isogeometric variational multiscale modeling of wall bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes abstract in this work we combine i nurbs based isogeometric analysis ii residual driven turbulence modeling and iii weak imposition of no slip and no penetration dirichlet boundary conditions on unstretched meshes to compute wall bounded turbulent flows while the first two ingredients were shown to be successful for turbulence computations at medium to high reynolds number i akkerman y bazilevs v m calo t j r hughes s hulshoff the role of continuity in residual based variational multiscale modeling of turbulence comput mech 41 2008 371 378 y bazilevs v m calo j a cottrell t j r hughes a reali g scovazzi variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows comput methods appl mech engrg 197 2007 173 201 it is the weak imposition of no slip boundary conditions on coarse uniform meshes that maintains the good performance of the proposed methodology at higher reynolds number y bazilevs t j r hughes weak imposition of dirichlet boundary conditions in fluid mechanics comput fluids 36 2007 12 26 y bazilevs c michler v m calo t j r hughes weak dirichlet boundary conditions for wall bounded turbulent flows comput methods appl mech engrg 196 2007 4853 4862 these three ingredients form a basis of a possible practical strategy for computing engineering flows somewhere between rans and les in complexity we demonstrate this by solving two challenging incompressible turbulent benchmark problems channel flow at friction velocity reynolds number 2003 and flow in a planar asymmetric diffuser we observe good agreement between our calculations of mean flow quantities and both reference computations and experimental data this lends some credence to the proposed approach which we believe may become a viable engineering tool

analysis of a modified first order system least squares method for linear elasticity with improved momentum balance a modified first order system least squares formulation for linear elasticity obtained by adding the antisymmetric displacement gradient in the test space is analyzed this approach leads to surprisingly small momentum balance error compared to standard least squares approaches it is shown that the modified least squares formulation is well posed and its performance is illustrated by adaptive finite element computation based on using a closely related least squares functional as a posteriori error estimator the results of our numerical computations show that for the modified least squares approach the momentum balance error converges at a much faster rate than the overall error we prove that this is due to a strong connection of the stress approximation to that obtained from a mixed formulation based on the hellinger reissner principle with exact local momentum balance the practical significance is that our proposed approach is almost momentum conservative at a smaller number of degrees of freedom than mixed approximations with exact local momentum balance

isogeometric structural shape optimization an old dilemma in structural shape optimization is the needed tight link between design model or geometric description and analysis model the intention of this paper is to show that isogeometric analysis offers a potential and promising way out of this dilemma to this end we show a structural shape optimization framework based on the isogeometric analysis approach with the discretization based on non uniform rational b splines nurbs the analysis model represents the structural geometry exactly furthermore nurbs enable efficient geometry control together with smooth boundaries they are the de facto standard in cad systems but are also widely used in a shape optimal design context to define the geometry representation and the design variables with the presented isogeometric approach to shape optimization the analysis model is inherently merged with the design model omitting the typically involved interplay between both we derive analytical sensitivities for nurbs discretizations which allow application of efficient gradient based optimization algorithms the present contribution is restricted to two dimensional problems of linear elasticity but the extension to three dimensions and other problem classes is straightforward some representative examples demonstrate and validate the methodology further the potential of boundary continuity control within isogeometric structural shape optimization is explored to trigger smooth or less smooth angular designs

subdivision based mixed methods for isogeometric analysis of linear and nonlinear nearly incompressible materials this paper addresses the use of isogeometric analysis to solve solid mechanics problems involving nearly incompressible materials the present work is focused on extension of two field mixed variational formulations in both small and large strains to isogeometric analysis inf sup stable displacement pressure combinations for mixed formulations are developed based on the subdivision property of nurbs stability and convergence properties of the proposed displacement pressure combinations are illustrated by computing numerical inf sup constants and error norms the performance of the proposed formulations is assessed by studying several benchmark examples involving nearly incompressible and incompressible elastic and elasto plastic materials in both small and large strain regime

