent of temperature the two cases of initially compressed plates and of initially heated plates are considered the formulations are based on reissner mindlin first order shear deformation plate theory and include the plate foundation interaction and thermal effects a set of admissible functions is developed for the dynamic response analysis of moderately thick plates with four free edges the galerkin method the gauss legendre quadrature procedure and the runge kutta technique are employed in conjunction with this set of admissible functions to determine the deflection time and bending moment time curves as well as shape mode curves an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region the numerical illustrations concern moderately thick plates with four free edges resting on tensionless elastic foundations of the winkler type and pasternak type from which results for conventional elastic foundations are obtained as comparators the results confirm that the plate will have stronger dynamic behavior than its counterpart when it is supported by a tensionless elastic foundation

asymptotic distribution of quadratic forms we consider quadratic forms q n a jh x j x k 1 j k n where x j are i i d random variables with finite third moment we obtain optimal bounds for the kolmogorov distance between the distribution of q n and the distribution of the same quadratic forms with x j replaced by corresponding gaussian random variables these bounds are applied to toeplitz and random matrices as well as to nonstationary ar 1 processes

the birth of strange nonchaotic attractors abstract a mechanism is described for the development of strange nonchaotic attractors from two frequency quasiperiodic attractors in quasiperiodically driven maps this mechanism is intimately tied to the phenomenon of torus doubling the transition to strange nonchaotic behavior occurs when a period doubled torus collides with its unstable parent torus as the collision is approached the period doubled torus becomes extremely wrinkled ultimately becoming fractal at the collision the lyapunov exponent remains negative through the collision these collisions are shown to be a new type of attractor merging crisis the new feature is the possibility of nonchaotic attractors taking part in the crisis this mechanism is illustrated via numerical and analytical studies of a quasiperiodically driven logistic map

universal analytical solution of the steady state response of an infinite beam on a pasternak elastic foundation under moving load abstract in this paper the steady state response of a uniform infinite euler bernoulli elastic beam resting on a pasternak elastic foundation and subjected to a concentrated load moving at a constant velocity along the beam is analytically investigated a universal closed form analytical solution is derived through fourier transform apt to represent the response for all possible beam foundation parameters a rigorous mathematical procedure is formulated for classifying the parametric behavior of the solution including for viscous damping depending on such a classification different types of bending wave shapes are shown to propagate within the beam ahead and behind the moving load position and crucial physical characteristics such as critical velocity and critical damping are reinterpreted into a wholly exact and complete mathematical framework mechanical features of the solution are revealed for the steady state response in terms of normalized deflection cross section rotation bending moment and shear force

differentiable generalized synchronization of chaos we consider simple lyapunov exponent based conditions under which the response of a system to a chaotic drive is a ital smooth function of the drive state we call this ital differentiable generalized synchronization dgs when dgs does not hold we quantify the degree of nondifferentiability using the h umlt o lder exponent we also discuss the consequences of dgs and give an illustrative numerical example copyright ital 1997 ital the american physical society

characteristic distributions of finite time lyapunov exponents we study the probability densities of finite time or local lyapunov exponents in low dimensional chaotic systems while the multifractal formalism describes how these densities behave in the asymptotic or long time limit there are significant finite size corrections which are coordinate dependent depending on the nature of the dynamical state the distribution of local lyapunov exponents has a characteristic shape for intermittent dynamics and at crises dynamical correlations lead to distributions with stretched exponential tails while for fully developed chaos the probability density has a cusp exact results are presented for the logistic map stackrel ensuremath rightarrow x 4x 1 ensuremath x at intermittency the density is markedly asymmetric while for typical chaos it is known that the central limit theorem obtains and a gaussian density results local analysis provides information on the variation of predictability on dynamical attractors these densities which are used to characterize the nonuniform spatial organization on chaotic attractors are robust to noise and can therefore be measured from experimental data

edgeworth expansion for u statistics under minimal conditions berry esseen bounds for u statistics under the optimal moment conditions were derived by koroljuk and borovskich and friedrich under the same optimal moment assumptions with an additional nonlattice condition we establish a one term edgeworth expansion with remainder o n 1 2 for u statistics

