global format for energy momentum based time integration in nonlinear dynamics summary a global format is developed for momentum and energy consistent time integration of second order dynamic systems with general nonlinear stiffness the algorithm is formulated by integrating the state space equations of motion over the time increment the internal force is first represented in fourth order form consisting of the end point mean value plus a term containing the stiffness matrix increment this form gives energy conservation for systems with internal energy as a quartic function of the displacement components this representation is then extended to general energy conservation via a discrete gradient representation the present procedure works directly with the internal force and the stiffness matrix at the time integration interval end points and in contrast to previous energy conserving algorithms it does not require any special form of the energy function nor use of mean value products at the element level or explicit use of a geometric stiffness matrix an optional monotonic algorithmic damping increasing with response frequency is developed in terms of a single damping parameter in the solution procedure the velocity is eliminated and the nonlinear iterations are based on the displacement components alone the procedure represents an energy consistent alternative to available collocation methods with an equally simple implementation copyright 2014 john wiley sons ltd

posterior distribution of hierarchical models using car 1 distributions summary we examine properties of the conditional autoregressive model or car 1 model which is commonly used to represent regional effects in bayesian analyses of mortality rates we consider a bayesian hierarchical linear mixed model where the fixed effects have a vague prior such as a constant prior and the random effect follows a class of car 1 models including those whose joint prior distribution of the regional effects is improper we give sufficient conditions for the existence of the posterior distribution of the fixed and random effects and variance components we then prove the necessity of the conditions and give a one way analysis of variance example where the posterior may or may not exist finally we extend the result to the generalised linear mixed model which includes as a special case the poisson log linear model commonly used in disease mapping

a lie algebraic approach to numerical integration of stochastic differential equations in this article composition methods or operator splitting methods for autonomous stochastic differential equations sdes are formulated to produce numerical approximation schemes for the equations in the proposed methods the exponential map which is given by the solution of an sde is approximated by composition of the stochastic flows derived from simpler and exactly integrable vector field operators having stochastic coefficients the local and global errors of the numerical schemes derived from the stochastic composition methods are investigated the new schemes are advantageous to preserve the special character of sdes numerically and are useful for approximations of the solutions to stochastic nonlinear equations to examine their superiority several numerical simulations on the basis of the proposed schemes are carried out for sdes which arise in mathematical finance and stochastic hamiltonian dynamical systems

generalized linear latent variable models for repeated measures of spatially correlated multivariate data summary observations of multiple response variables across space and over time occur often in environmental and ecological studies compared to purely spatial models for a single response variable in the exponential family of distributions fewer statistical tools are available for multiple response variables that are not necessarily gaussian an exception is a common factor model developed for multivariate spatial data by wang and wall 2003 biostatistics 4 569 582 the purpose of this article is to extend this multivariate space only model and develop a flexible class of generalized linear latent variable models for multivariate spatial temporal data for statistical inference maximum likelihood estimates and their standard deviations are obtained using a monte carlo em algorithm we also use a novel way to automatically adjust the monte carlo sample size which facilitates the convergence of the monte carlo em algorithm the methodology is illustrated by an ecological study of red pine trees in response to bark beetle challenges in a forest stand of wisconsin

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

arbitrary order numerical methods conserving integrals for solving dynamic equations abstract a number of problems in celestial mechanics some hamiltonian systems and non hamiltonian ones may be solved numerically by a modification of polynomial extrapolation which conserves integrals it means that it is possible to get numerical solutions of dynamic equations which possess the same properties that follow from the theoretical study this paper is a survey of problems for which this modification may be applied

conservative numerical methods for x f x abstract two distinctly different numerical methods are developed for solving the conservative initial value problem x f x x o dot x o both methods conserve exactly the same total energy as does the given differential equation computer examples are described and

