an extension of a bound for functions in sobolev spaces with applications to m s spline interpolation and smoothing given a function f on a bounded open subset of mathbb r n with a lipschitz continuous boundary we obtain a sobolev bound involving the values of f at finitely many points of overline omega this result improves previous ones due to narcowich et al math comp 74 743 763 2005 and wendland and rieger numer math 101 643 662 2005 we then apply the sobolev bound to derive error estimates for interpolating and smoothing m s splines in the case of smoothing noisy data as well as exact data are considered

sobolev bounds on functions with scattered zeros with applications to radial basis function surface fitting in this paper we discuss sobolev bounds on functions that vanish at scattered points in a bounded lipschitz domain that satisfies a uniform interior cone condition the sobolev spaces involved may have fractional as well as integer order we then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions rbfs these estimates include situations in which the target function does not belong to the native space of the rbf

a mixed method for dirichlet problems with radial basis functions we present a simple discretization by radial basis functions for the poisson equation with dirichlet boundary condition a lagrangian multiplier using piecewise polynomials is used to accommodate the boundary condition this simplifies previous attempts to use radial basis functions in the interior domain to approximate the solution and on the boundary to approximate the multiplier which technically requires that the mesh norm in the interior domain is significantly smaller than that on the boundary numerical experiments confirm the theoretical results

the p version of the boundary element method for weakly singular operators on piecewise plane open surfaces we study piecewise polynomial approximations in negative order sobolev norms of singularities which are inherent to neumann data of elliptic problems of second order in polyhedral domains the worst case of exterior crack problems in three dimensions is included as an application we prove an optimal a priori error estimate for the p version of the bem with weakly singular operators on polyhedral lipschitz surfaces and piecewise plane open screens

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

modulated stochastic multiresonance in a single mode laser system driven by colored additive and multiplicative noises without external periodic force abstract the stochastic resonance phenomenon is studied in a single mode laser system driven by correlated multiplicative and additive colored noises without modulation by external periodic force we detect that there are multiple extrema maximum in the curve of the mean output laser intensity versus the multiplicative noise intensity this phenomenon called stochastic multiresonance reveals that the mean output laser intensity can be amplified at several values of the multiplicative noise intensity whose peaks are modulated by a sinusoidal function this kind of stochastic resonance differs with those reported by past references furthermore similar behaviors also exist in the variance and the skewness

preconditioners for pseudodifferential equations on the sphere with radial basis functions in a previous paper a preconditioning strategy based on overlapping domain decomposition was applied to the galerkin approximation of elliptic partial differential equations on the sphere in this paper the methods are extended to more general pseudodifferential equations on the sphere using as before spherical radial basis functions for the approximation space and again preconditioning the ill conditioned linear systems of the galerkin approximation by the additive schwarz method numerical results are presented for the case of hypersingular and weakly singular integral operators on the sphere mathbb s 2

multiscale analysis in sobolev spaces on bounded domains we study a multiscale scheme for the approximation of sobolev functions on bounded domains our method employs scattered data sites and compactly supported radial basis functions of varying support radii at scattered data sites the actual multiscale approximation is constructed by a sequence of residual corrections where different support radii are employed to accommodate different scales convergence theorems for the scheme are proven and it is shown that the condition numbers of the linear systems at each level are independent of the level thereby establishing for the first time a mathematical theory for multiscale approximation with scaled versions of a single compactly supported radial basis function at scattered data points on a bounded domain

the effect of interference of coloured additive and multiplicative white noises on escape rate in this paper we have calculated the escape rate from a meta stable state for coloured and correlated noise driven open systems based on the fokker planck description of the stochastic process we consider the effect of two correlation times due to the additive coloured noise and the correlation between additive coloured and multiplicative white noises the effect of the noise correlation strength on the rate has also been investigated

stochastic resonance between dissipative structures in a bistable noise sustained dynamics we study an extended system that without noise shows a monostable dynamics but when submitted to an adequate multiplicative noise an effective bistable dynamics arises the stochastic resonance between the attractors of the noise sustained dynamicsis investigated theoretically in terms of a two state approximation the knowledge of the exact nonequilibrium potential allows us to obtain the output signal to noise ratio its maximum is predicted in the symmetric case for which both attractors have the same nonequilibrium potential value

double stochastic resonance in an insect ecosystem with time delays abstract considering additive and multiplicative periodic signals we have investigated the stochastic resonance sr phenomenon in an insect ecosystem with two different types of time delays at which the insect dynamics is assumed to be disturbed by both additive and multiplicative noises the signal to noise ratio snr is calculated when two different weak periodic signals are added to the insect system it is shown from the snr that the additive and multiplicative periodic signals can cause the sr and double sr in the case of time delays in the stochastic and deterministic force respectively a detailed study of the snr depending on various noise characteristics is performed and the main results about sr are compared for two different cases of time delays

