fisher information in quantum statistics braunstein and caves braunstein s l and caves c m 1994 phys rev lett 72 3439 43 proposed to use helstrom s quantum information number to define meaningfully a metric on the set of all possible states of a given quantum system they showed that the quantum information is nothing other than the maximal fisher information in a measurement of the quantum system maximized over all possible measurements combining this fact with classical statistical results they argued that the quantum information determines the asymptotically optimal rate at which neighbouring states on some smooth curve can be distinguished based on arbitrary measurements on n identical copies of the given quantum system we show that the measurement which maximizes the fisher information typically depends on the true unknown state of the quantum system we close the resulting loophole in the argument by showing that one can still achieve the same optimal rate of distinguishability by a two stage adaptive measurement procedure when we consider states lying not on a smooth curve but on a manifold of higher dimension the situation becomes much more complex we show that the notion of distinguishability of close by states depends strongly on the measurement resources one allows oneself and on a further specification of the task at hand the quantum information matrix no longer seems to play a central role

a finite element level set redistancing method based on gradient recovery we introduce a new redistancing method for level set functions this method applies in a finite element setting and uses a gradient recovery technique based on the recovered gradient a quasi normal field on the zero level of the finite element level set function is defined and from this an approximate signed distance function is determined for this redistancing method rigorous error bounds are derived for example the distance between the original zero level and the zero level after redistancing can be shown to be bounded by ch k 1 if finite elements of degree k are used in the discretization

polynomial preserving recovery for a class of weak galerkin finite element methods abstract this paper presents the polynomial preserving recover ppr postprocessing technique for the weak galerkin wg finite element methods on triangular meshes the proposed technique involves a fine tuning parameter in a stabilizer that improves the convergence order of the finite element methods the supercloseness between the lagrangian interpolation and the wg solution is analyzed which leads to the main result about the superconvergence in the gradient of the wg solution numerical results are presented to illustrate the theoretical analysis

frechet integration and adaptive metric selection for interpretable covariances of multivariate functional data summary for multivariate functional data recorded for a sample of subjects on a common domain one 10 is often interested in the covariance between pairs of the component functions extending the notion of a covariance matrix for multivariate data to the functional case a straightforward approach is to integrate the pointwise covariance matrices over the functional time domain we generalize this approach by defining the frintegral which depends on the metric chosen for the space of covariance matrices and demonstrate that the ordinary integration is a special 15 case when the frobenius metric is used as the space of covariance matrices is nonlinear we propose a class of power metrics as alternatives to the frobenius metric for any such power metric the calculation of frintegrals is equivalent to transforming the covariance matrices with the chosen power applying the classical riemann integral to the transformed matrices and finally applying the inverse transformation to return to the original scale we also propose data 20 adaptive metric selection with respect to a user specified target criterion for example fastest decline of the eigenvalues establish consistency of the proposed procedures and demonstrate their effectiveness in a simulation the proposed functional covariance approach through fr echet integration is illustrated in a comparison of connectivity between brain voxels for normal subjects and alzheimer s patients based on fmri data 25

laplace s law of succession and universal encoding this correspondence shows that the known add half rule is not asymptotically optimal for predicting the n 1 st symbol after a sequence of n symbols whereas the add spl beta sub 0 rule spl beta sub 0 0 50922 spl middot spl middot spl middot is

averaging of directional derivatives in vertices of nonobtuse regular triangulations for a shape regular triangulation mathcal t h without obtuse angles of a bounded polygonal domain omega subset re 2 let mathcal l h be the space of continuous functions linear on the triangles from mathcal t h and h the interpolation operator from c overline omega to mathcal l h this paper is devoted to the following classical problem find a second order approximation of the derivative partial u partial z a in a direction z of a function u in c 3 overline omega in a vertex a in the form of a linear combination of the constant directional derivatives partial pi h u partial z on the triangles surrounding a an effective procedure for such an approximation is presented its error is proved to be of the size o h 2 an operator mbox w h mathcal l h longrightarrow mathcal l h times mathcal l h relating a second order approximation wh h u of nabla u to every u in c 3 overline omega is constructed and shown to be a so called recovery operator the accuracy of the presented approximation is compared with the accuracies of the local approximations by other known techniques numerically

