a semi analytical approach to molecular dynamics despite numerous computational advances over the last few decades molecular dynamics still favors explicit and thus easily parallelizable time integrators for large scale numerical simulation as a consequence computational efficiency in solving its typically stiff oscillatory equations of motion is hampered by stringent stability requirements on the time step size in this paper we present a semi analytical integration scheme that offers a total speedup of a factor 30 compared to the verlet method on typical md simulation by allowing over three orders of magnitude larger step sizes by efficiently approximating the exact integration of the strong harmonic forces of covalent bonds through matrix functions far improved stability with respect to time step size is achieved without sacrificing the explicit symplectic time reversible or fine grained parallelizable nature of the integration scheme we demonstrate the efficiency and scalability of our integrator on simulations ranging from dna strand unbinding and protein folding to nanotube resonators

semiparametric nonlinear mixed effects models and their applications nonlinear mixed effects models nlmms and self modeling nonlinear regression semor models are often used to fit repeated measures data they use a common function shared by all subjects to model variation within each subject and some fixed and or random parameters to model variation between subjects the parametric nlmm may be too restrictive and the semiparametric semor model ignores correlations within each subject in this article we propose a class of semiparametric nonlinear mixed effects models snmms that extend nlmms semor models and many other existing models in a natural way a snmm assumes that the mean function depends on some parameters and nonparametric functions the parameters provide an interpretable data summary the nonparametric functions provide flexibility to allow the data to decide some unknown or uncertain components such as the shape of the mean response over time a second stage model with fixed and random effects is used to model the parameters smoothing splines are us

a deconvolution approach to estimation of a common shape in a shifted curves model this paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model we show that this problem can be transformed into a linear inverse problem where the density of the random shifts plays the role of a convolution operator an adaptive estimator of the mean pattern based on wavelet thresholding is proposed we study its consistency for the quadratic risk as the number of observed curves tends to infinity and this estimator is shown to achieve a near minimax rate of convergence over a large class of besov balls this rate depends both on the smoothness of the common shape of the curves and on the decay of the fourier coefficients of the density of the random shifts hence this paper makes a connection between mean pattern estimation and the statistical analysis of linear inverse problems which is a new point of view on curve registration and image warping problems we also provide a new method to estimate the unknown random shifts between curves some numerical experiments are given to illustrate the performances of our approach and to compare them with another algorithm existing in the literature

combining registration and fitting for functional models a registration method can be defined as a process of aligning features of a sample of curves by monotone transformations of their domain the aligned curves exhibit only amplitude variation and the domain transformations called warping functions capture the phase variation in the original curves in this article we precisely define a new type of registration process in which the warping functions optimize the fit of a principal components decomposition to the aligned curves the principal components are effectively the features that this process aligns we discuss the relationship of registration to closure of a function space under convex operations and define consistency for registration methods we define an explicit decomposition of functional variation into amplitude and phase partitions and develop an algorithm for combining registration with principal components analysis and apply it to simulated and real data

on the performance of exponential integrators for problems in magnetohydrodynamics exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems while the results of these investigations showed that exponential integrators can provide significant computational savings the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages resistive magnetohydrodynamic mhd modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas in many problems numerical solution of mhd equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest in this paper we evaluate the performance of exponential integrators on large mhd problems and compare them to a state of the art implicit time integrator both the variable and constant time step exponential methods of epirk type are used to simulate magnetic reconnection and the kevin helmholtz instability in plasma performance of these methods which are part of the epic software package is compared to the variable time step variable order bdf scheme included in the cvode part of sundials library we study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as reynolds lundquist and prandtl numbers we find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for mhd problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as mhd

on optimal convergence rate of the rational krylov subspace reduction for electromagnetic problems in unbounded domains we solve an electromagnetic frequency domain induction problem in mathbf r 3 for a frequency interval using rational krylov subspace rks approximation the rks is constructed by spanning on the solutions for a certain a priori chosen set of frequencies we reduce the problem of the optimal choice of these frequencies to the third zolotaryov problem in the complex plane having an approximate closed form solution and determine the best cauchy hadamard convergence rate the theory is illustrated with numerical examples for maxwell s equations arising in 3d magnetotelluric geophysical exploration

