the dual tree of a recursive triangulation of the disk in the recursive lamination of the disk one tries to add chords one after another at random a chord is kept and inserted if it does not intersect any of the previously inserted ones curien and le gall ann probab vol 39 pp 2224 2270 2011 have proved that the set of chords converges to a limit triangulation of the disk encoded by a continuous process m based on a new approach resembling ideas from the so called contraction method in function spaces we prove that when properly rescaled the planar dual of the discrete lamination converges almost surely in the gromov hausdorff sense to a limit real tree t which is encoded by m this confirms a conjecture of curien and le gall 1 introduction and main results in 18 curien and le gall introduce the model of random recursive triangulations of the disk the construction goes as follows atn 1 two points are sampled independently with uniform distribution on the circle they are connected by a chord a straight line which splits the disk into two fragments later on at each step two independent points are sampled uniformly at random on the circle and are connected by a chord if the latter does not intersect any of the previously inserted chords in other words the two points are connected by a chord if they both fall in the same fragment this gives rise to a sequence of laminations of the disk for us a lamination will be a collection of chords which may only intersect at their end points at timen the lamination ln consists of the union of the chords inserted up to timen as an increasing closed subset of the disk ln converges and it is proved in 18 that

paper tracking error bounds of adaptive nonstationary filtering adaptive filtering with error gradient algorithm and constant step size is analyzed for a deterministic time variable optimum filtering vector the unrealistic assumption of independent observations is replaced by a bounded memory model largely justifiable in applications then the mean square tracking deviation msd between the optimum vector and the algorithm output is proved to include two contributions the stationary mode error characteristic of convergence accuracy which is proportional to the step size and the transient mode error reflecting the rapidity of tracking which is proportional to the squared ratio of the maximum optimum estimator increment to the step size this result agrees with the common intuition that there exists an optimum step size which compromises between convergence accuracy and tracking speed

smoothness priors transfer function estimation abstract a smoothness priors approach to transfer function estimation from stationary time series is shown an infinite order impulse response model plus an infinite order additive ar noise model is assumed this is algebraically equivalent to an infinite order armax plus white noise model a finite order armax model approximation to this model is actually fitted to data frequency domain smoothness priors are assumed on the armax polynomials and smoothness hyperparameters balance the tradeoff between the infidelity of the model to the data and the infidelity of model to the smoothness constraints the likelihood of the hyperparameters is maximized by a least squares gradient search computational procedure the method is illustrated by the analysis of the box jenkins series j data some of the statistical properties of the method are explored in monte carlo simulation studies keywords bayesian models linear regression models charts

output only identification and dynamic analysis of time varying mechanical structures under random excitation a comparative assessment of parametric methods this article addresses the problem of parametric time domain identification and dynamic analysis for time varying tv mechanical structures under unobservable random excitation the methods presented are based on time dependent autoregressive moving average tarma models and are classified according to the mathematical structure imposed on the tv parameter evolution as unstructured parameter evolution stochastic parameter evolution and deter ministic parameter evolution the features and relative merits of each class are outlined a representativ e method from each is then assessed through its application to the identification and dynamic analysis o f a laboratory tv structure consisting of a beam with a mass moving on it the results are mutually compared and contrasted to those obtained through frozen configuration multiple experiment bas eline identification

estimation of stationary structural system parameters from non stationary random vibration data a locally stationary model method abstract stationary structural system building natural frequency and damping parameters are estimated from a long non stationary ambient vibration time series record the non stationary vibration record is decomposed into continuous not necessarily equal duration stationary time series segments by a locally stationary autoregressive ar model method estimates of the stationary structural system parameters are extracted from each of the locally stationary ar models the final estimate of the structural system parameters is a time duration weighted average of the estimates in each stationary segment under reasonable conditions the theoretical variance of the structural system parameter estimates decreases with the duration of the long non stationary record the results of the analysis of a long duration non stationary record are compared with the results of an earlier approach in which the long duration non stationary record was decomposed into relatively short fixed duration vibration records and analyzed as stationary time series 1 the variances of the damping parameter estimates achieved by the current method are one half to one quarter of those obtained by the earlier method the sample variance of the structural system parameter estimates decreases with the reciprocal of the duration of the overall non stationary record

a smoothness priors long ar model method for spectral estimation a new smoothness priors long ar model method approach is taken to the short data span spectral estimation problem an autoregressive ar model that is relatively long compared to the data length is considered the smoothness priors are in the form of the integrated squared derivatives of the ar model whitening filter a smoothness tradeoff parameter or bayesian hyperparameter balances the tradeoff between the infidelity of the ar model to the data and the infidelity of the model to the smoothness constraint the critical computation of the likelihood of the hyperparameters of the bayesian model is realized by a constrained least squares computation numerical examples are shown the results of simulation studies using entropy comparison evaluations of the bayesian and minimum aic ar methods of spectral estimation are also shown

scaling limits of markov branching trees with applications to galton watson and random unordered trees we consider a family of random trees satisfying a markov branching property roughly this property says that the subtrees above some given height are independent with a law that depends only on their total size the latter being either the number of leaves or vertices such families are parameterized by sequences of distributions on partitions of the integers that determine how the size of a tree is distributed in its different subtrees under some natural assumption on these distributions stipulating that macroscopic splitting events are rare we show that markov branching trees admit the so called self similar fragmentation trees as scaling limits in the gromov hausdorff prokhorov topology applications include scaling limits of consistent markov branching model and convergence of galton watson trees towards the brownian and stable continuum random trees we also obtain that random uniform unordered trees have the brownian tree as a scaling limit hence extending a result by marckert miermont and fully proving a conjecture made by aldous

on a functional contraction method methods for proving functional limit laws are developed for sequences of stochastic processes which allow a recursive distributional decomposition either in time or space our approach is an extension of the so called contraction method to the space c 0 1 of continuous functions endowed with uniform topology and the space d 0 1 of cadlag functions with the skorokhod topology the contraction method originated from the probabilistic analysis of algorithms and random trees where characteristics satisfy natural distributional recurrences it is based on stochastic fixed point equations where probability metrics can be used to obtain contraction properties and allow the application of banach s fixed point theorem we develop the use of the zolotarev metrics on the spaces c 0 1 and d 0 1 in this context applications are given in particular a short proof of donsker s functional limit theorem is derived and recurrences arising in the probabilistic analysis of algorithms are discussed