approximate and asymptotic distributions of chi squared type mixtures with applications in this article we study how to approximate a random variable t of general chi squared type mixtures by a random variable of the form via matching the first three cumulants the approximation error bounds for the density functions of the chi squared approximation and the normal approximation are established applications of the results to some nonparametric goodness of fit tests including those tests based on orthogonal series smoothing splines and local polynomial smoothers are investigated two simulation studies are conducted to compare the chi squared approximation and the normal approximation numerically the chi squared approximation is illustrated using a real data example for polynomial goodness of fit tests

characterization of the parameter mismatching effect on the loss of chaos synchronization we investigate the effect of the parameter mismatch on the loss of chaos synchronization in coupled one dimensional maps loss of strong synchronization begins with a first transverse bifurcation of a periodic saddle embedded in the synchronous chaotic attractor sca and then the sca becomes weakly stable because of local transverse repulsion of the periodic repellers embedded in the weakly stable sca a typical trajectory may have segments of arbitrary length that have positive local transverse lyapunov exponents consequently the weakly stable sca becomes sensitive with respect to the variation of the mismatching parameter to quantitatively characterize such parameter sensitivity we introduce a quantifier called the parameter sensitivity exponent pse as the local transverse repulsion of the periodic repellers strengthens the value of the pse increases in terms of these pses we also characterize the parameter mismatching effect on the intermittent bursting and basin riddling occurring in the regime of weak synchronization

non linear analysis of beam like structures on unilateral foundations a lattice spring model abstract a computationally efficient method is presented for static and dynamic analysis of a beam like structure on a viscoelastic foundation with the unilateral contact constraint at their interface the non smooth dynamics of the system is modelled using the euler bernoulli theory for the beam and the bilinear winkler model for the substrate thus the unilateral contact is the only source of non linearity the proposed approach relies on reducing the non smooth continuous system to a piecewise smooth multi degree of freedom model the beam is represented as a chain of discrete units through the use of the lattice spring model lsm and consequently the phase space is divided into a number of subdomains hence the system smoothness is lost when the trajectory of lattice nodes cross the boundaries between these subdomains an effective algorithm has been developed to handle the unilateral constraints by tracking the trajectories and successively capturing the intervals that the nodes spend in each of the smooth regions unlike more commonly used methods it neither relies on any prior information such as the number and location of the lift off areas nor on the non linear solvers the accuracy and robustness of this numerical technique have been demonstrated in several application examples furthermore the developed algorithm is utilised in combination with the shooting method and continuation of the periodic motions to obtain the non linear normal modes nnms of the system we show that frequency stiffness i u k w plots can be used to describe the salient features of the nnms for the beam on the full foundation the first mode in the configuration space has a linear shape and thus the conventional bilinear formulation can accurately approximate the non linear frequency for higher modes the modal lines are open curves and the bilinear approximation loses its accuracy in addition internal resonances may occur once the frequencies are commensurate they are characterised as new multimodal motions emanating from the backbone in the frequency stiffness plot

a comparison of infinite timoshenko and euler bernoulli beam models on winkler foundation in the frequency and time domain abstract this paper deals with the dynamic analysis of infinite beam models the translational and the rotational dynamic stiffness of both timoshenko and euler bernoulli beams on winkler foundation are derived and compared in the frequency domain the situation of vanishing elastic foundation is included as a special case here special emphasis is placed on the asymptotic behaviour of the derived stiffness expressions for high frequencies since this is of importance in case of transient excitations it is shown that the dynamic stiffness of the infinite timoshenko beam follows a linear function of i whereas rational powers of i are involved in case of euler bernoulli s model the stiffness formulations can be transformed into the time domain using the mixed variables technique this is based on a rational approximation of the low frequency force displacement relationship and a subsequent algebraic splitting process at the same time the high frequency asymptotic dynamic stiffness is transformed into the time domain in closed form it is shown that the timoshenko beam is equivalent to a simple dashpot in the high frequency limit whereas euler bernoulli s beam model leads to fractional derivatives of the unknown state variables in an equivalent time domain description this finding confirms the superiority of timoshenko s model especially for high frequencies and transient excitations numerical examples illustrate the differences with respect to the two beam models and demonstrate the applicability of the proposed method for the time domain transformation of force displacement relationships