art adaptive residual time restarting for krylov subspace matrix exponential evaluations abstract in this paper a new restarting method for krylov subspace matrix exponential evaluations is proposed since our restarting technique essentially employs the residual some convergence results for the residual are given we also discuss how the restart length can be adjusted after each restart cycle which leads to an adaptive restarting procedure numerical tests arepresented to compare our restarting with three other restarting methods some of the algorithms described in this paper are a part of the octave matlab package expmarpack available at http team kiam ru botchev expm

numerical aspects of gram schmidt orthogonalization of vectors abstract several variants of gram schmidt orthogonalization are reviewed from a numerical point of view it is shown that the classical and modified variants correspond to the gauss jacobi and gauss seidel iterations for linear systems further it is shown that orthogonalization with respect to elliptic norms and biorthogonalization can be formulated as orthogonalization by oblique projections

galerkin projection methods for solving multiple linear systems in this paper we consider using conjugate gradient cg methods for solving multiple linear systems a i x i b i for 1 le i le s where the coefficient matrices a i and the right hand sides b i are different in general in particular we focus on the seed projection method which generates a krylov subspace from a set of direction vectors obtained by solving one of the systems called the seed system by the cg method and then projects the residuals of other systems onto the generated krylov subspace to get the approximate solutions the whole process is repeated until all the systems are solved most papers in the literature t f chan and w l wan it siam j sci comput 18 1997 pp 1698 1721 b parlett it linear algebra appl 29 1980 pp 323 346 y saad it math comp 48 1987 pp 651 662 v simoncini and e gallopoulos it siam j sci comput 16 1995 pp 917 933 c smith a peterson and r mittra it ieee trans antennas and propagation 37 1989 pp 1490 1493 considered only the case where the coefficient matrices a i are the same but the right hand sides are different we extend and analyze the method to solve multiple linear systems with varying coefficient matrices and right hand sides a theoretical error bound is given for the approximation obtained from a projection process onto a krylov subspace generated from solving a previous linear system finally numerical results for multiple linear systems arising from image restorations and recursive least squares computations are reported to illustrate the effectiveness of the method

locally adaptive bandwidth choice for kernel regression estimators abstract kernel estimators with a global bandwidth are commonly used to estimate regression functions on the other hand it is obvious that the choice of a local bandwidth can lead to better results because a larger class of kernel estimators is available evidently this may in turn affect variability the optimal bandwidths depend essentially on the regression function itself and on the residual variance and it is desirable to estimate them from the data in this article a local bandwidth estimator is studied a comparison with its global bandwidth equivalent is performed both in theory and in simulations as the main result it is shown that the possible gain in mean integrated squared error of the resulting regression estimator must be paid for by a larger variability of the estimator this may lead to worse results if the sample size is small an algorithm has been devised that puts special weight on stability aspects our simulation study shows that improvements over a global bandwidth estimator

derivations and invariant forms of jordan and alternative tori jordan and alternative tori are the coordinate algebras of extended affine lie algebras of types a 1 and a 2 in this paper we show that the derivation algebra of a jordan torus is a semidirect product of the ideal of inner derivations and the subalgebra of central derivations in the course of proving this result we investigate derivations of the more general class of division graded jordan and alternative algebras we also describe invariant forms of these algebras

a deflated version of the conjugate gradient algorithm we present a deflated version of the conjugate gradient algorithm for solving linear systems the new algorithm can be useful in cases when a small number of eigenvalues of the iteration matrix are very close to the origin it can also be useful when solving linear systems with multiple right hand sides since the eigenvalue information gathered from solving one linear system can be recycled for solving the next systems and then updated

conditional quantile analysis when covariates are functions with application to growth data summary motivated by the conditional growth charts problem we develop a method for conditional quantile analysis when predictors take values in a functional space the method proposed aims at estimating conditional distribution functions under a generalized functional regression framework this approach facilitates balancing of model flexibility and the curse of dimensionality for the infinite dimensional functional predictors its good performance in comparison with other methods both for sparsely and for densely observed functional covariates is demonstrated through theory as well as in simulations and an application to growth curves where the method proposed can for example be used to assess the entire growth pattern of a child by relating it to the predicted quantiles of adult height

nonparametric maximum likelihood estimation of the structural mean of a sample of curves a random sample of curves can be usually thought of as noisy realisations of a compound stochastic process x t z w t where z t produces random amplitude variation and w t produces random dynamic or phase variation in most applications it is more important to estimate the so called structural mean t e z t than the crosssectional mean e x t but this estimation problem is difficult because the process z t is not directly observable in this paper we propose a nonparametric maximum likelihood estimator of t this estimator is shown to be surd n consistent and asymptotically normal under the assumed model and robust to model misspecification simulations and a realdata example show that the proposed estimator is competitive with landmark registration often considered the benchmark and has the advantage of avoiding time consuming and often infeasible individual landmark identification