space time coding ambiguities in joint adaptive channel estimation and detection this paper studies the error propagation effect that is caused by certain ambiguities in joint data detection channel tracking algorithms for transmission diversity schemes here we use a space time st receiver based on the maximum a posteriori map method that takes into account the channel estimation error assuming the unknown channel to have a given complex multivariate gaussian probability density function pdf i e a ricean channel the decision criterion that is expressed in quadratic form represents either a linear detector or a noncoherent nonlinear detector in extreme cases then the channel pdf for the next iteration is updated by estimates of the second order statistics of the channel coefficients and a very simple decision directed adaptive algorithm is derived for adaptive channel estimation the adaptive algorithm can efficiently track a fast rayleigh fading channel and as a result achieves robust performance however the occurrence of two types of ambiguities initiated in deep fades result in error propagation some remedies called space time ambiguity remedies stars are proposed to prevent error propagation a new time varying space time coding tvst scheme is suggested as a bandwidth efficient method to combat the permutation ambiguity impairment this coding scheme in conjunction with a differential detector can resolve the ambiguity problem

stochastic adaptive control and martingale limit theory recently s p meyn and p e caines ibid vol ac 32 p 220 6 1987 have used ergodic theory for markov processes to give the first asymptotic stability analysis of a nontrivial stochastic adaptive control problem by nontrivial is meant a stochastic adaptive control problem whose parameter variation has finite nonzero power they correctly observed that the stochastic lyapunov function methods fail here because there is no almost sure parameter convergence it is shown here how martingale asymptotics can be used to produce many results close to those of meyn and caines as well as to supply some new observations strengths and weaknesses of both approaches are discussed

probabilistic and fractal aspects of levy trees we investigate the random continuous trees called levy trees which are obtained as scaling limits of discrete galton watson trees we give a mathematically precise definition of these random trees as random variables taking values in the set of equivalence classes of compact rooted trees which is equipped with the gromov hausdorff distance to construct levy trees we make use of the coding by the height process which was studied in detail in previous work we then investigate various probabilistic properties of levy trees in particular we establish a branching property analogous to the well known property for galton watson trees conditionally given the tree below level a the subtrees originating from that level are distributed as the atoms of a poisson point measure whose intensity involves a local time measure supported on the vertices at distance a from the root we study regularity properties of local times in the space variable and prove that the support of local time is the full level set except for certain exceptional values of a corresponding to local extinctions we also compute several fractal dimensions of levy trees including hausdorff and packing dimensions in terms of lower and upper indices for the branching mechanism function which characterizes the distribution of the tree we finally discuss some applications to super brownian motion with a general branching mechanism

mixture based extension of the ar model and its recursive bayesian identification an extension of the autoregressive ar model is studied which allows transformations and distortions on the regressor to be handled many important signal processing problems are amenable to this extended ar i e ear model it is shown that bayesian identification and prediction of the ear model can be performed recursively in common with the ar model itself the ear model does however require that the transformation be known when it is unknown the associated transformation space is represented by a finite set of candidates what follows is a mixture based ear model i e the mear model an approximate identification algorithm for mear is developed using a restricted variational bayes vb method this restores the elegant recursive update of sufficient statistics the mear model is applied to the robust identification of ar processes corrupted by outliers and burst noise respectively and to click removal for speech

some statistical methods for random process data from seismology and neurophysiology examples are presented of statistical techniques for the analysis of random process data and of their uses in the substantive fields of seismology and neurophysiology the problems addressed include frequency estimation for decaying cosinusoids signal estimation association measurement causal connection assessment estimation of speed and direction and structural modeling the techniques employed include complex demodulation nonlinear regression probit analysis deconvolution maximum likelihood singular value decomposition fourier analysis and averaging

random stable laminations of the disk we study large random dissections of polygons we consider random dissections of a regular polygon with n sides which are chosen according to boltzmann weights in the domain of attraction of a stable law of index 2 1 2 as n goes to infinity we prove that these random dissections converge in distribution towards a random compact set called the random stable lamination if 2 we recover aldous brownian triangulation however if 2 1 2 large faces remain in the limit and a dierent random compact set appears we show that the random stable lamination can be coded by the continuous time height function associated to the normalized excursion of a strictly stable spectrally positive levy process of index using this coding we establish that the hausdor dimension of the stable random lamination is almost surely 2 1

analysis of a new stabilized finite element method for the reaction convection diffusion equations with a large reaction coefficient abstract in this paper we propose and analyze a new stabilized finite element method using continuous piecewise linear or bilinear elements for solving 2d reaction convection diffusion equations the equation under consideration involves a small diffusivity e and a large reaction coefficient leading to high peclet number and high damkohler number in addition to giving error estimates of the approximations in l 2 and h 1 norms we explicitly establish the dependence of error bounds on the diffusivity the l norm of convection field the reaction coefficient and the mesh size our analysis shows that the proposed method is particularly suitable for problems with a small diffusivity and a large reaction coefficient or more precisely with a large mesh peclet number and a large mesh damkohler number several numerical examples exhibiting boundary or interior layers are given to illustrate the high accuracy and stability of the proposed method the results obtained are also compared with those of existing stabilization methods

the continuum random tree iii let mathscr r k k geq 1 be random trees with k leaves satisfying a consistency condition removing a random leaf from mathscr r k gives mathscr r k 1 then under an extra condition this family determines a random continuum tree mathscr l which it is convenient to represent as a random subset of l 1 this leads to an abstract notion of convergence in distribution as n rightarrow infty of rescaled random trees mathscr j n on n vertices to a limit continuum random tree mathscr l the notion is based upon the assumption that for fixed k the subtrees of mathscr j n determined by k randomly chosen vertices converge to mathscr r k as our main example under mild conditions on the offspring distribution the family tree of a galton watson branching process conditioned on total population size equal to n can be rescaled to converge to a limit continuum random tree which can be constructed from brownian excursion