statistical properties of generalized discrepancies when testing that a sample of n points in the unit hypercube 0 1 d comes from a uniform distribution the kolmogorov smirnov and the cramer von mises statistics are simple and well known procedures to encompass these measures of uniformity hickernell introduced the so called generalized p discrepancies these discrepancies can be used in numerical integration through monte carlo and quasi monte carlo methods design of experiments uniformity testing and goodness of fit tests the aim of this paper is to derive the statistical asymptotic properties of these statistics under monte carlo sampling in particular we show that under the hypothesis of uniformity of the sample of points the asymptotic distribution is a complex stochastic integral with respect to a pinned brownian sheet on the other hand if the points are not uniformly distributed then the asymptotic distribution is gaussian

forced vibrations of a beam on a tensionless foundation abstract this paper is concerned with the response of an elastic beam resting on a tensionless winkler foundation subjected to a concentrated load a uniformly distributed load and a concentrated load the external load are assumed to be time dependent and the non linear governing differential equation of forced vibrations is derived by employing the galerkin method the free vibration mode functions of the completely free beam are adopted as the co ordinate functions of the displacement function of the beam the results which represent the static and dynamic responses of the beam are presented in the figures it is concluded that the presence of the lift off affects the response of the beam markedly by changing the shape of the displacement curve as well as the foundation reactions

some mathematical problems in the theory of quantum chaos abstract we discuss the general problem of distribution of spacings between levels in quantum problems for the quantum kicked rotator model we formulate the results on the poisson distribution for spacings some general remarks concerning the reasons for the appearance of this distribution are given

non linear modal analysis of structural components subjected to unilateral constraints in this paper we present a detailed numerical study of the non linear dynamics in structural components under unilateral contact constraints here the unilateral term characterises the constitutive law of the restoring force in the constraints as they only sustain elastic reactions in one direction either compressive or tensile thus the non differentiability of the contact law at the discontinuity point is the only source of non linearity in our approach the discrete lattice method dlm is used to treat the continuous system as a piecewise linear model thus the trajectory of each node in the discrete model would be a sequence of smooth solutions with the switching times between them the application of the one step integration scheme allows us to detect the occurrence of contact i e the instants that the lattice nodes cross the discontinuity boundary and consequently update the active constraints we also consider embedding the bisection algorithm into the time integration procedure to localise the instants at which the nodes cross the boundary and minimise the accumulative error subsequently the resulting unconditionally stable integration scheme is utilised as the modelling tool in combination with the shooting technique to perform a novel non smooth modal analysis in analogy with the smooth non linear systems the evolution of non smooth periodic motions is presented in the frequency stiffness plots we apply our method to obtain non linear normal modes nnms for a number of representative problems including a bar obstacle system a beam substrate system and a granular chain with tensionless interactions these numerical examples demonstrate the efficiency of the solution procedure to trace the family of energy independent non linear modes across the range of contact stiffnesses moreover the stability analysis of the modes on the plot backbone reveal that they may become unstable due to the interaction with the higher modes or bifurcation of a new nnm with a period equal to the integer multiple of the main mode period our results also indicate that the bilinear formula can accurately predict the non linear frequencies only if the corresponding mode exhibits a smooth character regardless of the commutativity conditions of the system stiffness matrix however it is obvious that the assumption of smooth bilinear behaviour for non linear modes is not generally valid this highlights the importance of the present numerical framework for the computation of non smooth resonance frequencies

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

response of beams resting on viscoelastically damped foundation to moving oscillators the response of beams resting on viscoelastically damped foundation under moving sdof oscillators is scrutinized through a novel state space formulation in which a number of internal variables is introduced with the aim of representing the frequency dependent behaviour of the viscoelastic foundation a suitable single step scheme is provided for the numerical integration of the equations of motion and the dimensional analysis is applied in order to define the dimensionless combinations of the design parameters that rule the responses of beam and moving oscillator the effects of boundary conditions span length and number of modes of the beam along with those of the mechanical properties of oscillator and foundation are investigated in a new dimensionless form and some interesting trends are highlighted the inaccuracy associated with the use of effective values of stiffness and damping for the viscoelastic foundation as usual in the present state of practice is also quantified

extremal probabilities for gaussian quadratic forms denote by q an arbitrary positive semidefinite quadratic form in centered gaussian random variables such that e q 1 we prove that for an arbitrary x 0 inf q p q x p 2 n n x where n 2 is a chi square distributed rv with n n x degrees of freedom n x is a non increasing function of x n 1 iff x x 1 1 5364 n 2 iff x x 2 x 1 where x 2 1 2989 etc n x rank q a similar statement is not true for the supremum if 1 x 2 and z 1 z 2 are independent standard gaussian rv s then sup0 1 2p z 1 2 1 z 2 2 x is taken not at 0 or at 1 2 but at 0 x 1 2 where x is a continuous increasing function from 1 0 to 2 1 2 e g 1 5 15 applications of our theorems include asymptotic quantiles of u and v statistics signal detection and stochastic orderings of integrals of squared gaussian processes