on monotonicity of the lanczos approximation to the matrix exponential abstract we prove strictly monotonic error decrease in the euclidian norm of the krylov subspace approximation of exp a where and a are respectively a vector and a symmetric matrix in addition we show that the norm of the approximate solution grows strictly monotonically with the subspace dimension

functional convex averaging and synchronization for time warped random curves data that can be best described as a sample of curves are now fairly common in science and engineering when the dynamics of development growth or response over time are at issue subjects or experimental units may experience events at different temporal paces for functional data where trajectories may be individually time transformed it is usually inadequate to use commonly used sample statistics such as the cross sectional mean or median or the cross sectional sample variance if one observes time warped curve data i e random curves or random trajectories that exhibit random transformations of the time scale then the usual l2 norm and metric typically are inadequate one may then consider subjecting each observed curve to a time transformation in an attempt to reverse the warping of the time scale before further statistical analysis dynamic time warping alignment curve registration and landmark based methods have been put forward with the goal of finding adequate empirical time transforma

registration for exponential family functional data we consider the problem of aligning curves from exponential family distributions the approach is based on the combination of alignment and functional principal components analysis and is facilitated by recent extensions of fpca to non gaussian settings our work is motivated by the study of physical activity using accelerometers wearable devices that provide around the clock monitoring of activity and produce non gaussian measurements we apply the proposed methods to activity counts using a poisson distribution and to a binary active vs inactive indicator using a binomial distribution after alignment the trajectories show clear peaks of activity in the morning and afternoon with a dip in the middle of the day

analysis of projection methods for solving linear systems with multiple right hand sides we analyze a class of krylov projection methods but mainly concentrate on a specific conjugate gradient cg implementation by smith peterson and mittra ieee transactions on antennas and propogation 37 1989 pp 1490 1493 to solve the linear system ax b where a is symmetric positive definite and b is a multiple of right hand sides this method generates a krylov subspace from a set of direction vectors obtained by solving one of the systems called the seed system by the cg method and then projects the residuals of other systems orthogonally onto the generated krylov subspace to get the approximate solutions the whole process is repeated with another unsolved system as a seed until all the systems are solved we observe in practice a superconvergence behavior of the cg process of the seed system when compared with the usual cg process we also observe that only a small number of restarts is required to solve all the systems if the right hand sides are close to each other these two features together make the method particularly effective in this paper we give theoretical proof to justify these observations furthermore we combine the advantages of this method and the block cg method and propose a block extension of this single seed method

residual variance and residual pattern in nonlinear regression summary a nonparametric estimator of residual variance in nonlinear regression is proposed it is based on local linear fitting asymptotically the estimator has a small bias but a larger variance compared with the parametric estimator in linear regression finite sample properties are investigated in a simulation study including a comparison with other nonparametric estimators the method is also useful for spotting heteroscedasticity and outliers in the residuals at an early stage of the data analysis a further application is checking the fit of parametric models this is illustrated for longitudinal growth data

conjugate gradient type methods and preconditioning in this paper we consider various iterative methods for the numerical solution of very large sparse linear systems of equations which arise in the discretization of partial differential equations as the performance of the methods generally depends on the characteristics of the problems to be solved a judicious choice between the methods will require knowledge about the system the aim of this paper is to review the properties of the various iteration methods in order to assist the user in making a deliberate selection

on the orthogonality of residual polynomials of minimax polynomial preconditioning this paper studies polynomials used in polynomial preconditioning for solving linear systems of equations optimum preconditioning polynomials are obtained by solving some constrained minimax approximation problems the resulting residual polynomials are referred to as the de boor rice and grcar polynomials it will be shown in this paper that the de boor rice and grcar polynomials are orthogonal polynomials over several intervals more specifically each de boor rice or grcar polynomial belongs to an orthogonal family but the orthogonal family varies with the polynomial this orthogonality property is important because it enables one to generate the minimax preconditioning polynomials by three term recursive relations some results on the convergence properties of certain preconditioning polynomials are also presented

global scd algorithm for real positive definite linear systems with multiple right hand sides abstract in the present paper we present the left conjugate direction lcd method for linear systems with multiple right hand sides we define the method by using left and right conjugate direction matrices and petrov galerkin condition the method has no breakdown for real positive definite systems the method reduces to the usual cg type method when a is symmetric positive definite we also show how to apply these methods for solving the lyapunov matrix equation finally a numerical experiment is given to illustrate the result