upper and lower bounds of the misadjustment in the lms algorithm the misadjustment is a dimensionless measure of the difference between the optimal weiner performance and the actual performance of the lms least mean squares algorithm this difference is attributed to the gradient noise in the adaptive process present estimates relate the misadjustment to the convergence gain and the trace of the autocorrelation matrix the authors establish tighter lower bounds on the estimate of this misadjustment an upper bound on the misadjustment as a function of the convergence gain is found

changing spectrum estimation abstract an autoregressive ar model with time varying coefficients is used for the modeling of non stationary covariance time series a stochastically perturbed linear constraint model is presented as a model of time varying ar coefficients the overall model for the time series is fitted by using the kalman filter and akaike s aic criterion an estimate of a changing spectrum is obtained by the fitted model and the fixed interval smoother examples are given to illustrate the procedure

synchronized per survivor mlsd receiver using a differential kalman filter a synchronized per survivor processing psp maximum likelihood sequence detection mlsd receiver is presented for a fast frequency selective rayleigh fading channel and large carrier frequency offset it is shown that by incorporating the synchronization parameters the timing error carrier frequency and phase offsets into the channel impulse response cir and modifying the resulting state space model by a differential approach the time varying carrier frequency offset can be effectively tracked using a simple least mean square lms estimator new criteria are proposed based on the smoothness of the estimated channel derivatives new criteria are proposed based on this fact that for smoothly time varying cir and frequency offset the magnitude of the cir time derivative compared with the magnitude of cir should be very small it is illustrated that the new criteria and the conventional mean square error mse are complementary

a weak galerkin finite element scheme with boundary continuity for second order elliptic problems abstract a new weak galerkin wg finite element method for solving the second order elliptic problems on polygonal meshes by using polynomials of boundary continuity is introduced and analyzed the wg method is utilizing weak functions and their weak derivatives which can be approximated by polynomials in different combination of polynomial spaces different combination gives rise to different weak galerkin finite element methods which makes wg methods highly flexible and efficient in practical computation this paper explores the possibility of certain combination of polynomial spaces that minimize the degree of freedom in the numerical scheme yet without losing the accuracy of the numerical approximation error estimates of optimal order are established for the corresponding wg approximations in both a discrete h 1 norm and the standard l 2 norm in addition the paper also presents some numerical experiments to demonstrate the power of the wg method the numerical results show that the wg method achieves the optimal convergence order with a relatively low computational cost which reveals a great promise of the flexibility and accuracy of the wg method

analysis of variable degree hdg methods for convection diffusion equations part ii semimatching nonconforming meshes in this paper we provide a projection based analysis of the hversion of the hybridizable discontinuous galerkin methods for convectiondiffusion equations on semimatching nonconforming meshes made of simplexes the degrees of the piecewise polynomials are allowed to vary from element to element we show that for approximations of degree k on all elements the order of convergence of the error in the diffusive flux is k 1 and that that of a projection of the error in the scalar unknown is 1 for k 0 and k 2 for k 0 we also show that for the variable degree case the projection of the error in the scalar variable is h times the projection of the error in the vector variable provided a simple condition is satisfied for the choice of the degree of the approximation on the elements with hanging nodes these results hold for any bounded irregularity index of the nonconformity of the mesh moreover our analysis can be extended to hypercubes

tracking of time varying mobile radio channels 1 the wiener lms algorithm adaptation algorithms with constant gains are designed for tracking smoothly time varying parameters of linear regression models in particular channel models occurring in mobile radio communications in a companion paper an application to channel tracking in the is 136 tdma system is discussed the proposed algorithms are based on two key concepts first the design is transformed into a wiener filtering problem second the parameters are modeled as correlated arima processes with known dynamics this leads to a new framework for systematic and optimal design of simple adaptation laws based on prior information the algorithms can be realized as wiener filters called learning filters or as lms newton updates complemented by filters that provide predictions or smoothing estimates the simplest algorithm named the wiener lms is presented all parameters are here assumed governed by the same dynamics and the covariance matrix of the regressors is assumed known the computational complexity is of the same order of magnitude as that of lms for regressors which are either white or have autoregressive statistics the tracking performance is however substantially improved

non gaussian state space modeling of nonstationary time series abstract a non gaussian state space approach to the modeling of nonstationary time series is shown the model is expressed in state space form where the system noise and the observational noise are not necessarily gaussian recursive formulas of prediction filtering and smoothing for the state estimation and identification of the non gaussian state space model are given also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas significant merits of non gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples a typical application of this non gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes simple gaussian state space modeling is not adequate for this situation here the model with small system noise variance cannot detect jump whereas the one with large system noise variance yields unfavorable wiggle to work

performance of transform domain lms adaptive digital filters in this paper we analyze the performance particularly the convergence behavior of the transform domain least mean square lms adaptive digital filter adf using the discrete fourier transform and discrete orthogonal transforms such as discrete cosine and sine transforms we first obtain the optimum wiener solution and the minimum mean squared error mse in the transform domain it is shown that the two minimum mse s in the time and transform domains are identical independently of the transforms used we then study the convergence conditions and the steady state excess mse s of the transform domain lms trlms algorithms both for the cases of having a constant and a time varying convergence factors when a constant convergence factor is used the convergence behaviors of the lms and trlms adf s appear to be almost identical provided that each has an appropriate value of the convergence factor depending on the transform used also based on the concept of a self orthogonalizing algorithm in the transform domain it is shown that the convergence speed of the trlms adf can be improved significantly for the same excess mse as that of the lms adf in addition we compare the computational complexities of the lms and trlms adf s finally we investigate by computer simulation the effects of system parameter values and different transforms on the convergence behavior of the trlms adf

a property of the minimum vectors of a regularizing functional defined by means of the absolute norm we consider a regularizing functional defined by means of the l sub 1 norm where the regularization is obtained using first differences as is well known such a functional can be put in relation with recursive median filters of appropriate window length we show that at least one of the minima is reached at a vector whose components have values over the same discrete set of the given signal this suggests a simple method to refine the approximate solution to the regularization problem which can be obtained with recursive median filters of increasing order we also report an example of application where the refinement method is employed for a signal detection problem