energy preserving schemes for nonlinear hamiltonian systems of wave equations application to the vibrating piano string the problem of the vibration of a string is well known in its linear form describing the transversal motion of a string nevertheless this description does not explain all the observations well enough nonlinear coupling between longitudinal and transversal modes seams to better model the piano string as does for instance the geometrically exact model gem this report introduces a general class of nonlinear systems nonlinear hamiltonian systems of wave equations in which fits the gem mathematical study of these systems is lead in a first part showing central properties energy preservation existence and unicity of a global smooth solution finite propagation velocity ldots space discretization is made in a classical way variational formulation and time discretization aims at numerical stability using an energy technique a definition of preserving schemes is introduced and we show that explicit schemes or partially implicit schemes which are preserving according to this definition cannot be built unless the model is linear a general energy preserving second order accurate fully implicit scheme is built for any continuous system that fits the nonlinear hamiltonian systems of wave equations class

spatial modeling of regional variables abstract in this article accumulated sudden infant death syndrome sids data from 1974 1978 and 1979 1984 for the counties of north carolina are analyzed after a spatial exploratory data analysis markov random field models are fit to the data the spatial trend is meant to capture the large scale variation in the data and the variance and spatial dependence are meant to capture the small scale variation the trend could be a function of other explanatory variables or could simply be modeled as a function of spatial location both models are fit and compared the results give an excellent illustration of a phenomenon already well known in time series that autocorrelation in data can be due to an undiscovered explanatory variable indeed for 1974 1978 we confirm a dependence of sids rate on proportion of nonwhite babies born along with insignificant spatial correlation without this regressor variable however the spatial correlation is significant in 1979 1984 perhaps due to reporting bias o

compensatability and optimal compensation of systems with white parameters the optimal compensation problem is considered in the case of linear discrete time systems with stationary white parameters and quadratic criteria a generalization of the notion of mean square stabilizability namely mean square compensatability is introduced it is shown that suitable mean square compensatability and detectability conditions are sufficient and necessary in general for the existence of a unique optimal mean square stabilizing compensator tests are given to determine whether or not a system is mean square compensatable it is indicated how to calculate numerically the tests and the optimal mean square stabilizing compensator the results are illustrated with examples

conservative numerical methods for nonlinear strings in this article a class of numerical schemes for the simulation of nonlinear coupled longitudinal transverse string vibration is presented though there are various ways of arriving at such schemes special attention is paid here to energy conservation in nonlinear model systems and its transfer to an analogous discrete quantity in a difference scheme such exact numerical energy conservation can lead to simple global stability conditions which can be otherwise difficult to ascertain for nonlinear difference schemes in particular such conditions may be arrived at without any reliance on frequency domain concepts i e fourier or laplace transforms which are of only moderate utility in the analysis of nonlinear systems implementation details are discussed and numerical results are presented

latent variable analysis of multivariate spatial data multivariate spatial or geo referenced data arise naturally in such disciplines as ecology agriculture geology and atmospheric sciences in practice interest often lies in modeling underlying structure and representing interrelationships in terms of a smaller number of variables for such situations statistical analysis using a latent variable model is proposed we present a general model that incorporates spatial correlation and potential lagged or shifted dependencies and that can represent subject matter theory or serve as a practical exploratory model procedures for model fitting parameter estimation inferences and latent variable prediction are developed without restrictive assumptions on distribution and covariance function forms the properties and usefulness of the proposed approaches are assessed by asymptotic theory and an extensive simulation study an example from precision agriculture is also presented

inherently energy conserving time finite elements for classical mechanics in this paper we develop a finite element method for the temporal discretization of the equations of motion the continuous galerkin method is based upon a weighted residual statement of hamilton s canonical equations we show that the proposed finite element formulation is energy conserving in a natural sense a family of implicit one step algorithms is generated by specifying the polynomial approximation in conjunction with the quadrature formula used for the evaluation of time integrals the numerical implementation of linear quadratic and cubic time finite elements is treated in detail for the model problem of a circular pendulum in addition to that concerning dynamical systems with several degrees of freedom we address the design of nonstandard quadrature rules which retain the energy conservation property our numerical investigations assess the effect of numerical quadrature in time on the accuracy and energy conservation property of the time stepping schemes