a pairwise interaction model for multivariate functional and longitudinal data functional data vectors consisting of samples of multivariate data where each component is a random function are encountered increasingly often but have not yet been comprehensively investigated we introduce a simple pairwise interaction model that leads to an interpretable and straightforward decomposition of multivariate functional data and of their variation into component specific processes and pairwise interaction processes the latter quantify the degree of pairwise interactions between the components of the functional data vectors while the component specific processes reflect the functional variation of a particular functional vector component that cannot be explained by the other components thus the proposed model provides an extension of the usual notion of a covariance or correlation matrix for multivariate vector data to functional data vectors and generates an interpretable functional interaction map the decomposition provided by the model can also serve as a basis for subsequent analysis such as study of the network structure of functional data vectors the decomposition of the total variance into componentwise and interaction contributions can be quantified by an formula see text like decomposition we provide consistency results for the proposed methods and illustrate the model by applying it to sparsely sampled longitudinal data from the baltimore longitudinal study of aging examining the relationships between body mass index and blood fats

a new finite element gradient recovery method superconvergence property this is the first in a series of papers in which a new gradient recovery method is introduced and analyzed it is proved that the method is superconvergent for translation invariant finite element spaces of any order the method maintains the simplicity efficiency and superconvergence properties of the zienkiewicz zhu patch recovery method in addition for uniform triangular meshes the method is superconvergent for the linear element under the chevron pattern and ultraconvergent at element edge centers for the quadratic element under the regular pattern applications of this new gradient recovery technique will be discussed in forthcoming papers

ultraconvergence of the patch recovery technique ii the ultraconvergence property of a gradient recovery technique proposed by zienkiewicz and zhu is analyzed for the laplace equation in the two dimensional setting under the assumption that the pollution effect is not present or is properly controlled it is shown that the convergence rate of the recovered gradient at an interior node is two orders higher than the optimal global convergence rate when even order finite element spaces and local uniform rectangular meshes are used

superconvergent derivative recovery for lagrange triangular elements of degree p on unstructured grids in this paper we develop a postprocessing derivative recovery scheme for the finite element solution u h on general unstructured but shape regular triangulations in the case of continuous piecewise polynomials of degree p geq 1 by applying the global l 2 projection q h and a smoothing operator s h the recovered p th derivatives s h m q h partial p u h superconverge to the exact derivatives partial p u based on this technique we are able to derive a local error indicator depending only on the geometry of corresponding element and the p 1 st derivatives approximated by partial s h m q h partial p u h we provide several numerical examples illustrating the effectiveness of our schemes we also observe that higher order elements are likely to require more conservative refinement strategies to create meshes corresponding to optimal orders of convergence

a numerical study of some hessian recovery techniques on isotropic and anisotropic meshes spaces of continuous piecewise linear finite elements are considered to solve a poisson problem and several numerical methods are investigated to recover second derivatives numerical results on 2d and 3d isotropic and anisotropic meshes indicate that the quality of the results is strongly linked to the mesh topology and that no convergence can be insured in general

functional data analysis for sparse longitudinal data we propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data the method aims at irregularly spaced longitudinal data where the number of repeated measurements available per subject is small in contrast classical functional data analysis requires a large number of regularly spaced measurements per subject we assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random subject specific trajectory plus measurement errors basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories and the estimation of the variance of the measurement errors the eigenfunction basis is estimated from the data and functional principal components score estimates are obtained by a conditioning step this conditional estimation method is conceptually simple and straightforward to implement