an efficient solution methodology to study the response of a beam on viscoelastic and nonlinear unilateral foundation static response abstract many engineering materials and foundations such as soils demonstrate nonlinear and viscoelastic behaviour yet it is challenging to develop static and dynamic models of systems that include these materials and are able to predict the behaviour over a wide range of loading conditions this research is focused on a specific example a pinned pinned beam interacting with polyurethane foam foundation two cases when the foundation can react in tension and compression as well as only in compression are considered the model developed here is capable of predicting the response to static as well as dynamic forces whether concentrated or distributed galerkin s method is used to derive modal amplitude equations in the tensionless foundation case the contact region changes with beam motion and the estimation of the co ordinates of the lift off points is embedded into the solution procedure an efficient solution technique is proposed that is capable of handling cases where there are multiple contact and non contact regions depending on the loading profiles a high number of modes may need to be included in the solution and to speed up computation time a convolution method is used to evaluate the integral terms in the model the adaptability of the solution scheme to complicated loading patterns is demonstrated via examples the solution approach proposed is applicable to dynamic loadings as well and in these cases the automated treatment of complicated response patterns makes the convolution approach particularly attractive the influence of various parameters on the static response is discussed

non gaussian fluctuations of local lyapunov exponents at intermittency in intermittent dynamical systems the distributions of local lyapunov exponents are markedly non gaussian and tend to be asymmetric and fat tailed a comparative analysis of the different time scales in intermittency provides a heuristic explanation for the origin of the exponential tails for which we also obtain an analytic expression deriving from a more quantitative theory application is made to several examples of discrete dynamical systems displaying intermittent dynamics

strange attractors that are not chaotic abstract it is shown that in certain types of dynamical systems it is possible to have attractors which are strange but not chaotic here we use the word strange to refer to the geometry or shape of the attracting set while the word chaotic refers to the dynamics of orbits on the attractor in particular the exponential divergence of nearby trajectories we first give examples for which it can be demonstrated that there is a strange nonchaotic attractor these examples apply to a class of maps which model nonlinear oscillators continuous time which are externally driven at two incommensurate frequencies it is then shown that such attractore are persistent under perturbations which preserve the original system type i e there are two incommensurate external driving frequencies this suggests that for systems of the typw which we have considered nonchaotic strange attractors may be expected to occur for a finite interval of parameter values on the other hand when small perturbations which do not preserve the system type are numerically introduced the strange nonchaotic attractor is observed to be converted to a periodic or chaotic orbit thus we conjecture that in general continuous time systems flows which are not externally driven at two incommensurate frequencies should not be expected to have strange nonchaotic attractors except possibly on a set of measure zero in the parameter space

asymptotic expansions for the laplace approximations of sums of banach space valued random variables let x i n be i i d b valued random variables where b is a real separable banach space let be a smooth enough mapping from b into r an asymptotic evaluation of z n e exp n n i 1 x i n up to a factor 1 o 1 has been gotten in bolthausen probab theory related fields 72 1986 305 318 and kusuoka and liang probab theory related fields 116 2000 221 238 in this paper a detailed asymptotic expansion of z n as n is given valid to all orders and with control on remainders the results are new even in finite dimensions

finite element dynamic analysis of finite beams on a bilinear foundation under a moving load abstract the present paper is concerned with the behaviour of finite elastic beams acted by a moving transverse concentrated load interacting with elastic foundations of different stiffnesses in compression and in tension using finite element analyses the displacement amplitudes and the critical velocities of the load on a uic 60 rail are computed and their dependence with respect to the difference between the foundation s moduli in compression and in tension is evaluated the limit case of a tensionless foundation is as well analyzed the numerical algorithm relies on the internal force vectors and tangent stiffness matrices computed exactly with automatic symbolic manipulation