minimal representation of matrix valued white stochastic processes and u d factorisation of algorithms for optimal control two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria called the optimal compensation problem one describes the matrix valued white stochastic processes involved using a sum of deterministic matrices each one multiplied by a scalar stochastic process that is independent of the others another that is more general and concise uses kronecker products instead this article relates the statistics of both descriptions and shows their advantages and disadvantages as to the first description an important result that comes out is the minimum number of matrices multiplied by scalar independent stochastic processes needed to represent a certain matrix valued white stochastic process together with an associated minimal representation as to the second description an important result concerns the generation of all kronecker products that represent relevant st

the influence of uncertainty on stability and compensatability in this paper the influence of uncertainty of linear discrete time systems modelled with white parameters on the properties of mean square stability and compensatability is considered a measure for the uncertainty in the system matrices is introduced this measure is also a measure for the uncertainty in the system in the sense that stability and compensatability decreases if this system uncertainty increases it is indicated how to calculate numerically the mean square stability and compensatability the results are illustrated with examples

domain level covariance analysis for multilevel survey data with structured nonresponse health care quality surveys in the united states are administered to individual respondents i e hospital patients health plan members to evaluate the performance of health care organizations i e hospitals health plans which thus constitute estimation domains for better understanding and more parsimonious reporting of dimensions of quality we analyze relationships among quality measures at the domain level rather than specifying a full parametric model for the observed responses and the nonresponse patterns at the lower patient level we first fit generalized variance covariance functions that take into account nonresponse patterns in the survey responses then specify a likelihood function for the domain mean responses using these generalized variance covariance functions this allows us to model directly the relationships among domain means for different items because the response scales are bounded we assume that these means follow a truncated multivariate normal distribution we calcu

non linear dynamics of three dimensional rods exact energy and momentum conserving algorithms the long term dynamic response of non linear geometrically exact rods under going finite extension shear and bending accompanied by large overall motions is addressed in detail the central objective is the design of unconditionally stable time stepping algorithms which exactly preserve fundamental constants of the motion such as the total linear momentum the total angular momentum and for the hamiltonian case the total energy this objective is accomplished in two steps first a class of algorithms is introduced which conserves linear and angular momentum this result holds independently of the definition of the algorithmic stress resultants second an algorithmic counterpart of the elastic constitutive equations is developed such that the law of conservation of total energy is exactly preserved conventional schemes exhibiting no numerical dissipation symplectic algorithms in particular are shown to lead to unstable solutions when the high frequencies are not resolved compared to conventional schemes there is little if any additional computational cost involved in the proposed class of energy momentum methods the excellent performance of the new algorithm in comparison to other standard schemes is demonstrated in several numerical simulations

infinite horizon optimal control of linear discrete time systems with stochastic parameters the infinite horizon optimal control problem is considered in the general case of linear discrete time systems and quadratic criteria both with stochastic parameters which are independent with respect to time a stronger stabilizability property and a weaker observability property than usual for deterministic systems are introduced it is shown that the infinite horizon problem has a solution if the system has the first property if in addition the problem has the second property the solution is unique and the control system is stable in the mean square sense a simple necessary and sufficient condition explicit in the system matrices is given for the system to have the stronger stabilizability property this condition also holds for deterministic systems to be stabilizable in the usual sense the stronger stabilizability and weaker observability properties coincide with the usual ones if the parameters are deterministic

dynamical difference equations abstract dynamical difference equations are motivated and developed conservation and covariance laws are proved illustrative examples are described and discussed newtonian equations are stressed but extensions to relativity and quantum mechanics are indicated the physical problem of convergence to the limit as the time step goes to zero is shown to reveal an area in which quantum mechanics and relativity are in disagreement

conservative spline methods for second order ivps of odes abstract one of the most fundamental characteristics in physics are the conservation laws 1 therefore the numerical methods in computational physics should be conservative unfortunately the most popular numerical methods like runge kutta multistep and taylor expansion methods when they are applied to the second order nonlinear newtonian initial value problems do not preserve fundamental physical invariants like energy and momentum when these are present in 2 4 a family of spline methods proposed for the initial value problems of order n a variant of these methods are energy conserving approximations of order three four and five for the second order newtonian initial value problems furthermore it seems to be easy to extend for equations containing the first derivative of the unknown function even for coupled equations some applications and numerical results are presented 1999 elsevier science ltd all rights reserved