enhancing finite element approximation for eigenvalue problems by projection method abstract this paper establishes the superconvergence and the related recovery type a posteriori error estimators based on projection method for finite element approximation of the elliptic eigenvalue problems the projection method is a postprocessing procedure that constructs a new approximation by using the least squares method the results are based on some regularity assumption for the elliptic problem and are applicable to the finite element approximations of self adjoint elliptic eigenvalue problems with general quasi regular partitions therefore the result of this paper can be employed to provide useful a posteriori error estimators in adaptive finite element computation under unstructured meshes

minimax estimation of qubit states with bures risk the central problem of quantum statistics is to devise measurement schemes for the estimation of an unknown state given an ensemble of n independent identically prepared systems for locally quadratic loss functions the risk of standard procedures has the usual scaling of 1 n however it has been noticed that for fidelity based metrics such as the bures distance the risk of conventional non adaptive qubit tomography schemes scales as 1 n for states close to the boundary of the bloch sphere several proposed estimators appear to improve this scaling and our goal is to analyse the problem from the perspective of the maximum risk over all states we propose qubit estimation strategies based on separate adaptive measurements and collective measurements that achieve 1 n scalings for the maximum bures risk the estimator involving local measurements uses a fixed fraction of the available resource n to estimate the bloch vector direction the length of the bloch vector is then estimated from the remaining copies by measuring in the estimator eigenbasis the estimator based on collective measurements uses local asymptotic normality techniques which allows us to derive upper and lower bounds to its maximum bures risk we also discuss how to construct a minimax optimal estimator in this setup finally we consider quantum relative entropy and show that the risk of the estimator based on collective measurements achieves a rate o n 1 log n under this loss function furthermore we show that no estimator can achieve faster rates in particular the standard rate n 1

function gradient and hessian recovery using quadratic edge bump functions an approximate error function for the discretization error on a given mesh is obtained by projecting via the energy inner product the functional residual onto the space of continuous piecewise quadratic functions which vanish on the vertices of the mesh conditions are given under which one can expect this hierarchical basis error estimator to give efficient and reliable function recovery asymptotically exact gradient recovery and convergent hessian recovery in the square norms one does not find similar function recovery results in the literature the analysis given here is based on a certain superconvergence result which has been used elsewhere in the analysis of gradient recovery methods numerical experiments are provided which demonstrate the effectivity of the approximate error function in practice

the local superconvergence of the trilinear element for the three dimensional poisson problem abstract in this paper we shall combine the finite element theory of green s function presented in this paper the extrapolation technique and the local symmetric technique to investigate the local superconvergence of the trilinear element for the three dimensional poisson equation

interior maximum norm estimates for finite element methods part ii we consider bilinear forms a connected with second order elliptic problems and assume that for u h in a finite element space s h we have a u u h x f x for x in s h with local compact support we give local estimates for u u h in l and w 1 of the type local best approximation plus weak outside influences plus the local size of f

a more efficient anisotropic mesh adaptation for the computation of lagrangian coherent structures the computation of lagrangian coherent structures is more and more used in fluid mechanics to determine subtle fluid flow structures we present in this paper a new adaptive method for the efficient computation of finite time lyapunov exponent ftle from which the coherent lagrangian structures can be obtained this new adaptive method considerably reduces the computational burden without any loss of accuracy on the ftle field

asymptotically exact a posteriori error estimators part i grids with superconvergence in part i of this work we develop superconvergence estimates for piecewise linear finite element approximations on quasi uniform triangular meshes where most pairs of triangles sharing a common edge form approximate parallelograms in particular we first show a superconvergence of the gradient of the finite element solution uh and to the gradient of the interpolant ui we then analyze a postprocessing gradient recovery scheme showing that q h nabla u h is a superconvergent approximation to nabla u here qh is the global l2 projection in part ii we analyze a superconvergent gradient recovery scheme for general unstructured shape regular triangulations this is the foundation for an a posteriori error estimate and local error indicators