searching for structure in curve samples abstract the shape of a regression curve can to a large extent be characterized by the succession of structural features like extrema inflection points and so on when analyzing a sample of regression curves it is often important to know at an early stage of data analysis which structural features are occurring consistently in each curve of the sample such a definition is usually not easy due to substantial interindividual variation both in the x and the y axis and due to the influence of noise a method is proposed for identifying typical features without relying on an a priori specified functional model for the curves the approach is based on the frequencies of occurrence of structural features as for example maxima in the curve sample along the x axis important tools are nonparametric regression and differentiation and kernel density estimation apart from a theoretical foundation the usefulness of the method is documented by application to two interesting biomedical areas growth and develop

a flexible and fast method for automatic smoothing abstract the choice of smoothing parameter or bandwidth is crucial when applying nonparametric regression estimators such as kernel estimators the optimal choice depends on the data at hand a data driven bandwidth selection close to the optimal one would make these curve estimators objective more reliable and easier to use minimizing residual mean squared error criteria such as cross validation have been frequently proposed to estimate the optimal smoothing parameter empirical and theoretical evidence indicates that cross validation rules and related methods lead to rather variable estimated optimal bandwidths the method presented here builds on estimating the asymptotically optimal bandwidth from the data since estimators for the residual variance and for an asymptotic expression for the bias are plugged into the asymptotic formula such selection rules are called plug in estimators the functional that quantifies bias is approximated by the integrated squared second derivative of the regre

bayesian hierarchical curve registration functional data often exhibit a common shape but with variations in amplitude and phase across curves the analysis often proceeds by synchronization of the data through curve registration in this article we propose a bayesian hierarchical model for curve registration our hierarchical model provides a formal account of amplitude and phase variability while borrowing strength from the data across curves in the estimation of the model parameters we discuss extensions of the model by using penalized b splines in the representation of the shape and time transformation functions and by allowing temporal misalignment of the curves we discuss applications of our model to simulated data as well as to two data sets in particular we use our model in a nonstandard analysis aimed at investigating regulatory network in time course microarray data

bandwidth choice for nonparametric regression this paper is concerned with the problem of choosing a bandwidth parameter for nonparametric regression we analyze a tapered fourier series estimate and discuss the relationship of this estimate to a kernel estimate we first consider a method based on an unbiased estimate of mean square error and show that the bandwidth thus chosen is asymptotically optimal other methods are examined as well and are shown to be asymptotically equivalent a small simulation shows however that for small or moderate sample size the methods perform quite differently

unconditionally stable integration of maxwell s equations numerical integration of maxwell s equations is often based on explicit methods accepting a stability step size restriction in literature evidence is given that there is also a need for unconditionally stable methods as exemplified by the successful alternating direction implicit finite difference time domain scheme in this paper we discuss unconditionally stable integration for a general semi discrete maxwell system allowing non cartesian space grids as encountered in finite element discretizations such grids exclude the alternating direction implicit approach particular attention is given to the second order trapezoidal rule implemented with preconditioned conjugate gradient iteration and to second order exponential integration using krylov subspace iteration for evaluating the arising phi functions a three space dimensional test problem is used for numerical assessment and comparison with an economical second order implicit explicit integrator we further pay attention to the chebyshev series expansion for computing the exponential operator for skew symmetric matrices

the lanczos optimization of a splitting up method to solve homogeneous evolutionary equations abstract let the cauchy problem for a symmetrical homogeneous ode system be solved by a difference scheme and let s be the required number of matrix vector operations with the finite difference matrix in classical schemes s is proportional to the number of time steps the lanczos method is used to decrease s without essential increase of error a theoretical estimate is given which shows approximately the s advantage of such an approach its application to the 2d heat conduction equation is considered one and two cyclic alternating direction difference schemes are used some numerical experiments show that the arithmetical costs are reduced by a factor 3 up to 60 with respect to the classical approach combination of a splitting scheme and the lanczos method is also proposed for the computation of the lower part of the spectrum and for solving some other problems