iterative nonparametric estimation of a log optimal portfolio selection function let stock market vectors form a stationary ergodic sequence for fixed d spl isin n a log optimal portfolio selection function of the past d observed vectors is iteratively estimated on the basis of a training sequence by use of gradients and nonparametric regression strong consistency is obtained under a boundedness and spl alpha mixing condition without further assumptions on the distribution

nonparametric identification of wiener systems by orthogonal series a wiener system i e a system comprising a linear dynamic and a nonlinear memoryless subsystems connected in a cascade is identified both the input signal and disturbance are random white and gaussian the unknown nonlinear characteristic is strictly monotonous and differentiable and therefore the problem of its recovering from input output observations of the whole system is nonparametric it is shown that the inverse of the characteristic is a regression function and a class of orthogonal series nonparametric estimates recovering the regression is proposed and analyzed the estimates apply the trigonometric legendre and hermite orthogonal functions pointwise consistency of all the algorithms is shown under some additional smoothness restrictions the rates of their convergence are examined and compared an algorithm to identify the impulse response of the linear subsystem is proposed

approximate fokker planck equation of system driven by multiplicative colored noises with colored cross correlation abstract using the hanggi ansatz to truncate the evolution equation for probability density an approximate fokker planck equation afpe is derived this afpe is valid for one dimensional general systems driven by two multiplicative colored noises 1 0 and 2 0 that are correlated in color 3 0 under the condition for 1 2 and 3 to satisfy some inequalities we apply this afpe to a symmetrical bistable potential system driven by a colored multiplicative noise and a white additive noise with white cross correlation to verify the validity of our analytical approximation the numerical simulations for this system is performed we discovered a new phenomenon that the symmetry of stationary probability density broken by the correlation between the noises can be gradually recovered as the noise self correlation time is increased

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

meshless galerkin methods using radial basis functions we combine the theory of radial basis functions with the field of galerkin methods to solve partial differential equations after a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions

continuous time wiener system identification a continuous time wiener system is identified the system consists of a linear dynamic subsystem and a memoryless nonlinear one connected in a cascade the input signal is a stationary white gaussian random process the system is disturbed by stationary white random gaussian noise both subsystems are identified from input output observations taken at the input and output of the whole system the a priori information is very small and therefore resulting identification problems are nonparametric the impulse impulse of the linear part is recovered by a correlation method while the nonlinear characteristic is estimated with the help of the nonparametric kernel regression method the authors prove convergence of the proposed identification algorithms and examine their convergence rates

role of phase difference and colored cross correlation on current in multiplicative and additive noises driven systems abstract we have investigated the transport properties of multiplicative and additive noise driven spatially periodic system the phase difference between periodic potential and periodic function in multiplicative noise term and the cross correlation between multiplicative and additive noise can break the detail balance of the system independently to produce directed motion the magnitude of current due to phase difference is smaller in comparison to cross correlation between the noises the phase difference can be used to control the direction of the cross correlation induced current another interesting observation is that there is a current inversion with increase of cross correlation time the current increases linearly with the strength of cross correlation

stochastic resonance and generalized information measures abstract we use tsallis information measure and the recently advanced escort tsallis one in order to investigate the stochastic resonance sr phenomenon in particular on the basis of these generalized information measures gim both characterized by a non extensivity parameter q we study the effect of modifying the type of noise the gim are used to measure sr phenomenon comparing the input and output probability distributions finding that for the range of noise intensities enhancing sr q 0 gives the optimum measure an important advantage of using gim instead of shannon s measure is the possibility of detecting smaller signal amplitudes with the former than with the latter one

stochastic resonance in an asymmetric bistable system with coloured noises and periodic rectangular signal abstract in this paper we consider the phenomenon of stochastic resonance sr in an asymmetric bistable system with coloured noises and periodic rectangular signal expression of the signal to noise ratio snr has been obtained under the adiabatic limit we investigate the effect of any system parameter such as p q r 1 2 on the snr the plot of snr 1 shows sr for some values of the additive noise self correlation time 2 but not for the whole range of 2 the system bias r suppresses the snr when the intensity of additive noise q is increased the sr phenomenon disappears in the plot of snr p but the plot of snr q presents sr for almost all values of the multiplicative noise intensity p

additive schwarz method for the p version of the boundary element method for the single layer potential operator on a plane screen we analyze an additive schwarz preconditioner for the p version of the boundary element method for the single layer potential operator on a plane screen in the three dimensional euclidean space we decompose the ansatz space which consists of piecewise polynomials of degree p on a mesh of size h by introducing a coarse mesh of size h ge h after subtraction of the coarse subspace of piecewise constant functions on the coarse mesh this results in local subspaces of piecewise polynomials living only on elements of size h this decomposition yields a preconditioner which bounds the spectral condition number of the stiffness matrix by o log frac hhp 2 numerical results supporting the theory are presented