distance multivariance new dependence measures for random vectors we introduce two new measures for the dependence of n ge2 random variables distance multivariance and total distance multivariance both measures are based on the weighted l 2 distance of quantities related to the characteristic functions of the underlying random variables these extend distance covariance introduced by szekely rizzo and bakirov from pairs of random variables to n tuplets of random variables we show that total distance multivariance can be used to detect the independence of n random variables and has a simple finite sample representation in terms of distance matrices of the sample points where distance is measured by a continuous negative definite function under some mild moment conditions this leads to a test for independence of multiple random vectors which is consistent against all alternatives

energy level statistics of model quantum systems universality and scaling in a lattice point problem we investigate the statistics of the numbern r s of lattice pointsn z 2 in an annular domain r w r w a ra wherer w 0 herea is a fixed convex set with smooth boundary andw is chosen so that the area of r w iss the statistics comes fromr being taken as random with a smooth density in some interval c 1 t c 2 t c 2 c 1 0 we find that in the limitt the variance and distribution of n n r s s depend strongly on hows grows witht there is a saturation regimes t ast in which the fluctuations in n coming from the two boundaries of are independent then there is a scaling regime s t z 0 z in which the distribution depends onz in an almost periodic way going to a gaussian asz 0 the variance in this limit approachesz for generic a but can be larger for degenerate cases the former behavior is what one would expect from the poisson limit of a distribution for annuli of finite area

synchronization by noise we provide sufficient conditions for synchronization by noise i e under these conditions we prove that weak random attractors for random dynamical systems consist of single random points in the case of sde with additive noise these conditions are also essentially necessary in addition we provide sufficient conditions for the existence of a minimal weak point random attractor consisting of a single random point as a result synchronization by noise is proven for a large class of sde with additive noise in particular we prove that the random attractor for an sde with drift given by a multidimensional double well potential and additive noise consists of a single random point all examples treated in tearne probab theory relat fields 141 1 2 1 18 2008 are also included

asymptotics for self normalized random products of sums of i i d random variables abstract let x x i i 1 be a sequence of independent and identically distributed positive random variables which is in the domain of attraction of the normal law and t n be a positive integer random variable denote s n i 1 n x i v n 2 i 1 n x i x 2 where x denotes the sample mean then we show that the self normalized random product of the partial sums k 1 t n s k k v t n is still asymptotically lognormal under a suitable condition about t n

a kind of complete moment convergence for self normalized sums let x x n n 1 be a sequence of independent and identically distributed i i d random variables with x in the domain of attraction of the normal law and ex 0 in this note we obtain a new kind of complete moment convergence for self normalized sums

transition to weak generalized synchrony in chaotically driven flows we study regimes of strong and weak generalized synchronization in chaotically forced nonlinear flows the transition between these dynamical states can occur via a number of different routes and here we examine the onset of weak generalized synchrony through intermittency and blowout bifurcations the quantitative characterization of this dynamical transition is facilitated by measures that have been developed for the study of strange nonchaotic motion weak and strong generalized synchronous motion show contrasting sensitivity to parametric variation and have distinct distributions of finite time lyapunov exponents

fractalization of a torus as a strange nonchaotic attractor fractalization of a torus and its transition to chaos in a quasiperiodically forced logistic map is reinvestigated in relation to a strange nonchaotic attractor with the aid of a functional equation for the invariant curve the existence of a fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor as well as the fourier mode analysis mechanisms of the onset of a fractal torus and the transition to chaos are studied in connection with the intermittency

asymptotic properties of the spectral test diaphony and related quantities this paper presents the limit laws of discrepancies defined via exponential sums and algorithms with error bounds to approximate the corresponding distribution functions the results cover the weighted and the nonweighted spectral test of hellekalek and various instances of the general discrepancies of hiekernell and hoogland and kleiss for the exponential function system as well as classical quantities like the spectral test diaphony and the zaremba figure of merit

scenarios for generalized synchronization with chaotic driving in chaotically driven nonlinear dynamical systems weak generalized synchrony can arise through distinct scenarios or routes in a manner similar to the onset of low dimensional chaos or the creation of strange nonchaotic attractors in quasiperiodically driven systems the limit sets of the dynamics for weak generalized synchronization are nonchaotic the lyapunov exponent is nonpositive and are geometrically strange quantitative measures related to the parameter sensitivity exponent and finite time lyapunov exponent distributions can be defined in order to characterize generalized synchronization