conservation properties of a time fe method part i time stepping schemes forn body problems in the present paper one step implicit integration algorithms for the n body problem are developed the time stepping schemes are based on a petrov galerkin finite element method applied to the hamiltonian formulation of the n body problem the approach furnishes algorithmic energy conservation in a natural way the proposed time finite element method facilitates a systematic implementation of a family of time stepping schemes a particular algorithm is specified by the associated quadrature rule employed for the evaluation of time integrals the influence of various standard as well as non standard quadrature formulas on algorithmic energy conservation and conservation of angular momentum is examined in detail for linear and quadratic time elements copyright 2000 john wiley sons ltd

conservation properties of a time fe method part iii mechanical systems with holonomic constraints a galerkin based discretization method for index 3 differential algebraic equations pertaining to finite dimensional mechanical systems with holonomic constraints is proposed in particular the mixed galerkin mg methodis introduced which leads in a natural way to time stepping schemes that inherit major conservation properties of the underlying constrained hamiltonian system namely total energy and angular momentum in addition to that the constraints on the configuration level and on the velocity momentum level are fulfilled exactly the application of the mg method to specific mechanical systems such as the pendulum rigid body dynamics and the coupled motion of rigid and flexible bodies is presented related numerical examples are investigated to evaluate the numerical performance of the mg 1 and mg 2 method

conservation properties of a time fe method part iv higher order energy and momentum conserving schemes in the present paper a systematic development of higher order accurate time stepping schemes which exactly conserve total energy as well as momentum maps of underlying finite dimensional hamiltonian systems with symmetry is shown the result of this development is the enhanced galerkin eg finite element method in time the conservation of the eg method is generally related to its collocation property total energy conservation in particular is obtained by a new projection technique the eg method is moreover based on objective time discretization of the used strain measure this paper is concerned with particle dynamics and semi discrete non linear elastodynamics the related numerical examples show good performance in presence of stiffness as well as for calculating large strain motions copyright 2005 john wiley sons ltd

bayesian hierarchical multivariate formulation with factor analysis for nested ordinal data this article devises a bayesian multivariate formulation for analysis of ordinal data that records teacher classroom performance along multiple dimensions to assess aspects characterizing good instruction study designs for scoring teachers seek to measure instructional performance over multiple classroom measurement event sessions at varied occasions using disjoint intervals within each session and employment of multiple ratings on intervals scored by different raters a design which instantiates a nesting structure with each level contributing a source of variation in recorded scores we generally possess little a priori knowledge of the existence or form of a sparse generating structure for the multivariate dimensions at any level in the nesting that would permit collapsing over dimensions as is done under univariate modeling our approach composes a bayesian data augmentation scheme that introduces a latent continuous multivariate response linked to the observed ordinal scores with the latent response mean constructed as an additive multivariate decomposition of nested level means that permits the extraction of de noised continuous teacher level scores and the associated correlation matrix a semi parametric extension facilitates inference for teacher level dependence among the dimensions of classroom performance under multi modality induced by sub groupings of rater perspectives we next replace an inverse wishart prior specified for the teacher covariance matrix over dimensions of instruction with a factor analytic structure to allow the simultaneous assessment of an underlying sparse generating structure our formulation for bayesian factor analysis employs parameter expansion with an accompanying post processing sign re labeling step of factor loadings that together reduce posterior correlations among sampled parameters to improve parameter mixing in our markov chain monte carlo mcmc scheme we evaluate the performance of our formulation on simulated data and make an application for the assessment of the teacher covariance structure with a dataset derived from a study of middle and high school algebra teachers