statistical tools to analyze data representing a sample of curves the paper is concerned with data representing a sample of smooth curves which can be considered as independent realizations of an underlying biological chemical ldots process such samples of curves often possess the following features there is a typical structural pattern common to all curves of the sample on the other hand individual realizations of the typical shape show different dynamics and intensity in particular typical peaks are shifted from individual to individual differences in dynamics complicate the analysis of samples of curves for example the cross sectional average usually does not reflect an average pattern due to shifts structure is smeared or might even disappear our approach consists in synchronizing the individual curves before determining the average or any further statistics pointwise averaging of the synchronized curves then leads to an average curve which represents the common structure with average dynamics and average intensity the method requires the introduction of new statistical objects they are defined mathematically their properties are discussed and possible estimators are proposed the asymptotic bias and variance of the estimators are derived an application to visually evoked brain potentials illustrates the approach

kernels for nonparametric curve estimation summary the choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error imse the present proof of the optimality of the latter kernels is restricted up to order k 5 these kernels are also of interest for the nonparametric estimation of probability densities and spectral densities a finite sample study indicates that higher order kernels asymptotically improving the rate of convergence may become attractive for realistic finite sample size suitably modified kernels are considered for estimating at the extremities of the data in a way which allows to retain the order of the bias found for interior points

global lsmr gl lsmr method for solving general linear systems with several right hand sides abstract the global solvers are an attractive class of iterative solvers for solving linear systems with multiple right hand sides in this paper first a new global method for solving general linear systems with several right hand sides is presented this method is the global version of the lsmr algorithm presented by fong and saunders 2011 then some theoretical properties of the new method are discussed finally numerical experiments from real applications are used to confirm the effectiveness of the proposed method

application of a block modified chebyshev algorithmto the iterative solution of symmetric linear systemswith multiple right hand side vectors an adaptive richardson iteration method is described for the solution of large sparse symmetric positive definite linear systems of equations with multiple right hand side vectors this scheme learns about the linear system to be solved by computing inner products of residual matrices during the iterations these inner products are interpreted as block modified moments a block version of the modified chebyshev algorithm is presented which yields a block tridiagonal matrix from the block modified moments and the recursion coefficients of the residual polynomials the eigenvalues of this block tridiagonal matrix define an interval which determines the choice of relaxation parameters for richardson iteration only minor modifications are necessary in order to obtain a scheme for the solution of symmetric indefinite linear systems with multiple right hand side vectors we outline the changes required

amplitude and phase variation of point processes we develop a canonical framework for the study of the problem of registration of multiple point processes subjected to warping known as the problem of separation of amplitude and phase variation the amplitude variation of a real random function y x x is an element of 0 1 corresponds to its random oscillations in the y axis typically encapsulated by its co variation around a mean level in contrast its phase variation refers to fluctuations in the x axis often caused by random time changes we formalise similar notions for a point process and nonparametrically separate them based on realisations of i i d copies pi i of the phase varying point process a key element in our approach is to demonstrate that when the classical phase variation assumptions of functional data analysis fda are applied to the point process case they become equivalent to conditions interpretable through the prism of the theory of optimal transportation of measure we demonstrate that these induce a natural wasserstein geometry tailored to the warping problem including a formal notion of bias expressing over registration within this framework we construct nonparametric estimators that tend to avoid over registration in finite samples we show that they consistently estimate the warp maps consistently estimate the structural mean and consistently register the warped point processes even in a sparse sampling regime we also establish convergence rates and derivev root n consistency and a central limit theorem in the cox process case under dense sampling showing rate optimality of our structural mean estimator in that case

evaluation of matrix functions with the block lanczos algorithm abstract for the approximate eigenvalues and eigenvectors obtained from a block lanczos iteration characterizations are given in terms of vectors of polynomials it is proven that after r steps of block lanczos with selfadjoint iteration matrix s the application p s f of a matrix polynomial and the linear functional v q s f can be evaluated exactly if p and q are polynomials of degree r 1 and 2 r 1 respectively for that the lanczos starting block should contain the vectors f and v based on this property a priori error bounds for the evaluation of g s f and v g s f for more general functions g are derived the error bounds are applied to the case of calculating the dynamic response in forced vibration problems a numerical example is given

cache issues of algebraic multigrid methods for linear systems with multiple right hand sides this paper is concerned with the solution of a linear system with multiple right hand sides such problems arise from nonlinear time dependent inverse or optimization problems in order to solve these problems efficiently we use block variants of the conjugate gradient method and combine them with cache aware algorithms further we describe the acceleration of algebraic multigrid amg methods by using such cache aware algorithms finally numerical studies are presented that show the high efficiency of the proposed methods