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

least squares methods for stokes equations based on a discrete minus one inner product abstract the purpose of this paper is to develop and analyze least squares approximations for stokes and elasticity problems the major advantage of the least squares formulation is that it does not require that the classical ladyzhenskaya bab ska brezzi lbb condition be satisfied we provide two methods the first is posed in terms of the velocity pressure pair without the introduction of additional variables the second adds a vorticity variable in both cases we employ least squares functionals which involve a discrete inner product which is related to the inner product in h 1 the sobolev space of order minus one on the use of such inner products applied to second order problems was proposed in an earlier paper by bramble lazarov and pasciak 1994

isogeometric analysis of nearly incompressible solids this paper describes the use of isogeometric methods to solve problems in finite deformation solid mechanics in which compressible and nearly incompressible behavior may be encountered the work is based on a three field variational structures in which displacements mean stress and volume effects are independently approximated using this approach and tensor product nurbs approximations it is shown how the solution can be conducted in a standard approach where main variables are organized at nodes control points this leads to an efficient procedure to solve large problems of a general form without the need to develop special solution strategies the approach is demonstrated on some standard test problems copyright 2010 john wiley sons ltd

adaptive voting rules for k nearest neighbors classifiers a simple form of cooperation between the k nearest neighbors nn approach to classification and the neural like property of adaptation is explored a tunable high level k nearest neighbors decision rule is defined that comprehends most previous generalizations of the common majority rule a learning procedure is developed that applies to this rule and exploits those statistical features that can be induced from the training set the overall approach is tested on a problem of handwritten character recognition experiments show that adaptivity in the decision rule may improve the recognition and rejection capability of standard k nn classifiers

the kernel estimate is relatively stable consider the parzen rosenblatt kernel estimate f n 1 n sum limits i 1 n k h x x i whereh 0 is a constant k is an absolutely integrable function with integral one k h x 1 h andx 1 x n are iid random variables with common densityf onr d we show that for all e 0 mathop sup limits h 0 f p leqq 2e frac n varepsilon 2 32 mathop smallint limits 2 k we also establish thatf n is relatively stable i e frac int f n f e int f n f to 1 in probability as n to infty whenerver lim inf sqrt n e int f n f infty we also study what happens whenh is allowed to depend upon the data sequence

the lack of a priori distinctions between learning algorithms this is the first of two papers that use off training set ots error to investigate the assumption free relationship between learning algorithms this first paper discusses the senses in which there are no a priori distinctions between learning algorithms the second paper discusses the senses in which there are such distinctions in this first paper it is shown loosely speaking that for any two algorithms a and b there are as many targets or priors over targets for which a has lower expected ots error than b as vice versa for loss functions like zero one loss in particular this is true if a is cross validation and b is anti cross validation choose the learning algorithm with largest cross validation error this paper ends with a discussion of the implications of these results for computational learning theory it is shown that one cannot say if empirical misclassification rate is low the vapnik chervonenkis dimension of your generalizer is small and the training set is large then with high probability your ots error is small other implications for membership queries algorithms and punting algorithms are also discussed

the least squares finite element method for low mach number compressible viscous flows the present paper reports the development of the least squares finite element method lsfem for simulating compressible viscous flows at low mach numbers in which the incompressible flows pose as an extreme conventional approach requires special treatments for low speed flows calculations finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique and finite element methods rely on the mixed method and the operator splitting method in this paper however we show that such difficulty does not exist for the lsfem and no special treatment is needed the lsfem always leads to a symmetric positive definite matrix through which the compressible flow equations can be effectively solved two numerical examples are included to demonstrate the method first driven cavity flows at various reynolds numbers and buoyancy driven flows with significant density variation both examples are calculated by using full compressible flow equations

first order system least squares for darcy stokes flow the subject of this paper is a first order system least squares formulation for the stokes equation which remains uniformly valid in the limit of vanishing viscosity for this so called darcy stokes flow problem we establish continuity and coercivity of the corresponding least squares functional in appropriate norms two types of finite element spaces for the approximation of the velocity field are investigated in detail the well known raviart thomas elements and an element recently introduced by mardal tai and winther specifically for mixed approaches to darcy stokes flow the computational results derived with next to lowest order raviart thomas elements as well as the mardal tai winther elements confirm our analysis

design of simple low order finite elements for large strain analysis of nearly incompressible solids a simple four node quadrilateral and an eight node hexahedron for large strain analysis of nearly incompressible solids are proposed based on the concept of deviatoric volumetric split and the replacement of the compatible deformation gradient with an assumed modified counterpart the formulation developed is applicable to arbitrary material models the closed form of the corresponding exact tangent stiffnesses which have a particularly simple structure is derived it ensures asymptotically quadratic rates of convergence of the newton raphson scheme employed in the solution of the implicit finite element equilibrium equations from a practical point of view the incorporation of the proposed elements into existing codes is straightforward it requires only small changes in the routines of the standard displacement based 4 node quadrilateral and 8 node brick a comprehensive set of numerical examples involving hyperelasticity as well as multiplicative elasto plasticity is provided it illustrates the performance of the proposed elements over a wide range of applications including strain localisation problems metal forming simulation and adaptive analysis