invariant conserving finite difference algorithms for the nonlinear klein gordon equation a formalism for systematicaiiy deriving second order accurate finite difference algorithms which conserve certain invariant quantities in the original nonlinear pdes is presented three algorithms are derived for the nonlinear klein gordon equation nlkge based on the proposed formalism the local conservation laws of the nlkge form the basic starting point in our derivation which hinges essentially on the commutativity of certain finite difference operators such commutativity in the discrete approximations allows a preservation of the derivation properties of the continuous counterparts at the pde level with appropriate boundary conditions the proposed algorithms preserve in the discrete sense either the total system energy or the system s linear momentum several variants of the present algorithms and their relation to previously proposed algorithms are discussed an analysis of the accuracy and stability is conducted to compare the different variants of the proposed algorithms the preservation of energy of the present algorithms for the nlkge can also be viewed as providing a method of stabilization for conditionally stable algo thms for the linear wave equation the computer impiementation of the proposed algorithms with the treatment of the boundary conditions is presented in detail numerical examples are given concerning soliton collisions in the sine gordon equation the double sine gordon equation and the cb phi four equation the numerical results demonstrate that the present algorithms can preserve accurately up to 10 decimal digits the total system energy for a very coarse grid reliable algorithms for josephson junction models which contain dissipation damping mechanisms and driving bias current are obtained as direct by products of the proposed invariant conserving algorithms for the nlkge even though presented mainly for the 1 d case the proposed algorithms are generalizable to the 2 d and 3 d cases and to the case of complex valued nlkge

some energy preserving finite element schemes based on the discrete variational derivative method abstract in this paper we discuss energy preserving finite element scheme for partial differential equations we firstly consider linear heat equation and linear wave equation as the typical example to derive energy preserving finite element scheme we employ the discrete variational method as the application of nonlinear partial differential equations we consider allen cahn equation and fujita problem

a mixed variational framework for the design of energy momentum schemes inspired by the structure of polyconvex stored energy functions abstract a new approach to the design of energy momentum em consistent algorithms for nonlinear elastodynamics is proposed the underlying mixed variational formulation is motivated by the structure of polyconvex stored energy functions and benefits from the notion of a tensor cross product for second order tensors the structure preserving discretization in time of the mixed variational formulation yields an em consistent semi discrete formulation the semi discrete formulation offers several options for the discretization in space in the special case of a purely displacement based method a new form of the algorithmic stress formula is obtained several numerical examples are presented to evaluate the performance of the newly developed schemes

energy conserving schemes for the simulation of musical instrument contact dynamics abstract collisions are an innate part of the function of many musical instruments due to the nonlinear nature of contact forces special care has to be taken in the construction of numerical schemes for simulation and sound synthesis finite difference schemes and other time stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a newtonian description of the system however because impact forces are non analytic functions of the phase space variables algorithm stability can rarely be established this way this paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling the proposed numerical formulations follow from discretising hamilton s equations of motion generally leading to an implicit system of nonlinear equations that can be solved with newton s method the approach is first outlined for point mass collisions and then extended to distributed settings such as vibrating strings and beams colliding with rigid obstacles stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples the methodology is exemplified through a case study on tanpura string vibration with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument

continuous finite element methods which preserve energy properties for nonlinear problems abstract continuous finite elements are used to develop numerical methods which preserve energy properties for nonlinear ordinary and partial differential equations schemes are constructed that give high orders of accuracy time discretization algorithms for the cahn hilliard klein gordon korteweg de vries and schrodinger equations are presented comparisons are made with existing schemes

model choice a minimum posterior predictive loss approach summary model choice is a fundamental and much discussed activity in the analysis of datasets nonnested hierarchical models introducing random effects may not be handled by classical methods bayesian approaches using predictive distributions can be used though the formal solution which includes bayes factors as a special case can be criticised we propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values we obtain this criterion by minimising posterior loss for a given model and then for models under consideration selecting the one which minimises this criterion for a broad range of losses the criterion emerges as a form partitioned into a goodness of fit term and a penalty term we illustrate its performance with an application to a large dataset involving residential property transactions

detectability observability and lyapunov type theorems of linear discrete time varying stochastic systems with multiplicative noise abstractthe objective of this paper is to study detectability observability and related lyapunov type theorems of linear discrete time time varying stochastic systems with multiplicative noise some new concepts such as uniform detectability k exact detectability resp kwft exact detectability kft exact detectability kn exact detectability and k exact observability resp kwft exact detectability kft exact detectability kn exact detectability are introduced respectively and nice properties associated with uniform detectability exact detectability and exact observability are also obtained moreover some lyapunov type theorems associated with generalised lyapunov equations and exponential stability in mean square sense are presented under uniform detectability kn exact observability and kn exact detectability respectively