functional linear regression analysis for longitudinal data we propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data where both the predictor and response are functions of a covariate such as time predictor and response processes have smooth random trajectories and the data consist of a small number of noisy repeated measurements made at irregular times for a sample of subjects in longitudinal studies the number of repeated measurements per subject is often small and may be modeled as a discrete random number and accordingly only a finite and asymptotically nonincreasing number of measurements are available for each subject or experimental unit we propose a functional regression approach for this situation using functional principal component analysis where we estimate the functional principal component scores through conditional expectations this allows the prediction of an unobserved response trajectory from sparse measurements of a predictor trajectory the resulting technique is flexible and allows for different patterns regarding the timing of the measurements obtained for predictor and response trajectories asymptotic properties for a sample of n subjects are investigated under mild conditions as n oo and we obtain consistent estimation for the regression function besides convergence results for the components of functional linear regression such as the regression parameter function we construct asymptotic pointwise confidence bands for the predicted trajectories a functional coefficient of determination as a measure of the variance explained by the functional regression model is introduced extending the standard r 2 to the functional case the proposed methods are illustrated with a simulation study longitudinal primary biliary liver cirrhosis data and an analysis of the longitudinal relationship between blood pressure and body mass index

an updated lagrangian method with error estimation and adaptive remeshing for very large deformation elasticity problems the three dimensional case abstract solving large deformation problems of hyperelastic materials by the finite element method is still a challenging problem due to the severe mesh distortion that occurs during the computation in leger et al 2014 it was shown that combining an updated lagrangian method with an efficient adaptive remeshing algorithm an accurate transfer method for the deformation gradient tensor as well as an efficient continuation method leads to a very stable efficient and accurate algorithm to solve two dimensional very large deformation problems in this paper we show that this method can also be generalized to solve three dimensional problems a number of static problems will be presented and analyzed

minimax quantum tomography estimators and relative entropy bounds a minimax estimator has the minimum possible error risk in the worst case we construct the first minimax estimators for quantum state tomography with relative entropy risk the minimax risk of nonadaptive tomography scales as o 1 sqrt n in contrast to that of classical probability estimation which is o 1 n where n is the number of copies of the quantum state used we trace this deficiency to sampling mismatch future observations that determine risk may come from a different sample space than the past data that determine the estimate this makes minimax estimators very biased and we propose a computationally tractable alternative with similar behavior in the worst case but superior accuracy on most states

can we have superconvergent gradient recovery under adaptive meshes we study adaptive finite element methods for elliptic problems with domain corner singularities our model problem is the two dimensional poisson equation results of this paper are twofold first we prove that there exists an adaptive mesh gauged by a discrete mesh density function under which the recovered gradient by the polynomial preserving recovery ppr is superconvergent second we demonstrate by numerical examples that an adaptive procedure with an a posteriori error estimator based on ppr does produce adaptive meshes that asatisfy our mesh density assumption and the recovered gradient by ppr is indeed superconvergent in the adaptive process

dynamical correlation for multivariate longitudinal data nonparametric methodology for longitudinal data analysis is becoming increasingly popular the analysis of multivariate longitudinal data where data on several time courses are recorded for each subject has received considerably less attention despite its importance for practical data analysis in particular there is a need for measures and estimates to capture dependency between the components of vector valued longitudinal data we propose and analyze a simple and effective nonparametric method to quantify the covariation of components of multivariate longitudinal observations which are viewed as realizations of a random process this includes the notion of a correlation between derivatives and time shifted versions the concept of dynamical correlation is based on a scalar product obtained from pairs of standardized smoothed curves the proposed method can be used when observation times are irregular and not matching between subjects or between responses within a subject for higher dimensional dat

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

comparing the shapes of regression functions summary does a regression function follow a specified shape do two regression functions have the same shape how can regression functions be grouped based on shape these questions can occur when investigating monotonicity when counting local maxima or when studying variation in families of curves one can address these questions by considering the rank correlation coefficient between two functions this correlation is a generalisation of the rank correlation between two finite sets of numbers and is equal to one if and only if the two functions have the same shape a sample rank correlation based on smoothed estimates of the regression functions consistently estimates the true correlation this sample rank correlation can be used as a measure of similarity between functions in cluster analysis and as a measure of monotonicity or modality