generalization of the escape rate from a metastable state driven by external cross correlated noise processes we propose generalization of the escape rate from a metastable state for externally driven correlated noise processes in one dimension in addition to the internal non markovian thermal fluctuations the external correlated noise processes we consider are gaussian stationary in nature and are of ornstein uhlenbeck type based on a fokker planck description of the effective noise processes with finite memory we derive the generalized escape rate from a metastable state in the moderate to large damping limit and investigate the effect of degree of correlation on the resulting rate comparison of the theoretical expression with numerical simulation gives a satisfactory agreement and shows that by increasing the degree of external noise correlation one can enhance the escape rate through the dressed effective noise strength

stochastic system with coupling between non gaussian and gaussian noise terms a stochastic system with coupling between non gaussian and gaussian noise terms is investigated a general approximate fokker planck equation of the system is derived through a path integral approach for a bistable system the coupling between noise terms can induce the reentrance like phase transition while the parameter q of the departure from the gaussian noise can induce the first order like phase transition both the coupling and the parameter q can change the curve of the mean first passage time mfpt from monotonically decreasing function to a peak in the mfpt numerical simulations are carried out to check the approximate theoretical results reasonably good agreement is obtained

a unified theory of radial basis functions native hilbert spaces for radial basis functions ii abstract this contribution provides a new formulation of the theory of radial basis functions in the context of integral operators instead of fourier transforms the most important tools now are expansions into eigenfunctions this unifies the theory of radial basis functions in r d with the theory of zonal functions on the sphere sd 1 and the theory of kernel functions on riemannian manifolds new characterizations of native spaces and positive definite functions are included the paper is a self contained continuation of an earlier survey r schaback international series of numerical mathematics vol 132 birkhauser basel 1999 pp 255 282 over the native spaces associated to not necessarily radial basis functions

optimal range of a nonlocal kernel for stochastic resonance in extended systems abstract here we study stochastic resonance sr in a spatially extended system described by a reaction diffusion equation for a scalar activator like field including a nonlocal contribution we assume that such a contribution arises from an effective adiabatic elimination of an auxiliary inhibitor like field our aim is to study the role played by the range of the nonlocal kernel on the sr phenomena we have found that increasing the nonlocal coupling reduces the system s response and that similar to the so called system size sr there is an optimal value of the kernel s range yielding a maximum in the system s response

graph laplacians and their convergence on random neighborhood graphs given a sample from a probability measure with support on a submanifold in euclidean space one can construct a neighborhood graph which can be seen as an approximation of the submanifold the graph laplacian of such a graph is used in several machine learning methods like semi supervised learning dimensionality reduction and clustering in this paper we determine the pointwise limit of three different graph laplacians used in the literature as the sample size increases and the neighborhood size approaches zero we show that for a uniform measure on the submanifold all graph laplacians have the same limit up to constants however in the case of a non uniform measure on the submanifold only the so called random walk graph laplacian converges to the weighted laplace beltrami operator

rate laws of the self induced aggregation kinetics of brownian particles abstract in this paper we have studied the self induced aggregation kinetics of brownian particles in the presence of both multiplicative and additive noises in addition to the drift due to the self aggregation process the environment may induce a drift term in the presence of a multiplicative noise then there would be an interplay between the two drift terms it may account qualitatively the appearance of the different laws of aggregation process at low strength of white multiplicative noise the cluster number decreases as a gaussian function of time if the noise strength becomes appreciably large then the variation of cluster number with time is fitted well by the mono exponentially decaying function of time for additive noise driven case the decrease of cluster number can be described by the power law but in case of multiplicative colored driven process cluster number decays multi exponentially however we have explored how the rate constant in the mono exponentially cluster number decaying case depends on strength of interference of the noises and their intensity we have also explored how the structure factor at long time depends on the strength of the cross correlation cc between the additive and the multiplicative noises

stochastic resonance driven by time modulated correlated white noise sources we analyze the effects caused by the simultaneous presence of correlated additive and multiplicative noises for stochastic resonance besides the standard potential modulation we also consider a time periodic variation of the correlation between the two noise sources as a foremost result we find that stochastic resonance as characterized by the signal to noise ratio and the spectral amplification becomes characteristically broadened the broadening can be controlled by varying the relative phase shift between the two types of modulation force

nonparametric identification of wiener systems a wiener system i e a system in which a linear dynamic part is followed by a nonlinear and memoryless one is identified no parametric restriction is imposed on the functional form of the nonlinear characteristic of the memoryless subsystem and a nonparametric algorithm recovering the characteristic from input output observations of the whole system is proposed its consistency is shown and the rate of convergence is given an idea for identification of the impulse response of the linear subsystem is proposed results of numerical simulation are also presented

