efficient bounds for the monte carlo neumann solution of stochastic systems the numerical solution of uncertainty propagation problems in mechanics can be computationally demanding in this article a well known property of the neumann series is explored in order to derive lower and upper bounds for expected value and autocorrelation of stochastic system responses uncertainties in system parameters are represented as parameterized stochastic processes monte carlo simulation is employed to obtain samples of system response from which lower and upper bounds of expected value and autocorrelation are computed the proposed methodology is applied to two example problems involving beam bending and axial thermo elasticity it is shown that accurate and efficient bounds can be obtained for a proper choice of operator norm with as few as one or two terms in the neumann expansion the monte carlo neumann bounding scheme proposed herein is shown to be an efficient alternative for the solution of uncertainty propagation problems in mechanics

solving elliptic boundary value problems with uncertain coefficients by the finite element method the stochastic formulation this work studies a linear elliptic problem with uncertainty the introduction gives a survey of different formulations of the uncertainty and resulting numerical approximations the major emphasis

high energy limits of laplace type and dirac type eigenfunctions and frame flows we relate high energy limits of laplace type and dirac type operators to frame flows on the corresponding manifolds and show that the ergodicity of frame flows implies quantum ergodicity in an appropriate sense for those operators observables for the corresponding quantum systems are matrix valued pseudodifferential operators and therefore the system remains non commutative in the high energy limit we discuss to what extent the space of stationary high energy states behaves classically

a statistical view of some chemometrics regression tools chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis in addition to borrowing many techniques from the statistics and engineering literatures chemometrics itself has given rise to several new data analytical methods this article examines two methods commonly used in chemometrics for predictive modeling partial least squares and principal components regression from a statistical perspective the goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations these methods include ordinary least squares variable subset selection and ridge regression

sparse partial least squares regression for simultaneous dimension reduction and variable selection partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s it has recently gained much attention in the analysis of high dimensional genomic data we show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm we derive a similar result for a multivariate response regression with partial least squares we then propose a sparse partial least squares formulation which aims simultaneously to achieve good predictive performance and variable selection by producing sparse linear combinations of the original predictors we provide an efficient implementation of sparse partial least squares regression and compare it with well known variable selection and dimension reduction approaches via simulation experiments we illustrate the practical utility of sparse partial least squares regression in a joint analysis of gene expression and genomewide binding data

iterative partial least squares with right censored data analysis a comparison to other dimension reduction techniques summary in the linear model with right censored responses and many potential explanatory variables regression parameter estimates may be unstable or when the covariates outnumber the uncensored observations not estimable we propose an iterative algorithm for partial least squares based on the buckley james estimating equation to estimate the covariate effect and predict the response for a future subject with a given set of covariates we use a leave two out cross validation method for empirically selecting the number of components in the partial least squares fit that approximately minimizes the error in estimating the covariate effect of a future observation simulation studies compare the methods discussed here with other dimension reduction techniques data from the aids clinical trials group protocol 333 are used to motivate the methodology

partial least squares algorithm yields shrinkage estimators we give a geometric proof that the estimates of a regression model derived by using partial least squares shrink the ordinary least squares estimates the proof is based on a sequential construction algorithm of partial least squares a discussion of the nature of shrinkage is included

semiclassical limit for multistate klein gordon systems almost invariant subspaces and scattering theory by using the method of helffer and sjostrand to construct moyal projections we extend the almost invariant subspace theory to the semiclassical context applications to the semiclassical limit for two component klein gordon hamiltonian are given more precisely under the conditions that the potential is analytic and its eigenvalues never cross we prove that the scattering matrix is block diagonal up to exponentially small errors also we show how the existence of almost invariant subspaces leads to the existence of quasimodes with exponentially long lifetimes

quantum normal forms moyal star product and bohr sommerfeld approximation a normal form transformation is carried out on one dimensional quantum hamiltonians that transforms them into functions of the quantum harmonic oscillator the method works with the weyl transform or symbol of the hamiltonian the moyal star product is used to carry out the normal form transformation at the level of symbols diagrammatic techniques are developed for handling the expressions that result from higher order terms in the moyal series once the normal form is achieved the bohr sommerfeld formula for the eigenvalues including higher order corrections follows easily

characterization of estimators uniformly shrinking on subspaces abstract shrinkage factors play an important role in the behaviour of biased estimators in this paper we first show that the only way to have bounded shrinkage factors on a subspace is to shrink uniformly on this subspace then we characterize regressions on components that shrink uniformly on the subspaces spanned by their associated weight vectors we show that this problem is equivalent to solving a set of linear equations involving two different projectors we define a class of matrices whose eigen decompositions give the solution

an efficient 3d stochastic finite element method real life structural systems are characterized by their inherent or externally induced uncertainties in the design parameters this study proposes a stochastic finite element tool efficient to take account of these uncertainties here uncertain structural parameter is modeled as homogeneous gaussian stochastic field and commonly used two dimensional 2d local averaging technique is extended and generalized for 3d random field this is followed by cholesky decomposition of respective covariance matrix for digital simulation by expanding uncertain stiffness matrix about its reference value the neumann expansion method is introduced blended with direct monte carlo simulation this approach involves decomposition of stiffness matrix only once for the entire simulated structure thus substantial saving of cpu time and also the scope of tackling several stochastic fields simultaneously are the basic advantages of the proposed algorithm accuracy and efficiency of this method with reference to example problem is also studied here and numerical results validate its superiority over direct simulation method or first order perturbation approach