metric tensors for anisotropic mesh generation it has been amply demonstrated that significant improvements in accuracy and efficiency can be gained when a properly chosen anisotropic mesh is used in the numerical solution for a large class of problems which exhibit anisotropic solution features in practice an anisotropic mesh is commonly generated as a quasi uniform mesh in the metric determined by a tensor specifying the shape size orientation of elements thus it is crucial to choose an appropriate metric tensor for anisotropic mesh generation and adaptation in this paper we develop a general formula for the metric tensor for use in any spatial dimension the formulation is based on error estimates for polynomial preserving interpolation on simiplicial elements numerical results in two dimensions are presented to demonstrate the ability of the metric tensor to produce anisotropic meshes with correct mesh concentration and good overall quality the procedure developed in this paper for defining the metric tensor can also be applied to other types of error estimates

superconvergence of the h p version of the finite element method in one dimension in this paper we investigate the superconvergence properties of the h p version of the finite element method fem for two point boundary value problems a postprocessing technique for the h p finite element approximation is analyzed the analysis shows that the postprocess improves the order of convergence furthermore we obtain asymptotically exact a posteriori error estimators based on the postprocessing results numerical examples are included to illustrate the theoretical analysis

adaptive variational multiscale methods for incompressible flow based on two local gauss integrations we consider variational multiscale vms methods with h adaptive technique for the stationary incompressible navier stokes equations the natural combination of vms with adaptive strategy retains the best features of both methods and overcomes many of their deficits a reliable a posteriori projection error estimator is derived which can be computed by two local gauss integrations at the element level finally some numerical tests are presented to illustrate the method s efficiency

hedged maximum likelihood quantum state estimation this letter proposes and analyzes a new method for quantum state estimation called hedged maximum likelihood hmle hmle is a quantum version of lidstone s law also known as the add rule a straightforward modification of maximum likelihood estimation mle it can be used as a plug in replacement for mle the hmle estimate is a strictly positive density matrix slightly less likely than the ml estimate but with much better behavior for predictive tasks single qubit numerics indicate that hmle beats mle according to several metrics for nearly all true states for nearly pure states mle does slightly better but neither method is optimal

a posteriori error estimates based on the polynomial preserving recovery superconvergence of order o h 1 rho for some rho 0 is established for the gradient recovered with the polynomial preserving recovery ppr when the mesh is mildly structured consequently the ppr recovered gradient can be used in building an asymptotically exact a posteriori error estimator

superconvergence property of an over penalized discontinuous galerkin finite element gradient recovery method a polynomial preserving recovery method is introduced for over penalized symmetric interior penalty discontinuous galerkin solutions to a quasi linear elliptic problem as a post processing method the polynomial preserving recovery is superconvergent for the linear and quadratic elements under specified meshes in the regular and chevron patterns as well as general meshes satisfying condition by means of the averaging technique we prove the polynomial preserving recovery method for averaged solutions is superconvergent satisfying similar estimates as those for conforming finite element methods we deduce superconvergence of the recovered gradient directly from discontinuous solutions and naturally construct an a posteriori error estimator consequently the a posteriori error estimator based on the recovered gradient is asymptotically exact extensive numerical results consistent with our analysis are presented

superconvergence analysis for the explicit polynomial recovery method a new recovery technique explicit polynomial recovery epr is analyzed for finite element methods epr reconstructs the value at edge centers by solving a local problem in combination with the finite element solution at the vertex a quadratic approximation is constructed besides improving the accuracy it can also be applied in building the epr based error estimator for the poisson equation the element center is a superconvergent point of the gradient of the epr recovered function on an equilateral triangulation numerical examples are presented to verify the theoretical results and to show the performance of the epr in the adaptive finite element method