f bar based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids part i formulation and benchmarking this paper proposes a new technique which allows the use of simplex finite elements linear triangles in 2d and linear tetrahedra in 3d in the large strain analysis of nearly incompressible solids the new technique extends the f bar method proposed by de souza neto et al int j solids and struct 1996 33 3277 3296 and is conceptually very simple it relies on the enforcement of near incompressibility over a patch of simplex elements rather than the point wise enforcement of conventional displacement based finite elements within the framework of the f bar method this is achieved by assuming for each element of a mesh a modified f bar deformation gradient whose volumetric component is defined as the volume change ratio of a pre defined patch of elements the resulting constraint relaxation effectively overcomes volumetric locking and allows the successful use of simplex elements under finite strain near incompressibility as the original f bar procedure the present methodology preserves the displacement based structure of the finite element equations as well as the strain driven format of standard algorithms for numerical integration of path dependent constitutive equations and can be used regardless of the constitutive model adopted the new elements are implemented within an implicit quasi static environment in this context a closed form expression for the exact tangent stiffness of the new elements is derived this allows the use of the full newton raphson scheme for equilibrium iterations the performance of the proposed elements is assessed by means of a comprehensive set of benchmarking two and three dimensional numerical examples

isogeometric analysis of the isothermal navier stokes korteweg equations this paper is devoted to the numerical simulation of the navier stokes korteweg equations a phase eld model for water water vapor two phase ows we develop a numerical formulation based on isogeometric analysis that permits straightforward treatment of the higher order partial dierenti al operator that represents capillarity we introduce a new renement methodology that desensitizes the numerical solution to the computational mesh and achieves mesh invariant solutions finally we present several numerical examples in two and three dimensions that illustrate the eectiveness and robustness of our approach

analysis of least squares finite element methods for the navier stokes equations in this paper we study finite element methods of least squares type for the stationary incompressible navier stokes equations in two and three dimensions we consider methods based on velocity vorticity pressure form of the navier stokes equations augmented with several nonstandard boundary conditions least squares minimization principles for these boundary value problems are developed with the aid of the agmon douglis nirenberg adn elliptic theory among the main results of this paper are optimal error estimates for conforming finite element approximations and analysis of some nonstandard boundary conditions results of several computational experiments with least squares methods which illustrate among other things the optimal convergence rates are also reported

local discriminative distance metrics ensemble learning the ultimate goal of distance metric learning is to incorporate abundant discriminative information to keep all data samples in the same class close and those from different classes separated local distance metric methods can preserve discriminative information by considering the neighborhood influence in this paper we propose a new local discriminative distance metrics lddm algorithm to learn multiple distance metrics from each training sample a focal sample and in the vicinity of that focal sample focal vicinity to optimize local compactness and local separability those locally learned distance metrics are used to build local classifiers which are aligned in a probabilistic framework via ensemble learning theoretical analysis proves the convergence rate bound the generalization bound of the local distance metrics and the final ensemble classifier we extensively evaluate lddm using synthetic datasets and large benchmark uci datasets

first order system least squares for geometrically nonlinear elasticity we present a first order system least squares fosls method to approximate the solution to the equations of geometrically nonlinear elasticity in two dimensions with assumptions of regularity on the problem we show h 1 equivalence of the norm induced by the fosls functional in the case of pure displacement boundary conditions as well as local convergence of newton s method in a nested iteration setting theoretical results hold for deformations satisfying a small strain assumption a set we show to be largely coincident with the set of deformations allowed by the model numerical results confirm optimal multigrid performance and finite element approximation rates of the discrete functional with a total work bounded by about 25 fine grid relaxation sweeps