nonparametric input estimation in physiological systems problems methods and case studies input estimation from output data is an important problem in the analysis of physiological systems because many signals of interest are not directly accessible to measurement when the system is time invariant this problem is often referred to as deconvolution three representative physiological problems regarding hormone secretion insulin dynamics and hepatic glucose production are used to illustrate the major challenges ill conditioning confidence intervals assessment infrequent and nonuniform sampling nonnegativity constraints and computational efficiency the paper provides a critical overview of the existing techniques focusing on regularization theory and bayesian estimation in order to overcome some inadequacies of the existing methods some new results are derived in particular the connection between the maximum likelihood estimate of the regularization parameter and the notion of equivalent degree of freedom is studied moreover a fast svd based numerical algorithm is developed that includes the optimization of the regularization parameter and the computation of confidence intervals the proposed techniques are validated on a benchmark problem and are shown to provide effective solutions to the three physiological case studies

estimating time varying parameters by the kalman filter based algorithm stability and convergence convergence and stability properties of the kalman filter based parameter estimator are established for linear stochastic time varying regression models the main features are both the variances and sample path averages of the parameter tracking error are shown to be bounded the regression vector includes both stochastic and deterministic signals and no assumptions of stationarity or independence are requires and the unknown parameters are only assumed to have bounded variations in an average sense

discontinuous galerkin methods for advection diffusion reaction problems we apply the weighted residual approach recently introduced in f brezzi et al comput methods appl mech engrg 195 2006 pp 3293 3310 to derive discontinuous galerkin formulations for advection diffusion reaction problems we devise the basic ingredients to ensure stability and optimal error estimates in suitable norms and propose two new methods

the weak galerkin finite element method for the symmetric hyperbolic systems abstract in this paper we present and analyze a weak galerkin finite element wg method for solving the symmetric hyperbolic systems this method is highly flexible by allowing the use of discontinuous finite elements on element and its boundary independently of each other by introducing special weak derivative we construct a stable weak galerkin scheme and derive the optimal l 2 error estimate of o h k 1 2 order for the discrete solution when the k order polynomials are used for k 0 as application we discuss this wg method for solving the singularly perturbed convection diffusion reaction equation and derive an e uniform error estimate of order k 1 2 numerical examples are provided to show the effectiveness of the proposed wg method

a priori error analysis of residual free bubbles for advection diffusion problems we develop an a priori error analysis of a finite element approximation to the elliptic advection diffusion equation eps delta u conv cdot nabla u f subject to a homogeneous dirichlet boundary condition based on the use of residual free bubble functions an optimal order error bound is derived in the so called stability norm biggl eps nabla v 2 l 2 omega sum t h t conv cdot nabla v 2 l 2 t biggr 1 2 where ht denotes the diameter of element t in the subdivision of the computational domain

analysis of a multiscale discontinuous galerkin method for convection diffusion problems we study a multiscale discontinuous galerkin method introduced in t j r hughes g scovazzi p bochev and a buffa comput meth appl mech engrg 195 2006 pp 2761 2787 that reduces the computational complexity of the discontinuous galerkin method seemingly without adversely affecting the quality of results for a stabilized variant we are able to obtain the same error estimates for the convection diffusion equation as for the usual discontinuous galerkin method we assess the stability of the unstabilized case numerically and find that the inf sup constant is positive bounded uniformly away from zero and very similar to that for the usual discontinuous galerkin method

a new weak galerkin finite element scheme for general second order elliptic problems abstract a new weak galerkin wg finite element scheme is presented for general second order elliptic problems in this paper in this new scheme a skew symmetric form has been used for handling the convection term the advantage of the new scheme is that the system of linear equations from the scheme is positive definite and one might easily get the well posedness of the system in this scheme the wg elements are designed to have the form of p k t p k 1 e that is we choose the polynomials of degree k 1 on each element and the polynomials of degree k 1 on the edge face of each element as a result fewer degrees of freedom are generated in the new wg finite element scheme it is also worth pointing out that the wg finite element scheme is established on finite element partitions consisting of arbitrary shape of polygons polyhedra which are shape regular optimal order error estimates are presented for the corresponding numerical approximation in various norms some numerical results are reported to confirm the theory

tracking of time varying channels using two step lms type adaptive algorithm this paper presents a modified version of the two step least mean square lms type adaptive algorithm motivated by the work of gazor we describe the nonstationary adaptation characteristics of this modified two step lms mg lms algorithm for the system identification problem it ensures stable behavior during convergence as well as improved tracking performance in the smoothly time varying environments the estimated weight increment vector is used for the prediction of weight vector for the next iteration the proposed modification includes the use of a control parameter to scale the estimated weight increment vector in addition to a smoothing parameter used in the two step lms g lms algorithm which controls the initial oscillatory behavior of the algorithm the analysis focuses on the effects of these parameters on the lag misadjustment in the tracking process the mathematical analysis for a nonstationary case where the plant coefficients are assumed to follow a first order markov process shows that the mg lms algorithm contributes less lag misadjustment than the conventional lms and g lms algorithms further the stability criterion imposes upper bound on the value of the control parameter these derived analytical results are verified and demonstrated with simulation examples which clearly show that the lag misadjustment reduces with increasing values of the smoothing and control parameters under permissible limits

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

nonparametric estimation of large covariance matrices of longitudinal data summary estimation of an unstructured covariance matrix is difficult because of its positivedefiniteness constraint this obstacle is removed by regressing each variable on its predecessors so that estimation of a covariance matrix is shown to be equivalent to that of estimating a sequence of varying coefficient and varying order regression models our framework is similar to the use of increasing order autoregressive models in approximating the covariance matrix or the spectrum of a stationary time series as an illustration we adopt fan zhang s 2000 two step estimation of functional linear models and propose nonparametric estimators of covariance matrices which are guaranteed to be positive definite for parsimony a suitable order for the sequence of auto regression models is found using penalised likelihood criteria like aic and bic some asymptotic results for the local polynomial estimators of components of a covariance matrix are established two longitudinal datasets are analysed to illustrate the methodology a simulation study reveals the advantage of the nonparametric covariance estimator over the sample covariance matrix for large covariance matrices

partial match retrieval of multidimensional data a precise analysis of partial match retrieval of multidimensional data is presented the structures considered here are multidimensional search trees k d trees and digital tries k d tries as well as structures designed for efficient retrieval of information stored on external devices the methods used include a detailed study of a differential system around a regular singular point in conjunction with suitable contour integration techniques for the analysis of k d trees and properties of the mellin integral transform for k d tries and extendible cell algorithms