canonical correlation analysis when the data are curves summary it is not immediately straightforward to extend canonical correlation analysis to the context of functional data analysis where the data are themselves curves or functions the obvious approach breaks down and it is necessary to use a method involving smoothing in some way such a method is introduced and discussed with reference to a data set on human gait the breakdown of the unsmoothed method is illustrated in a practical context and is demonstrated theoretically a consistency theorem for the smoothed method is proved in an increasing number of problems in a wide range of fields the data observed are not the univariate or multivariate observations of classical statistics but are func tions observed continuously ramsay and dalzell 1991 give the name functional data analysis to the analysis of data of this kind in most cases the observations will be functions of time or a closely related variable but there are clearly applications where the functions are surfaces observed over two or three dimensional space the motivating example for the present paper is a set of data on children s gait collected by the motion analysis laboratory at children s hospital san diego california see olshen et al 1989 for full details for each of a number of children several angles made by the child s joints knee hip etc are observed during the child s gait cycle one aim of the study is to gain understanding of the gait cycle of a normal child to make comparisons with children suffering from walking diffi culties these data motivated rice and silverman 1991 to discuss the extension of principal component analysis to the functional setting and to explain how smoothing can be incorporated into the analysis in a natural way in a substantial complemen tary paper ramsay and dalzell 1991 discuss different approaches to regression and principal component analysis in functional data analysis illustrating their work by a meteorological example the insights of functional data analysis may be helpful in chemometrics for instance a standard chemometric problem is the analysis of spectra observed in chromatography and these are to all intents and purposes functional observations another obvious area of potential relevance is the analysis of growth curve data the focus in the present paper will be on canonical correlation analysis cca in the gait example one might ask how variability in the knee angle cycle is related to

enhancing eigenvalue approximation by gradient recovery the polynomial preserving recovery ppr is used to enhance the finite element eigenvalue approximation remarkable fourth order convergence is observed for linear elements under structured meshes as well as unstructured initial meshes produced by the delaunay triangulation with the conventional bisection refinement

functional singular component analysis summary aiming at quantifying the dependence of pairs of functional data x y we develop the concept of functional singular value decomposition for covariance and functional singular component analysis building on the concept of canonical expansion of compact operators in functional analysis we demonstrate the estimation of the resulting singular values functions and components for the practically relevant case of sparse and noise contaminated longitudinal data and provide asymptotic consistency results expanding bivariate functional data into singular functions emerges as a natural extension of the popular functional principal component analysis for single processes to the case of paired processes a natural application of the functional singular value decomposition is a measure of functional correlation owing to the involvement of an inverse operation most previously considered functional correlation measures are plagued by numerical instabilities and strong sensitivity to the choice of smoothing parameters these problems are exacerbated for the case of sparse longitudinal data on which we focus the functional correlation measure that is derived from the functional singular value decomposition behaves well with respect to numerical stability and statistical error as we demonstrate in a simulation study practical feasibility for applications to longitudinal data is illustrated with examples from a study on aging and on line auctions

a posteriori analysis and improved accuracy for an operator decomposition solution of a conjugate heat transfer problem we consider the accuracy of an operator decomposition finite element method for a conjugate heat transfer problem consisting of two materials coupled through a common boundary we derive accurate a posteriori error estimates that account for the transfer of error between components of the operator decomposition method as well as the differences between the adjoints of the full problem and the discrete iterative system we use these estimates to guide adaptive mesh refinement in addition we address a loss of order of convergence that results from the decomposition and show that the order of convergence is limited by the accuracy of the transferred gradient information we employ a boundary flux recovery method to regain the expected order of accuracy in an efficient manner

analysis of recovery type a posteriori error estimators for mildly structured grids some recovery type error estimators for linear finite elements are analyzed under o h 1 0 regular grids superconvergence of order o h 1 0 p is established for recovered gradients by three different methods as a consequence a posteriori error estimators based on those recovery methods are asymptotically exact

optimal anisotropic meshes for minimizing interpolation errors in l p norm in this paper we present a new optimal interpolation error estimate in l p norm 1 p for finite element simplicial meshes in any spatial dimension a sufficient condition for a mesh to be nearly optimal is that it is quasi uniform under a new metric defined by a modified hessian matrix of the function to be interpolated we also give new functionals for the global moving mesh method and obtain optimal monitor functions from the viewpoint of minimizing interpolation error in the l p norm some numerical examples are also given to support the theoretical estimates