geometry of the transport equation in multicomponent wkb approximations although the wkb approximation for multicomponent systems has been intensively studied in the literature its geometric and global aspects are much less well understood than in the scalar case in this paper we give a completely geometric derivation of the transport equation without using local sections and without assuming complete diagonalizability of the matrix valued principal symbol or triviality of its eigenbundles the term unnamed in the previous literature appearing in the transport equation in addition to the covariant derivative with respect to a natural projected connection is a tensor independent of the choice of any sections we give a goemetric interpretation of this tensor involving the contraction of the curvature of the eigenbundle and an analog of the second fundamental form with the poisson tensor in phase space in the non degenerate case this term may be rewritten in an even simpler geometric form finally we discuss obstructions to the existence of wkb states and give a geometric description of the quantization condition for wkb states for a non degenerate eigenvalue function

multicomponent wentzel kramers brillouin approximation on arbitrary symplectic manifolds a star product approach it is known that in the wentzel kramers brillouin approximation of multicomponent systems like the dirac equation or born oppenheimer approximation an additional phase appears apart from the berry phase so far this phase was only examined in special cases or under certain restrictive assumptions namely that the eigenspaces of the matrix or endomorphism valued symbol of the hamiltonian form trivial bundles we give a completely global derivation of this phase which does not depend on any choice of local trivializing sections this is achieved using a star product approach to quantization furthermore we give a systematic and global approach to a reduction of the problem to a problem defined completely on the different polarizations finally we discuss to what extent it is actually possible to reduce the problem to a really scalar one and make some comments on obstructions to the existence of global quasiclassical states

the peculiar shrinkage properties of partial least squares regression partial least squares regression has been widely adopted within some areas as a useful alternative to ordinary least squares regression in the manner of other shrinkage methods such as principal components regression and ridge regression in this paper we examine the nature of this shrinkage and demonstrate that partial least squares regression exhibits some undesirable properties

quantal phase factors accompanying adiabatic changes a quantal system in an eigenstate slowly transported round a circuit c by varying parameters r in its hamiltonian r will acquire a geometrical phase factor exp i c in addition to the familiar dynamical phase factor an explicit general formula for c is derived in terms of the spectrum and eigenstates of r over a surface spanning c if c lies near a degeneracy of c takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy as an illustration c is calculated for spinning particles in slowly changing magnetic fields although the sign reversal of spinors on rotation is a special case the effect is predicted to occur for bosons as well as fermions and a method for observing it is proposed it is shown that the aharonov bohm effect can be interpreted as a geometrical phase factor

a semiclassical egorov theorem and quantum ergodicity for matrix valued operators we study the semiclassical time evolution of observables given by matrix valued pseudodifferential operators and construct a decomposition of the hilbert space l2 open image in new windowd open image in new windown into a finite number of almost invariant subspaces for a certain class of observables that is preserved by the time evolution we prove an egorov theorem we then associate with each almost invariant subspace of l2 open image in new windowd open image in new windown a classical system on a product phase space t open image in new windowd open image in new window where open image in new window is a compact symplectic manifold on which the classical counterpart of the matrix degrees of freedom is represented for the projections of eigenvectors of the quantum hamiltonian to the almost invariant subspaces we finally prove quantum ergodicity to hold if the associated classical systems are ergodic

continuum regression cross validated sequentially constructed prediction embracing ordinary least squares partial least squares and principal components regression read before the royal statistical society at a meeting organized by the research section on wednesday october 25th 1989 professor d v hinkley in the chair summary the paper addresses the evergreen problem of construction of regressors for use in least squares multiple regression in the context of a general sequential procedure for doing this it is shown that with a particular objective criterion for the construction the procedures of ordinary least squares and principal components regression occupy the opposite ends of a continuous spectrum with partial least squares lying in between there are two adjustable parameters controlling the procedure alpha in the continuum 0 11 and omega the number of regressors finally accepted these control parameters are chosen by crossvalidation the method is illustrated by a range of examples of its application

on the propagation of polarization sets for systems of real principal type we define and study the polarization sets for vector valued distributions systems of real principal type are defined and we prove that for such systems of pseudodifferential operators we have a unique propagation of the polarization sets for the solutions

explicit solution to the stochastic system of linear algebraic equations α1a1 α2a2 αmam x b abstract this paper presents a novel solution strategy to the stochastic system of linear algebraic equations 1 a 1 2 a 2 m a m x b arising from stochastic finite element modelling in computational mechanics in which i i 1 m denote random variables a i i 1 m real symmetric deterministic matrices b a deterministic random vector and x the unknown random vector to be solved the system is first decoupled by simultaneously diagonalizing all the matrices a i via a similarity transformation and then it is trivial to invert the sum of the diagonalized stochastic matrices to obtain the explicit solution of the stochastic equation system unless all the matrices a i share exactly the same eigen structure the joint diagonalization can only be approximately achieved hence the solution is approximate and corresponds to a particular average eigen structure of the matrix family specifically the classical jacobi algorithm for the computation of eigenvalues of a single matrix is modified to accommodate multiple matrices and the resulting jacobi like joint diagonalization algorithm preserves the fundamental properties of the original version including its convergence and an explicit solution for the optimal givens rotation angle three numerical examples are provided to illustrate the performance of the method