on the distribution of positive definite gaussian quadratic forms quadratic signal processing is used in detection and estimation of random signals to describe the performance of quadratic signal processing the probability distribution of the output of the processor is needed only positive definite gaussian quadratic forms are considered the quadratic form is diagonalized in terms of independent gaussian variables and its mean moment generating function and cumulants are computed conditions are given for the quadratic form to be chi 2 distributed and distributed like a sum of independent random variables having a gamma distribution a new method is proposed to approximate its probability distribution using an expansion in laguerre polynomials for the central case and in generalized chi 2 distributions in the noncentral case the series coefficients and bounds on truncation error are evaluated some applications in average power and power spectrum estimation and in detection illustrate our method

monte carlo approximations in bayesian decision theory abstract in decision making problems the bayesian action and its posterior expected loss usually cannot be obtained analytically in this article we study a monte carlo method for approximating the bayesian action and its posterior expected loss the monte carlo approximation to the bayesian action is obtained through a approximating the posterior expected loss function by using the monte carlo integration method and b searching the minimum of the approximated posterior expected loss function as the monte carlo sample size diverges to infinity the monte carlo approximations are shown to be convergent in general situations the rates of the convergence are also obtained under some regularity conditions on the loss function two accuracy measures of the monte carlo approximations are proposed some examples are presented for illustration

expected conditional characteristic function based measures for testing independence we propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions the

a perturbed lagrangian formulation for the finite element solution of contact problems making use of a perturbed lagrangian formulation a finite element procedure for contact problems is developed for the general case in which node to node contact no longer holds the proposed procedure leads naturally to a discretization of the contact interface into contact segments within the context of a bilinear interpolation for the displacement field a mixed finite element approximation is introduced by assuming discont naous contact pressure constant on the contact segment because of this piece wise constant approximation the gap function enters into the formulation in an average sense instead of through a point wise definition numerical examples are presented that illustrate the performance of the proposed procedure current finite element formulations for contact problems based on either the classical lagrange parameter procedure l 3 12 203 or the penalty function method 4 6 11 are characterized by a point wise enforcement of the contact constraint condition in the sense that penetration of the bodies is established on a nodal basis moreover in this methods the recovery of the contact pressure over the element from the contact nodal forces generally requires an additional procedure within the framework of classical lagrange multiplier methods the contact condition is exactly satisfied by transforming the constrained problem into an unconstrained one with the introduction of additional variables lagrange multipliers these extra variables add computational effort to the solution process which often requires special procedures to handle the presence of zero diagonal terms penalty methods on the other hand enable one to transform the constrained problem into an unconstrained one without introducing additional variables the constraint condition is now satisfied only approximately for finite values of the penalty parameter the main difhculty associated with these methods however lies in the poor conditioning of the problem as the penalty is increased to more accurately enforce the constraint condition this is a well understood phenomenon particularly in the context of the incompressible and nearly incompressible problem in solid and fluid mechanics e g see l 22 25 for a review recently augmented lagrangian procedures have been proposed as a promising way to partially overcome these difficulties and regularize the penalty formulation e g see the survey in 7 8 within the framework of zinearited e u c it is possible to restrict the finite element formulation of contact problems by assuming that node to node contact occurs this is in fact the case often considered in the literature l 2 4 6 12 20 211 in the general context of fully

simultaneous perturbation stochastic approximation of nonsmooth functions abstract a simultaneous perturbation stochastic approximation spsa method has been developed in this paper using the operators of perturbation with the lipschitz density function this model enables us to use the approximation of the objective function by twice differentiable functions and to present their gradients by volume integrals the calculus of the stochastic gradient by means of this presentation and likelihood ratios method is proposed that can be applied to create spsa algorithms for a wide class of perturbation densities the convergence of the spsa algorithms is proved for lipschitz objective functions under quite general conditions the rate of convergence o 1 k 1 2 of the developed algorithms has been established for functions with a sharp minimum as well as the dependence of the rate of convergence is explored theoretically as well as by computer simulation the applicability of the presented algorithm is demonstrated by applying it to minimization of the mean absolute pricing error for the calibration of the heston stochastic volatility model

non linear vibrations of a beam on an elastic foundation the non linear vibrations of an elastic beam resting on a non linear tensionless winkler foundation subjected to a concentrated load at the centre is presented in this paper since the foundation is assumed to be tensionless the beam may lift off the foundation and there exists different regions namely contact and non contact regions since the contact regions are not known in advance the problem appears as a non linear one even though there is no non linear term in the foundation model in this case the calculation of the roots of a non linear equation is needed to obtain contact lengths the perturbation technique is used to solve the non linear governing equation associated with the problem using this technique the non linear problem is reduced to the solution of a set of linearized partial differential equations the lift off points and the displacements are obtained in linear and non linear cases and the variation of these points with respect to various parameters are presented it is concluded that the contact length varies with the magnitude of the load because of the non linearity