least squares finite element formulations for viscous incompressible and compressible fluid flows abstract we present least squares based finite element formulations for the numerical solution of viscous fluid flows governed by the navier stokes equations as an alternate approach to the well known weak form galerkin finite element formulations the use of least squares principles leads to a variational unconstrained minimization problem where compatibility conditions between approximation spaces never arise and the resulting linear algebraic problem will have a symmetric positive definite coefficient matrix we address the issue of norm equivalence of the least squares functional and its implications on the resulting finite element model in particular we develop an understanding of the compromise that must exist between the optimality and practicality of the finite element model the latter measured in terms of c k regularity across inter element boundaries we show through numerical examples that for the traditional c 0 basis such a compromise is possible when high p levels are used to span the finite element spaces when a low p level solution is desired guidelines are presented to obtain a reliable least squares collocation solution numerical examples are presented to demonstrate the high and low p level approaches these include incompressible flow past two circular cylinders in a side by side arrangement for gap sizes s d 2 0 and 0 85 incompressible flow past a square cylinder and subsonic transonic and supersonic compressible flow past a circular cylinder in addition we present a discontinuous least squares formulation where c k regularity across inter element boundaries is enforced in a weak sense through the least squares functional allowing for h and p type non conformities in the computational domain

the equivalence of weak strong and complete convergence in l_1 for kernel density estimates theorem 1 let k be a nonnegative borel measurable function on rd with f k x dx 1 then the following conditions are equivalent i j 0 in probability as n oo some f ii jn o 0 in probability as n s oo all f iii jn s 0 almost surely as n oo all f iv jn 0 exponentially as n oc i e for all e 0 there exist r no 0 such that p jne no all f v lim0h 0 and limnnhd oo also v implies iv when k is merely absolutely integrable and f k x dx 1 0

v matrix method of solving statistical inference problems this paper presents direct settings and rigorous solutions of the main statistical inference problems it shows that rigorous solutions require solving multidimensional fredholm integral equations of the first kind in the situation where not only the right hand side of the equation is an approximation but the operator in the equation is also defined approximately using stefanuyk vapnik theory for solving such ill posed operator equations constructive methods of empirical inference are introduced these methods are based on a new concept called v matrix this matrix captures geometric properties of the observation data that are ignored by classical statistical methods

an adaptive least squares mixed finite element method for elasto plasticity a least squares mixed finite element method for the incremental formulation of elasto plasticity using a plastic flow rule of von mises type with isotropic hardening is presented this approach is based on the use of the stress tensor in addition to the displacement field as independent process variables the nonlinear least squares functional is shown to constitute an a posteriori error estimator on which an adaptive refinement strategy may be based for the finite element implementation under plane strain conditions quadratic i e next to lowest order raviart thomas elements are used for the stress approximation while the displacement is represented by standard quadratic conforming elements computational results for a benchmark problem of elasto plasticity under plane strain conditions are presented in order to illustrate the effectiveness of the least squares approach

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

least squares mixed finite elements for small strain elasto viscoplasticity the main aim of this contribution is to provide a mixed finite element for small strain elasto viscoplastic material behavior based on the least squares method the l2 norm minimization of the residuals of the given first order system of differential equations leads to a two field functional with displacements and stresses as process variables for the continuous approximation of the stresses lowest order raviart thomas elements are used whereas for the displacements standard conforming elements are employed it is shown that the non linear least squares functional provides an a posteriori error estimator which establishes ellipticity of the proposed variational approach further on details about the implementation of the least squares mixed finite elements are given and some numerical examples are presented copyright 2008 john wiley sons ltd

weak convergence of k nn density and regression estimators with varying k and applications on considere le probleme sous une condition de lissite du second ordre dans le cas unidimensionnel

nonparametric density estimation the l 1 view differentiation of integrals consistency lower bounds for rates of convergence rates of convergence in l1 the automatic kernel estimate l1 and pointwise convergence estimates related to the kernel estimate and the histogram estimate simulation inequalities and random variate generation the transformed kernel estimate applications in discrimination operations on density estimates estimators based on orthogonal series index

optimal learning rates for localized svms one of the limiting factors of using support vector machines svms in large scale applications are their super linear computational requirements in terms of the number of training samples to address this issue several approaches that train svms on many small chunks separately have been proposed in the literature with the exception of random chunks which is also known as divide and conquer kernel ridge regression however these approaches have only been empirically investigated in this work we investigate a spatially oriented method to generate the chunks for the resulting localized svm that uses gaussian kernels and the least squares loss we derive an oracle inequality which in turn is used to deduce learning rates that are essentially minimax optimal under some standard smoothness assumptions on the regression function in addition we derive local learning rates that are based on the local smoothness of the regression function we further introduce a data dependent parameter selection method for our local svm approach and show that this method achieves the same almost optimal learning rates finally we present a few larger scale experiments for our localized svm showing that it achieves essentially the same test error as a global svm for a fraction of the computational requirements in addition it turns out that the computational requirements for the local svms are similar to those of a vanilla random chunk approach while the achieved test errors are significantly better