mellin transforms and asymptotics finite differences and rice s integrals high order differences of simple number sequences may be analysed asymptotically by means of integral representations residue calculus and contour integration this technique akin to mellin transform asymptotics is put in perspective and illustrated by means of several examples related to combinatorics and the analysis of algorithms like digital tries digital search trees quadtrees and distributed leader election

variational bayes for generalized autoregressive models we describe a variational bayes vb learning algorithm for generalized autoregressive gar models the noise is modeled as a mixture of gaussians rather than the usual single gaussian this allows different data points to be associated with different noise levels and effectively provides robust estimation of ar coefficients the vb framework is used to prevent overfitting and provides model order selection criteria both for ar order and noise model order we show that for the special case of gaussian noise and uninformative priors on the noise and weight precisions the vb framework reduces to the bayesian evidence framework the algorithm is applied to synthetic and real data with encouraging results

on the statistical efficiency of the lms algorithm with nonstationary inputs a fundamental relationship exists between the quality of an adaptive solution and the amount of data used in obtaining it quality is defined here in terms of misadjustment the ratio of the excess mean square error mse in an adaptive solution to the minimum possible mse the higher the misadjustment the lower the quality is the quality of the exact least squares solution is compared with the quality of the solutions obtained by the orthogonalized and the conventional least mean square lms algorithms with stationary and nonstationary input data when adapting with noisy observations a filter trained with a finite data sample using an exact least squares algorithms will have a misadjustment given by m frac n n frac number of weights number of training samples if the same adaptive filter were trained with a steady flow of data using an ideal orthogonalized lms algorithm the misadjustment would be m frac n 4 tau mse frac number of weights number of training samples thus for a given time constant tau mse of the learning process the ideal orthogonalized lms algorithm will have about as low a misadjustment as can be achieved since this algorithm performs essentially as an exact least squares algorithm with exponential data weighting it is well known that when rapid convergence with stationary data is required exact least squares algorithms can in certain cases outperform the conventional widrow hoff lms algorithm it is shown here however that for an important class of nonstationary problems the misadjustment of conventional lms is the same as that of orthogonalized lms which in the stationary case is shown to perform essentially as an exact least squares algorithm

a robust wg finite element method for convection diffusion reaction equations this paper proposes and analyzes a weak galerkin wg finite element method for 2 and 3 dimensional convection diffusion reaction problems on conforming or nonconforming polygon polyhedral meshes the wg method uses piecewise polynomial approximations of degrees k k 0 for both the scalar function and its trace on the inter element boundaries we show that the method is robust in the sense that the derived a priori error estimates is uniform with respect to the coefficients for sufficient smooth true solutions numerical experiments confirm the theoretical results

a weak galerkin finite element method with polynomial reduction the weak galerkin wg is a novel numerical method based on variational principles for weak functions and their weak partial derivatives defined as distributions in the implementation the weak partial derivatives and the weak functions are approximated by polynomials with various degrees of freedom the accuracy and the computational complexity of the corresponding wg scheme is significantly impacted by the selection of such polynomials this paper presents an optimal combination for the polynomial spaces that minimize the number of unknowns in the numerical scheme without compromising the accuracy of the numerical approximation for illustrative purpose the authors use the second order elliptic equation to demonstrate the basic ideas of polynomial reduction consequently a new weak galerkin finite element method is proposed and analyzed error estimates of optimal order are established for the corresponding wg approximations in both a discrete h 1 norm and the standard l 2 norm in addition the paper presents some numerical results to demonstrate the power of the wg method in dealing with finite element partitions with arbitrary polygons in 2d or polyhedra in 3d the numerical examples include various finite element partitions such as triangular mesh quadrilateral mesh honeycomb mesh in 2d and mesh with deformed cubes in 3d

an algorithm for the minimization of mixed l sub 1 and l sub 2 norms with application to bayesian estimation the regularizing functional approach is widely used in many estimation problems in practice the solution is defined as one minimum point of a suitable functional the main part of which accounts for the underlying physical model whereas the regularizing part represents some prior information about the unknowns in the bayesian interpretation one has a maximum a posteriori map estimator in which the main and regularizing parts are represented respectively by likelihood and prior distributions when either the prior or likelihood is a laplace distribution and the other is a gaussian distribution one is led to consider functionals that include both absolute and square norms the authors present a characterization of the minimum points of such functionals together with a descent type algorithm for numerical computations the results of monte carlo simulations are also reported

residual free bubbles for advection diffusion problems the general error analysis we develop the general a priori error analysis of residual free bubble finite element approximations to linear elliptic convection dominated diffusion problems subject to homogeneous dirichlet boundary condition optimal order error bounds are derived in various norms using piecewise polynomial finite elements of degree greater than or equal to 1

markov and recursive least squares methods for the estimation of data with discontinuities an algorithm is presented for smoothing data piecewise modeled by linear equations within regions of a one dimensional or two dimensional field from measurements corrupted by additive noise its main feature is the combination of markov random field mrf models with recursive least squares rls techniques in order to estimate the model parameters within the regions applications to one dimensional and two dimensional data are given with particular emphasis on the segmentation of images with piecewise constant intensity levels

a sequential smoothing algorithm with linear computational cost in this paper we propose a new particle smoother that has a computational complexity of o n where n is the number of particles this compares favourably with the o n2 computational cost of most smoothers the new method also overcomes some degeneracy problems in existing algorithms through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost it is shown both through these simulation studies and by the analysis of an athletics dataset that our new method also substantially outperforms the simple filter smoother the only other smoother with computational cost that is o n

smoothing of discontinuous signals the competitive approach discontinuous signals buried in noise cannot be recovered by linear filtering methods this paper presents a new class of nonlinear filters in which sets of forward and backward linear predictors and smoothers compete with each other at each timestep the winner of each competition is granted the right to produce the smoothed estimate at that timestep this conceptually simple approach to nonlinear filtering called the competitive smoothing approach is justified by considering sets of kalman filters corresponding to the hypotheses used in the bayesian framework which are used to derive model credibility coefficients these are shown to essentially switch between the various models we argue that the concept of competitive smoothing is considerably more general than just the kalman setting and can be used with almost any predictors and or smoothers several examples are presented which demonstrate the efficacy of the approach at both smoothing and preserving jump discontinuities comparisons are made with the other main nonlinear filtering approach the median filter