polynomial preserving recovery on boundary in this paper we propose two systematic strategies to recover the gradient on the boundary of a domain the recovered gradient has comparable superconvergent property on the boundary as that in the interior of the domain this superconvergence property has been validated by several numerical experiments

gradient recovery for elliptic interface problem ii immersed finite element methods abstract this is the second paper on the study of gradient recovery for elliptic interface problem in our previous work guo and yang 2016 17 we developed a novel gradient recovery technique for finite element method based on the body fitted mesh in this paper we propose new gradient recovery methods for two immersed interface finite element methods symmetric and consistent immersed finite method ji et al 2014 23 and petrov galerkin immersed finite element method hou et al 2004 22 and hou and liu 2005 20 compared to the body fitted mesh based gradient recovery method the new methods provide a uniform way of recovering gradient on regular meshes numerical examples are presented to confirm the superconvergence of both gradient recovery methods moreover they provide asymptotically exact a posteriori error estimators for both immersed finite element methods

smoothed functional principal components analysis by choice of norm the principal components analysis of functional data is often enhanced by the use of smoothing it is shown that an attractive method of incorporating smoothing is to replace the usual l 2 orthonormality constraint on the principal components by orthonormality with respect to an inner product that takes account of the roughness of the functions the method is easily implemented in practice by making use of appropriate function transforms fourier transforms for periodic data and standard principal components analysis programs several alternative possible interpretations of the smoothed principal components as obtained by the method are presented some theoretical properties of the method are discussed the estimates are shown to be consistent under appropriate conditions and asymptotic expansion techniques are used to investigate their bias and variance properties these indicate that the form of smoothing proposed is advantageous under mild conditions indeed milder than those for existing methods of smoothed functional principal components analysis the choice of smoothing parameter by cross validation is discussed the methodology of the paper is illustrated by an application to a biomechanical data set obtained in the study of the behaviour of the human thumb forefinger system

modeling and forecasting daily electricity load curves a hybrid approach we propose a hybrid approach for the modeling and the short term forecasting of electricity loads two building blocks of our approach are 1 modeling the overall trend and seasonality by fitting a generalized additive model to the weekly averages of the load and 2 modeling the dependence structure across consecutive daily loads via curve linear regression for the latter a new methodology is proposed for linear regression with both curve response and curve regressors the key idea behind the proposed methodology is dimension reduction based on a singular value decomposition in a hilbert space which reduces the curve regression problem to several ordinary i e scalar linear regression problems we illustrate the hybrid method using french electricity loads between 1996 and 2009 on which we also compare our method with other available models including the electricite de france operational model supplementary materials for this article are available online

peter hall functional data analysis and random objects functional data analysis has become a major branch of nonparametric statistics and is a fast evolving field peter hall has made fundamental contributions to this area and its theoretical underpinnings he wrote more than 25 papers in functional data analysis between 1998 and 2016 and from 2005 on was a tenured faculty member with a 25 appointment in the department of statistics at the university of california davis this article describes aspects of his appointment and academic life in davis and also some of his major results in functional data analysis along with a brief history of this area it concludes with an outlook on new types of functional data and an emerging field of random objects that subsumes functional data analysis as it deals with more complex data structures

anisotropic residual based a posteriori mesh adaptation in 2d element based approach abstract an element based adaptation method is developed for an anisotropic a posteriori error estimator the adaptation does not make use of a metric but instead equidistributes the error over elements using local mesh modifications numerical results are reported comparing with three popular anisotropic adaptation methods currently in use it was found that the new method gives favourable results for controlling the energy norm of the error in terms of degrees of freedom at the cost of increased cpu usage additionally we considered a new l 2 variant of the estimator the estimator is shown to be conditionally equivalent to the exact l 2 error we provide examples of adapted meshes with the l 2 estimator and show that it gives greater control of the l 2 error compared with the original estimator