first order system least squares for coupled stokes darcy flow the coupled problem with stokes flow in one subdomain and a darcy flow model in a second subdomain is studied in this paper both flow problems are treated as first order systems involving pseudostress and velocity in the stokes case and using a flux pressure formulation in the darcy subdomain as process variables respectively the beavers joseph saffman interface conditions are treated by an appropriate interface functional which is added to the least squares functional associated with the subdomain problems a combination of h mathrm div conforming raviart thomas and standard h 1 conforming elements is used for the stokes as well as for the darcy subsystem the homogeneous least squares functional is shown to be equivalent to an appropriate norm allowing the use of standard finite element approximation estimates it also establishes the fact that the local evaluation of the least squares functional itself constitutes an a posteriori error estimator to be used for adaptive refinement strategies

detrended fluctuation analysis of time series of a firing fusimotor neuron abstract we study the interspike intervals isi time series of the spontaneous fusimotor neuron activity by applying the detrended fluctuation analysis that is a modification of the random walk model analysis thus we have found evidence for the white noise characteristics of the isi time series which means that the fusimotor activity does not possess temporal correlations we conclude that such an activity represents the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles

beneficial randomness of signals in a neuronal circuit abstract we have analyzed spontaneous discharge dynamics of fusimotor neurons by applying the so called detrended fluctuation analysis which is a modification of the random walk model analysis besides we applied the wavelet analysis method to the same problem by using these methods we have found evidence for the white noise characteristics of the time series generated by the neuron discharges we concluded that such a discharge dynamics represents the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles this finding appears to be very intriguing since it provided for the first time statistical characterization of the neuronal noise

least squares methods for linear elasticity this paper develops least squares methods for the solution of linear elastic problems in both two and three dimensions our main approach is defined by simply applying the l2 norm least squares principle to a stress displacement system the constitutive and the equilibrium equations it is shown that the homogeneous least squares functional is elliptic and continuous in the h rm div omega d times h 1 omega d norm this immediately implies optimal error estimates for finite element subspaces of h rm div omega d times h 1 omega d it admits optimal multigrid solution methods as well if raviart thomas finite element spaces are used to approximate the stress tensor our method does not degrade when the material properties approach the incompressible limit least squares methods that impose boundary conditions weakly and use an inverse norm are also considered numerical results for a benchmark test problem of planar elasticity are included in order to illustrate the robustness of our

the least squares finite element method in elasticity part i plane stress or strain with drilling degrees of freedom a new least squares finite element method lsfem for plane elasticity problems is developed based on the first order displacement stress rotation formulation which includes two new first order compatibility constraints among the stresses and the drilling rotation this lsfem can accommodate all kinds of equal order interpolations numerical experiments on various examples including incompressible materials show that the method achieves an optimal rate of convergence for all variables copyright 2001 john wiley sons ltd

a modified least squares mixed finite element with improved momentum balance the main goal of this contribution is to provide an improved mixed finite element for quasi incompressible linear elasticity based on a classical least squares formulation a modified weak form with displacements and stresses as process variables is derived this weak form is the basis for a finite element with an advanced fulfillment of the momentum balance and therefore with a better performance for the continuous approximation of stresses and displacements on the triangular and tetrahedral elements lowest order raviart thomas and linear standard lagrange interpolations can be used it is shown that coercivity and continuity of the resulting asymmetric bilinear form could be established with respect to appropriate norms further on details about the implementation of the least squares mixed finite elements are given and some numerical examples are presented in order to demonstrate the performance of the proposed formulation copyright 2009 john wiley sons ltd

vapnik chervonenkis generalization bounds for real valued neural networks we show how lower bounds on the generalization ability of feedforward neural nets with real outputs can be derived within a formalism based directly on the concept of vc dimension and vapnik s theorem on uniform convergence of estimated probabilities