mortar boundary elements we establish a mortar boundary element scheme for hypersingular boundary integral equations representing elliptic boundary value problems in three dimensions we prove almost quasi optimal convergence of the scheme in broken sobolev norms of order 1 2 subdomain decompositions can be geometrically nonconforming and meshes must be quasi uniform only on subdomains numerical results confirm the theory

kernel smoothing of data with correlated errors abstract kernel smoothing is a common method of estimating the mean function in the nonparametric regression model y f x e where f x is a smooth deterministic mean function and e is an error process with mean zero in this article the mean squared error of kernel estimators is computed for processes with correlated errors and the estimators are shown to be consistent when the sequence of error processes converges to a mixing sequence the standard techniques for bandwidth selection such as cross validation and generalized cross validation are shown to perform very badly when the errors are correlated standard selection techniques are shown to favor undersmoothing when the correlations are predominantly positive and oversmoothing when negative the selection criteria can however be adjusted to correct for the effect of correlation in simulations the standard selection criteria are shown to behave as predicted the corrected criteria are shown to be very effective when the correlation functi

hammerstein system identification by non parametric regression estimation a discrete time multiple input non linear hammerstein system is identified the dynamical subsystem is recovered using the standard correlation method the main results concern estimation of the non linear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a non parametric kernel estimate of the regression function calculated from the dependent data it is shown that the algorithm converges to the characteristic of the subsystem in the pointwise as well as the global sense for sufficiently smooth characteristics the rate of convergence is o n 1 2 d in probability where d is the dimension of the input variable

on almost sure convergence of conditional empirical distribution functions on etudie la convergence presque sure d une distribution empirique conditionnelle de type noyau a la fois en norme sup et en norme sup ponderee

radial basis functions for the solution of hypersingular operators on open surfaces we analyze the approximation by radial basis functions of a hypersingular integral equation on an open surface in order to accommodate the homogeneous essential boundary condition along the surface boundary scaled radial basis functions on an extended surface and lagrangian multipliers on the extension are used we prove that our method converges quasi optimally approximation results for scaled radial basis functions indicate that for highly regular radial basis functions the achieved convergence rates are close to the one of low order conforming boundary element schemes numerical experiments confirm our conclusions

stochastic resonance driven by two different kinds of colored noise in a bistable system the phenomenon of stochastic resonance in a bistable nonlinear system is investigated when both the multiplicative noise and the coupling between additive and multiplicative noise are colored with different values of noise correlation time ensuremath tau 1 and ensuremath tau 2 combining the functional analysis and unified colored noise approximation the two different kinds of colored noise in the nonlinear system can be simplified the signal to noise ratio is calculated when a weakly periodic signal is added to the system it is found that there appears a transition between one peak and two peaks in the curve of the signal to noise ratio when either the noise correlation time ensuremath tau 1 and ensuremath tau 2 or the coupling strength ensuremath lambda between additive and multiplicative noise is increased the transition between one and two peaks depending on ensuremath tau 1 and ensuremath lambda is more complex than that depending on ensuremath tau 2

dynamical properties of a logistic growth model with cross correlated noises abstract a logistic growth model driven by additive and multiplicative noises which are correlated with each other is investigated using the novikov theorem and the projection operator method we obtain the analytic expressions of the stationary probability distribution p s t x the relaxation time t c and the normalized correlation function c s of this system the computational results show that the relaxation time t c increases as the cross correlated time increases but decreases while the cross correlated strength increases the relationship between the relaxation time c s and the decay time s is given correlation time and correlation strength play an opposite role on dynamic properties in this logistic growth model

on the h p version of the boundary element method for symm s integral equation on polygons abstract in this paper we present the numerical implementation of and numerical experiments for the galerkin approximation of symm s integral equation using the h p and h p methods numerical results obtained using an adaptive algorithm are also given the theoretical results for these methods are summarized and are compared with the experimental results

different delays induced regime shifts in a stochastic insect outbreak dynamics abstract considering time delays in the deterministic and stochastic forces we construct stochastic delayed differential equations to investigate the regime shifts in an insect ecosystem the stationary probability distribution spd and mean first passage time mfpt are obtained respectively our main results show i the multiplicative noise positive cross correlation noise between two noises and time delays can induce the regime shifts from the boom outbreak state to the bust one but the additive noise and negative cross correlation can induce the regime shifts from the bust outbreak state to the boom one ii for the negative cross correlation the mfpt as a function of noise strengths exhibits one maximum which shows the characteristic of the noise delayed switching for the boom outbreak state but for the no cross correlation or positive cross correlation the mfpt decreases with the noise strengths iii two different types of time delays play same roles on the maximal mfpt with additive noise and play opposite roles on the maximal mfpt with multiplicative noise the mechanisms for noises and delays induced regime shifts between two states can be explained physically through the effective potential of ecological model