regularized fast recursive least squares algorithms for adaptive filtering fast recursive least squares frls algorithms are developed by using factorization techniques which represent an alternative way to the geometrical projections approach or the matrix partitioning based derivations the estimation problem is formulated within a regularization approach and priors are used to achieve a regularized solution which presents better numerical stability properties than the conventional least squares one the numerical complexity of the presented algorithms is explicitly related to the displacement rank of the a priori covariance matrix of the solution it then varies between o 5m and that of the slow rls algorithms to update the kalman gain vector m being the order of the solution an important advantage of the algorithms is that they admit a unified formulation such that the same equations may equally treat the prewindowed and the covariance cases independently from the used priors the difference lies only in the involved numerical complexity which is modified through a change of the dimensions of the intervening variables simulation results are given to illustrate the performances of these algorithms

performance of lms based adaptive filters in tracking a time varying plant the article gives a general analysis of the lms based adaptive filters when used for tracking a class of time varying plants the algorithms covered are the conventional lms the transform domain normalized lms and the lms newton algorithm an important fact that we observe is that in comparing these algorithms better initial convergence does not necessarily mean better tracking a few special cases are presented that show the contrary

shaping frequency dependent time resolution when estimating spectral properties with parametric methods the problem of tracking time varying properties of a signal is studied the somewhat contradictory notion of time varying spectrum and how to estimate the current spectrum in an on line fashion is discussed the traditional concepts and relations between time and frequency resolution are crucial for this problem we introduce two definitions for the time resolution of filters essentially measuring the effective number of past data that are used to form the estimate in for example wavelet transform techniques frequency dependent time resolutions are used so that fewer data are used at higher frequencies thus enabling faster tracking of high frequency components at the price of worse frequency resolution the main contribution of the paper is to show how this same feature can be introduced when estimating spectra via a time varying autoregressive model of the signal this is achieved by a special choice of nominal covariance matrix for the underlying parameter changes

a hybridizable discontinuous galerkin method for steady state convection diffusion reaction problems in this article we propose a novel discontinuous galerkin method for convection diffusion reaction problems characterized by three main properties the first is that the method is hybridizable this renders it efficiently implementable and competitive with the main existing methods for these problems the second is that when the method uses polynomial approximations of the same degree for both the total flux and the scalar variable optimal convergence properties are obtained for both variables this is in sharp contrast with all other discontinuous methods for this problem the third is that the method exhibits superconvergence properties of the approximation to the scalar variable this allows us to postprocess the approximation in an element by element fashion to obtain another approximation to the scalar variable which converges faster than the original one in this paper we focus on the efficient implementation of the method and on the validation of its computational performance with this aim e

digital filters as absolute norm regularizers a variational formulation of the digital filtering problem based on a certain regularizing functional is presented in particular the special case where the regularizing functional is defined by means of l sub 1 norm is considered and a characterization of its minima is presented it is shown that for a certain class of signals one solution to the regularization problem can be obtained by means of a suitable recursive median filter some examples and a possible extension of the variational approach are also discussed

branching processes in levy processes the exploration process the main idea of the present work is to associate with a general continuous branching process an exploration process that contains the desirable information about the genealogical structure the exploration process appears as a simple local time functional of a levy process with no negative jumps whose laplace exponent coincides with the branching mechanism function this new relation between spectrally positive levy processes and continuous branching processes provides a unified perspective on both theories in particular we derive the adequate formulation of the classical ray knight theorem for such levy processes as a consequence of this theorem we show that the path continuity of the exploration process is equivalent to the almost sure extinction of the branching process

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

weak galerkin method with implicit θ schemes for second order parabolic problems abstract we introduce a new weak galerkin finite element method whose weak functions on interior edges are double valued and approximation spaces are based on pk t pk e rtk t elements it is natural to develop a semi discrete stable scheme for parabolic problems and then fully discrete approaches are formulated with implicit schemes in time for 1 2 1 which include first order backward euler 1 and second order crank nicolson schemes 1 2 furthermore optimal convergence rates in the l2 and energy norms are derived numerical results are given to verify the theory

optimization of adaptive identification for time varying filters adaptive identification in a time varying context is studied when controlled by the lms algorithm with constant gain under the assumption of correlated successive input vectors it is well known by experience that the tracking mean square error mse epsilon mu results from the tradeoff between the gradient part which is increasing and the lag contribution which is decreasing in this note we clarify the relative roles of the gradient and lag errors by proving their decoupled character this property relies upon independence between the additive noise at the output of the plant to be identified and the information vector at the plant input convergence of the mse is established rather than assumed quantitative evaluations of upper and lower bounds allow an approximate optimization of the gain in two important cases the optimum is exact one of these cases is slow variations it is defined in a quantitative manner thanks to the ratio of the variation noise to the output additive noise

poincare friedrichs inequalities for piecewise h 1 functions poincare friedrichs inequalities for piecewise h1 functions are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

recursive self similarity for random trees random triangulations and brownian excursion recursive self similarity for a random object is the property of being decomposable into independent rescaled copies of the original object certain random combinatorial objects trees and triangulations possess approximate versions of recursive self similarity and then their continuous limits possess exact recursive self similarity in particular since the limit continuum random tree can be identified with brownian excursion we get a nonobvious recursive self similarity property for brownian excursion

interior penalty discontinuous approximations of convection diffusion problems with parabolic layers a nonsymmetric discontinuous galerkin finite element method with interior penalties is considered for two dimensional convection diffusion problems with regular and parabolic layers on an anisotropic shishkin type mesh with bilinear elements we prove error estimates uniformly in the perturbation parameter in an integral norm associated with this method on different types of interelement edges we derive the values of discontinuity penalization parameters numerical experiments complement the theoretical results

partial match queries in random k d trees we solve the open problem of characterizing the leading constant in the asymptotic approximation to the expected cost used for random partial match queries in random k d trees our approach is new and of some generality in particular it is applicable to many problems involving differential equations or difference equations with polynomial coefficients