modified newmark family for non linear dynamic analysis a simple modification of the newmark scheme is suggested which keeps the total energy of mechanical systems constant and thereby enhances the unconditional stability in non linear dynamic analysis numerical damping which is formulated on an energy basis is also introduced and the dissipative character of the algorithm is guaranteed in the non linear regime representative examples in support of such a modified newmark family are presented copyright 2004 john wiley sons ltd

conservative difference formulations of calogero and toda hamiltonian systems abstract calogero and toda hamiltonian systems are reformulated using only differences the formulations prove to have the same fundamental invariants as the continuous systems and in addition are readily implementable on modern digital computers

regular article finite difference schemes for u t x α δg δu that inherit energy conservation or dissipation property we propose a new procedure for designing by rote finite difference schemes that inherit energy conservation or dissipation property from nonlinear partial differential equations such as the korteweg de vries kdv equation and the cahn hilliard equation the most important feature of our procedure is a rigorous discretization of variational derivatives using summation by parts which implies that the inherited properties are satisfied exactly since the inherited properties are kept even if the time mesh size changes in the time evolution process we can use some appropriate time mesh adaptive methods to obtain numerical solutions through the derived schemes because of these properties the derived schemes are expected to be numerically stable and yield solutions converging to pde solutions and sufficiently flexible to treat the inheritance of the energy conservation and dissipation properties are verified numerically for the kdv equation and the cahn hilliard equation

the time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems hence the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging in this work we show that time finite element methods because of their inherent energy momentum conserving property in the case of linear and nonlinear elastodynamics provide a robust time stepping method for nonlinear dynamic equations including chaotic systems we also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework thus the time finite element provides a unification of time stepping schemes used in diverse disciplines we demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic

latent variable models with fixed effects we discuss latent variable models that allow for fixed effect covariates as well as covariates affecting the latent variable directly restricted maximum likelihood and maximum likelihood are used to estimate model parameters a generalized likelihood ratio test can be used to test significance of the covariates effecting the latent outcomes special cases of the proposed model correspond to factor analysis mixed models random effects models and simultaneous equations the model is applied to birth defects data where continuous data on the size of infants who were exposed to anticonvulsant medications in utero are compared to controls

bayesian factor analysis for spatially correlated data with application to summarizing area level material deprivation from census data this article describes a bayesian hierarchical model for factor analysis of spatially correlated multivariate data the first level specifies for each area on a map the distribution of a vector of manifest variables conditional on an underlying latent factor at the second level the area specific latent factors have a joint distribution that incorporates spatial correlation the framework allows for both marginal and conditional e g conditional autoregressive specifications of spatial correlation the model is used to quantify material deprivation at the census tract level using data from the 1990 u s census in rhode island an existing and widely used measure of material deprivation is the townsend index an unweighted sum of four standardized census variables i e z scores corresponding to area level proportions of unemployment car ownership crowding and home ownership the townsend and many related indices are computed as linear combinations of measured census variables which motivates t

factor copula models for replicated spatial data abstractwe propose a new copula model that can be used with replicated spatial data unlike the multivariate normal copula the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all measurements of the process moreover the proposed copula can model tail dependence and tail asymmetry the model is parameterized in terms of a covariance function that may be chosen from the many models proposed in the literature such as the matern model for some choice of common factors the joint copula density is given in closed form and therefore likelihood estimation is very fast in the general case one dimensional numerical integration is needed to calculate the likelihood but estimation is still reasonably fast even with large datasets we use simulation studies to show the wide range of dependence structures that can be generated by the proposed model with different choices of common factors we apply the proposed model to spatial temperature data and com