consistency and localizability we show that all consistent learning methods that is that asymptotically achieve the lowest possible expected loss for any distribution on x y are necessarily localizable by which we mean that they do not significantly change their response at a particular point when we show them only the part of the training set that is close to that point this is true in particular for methods that appear to be defined in a non local manner such as support vector machines in classification and least squares estimators in regression aside from showing that consistency implies a specific form of localizability we also show that consistency is logically equivalent to the combination of two properties 1 a form of localizability and 2 that the method s global mean over the entire x distribution correctly estimates the true mean consistency can therefore be seen as comprised of two aspects one local and one global

the weighted nearest neighbor estimate for hammerstein system identification this paper concerns the nonparametric identification problem for a class of nonlinear discrete time dynamical systems that is characterized by its cascade structure this is a hammerstein system being a series connection of a nonlinear memoryless element followed by a linear dynamic system the input output training data generated from the system are dependent and they do not reveal the strong mixing property the nonlinear part of the system is recovered with the weighted k nearest neighbor regression estimate the a priori information is nonparametric both the nonlinear characteristic and the impulse response of the linear part are completely unknown and can be of any form local and global properties of the estimate are examined whatever the probability density of the input signal the estimate converges at every continuity point of the characteristic as well as in the global sense we derive the formulas for asymptotic bias and the variance and evaluate the corresponding rate of convergence the convergence rate is independent of the shape of the input density and is proved to be optimal these results allow us to find a set of optimal nonnegative weights that further improve the accuracy of our estimation algorithm our findings are supported by simulation experiments

space time coupled spectral hp least squares finite element formulation for the incompressible navier stokes equations we consider least squares finite element models for the numerical solution of the non stationary navier stokes equations governing viscous incompressible fluid flows the paper presents a formulation where the effects of space and time are coupled resulting in a true space time least squares minimization procedure as opposed to a space time decoupled formulation where a least squares minimization procedure is performed in space at each time step the formulation is first presented for the linear advection diffusion equation and then extended to the navier stokes equations the formulation has no time step stability restrictions and is spectrally accurate in both space and time to allow the use of practical c0 element expansions in the resulting finite element model the navier stokes equations are expressed as an equivalent set of first order equations by introducing vorticity as an additional independent variable and the least squares method is used to develop the finite element model of the governing equations high order element expansions are used to construct the discrete model the discrete model thus obtained is linearized by newton s method resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix free form spectral convergence of the l2 least squares functional and l2 error norms in space time is verified using a smooth solution to the two dimensional non stationary incompressible navier stokes equations numerical results are presented for impulsively started lid driven cavity flow oscillatory lid driven cavity flow transient flow over a backward facing step and flow around a circular cylinder the results demonstrate the predictive capability and robustness of the proposed formulation even though the space time coupled formulation is emphasized we also present the formulation and numerical results for least squares space time decoupled finite element models the numerical results show that the space time coupled formulation has superior predictive capabilities for flows demanding high space time resolution exemplified here by the transient flow over a backward facing step

first order system least squares for the stress displacement formulation linear elasticity this paper develops a least squares finite element method for linear elasticity in both two and three dimensions the least squares functional is based on the stress displacement formulation with the symmetry condition of the stress tensor imposed in the first order system for the respective displacement and stress using the crouzeix raviart and raviart thomas finite element spaces our least squares finite element method is shown to be optimal in the broken h1 and h div norms uniform in the incompressible limit

on convergence properties of pocket algorithm the problem of finding optimal weights for a single threshold neuron starting from a general training set is considered among the variety of possible learning techniques the pocket algorithm has a proper convergence theorem which asserts its optimality however the original proof ensures the asymptotic achievement of an optimal weight vector only if the inputs in the training set are integer or rational this limitation is overcome in this paper by introducing a different approach that leads to the general result furthermore a modified version of the learning method considered called pocket algorithm with ratchet is shown to obtain an optimal configuration within a finite number of iterations independently of the given training set

distribution free consistency of a nonparametric kernel regression estimate and classification it is shown that the kernel estimate of the regression e y x x is weakly or strongly consistent for almost all x mu where mu is the probability measure of x the result is valid for any distribution of x the asymptotical optimality of classification rules derived from the estimate is examined the optimality is independent of class distributions i e it is distribution free