fitting time series models to nonstationary processes a general minimum distance estimation procedure is presented for nonstationary time series models that have an evolutionary spectral representation the asymptotic properties of the estimate are derived under the assumption of possible model misspecification for autoregressive processes with time varying coefficients the estimate is compared to the least squares estimate furthermore the behavior of estimates is explained when a stationary model is fitted to a nonstationary process

nonparametric time variant frequency response function estimates using arbitrary excitations the time variant frequency response function tv frf uniquely characterises the dynamic behaviour of a linear time variant ltv system this paper proposes a method for estimating nonparametrically the dynamic part of the tv frf from known input noisy output observations the arbitrary time variation of the tv frf is modelled by legendre polynomials in opposition to existing solutions the proposed method is applicable to arbitrary inputs

brief paper fast computation of smoothing splines subject to equality constraints the issue of constructing periodic smoothing splines has been recently formulated as a controlled two point boundary value problem which admits a state space description in the context of minimum norm problems in hilbert spaces it has been shown that the solution is the sum of a finite number of basis functions and can be obtained with a number of operations which scales with the cube of the sum of the number of measurements and boundary constraints in this paper we consider a more general class of variational problems subject to equality constraints which contains the periodic smoothing spline problem as a special case using the theory of reproducing kernel hilbert spaces we derive a solution to the problem which has the same computational complexity as that recently proposed next assuming that the problem admits a state space representation we obtain an algorithm whose complexity is linear in the number of measurements we also show that the solution of the problem admits the structure of a particular regularization network whose weights can be computed in linear time closed form expressions for the basis functions associated with the periodic cubic smoothing spline problem are finally derived

prediction in lms type adaptive algorithms for smoothly time varying environments the aim of this correspondence is to improve the performance of the least mean square lms and normalized lms nlms adaptive algorithms in tracking of time varying models a new procedure for estimation of weight increments for including in the lms type adaptive algorithms is proposed this procedure applies a simple smoothing on the increment of the estimated weights to estimate the speed of weights the estimated speeds are then used to predict the weights for the next iteration the efficiency of the algorithm is confirmed by simulation results the algorithm has a very low order of arithmetic complexity moreover this procedure could be combined with a wide class of adaptive filters e g rls gradient lattice algorithm etc to improve their behaviors the proposed algorithm is obtained by simplifying a kalman filter to this end a markov model of second order is considered for the weight vector this model shows that the estimation of parameter increments inferred from the predicted parameters improves the tracking performance

evolutionary periodogram for nonstationary signals presents a novel estimator for the time dependent spectrum of a nonstationary signal by modeling the signal at any given frequency as having a time varying amplitude accurately represented by an orthonormal basis expansion the authors are able to compute a minimum mean squared error estimate of this time varying amplitude repeating the process over all frequencies they obtain a power distribution as a function of time and frequency that is consistent with the wold cramer evolutionary spectrum based on the model assumptions the authors develop the evolutionary periodogram ep for nonstationary signals an estimator analogous to the periodogram used in the stationary case they also derive the time frequency resolution of the new estimator the approach is free of some of the drawbacks of the bilinear distributions and of the short time fourier transform spectral estimates it is guaranteed to produce nonnegative spectra without the cross term behavior of the bilinear distributions and it does not require windowing of data in the time domain examples illustrating the new estimator are given

discontinuous galerkin finite element methods for interface problems a priori and a posteriori error estimations discontinuous galerkin dg finite element methods were studied by many researchers for second order elliptic partial differential equations and a priori error estimates were established when the solution of the underlying problem is piecewise h 3 2 epsilon smooth with epsilon 0 however elliptic interface problems with intersecting interfaces do not possess such a smoothness in this paper we establish a quasi optimal a priori error estimate for interface problems whose solutions are only h 1 alpha smooth with alpha in 0 1 and hence fill a theoretical gap of the dg method for elliptic problems with low regularity the second part of the paper deals with the design and analysis of robust residual and recovery based a posteriori error estimators theoretically we show that the residual and recovery estimators studied in this paper are robust with respect to the dg norm i e their reliability and efficiency bounds do not depend on the jump provided that the distribution of coefficients is locally quasi monotone

weak galerkin finite element method for biots consolidation problem in this paper a fully discrete weak galerkin wg finite element method is proposed to solve biots consolidation problem where weakly defined gradient and divergence operators over discontinuous functions are introduced plpl l1 finite element combination is used for the displacement and pressure approximations in the interior of the elements and plpl1 combination for the corresponding trace approximations on the interfaces of the finite element partition the existence and uniqueness of the discrete linear system at each time step is derived and error estimates for the approximation of displacement and pressure are obtained numerical experiments confirm the theoretical results and show that the proposed wg method is capable of overcoming pressure oscillations

wiener design of adaptation algorithms with time invariant gains a design method is presented that extends least mean squared lms adaptation of time varying parameters by including general linear time invariant filters that operate on the instantaneous gradient vector the aim is to track time varying parameters of linear regression models in situations where the regressors are stationary or have slowly time varying properties the adaptation law is optimized with respect to the steady state parameter error covariance matrix for time variations modeled as vector arima processes the design method systematically uses prior information about time varying parameters to provide filtering prediction or fixed lag smoothing estimates for arbitrary lags the method is based on a transformation of the adaptation problem into a wiener filter design problem the filter works in open loop for slow parameter variations whereas a time varying closed loop has to be considered for fast variations in the latter case the filter design is performed iteratively the general form of the solution at each iteration is obtained by a bilateral diophantine polynomial matrix equation and a spectral factorization for white gradient noise the diophantine equation has a closed form solution further structural constraints result in very simple design equations under certain model assumptions the wiener designed adaptation laws reduce to lms adaptation compared with kalman estimators the channel tracking performance becomes nearly the same in mobile radio applications whereas the complexity is in general much lower

a smoothness priors time varying ar coefficient modeling of nonstationary covariance time series a smoothness priors time varying ar coefficient model approach for the modeling of nonstationary in the covariance time series is shown smoothness priors in the form of a difference equation constraint excited by an independent white noise are imposed on each ar coefficient the unknown white noise variances are hyperparameters of the ar coefficient distribution the critical computation is of the likelihood of the hyperparameters of the bayesian model this computation is facilitated by a state space representation kalman filter implementation the best difference equation order best ar model order best hyperparameter model locally in time is selected using the minimum aic method also an instantaneous spectral density is defined in terms of the instantaneous ar model coefficients and a smoothed estimate of the instantaneous time series variance an earthquake record is analyzed the changing spectral analysis of the original data and of simulations from a time varying ar coefficient model of that data are shown