discrete time quantum mechanics abstract this paper summarizes a research program that has been underway for a decade the objective is to find a fast and accurate scheme for solving quantum problems which does not involve a monte carlo algorithm we use an alternative strategy based on the method of finite elements we are able to formulate fully consistent quantum mechanical systems directly on a lattice in terms of operator difference equations one advantage of this discretized formulation of quantum mechanics is that the ambiguities associated with operator ordering are eliminated furthermore the scheme provides an easy way in which to obtain the energy levels of the theory numerically a generalized version of this discretization scheme can be applied to quantum field theory problems the difficulties normally associated with fermion doubling are eliminated also one can incorporate local gauge invariance in the finite element formulation results for some field theory models are summarized in particular we review the calculation of the anomaly in two dimensional quantum electrodynamics the schwinger model finally we discuss nonabelian gauge theories

on a stress resultant geometrically exact shell model part vi conserving algorithms for non linear dynamics in parts i to v of the present work the formulation and finite element implementation of a non linear stress resultant shell model are considered in detail this paper is concerned with the extension of these results to incorporate completely general non linear dynamic response of special interest here is the dynamics of very flexible shells undergoing large overall motion which conserves the total linear and angular momentum and for the hamiltonian case the total energy a main goal of this paper is the design of non linear time stepping algorithms and the construction of finite element interpolations which preserve exactly these fundamental constants of motion it is shown that only a very special class of algorithms namely a formulation of the mid point rule in conservation form exactly preserves the total linear and angular momentum for the hamiltonian case a somewhat surprising result is proved regardless of the degree of non linearity in the stored energy function a generalized mid point rule algorithm always exists which exactly conserves energy the conservation properties of a time stepping algorithm need not and in general will not be preserved by the spatial discretization precise conditions which ensure preservation of these conservation properties are derived a number of numerical simulations are presented which illustrate the exact conservation properties of the proposed methodology

optimal projection equations for discrete time fixed order dynamic compensation of linear systems with multiplicative white noise the optimal projection equations for discrete time reduced order dynamic compensation are generalized to include the effects of state control and measurement dependent noise in addition the discrete time static output feedback problem with multiplicative disturbances is considered for both problems the design equations are presented in a concise unified manner to facilitate their accessibility for developing numerical algorithms for practical applications

finite difference calculus invariant structure of a class of algorithms for the nonlinear klein gordon equation in a previous work the authors have presented a formalism for deriving systematically invariant symmetric finite difference algorithms for nonlinear evolution differential equations that admit conserved quantities this formalism is herein cast in the context of exact finite difference calculus the algorithms obtained from the proposed formalism are shown to derive exactly from discrete scalar potential functions using finite difference calculus in the same sense as that of the corresponding differential equation being derivable from its associated energy function a conserved quantity a clear ramification of this result is that the derived algorithms preserve certain discrete invariant quantities which are the consistent counterpart of the invariant quantities in the continuous case results on the nonlinear stability of a class of algorithms that are derived using the proposed formalism and that preserve energy or linear momentum are discussed in the context of finite difference calculus some

unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum we show that for rigid body dynamics the mid point rule formulated in body co ordinates exactly conserves energy and the norm of the angular momentum for incremental force free motions but fails to conserve the direction of the angular momentum vector further we show that the mid point rule formulated in the spatial representation is in general physically and geometrically meaningless an alternative algorithm is developed which exactly preserves energy and the total spatial angular momentum in incremental force free motions the implicit version of this algorithm is unconditionally stable and second order accurate the explicit version conserves exactly angular momentum in incremental force free motions numerical simulations are presented which illustrate the excellent performance of the proposed procedure even for incremental rotations over 65 degrees the procedure is directly applicable to transient dynamic calculations of geometrically exact rods and shells

bayesian estimates of disease maps how important are priors in the fully bayesian fb approach to disease mapping the choice of the hyperprior distribution of the dispersion parameter is a key issue in this context we investigated the sensitivity of the rate ratio estimates to the choice of the hyperprior via a simulation study we also compared the performance of the fb approach to mapping disease risk to the conventional approach of mapping maximum likelihood ml estimates and p values the study was modelled on the incidence data of insulin dependent diabetes mellitus iddm as observed in the communes of sardinia