wavelet analysis of discharge dynamics of fusimotor neurons abstract we study the interspike intervals isi time series of the spontaneous fusimotor neuron activity by applying the wavelet transform analysis and confirm the existence of the white noise characteristics of the isi time series this means that the neuron activity may serve as the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles besides we apply the multifractal formalism adapted for the wavelet transform time series analysis thus we have established the multifractality of the isi data and achieved an additional insight into fusimotor discharge dynamics

nurbs based least squares finite element methods for fluid and solid mechanics summary this contribution investigates the performance of a least squares finite element method based on non uniform rational b splines nurbs basis functions the least squares functional is formulated directly in terms of the strong form of the governing equations and boundary conditions thus the introduction of auxiliary variables is avoided but the order of the basis functions must be higher or equal to the order of the highest spatial derivatives the methodology is applied to the incompressible navier stokes equations and to linear as well as nonlinear elastic solid mechanics the numerical examples presented feature convective effects and incompressible or nearly incompressible material the numerical results which are obtained with equal order interpolation and without any stabilisation techniques are smooth and accurate it is shown that for p and h refinement the theoretical rates of convergence are achieved copyright 2014 john wiley sons ltd

singularity spectrum of fractal signals from wavelet analysis exact results the multifractal formalism for singular measures is revisited using the wavelet transform for bernoulli invariant measures of some expanding markov maps the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima the generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures it is demonstrated that the hausdorff dimensiond h of the set of singularities of holder exponenth can be directly determined from the wavelet transform modulus maxima the singularity spectrum so obtained is shown to be not disturbed by the presence in the signal of a superimposed polynomial behavior of ordern provided one uses an analyzing wavelet that possesses at leastn n vanishing moments however it is shown that ac behavior generally induces a phase transition in thed h singularity spectrum that somewhat masks the weakest singularities this phase transition actually depends on the numbern of vanishing moments of the analyzing wavelet its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal these theoretical results are illustrated with numerical examples they are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional brownian motions and turbulent velocity signals

wavelet transform analysis of time series generated by the stimulated neuronal activity abstract we have studied the stimulated discharge dynamics of fusimotor neurons by applying the wavelet transform technique and by adopting that the neuronal discharge dynamics is manifested by the random time series of interspike intervals we found two different power law type behaviors along interspike intervals isi time scale which implies existence of two different types of neuronal noise which are separated by a crossover region our results reveal that complex neuronal dynamics in the presence of external stimulation is manifested with long range correlated noise in the region before the crossover on the isi time scale

detecting long range correlations in time series of neuronal discharges abstract we have studied the discharge dynamics of dorsal horn neurons dhn by applying the detrended fluctuation analysis dfa and the wavelet transform wt technique we have adopted that discharge dynamics is manifested by the random time series of the interspike intervals isi that is by intervals between two consecutive neuronal electrical activities in all cases studied we found two different power law type behaviors across isi enumeration scale that are separated by a crossover region our results reveal that complex neuronal dynamics may change in the presence of external stimulation which is manifested by changing the noise characteristics that appear before the crossover region the noise after the crossover region is of the 1 f type

dynamics of beryllium 7 specific activity in relation to meteorological variables tropopause height teleconnection indices and sunspot number abstract the dynamics of the beryllium 7 specific activity in surface air over 1987 2011 is analyzed using wavelet transform wt analysis and time dependent detrended moving average tddma method wt analysis gives four periodicities in the beryllium 7 specific activity one month three months one year and three years these intervals are further used in tddma to calculate local autocorrelation exponents for precipitation tropopause height and teleconnection indices our results show that these parameters share common periods with the beryllium 7 surface concentration tddma method indicates that on the characteristic intervals of one year and shorter the beryllium 7 specific activity is strongly autocorrelated on the three year interval the beryllium 7 specific activity shows periods of anticorrelation implying slow changes in its dynamics that become evident only over a prolonged period of time a comparison of the hurst exponents of all the variables on the one and three year intervals suggest some similarities in their dynamics overall a good agreement in the behavior of the teleconnection indices and specific activity of beryllium 7 in surface air is noted

local algorithms for pattern recognition and dependencies estimation in previous publications bottou and vapnik 1992 vapnik 1992 we described local learning algorithms which result in performance improvements for real problems we present here the theoretical framework on which these algorithms are based first we present a new statement of certain learning problems namely the local risk minimization we review the basic results of the uniform convergence theory of learning and extend these results to local risk minimization we also extend the structural risk minimization principle for both pattern recognition problems and regression problems this extended induction principle is the basis for a new class of algorithms