the gautschi time stepping scheme for edge finite element discretizations of the maxwell equations for the time integration of edge finite element discretizations of the three dimensional maxwell equations we consider the gautschi cosine scheme where the action of the matrix function is approximated by a krylov subspace method first for the space discretized edge finite element maxwell equations the dispersion error of this scheme is analyzed in detail and compared to that of two conventional schemes second we show that the scheme can be implemented in such a way that a higher accuracy can be achieved within less computational time as compared to other implicit schemes we also analyzed the error made in the krylov subspace matrix function evaluations although the new scheme is unconditionally stable it is explicit in structure as an explicit scheme it requires only the solution of linear systems with the mass matrix

second order comparison of gaussian random functions and the geometry of dna minicircles given two samples of continuous zero mean iid gaussian processes on 0 1 we consider the problem of testing whether they share the same covariance structure our study is motivated by the problem of determining whether the mechanical properties of short strands of dna are significantly affected by their base pair sequence though expected to be true had so far not been observed in three dimensional electron microscopy data the testing problem is seen to involve aspects of ill posed inverse problems and a test based on a karhunen loeve approximation of the hilbert schmidt distance of the empirical covariance operators is proposed and investigated when applied to a dataset of dna minicircles obtained through the electron microscope our test seems to suggest potential sequence effects on dna shape supplemental material available online

an iterative solution method for solving f a x b using krylov subspace information obtained for the symmetric positive definite matrix a abstract the conjugate gradients method generates successive approximations x i for the solution of the linear system ax b where a is symmetric positive definite and usually sparse it will be shown how intermediate information obtained by the conjugate gradients cg algorithm or by the closely related lanczos algorithm can be used to solve f a x b iteratively in an efficient way for suitable functions f the special case f a a 2 is discussed in particular we also consider the problem of solving ax b for different right hand sides b a variant on a well known algorithm for that problem is proposed which does not seem to suffer from the usual loss of orthogonality in the standard cg and lanczos algorithms

functional quasi likelihood regression models with smooth random effects summary we propose a class of semiparametric functional regression models to describe the influence of vector valued covariates on a sample of response curves each observed curve is viewed as the realization of a random process composed of an overall mean function and random components the finite dimensional covariates influence the random components of the eigenfunction expansion through single index models that include unknown smooth link and variance functions the parametric components of the single index models are estimated via quasi score estimating equations with link and variance functions being estimated nonparametrically we obtain several basic asymptotic results the functional regression models proposed are illustrated with the analysis of a data set consisting of egg laying curves for 1000 female mediterranean fruit flies medflies

pairwise curve synchronization for functional data summary data collected by scientists are increasingly in the form of trajectories or curves often these can be viewed as realizations of a composite process driven by both amplitude and time variation we consider the situation in which functional variation is dominated by time variation and develop a curve synchronization method that uses every trajectory in the sample as a reference to obtain pairwise warping functions in the first step these initial pairwise warping functions are then used to create improved estimators of the underlying individual warping functions in the second step a truncated averaging process is used to obtain robust estimation of individual warping functions the method compares well with other available time synchronization approaches and is illustrated with berkeley growth data and gene expression data for multiple sclerosis

distribution on warp maps for alignment of open and closed curves alignment of curve data is an integral part of their statistical analysis and can be achieved using model or optimization based approaches the parameter space is usually the set of monotone con

solution of 3d time domain electromagnetic problems using optimal subspace projection abstracttime domain problems for controlled source electromagnetic exploration require accurate discretization of the solution for multiple spacial and temporal scales therefore forward simulation using conventional computational methods becomes computationally expensive even without accounting for induced polarization ip effects these effects create another complication caused by the presence of a convolution integral in the time domain maxwell system we suggested a novel fast and robust algorithm to solve the 3d time domain electromagnetic em problems that can be considered as a generalization of the spectral lanczos decomposition method the new method also allowed us to incorporate the ip effects without significant cost increase the discretized large scale maxwell system was projected onto a small subspace consisting of the laplace domain solutions the so called parameter dependent krylov subspace for an optimally chosen set of laplace parameters the projected system preserved stabilit