random minimality and continuity of invariant graphs in random dynamical systems we study dynamical systems forced by a combination of random and deterministic noise and provide criteria in terms of lyapunov exponents for the existence of random attractors with continuous structure in the fibres for this purpose we provide suitable random versions of the semiuniform ergodic theorem and also introduce and discuss some basic concepts of random topological dynamics 2010 mathematics subject classification 37a30 37h15 34d45

nonlinear stochastic programming by monte carlo estimators abstract methods for solving stochastic programming sp problems by a finite series of monte carlo samples are considered the accuracy of solution is treated in a statistical manner testing the hypothesis of optimality according to statistical criteria the rule for adjusting the monte carlo sample size is introduced to ensure the convergence and to find the solution of the sp problem using a reasonable number of monte carlo trials issues of implementation of the developed approach in decision making and other applicable fields are considered too

a high dimensional clt in mathcal w _2 w 2 distance with near optimal convergence rate let x 1 ldots x n be i i d random vectors in mathbb r d with vert x 1 vert le beta then we show that begin aligned frac 1 sqrt n left x 1 cdots x n right end aligned converges to a gaussian in quadratic transportation also known as kantorovich or wasserstein distance at a rate of o left frac sqrt d beta log n sqrt n right improving a result of valiant and valiant the main feature of our theorem is that the rate of convergence is within log n of optimal for n d rightarrow infty

smoothed functionals in stochastic optimization we consider the problem of finding a global extremum for a nonconvex function by constructing another smoothed function which has a better behavior than the original one then operating only with the smoothed function we find the global extremum for the original function

absolute versus relative formulations of the moving oscillator problem in the general framework of the bridge vehicle dynamic interaction the so called moving oscillator problem is revisited in order to provide a deeper insight into some analytical and physical aspects not specifically analyzed in previous investigations without lack of generality the case of a stream of moving oscillators crossing a simply supported beam with arbitrary time law is considered the formulations in terms of both absolute and relative displacements of the moving oscillators are critically reviewed and compared and alternative sets of differential equations with time dependent coefficients are derived the study enlightens both theoretically and numerically that impulsive contributions to the dynamic response appear in the relative displacement formulation at the time instants in which each vehicle enters or exits the bridge it is demonstrated that such contributions somehow hidden in the absolute displacement formulation may have a significant influence on the vibration of the moving oscillators and thus cannot be a priori neglected in the analysis it is also shown that the analytical and computational difficulties associated with these additional impulses make preferable the use of the absolute displacement formulation far from being restricted to the case of simply supported beams these findings are valid for any type of bridge structure which induces a discontinuity in the slope of the road profile experienced by the vehicles

constrained euler buckling an interplay of computation and analysis we consider elastic buckling of an inextensible beam with hinged ends and fixed end displacements confined to the plane and in the presence of rigid frictionless sidewalls which constrain overall lateral displacements we formulate the geometrically nonlinear euler problem and develop global search and path following algorithms to find equilibria in various classes satisfying different contact patterns and hence boundary conditions we derive complete analytical results for the case of line contacts with the sidewalls and partial results for point contact and mixed cases the analysis is essential to understanding the numerical results for in contrast to the unconstrained problem we find a very rich bifurcation structure with the cardinality of branches growing exponentially with mode number

nature of weak generalized synchronization in chaotically driven maps weak generalized synchrony in a drive response system occurs when the response dynamics is a unique but nondifferentiable function of the drive in a manner that is similar to the formation of strange nonchaotic attractors in quasiperiodically driven dynamical systems we consider a chaotically driven monotone map and examine the geometry of the limit set formed in the regime of weak generalized synchronization the fractal dimension of the set of zeros is studied both analytically and numerically we further examine the stable and unstable sets formed and measure the regularity of the coupling function the stability index as well as the dimension spectrum of the equilibrium measure can be computed analytically

estimates for the closeness of successive convolutions of multidimensional symmetric distributions let 1 2 be i i d random vectors in k with a common distribution i f i 1 2 let s n 1 n we investigate how small is the difference between s n and s n m in the case when i have symmetric distributions