hammerstein system identification with the nearest neighbor algorithm the nonlinear characteristic in a hammerstein system i e a system in which a nonlinear memoryless subsystem and a linear dynamic are connected in a cascade is recovered with the nonparametric nearest neighbor regression estimate the a priori information is nonparametric both the nonlinear characteristic and the impulse response are completely unknown and can be of any form local and global properties of the estimate are examined whatever the probability density of the input signal the estimate converges at every continuity point of the characteristic as well as in the global sense we derive the asymptotic bias and variance of the proposed estimate as a result the optimal rate of convergence is established that additionally is independent of the shape of the input density results of numerical simulations are also presented

stochastic resonance of ensemble neurons for transient spike trains wavelet analysis by using the wavelet transformation wt i have analyzed the response of an ensemble of n 1 10 100 and 500 hodgkin huxley neurons to transient m pulse spike trains m i to 3 with independent gaussian noises thecross correlation between the input and output signals is expressed in terms of the wt expansion coefficients the signal to noise ratio snr is evaluated by using the denoising method within the wt by which the noise contribution is extracted from the output signals although the response of a single n 1 neuron to subthreshold transient signals with noises is quite unreliable the transmission fidelity assessed by the cross correlation and snr is shown to be much improved by increasing the value of n a population of neurons plays an indispensable role in the stochastic resonance sr for transient spike inputs it is also shown that in a large scale ensemble the transmission fidelity for suprathreshold transient spikes is not significantly degraded by a weak noise which is responsible to sr for subthreshold inputs

local minimax learning of functions with best finite sample estimation error bounds applications to ridge and lasso regression boosting tree learning kernel machines and inverse problems optimal local estimation is formulated in the minimax sense for inverse problems and nonlinear regression this theory provides best mean squared finite sample error bounds for some popular statistical learning algorithms and also for several optimal improvements of other existing learning algorithms such as smoothing splines and kernel regularization the bounds and improved algorithms are not based on asymptotics or bayesian assumptions and are truly local for each query not depending on cross validating estimates at other queries to optimize modeling parameters results are given for optimal local learning of approximately linear functions with side information context using real algebraic geometry in particular finite sample error bounds are given for ridge regression and for a local version of lasso regression the new regression methods require only quadratic programming with linear or quadratic inequality constraints for implementation greedy additive expansions are then combined with local minimax learning via a change in metric an optimal strategy is presented for fusing the local minimax estimators of a class of experts providing optimal finite sample prediction error bounds from random forests local minimax learning is extended to kernel machines best local prediction error bounds for finite samples are given for tikhonov regularization the geometry of reproducing kernel hilbert space is used to derive improved estimators with finite sample mean squared error mse bounds for class membership probability in two class pattern classification problems a purely local cross validation free algorithm is proposed which uses fisher information with these bounds to determine best local kernel shape in vector machine learning finally a locally quadratic solution to the finite fourier moments problem is presented after reading the first three sections the reader may proceed directly to any of the subsequent applications sections

universal consistency of localized versions of regularized kernel methods in supervised learning problems global and local learning algorithms are used in contrast to global learning algorithms the prediction of a local learning algorithm in a testing point is only based on training data which are close to the testing point every global algorithm such as support vector machines svm can be localized in the following way in every testing point the global learning algorithm is not applied to the whole training data but only to the k nearest neighbors knn of the testing point in case of support vector machines the success of such mixtures of svm and knn called svm knn has been shown in extensive simulation studies and also for real data sets but only little has been known on theoretical properties so far in the present article it is shown how a large class of regularized kernel methods including svm can be localized in order to get a universally consistent learning algorithm

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

on the strong universal consistency of nearest neighbor regression function estimates two results are presented concerning the consistency of the k nearest neighbor regression estimate we show that all modes of convergence in l 1 in probability almost sure complete are equivalent if the regression variable is bounded under the additional condition k log n we also obtain the strong universal consistency of the estimate

the rates of convergence of kernel regression estimates and classification rules both nonrecursive and recursive nonparametric regression estimates are studied the rates of weak and strong convergence of kernel estimates as well as corresponding multiple classification errors are derived without assuming the existence of the density of the measurements an application of the obtained results to a nonparametric bayes predication is presented