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

a multiresolution approach to time warping achieved by a bayesian prior posterior transfer fitting strategy summary warping is an approach to the reduction and analysis of phase variability in functional observations by applying a smooth bijection to the function argument we propose a natural representation of warping functions in terms of a new type of elementary functions named warping component functions or warplets which are combined into the warping function by composition the inverse warping function is trivial and explicit to obtain a sequential bayesian estimation strategy is introduced which fits a series of models and transfers the posterior of the previous fit into the prior of the next fit model selection is based on a warping analogue to wavelet thresholding combined with bayesian inference

a new class of split exponential propagation iterative methods of runge kutta type sepirk for semilinear systems of odes abstract in this paper the framework of the exponential propagation iterative methods of runge kutta type epirk is extended to construct split epirk sepirk integrators for semilinear systems of odes the structure of the sepirk methods possesses the flexibility and generality that allows construction of very efficient schemes we demonstrate how bicolored trees based b series can be used to derive the order conditions for the new integrators an algorithm is developed to solve the order conditions up to order three and several new schemes with desirable properties are proposed the numerical results illustrate the advantages offered by the new class of integrators the experiments also address the comparative performance of split vs non split epirk methods and the question of improving efficiency by optimizing coefficients of the sepirk schemes it is shown that specific schemes can be custom built to improve computational efficiency for a particular problem

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

semiparametric curve alignment and shift density estimation for biological data we observe a large number of signals all of them with identical although unknown shape but with a different random shift the objective is to estimate the individual time shifts and their distribution such an objective appears in several biological applications like neuroscience or ecg signal processing in which the estimation of the distribution of the elapsed time between repetitive pulses with a possibly low signal noise ratio and without a knowledge of the pulse shape is of interest we suggest an m estimator leading to a three stage algorithm we first split our data set in blocks then the shift estimation in each block is done by minimizing a cost function based on the periodogram the estimated shifts are eventually plugged into a standard density estimator we show that under mild regularity assumptions the density estimate converges weakly to the true shift distribution the theory is applied both to simulations and to alignment of real ecg signals the proposed approach outperforms the standard methods for curve alignment and shift density estimation even in the case of low signal to noise ratio and is robust to numerous perturbations common in ecg signals

asymptotically optimal difference based estimation of variance in nonparametric regression summary we define and compute asymptotically optimal difference sequences for estimating error variance in homoscedastic nonparametric regression our optimal difference sequences do not depend on unknowns such as the mean function and provide substantial improvements over the suboptimal sequences commonly used in practice for example in the case of normal data the usual variance estimator based on symmetric second order differences is only 64 efficient relative to the estimator based on optimal second order differences the efficiency of an optimal mth order difference estimator relative to the error sample variance is 2m 2m 1 again this is for normal data and increases as the tails of the error distribution become heavier

on the lanczos method for solving symmetric linear systems with several right hand sides this paper analyzes a few methods based on the lanczos algorithm for solving large sparse symmetric linear systems with several right hand sides the methods examined are suitable for the situation when the right sides are not too different from one another as is often the case in time dependent or parameter dependent problems we propose a theoretical error bound for the approximation obtained from a projection process onto a krylov subspace generated from processing a previous right hand side

smoothing iterative block methods for linear systems with multiple right hand sides in the present paper we present smoothing procedures for iterative block methods for solving nonsymmetric linear systems of equations with multiple right hand sides these procedures generalize those known when solving one right hand linear systems we give some properties of these new methods and then using these procedures we show connections between some known iterative block methods finally we give some numerical examples

integral shape averaging and structural average estimation a comparative study classical signal averaging is an important operation in signal processing applications but is meaningless if shape or time variability is present among the signals being averaged structural average estimation sae and integral shape averaging isa are recent methods that deal with these types of variability by providing a structural average for sae and a mean shape signal for isa that can act as a complement to the classical average in signal analysis in this paper these two techniques are regarded from the perspective of the time warping problem we approach isa using a new formalism that emphasizes the theoretical connections between the two techniques a simulation study is then carried out to compare the two methods in three kinds of time fluctuation two sae algorithms are employed namely dynamic time warping dtw and self modeling registration smr the discussion of the results obtained in this comparison offers specific guidelines for the application dependent use of each approach

projection techniques for iterative solution of ax b with successive right hand sides we present two projection techniques for computing approximate solutions to linear systems of the form ax n b n for a sequence n 1 2 e g such as arises from time discretization of a partial differential equation the inexpensive approximate solutions can be used as initial guesses for iterative solution of the system resulting in significantly reduced computational expense examples of two and three dimensional incompressible navier stokes calculations are presented in which x represents the pressure and a is a discrete poisson operator in flows containing significant dynamic activity these projection techniques lead to as much as a two fold reduction in solution time