the scaling limit of the minimum spanning tree of the complete graph consider the minimum spanning tree mst of the complete graph with nn vertices when edges are assigned independent random weights endow this tree with the graph distance renormalized by n1 3n1 3 and with the uniform measure on its vertices we show that the resulting space converges in distribution as n n to a random compact measured metric space in the gromov hausdorff prokhorov topology we additionally show that the limit is a random binary rr tree and has minkowski dimension 33 almost surely in particular its law is mutually singular with that of the brownian continuum random tree or any rescaled version thereof our approach relies on a coupling between the mst problem and the erd s renyi random graph we exploit the explicit description of the scaling limit of the erd s renyi random graph in the so called critical window established in probab theory related fields 152 2012 367 406 and provide a similar description of the scaling limit for a critical minimum spanning forest contained within the mst in order to accomplish this we introduce the notion of rr graphs which generalise rr trees and are of independent interest

mixed virtual element methods for elastodynamics with weak symmetry abstract we propose and analyze a mixed virtual element method for linear elastodynamics in velocity stress formulation with weak symmetry in this formulation the symmetry of the stress is relaxed by the rotation of the displacement and the system of second order differential equation in time is reduced to first order differential equations in time by introducing velocity the proposed method uses h div conforming virtual element space of order k k 1 for the stress and discontinuous piecewise polynomial spaces of degree k for the velocity and rotation for time discretization we use the crank nicolson scheme both semidiscrete and fully discrete error estimates are robust for nearly incompressible materials numerical experiments confirm our theoretical predictions

difference equation representation of chirp signals and instantaneous frequency amplitude estimation we present a time varying coefficient difference equation representation for sinusoidal signals with time varying amplitudes and frequencies we first obtain a recursive equation for a single chirp signal then using this result we obtain time varying coefficient difference equation representations for signals composed of multiple chirp signals we analyze these equations using the skew shift operators we show that the phases of the poles of the difference equations produce instantaneous frequencies if and the magnitudes are proportional to the ratio of successive values of the instantaneous amplitudes ia then algorithms are presented for the estimation of instantaneous frequencies and instantaneous amplitudes for multicomponent signals composed of chirps using the difference equation representation the first algorithm we propose is based on the skew shift operators next we derive the conditions under which we can use the so called frozen time approach we propose an algorithm for if and ia estimation based on the frozen time approach then we propose an automatic signal separation method finally we apply the proposed algorithms to single and multicomponent signals and compare the results with some existing methods

stabilization mechanisms in discontinuous galerkin finite element methods in this paper we propose a new general framework for dg methods which allows to uncover a basic mechanism that ensures suitable stability properties of the methods we show that such a mechanism is essentially the same for apparently unrelated stabilizations such as jump penalty upwinding and hughes franca type residual based stabilizations

a weak galerkin mixed finite element method for second order elliptic problems abstract a new weak galerkin wg method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations this method called wg mfem is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary shape of polygons polyhedra the wg mfem is capable of providing very accurate numerical approximations for both the primary and flux variables allowing the use of discontinuous approximating functions on arbitrary shape of polygons polyhedra makes the method highly flexible in practical computation optimal order error estimates in both discrete h and l norms are established for the corresponding weak galerkin mixed finite element solutions

a weak galerkin finite element method for second order elliptic problems this paper introduces a finite element method by using a weakly defined gradient operator over generalized functions the use of weak gradients and their approximations results in a new concept called discrete weak gradients which is expected to play an important role in numerical methods for partial differential equations this article intends to provide a general framework for managing differential operators on generalized functions as a demonstrative example the discrete weak gradient operator is employed as a building block in the design of numerical schemes for a second order elliptic problem in which the classical gradient operator is replaced by the discrete weak gradient the resulting numerical scheme is called a weak galerkin wg finite element method it can be seen that the weak galerkin method allows the use of totally discontinuous functions in the finite element procedure for the second order elliptic problem an optimal order error estimate in both a discrete h 1 and l 2 norms are established for the corresponding weak galerkin finite element solutions a superconvergence is also observed for the weak galerkin approximation

locally adaptive cooperative kalman smoothing and its application to identification of nonstationary stochastic systems one of the central problems of the stochastic approximation theory is the proper adjustment of the smoothing algorithm to the unknown and possibly time varying rate and mode of variation of the estimated signals parameters in this paper we propose a novel locally adaptive parallel estimation scheme which can be used to solve the problem of fixed interval kalman smoothing in the presence of model uncertainty the proposed solution is based on the idea of cooperative smoothing the bayesian extension of the leave one out cross validation approach to model selection within this approach the smoothed estimates are evaluated as a convex combination of the estimates provided by several competing smoothers we derive computationally attractive algorithms allowing for cooperative kalman smoothing and show how the proposed approach can be applied to identification of nonstationary stochastic systems

adaptive scheme for elimination of broadband noise and impulsive disturbances from ar and arma signals the problem of elimination of measurement noise and impulsive disturbances from autoregressive and autoregressive moving average signals is considered it is shown that the task of simultaneous detection tracking restoration can be stated as a nonlinear filtering problem and solved using the theory of extended kalman filter numerical tests carried out for real audio signals corrupted by both real and artificially generated disturbances confirm very good properties of the proposed algorithm

discontinuous hp finite element methods for advection diffusion reaction problems we consider the hp version of the discontinuous galerkin finite element method dgfem for second order partial differential equations with nonnegative characteristic form this class of equations includes second order elliptic and parabolic equations advection reaction equations as well as problems of mixed hyperbolic elliptic parabolic type our main concern is the error analysis of the method in the absence of streamline diffusion stabilization in the hyperbolic case an hp optimal error bound is derived here we consider only advection reaction problems which satisfy a certain standard positivity condition in the self adjoint elliptic case an error bound that is h optimal and p suboptimal by frac 1 2 a power of p is obtained these estimates are then combined to deduce an error bound in the general case for elementwise analytic solutions the method exhibits exponential rates of convergence under p refinement the theoretical results are illustrated by numerical experiments