choice of bandwidth for kernel regression when residuals are correlated summary standard techniques for selecting the bandwidth of a kernel estimator from the data in a nonparametric regression model perform badly when the errors are correlated in this paper we propose a modified version of an existing plug in bandwidth selector the method is generalized to stationary error variables by estimating a functional of the residual covariance function the proposed bandwidth selector shows good properties in asymptotic theory and in simulations without assuming a parametric model for the error process

the block least squares method for solving nonsymmetric linear systems with multiple right hand sides abstract in this paper we present the block least squares method for solving nonsymmetric linear systems with multiple right hand sides this method is based on the block bidiagonalization we first derive two algorithms by using two different convergence criteria the first one is based on independently minimizing the 2 norm of each column of the residual matrix and the second approach is based on minimizing the frobenius norm of residual matrix we then give some properties of these new algorithms finally some numerical experiments on test matrices from harwell boeing collection are presented to show the efficiency of the new method

exponential rosenbrock methods of order five construction analysis and numerical comparisons the aim of this paper is to construct high order exponential rosenbrock methods and to analyze their convergence properties for the time discretization of large scale systems of stiff differential equations we present a new and simple approach for deriving the stiff order conditions these conditions allow us to construct new pairs of embedded methods of high order as an example we present a fifth order method with five stages for particular problems the order conditions can be simplified it is then even possible to construct a method of order 5 with three stages only the error analysis is performed in an abstract framework of strongly continuous semigroups that allows us to treat semilinear evolution equations in banach spaces convergence results are proved for variable step size implementations to demonstrate the efficiency of the new integrators we give some numerical experiments in matlab in particular numerical comparisons for semilinear parabolic pdes in one and two space dimensions are presented

on the finite difference approximation to the convection diffusion equation abstract in this paper the system of ordinary differential equations arisen from discretizing the convection diffusion equation with respect to the space variable to compute its approximate solution along a time level is considered this system involves in computing e k a y for some vector y where k is the time step size and a is a large tridiagonal toeplitz matrix the common ways to compute an approximate solution of the convection diffusion equation are based on replacing e k a y by an its approximation we give an explicit expression for the exact value of e k a y and then the numerical results of our method with that of some well known methods are compared

clustering multivariate functional data with phase variation when functional data come as multiple curves per subject characterizing the source of variations is not a trivial problem the complexity of the problem goes deeper when there is phase variation in addition to amplitude variation we consider clustering problem with multivariate functional data that have phase variations among the functional variables we propose a conditional subject specific warping framework in order to extract relevant features for clustering using multivariate growth curves of various parts of the body as a motivating example we demonstrate the effectiveness of the proposed approach the found clusters have individuals who show different relative growth patterns among different parts of the body

analysis of projection methods for rational function approximation to the matrix exponential krylov subspace methods for approximating the action of the matrix exponential exp a on a vector v are analyzed with a hermitian and negative semidefinite our approach is based on approximating the exponential with the commonly employed diagonal pade and chebyshev rational functions which yield a system of equations with a polynomial coefficient matrix we derive optimality properties and error bounds for the convergence of a galerkin type approximation and of a computationally feasible and extensively used alternative as complementary results we theoretically justify the use of a popular a posteriori error estimate and we provide upper bounds for the components of the solution vector our theoretical and numerical results show that this methodology may provide an appropriate framework to devise new strategies such as more powerful acceleration schemes

global least squares method gl lsqr for solving general linear systems with several right hand sides abstract in this paper we propose a new method for solving general linear systems with several right hand sides this method is based on global least squares method and reduces the original matrix to the lower bidiagonal form we derive a simple recurrence formula for generating the sequence of approximate solutions x k some theoretical properties of the new method are discussed and we also show that how this method can be implemented for the sylvester equation finally some numerical experiments on test matrices are presented to show the efficiency of the new method

clustering objects on subsets of attributes with discussion read before the royal statistical society at a meeting organized by the research section on wednesday may 5th 2004 professor j t kent in the chair summary a new procedure is proposed for clustering attribute value data when used in conjunction with conventional distance based clustering algorithms this procedure encourages those algorithms to detect automatically subgroups of objects that preferentially cluster on subsets of the attribute variables rather than on all of them simultaneously the relevant attribute subsets for each individual cluster can be different and partially or completely overlap with those of other clusters enhancements for increasing sensitivity for detecting especially low cardinality groups clustering on a small subset of variables are discussed applications in different domains including gene expression arrays are presented