adaptive bayesian wavelet shrinkage abstract when fitting wavelet based models shrinkage of the empirical wavelet coefficients is an effective tool for denoising the data this article outlines a bayesian approach to shrinkage obtained by placing priors on the wavelet coefficients the prior for each coefficient consists of a mixture of two normal distributions with different standard deviations the simple and intuitive form of prior allows us to propose automatic choices of prior parameters these parameters are chosen adaptively according to the resolution level of the coefficients typically shrinking high resolution frequency coefficients more heavily assuming a good estimate of the background noise level we obtain closed form expressions for the posterior means and variances of the unknown wavelet coefficients the latter may be used to assess uncertainty in the reconstruction several examples are used to illustrate the method and comparisons are made with other shrinkage methods

dilatation and order of contact for holomorphic self maps of strongly convex domains let d be a bounded strongly convex domain and let f be a holomorphic self map of d in this paper we introduce and study the dilatation alpha f of f defined if f has no fixed points in d as the usual boundary dilatation coefficient of f at its wolff point or if f has some fixed points in d as the ratio of shrinking of the kobayashi balls around a fixed point of f in particular we show that the map alpha defined as alpha f mapsto alpha f in 0 1 is lower semicontinuous among other things this allows us to study the limits of a family of holomorphic self maps of d in the case of an inner fixed point the dilatation is an intrinsic measure of the order of contact of f d to partial d finally using complex geodesics we define and study a directional dilatation which is a measure of the shrinking of the domain along a given direction again results of semicontinuity are given and applied to a family of holomorphic self maps

a high precision integration scheme for the spectral element time domain method in electromagnetic simulation a high precision integration hpi scheme combined with the spectral element time domain setd method is presented to solve the time dependent maxwell s equations spatial discretization by spectral elements will lead to block diagonal mass matrices thus greatly alleviating the computational burden of inverting the mass matrices a high precision time integration method based on the matrix exponential is then employed to solve the discretized setd system numerical examples demonstrate that this algorithm is unconditionally stable and very accurate

numerical dispersion in dg fetd method using brick and tetrahedral edge elements a numerical dispersion analysis nda of the discontinuous galerkin finite element time domain dg fetd method is presented vector basis functions under the nda are with brick and tetrahedral elements this nda shows that there exist both normal and spurious modes in the dg fetd method a dg fetd modeling of transverse electromagnetic tem wave propagation in a parallel waveguide is applied to verify the nda for zeroth order vector bases the effect of wave propagation direction and electrical size of elements on numerical dispersion is investigated it is shown from the nda for higher order interpolatory vector bases that the phase error of normal modes can be significantly reduced by using higher order bases

rigidity of holomorphic mappings and a new schwarz lemma at the boundary a rigidity theorem for holomorphic mappings in the nature of the uniqueness statement of the classical one variable schwarz lemma is proved at the boundary of a strongly pseudoconvex domain the result reduces to an interesting and apparently new result even in one complex dimension the theorem has a variety of geometric and analytic interpretations department of mathematics university of michigan ann arbor michigan 48109 department of mathematics box 1146 washington university in st louis st louis missouri 63130 this content downloaded from 40 77 167 14 on wed 15 jun 2016 05 36 04 utc all use subject to http about jstor org terms

high order symplectic integration methods for finite element solutions to time dependent maxwell equations in this paper we motivate the use of high order integration methods for finite element solutions of the time dependent maxwell equations in particular we present a symplectic algorithm for the integration of the coupled first order maxwell equations for computing the time dependent electric and magnetic fields symplectic methods have the benefit a conserving total electromagnetic field energy and are therefore preferred over dissipative methods such as traditional runge kutta in applications that require high accuracy and energy conservation over long periods of time integration we show that in the context or symplectic methods several popular schemes can be elegantly cast in a single algorithm we conclude with some numerical examples which demonstrate the superior performance of high order time integration methods

a vector finite element time domain method for solving maxwell s equations on unstructured hexahedral grids in this paper the vector finite element time domain vfetd method is derived analyzed and validated the vfetd method uses edge vector finite elements as a basis for the electric field and face vector finite elements as a basis for the magnetic flux density the galerkin method is used to convert maxwell s equations to a coupled system of ordinary differential equations the leapfrog method is used to advance the fields in time the method is shown to be stable and to conserve energy and charge for arbitrary hexahedral grids a numerical dispersion analysis shows the method to be second order accurate on distorted hexahedral grids several computational experiments are performed to determine the accuracy and efficiency of the method

a symplectic integration algorithm for separable hamiltonian functions abstract we derive an algorithm to numerically integrate differential equations derivable from a separable hamiltonian function this symplectic algorithm is accurate to fourth order in the time step and preserves exactly the poincare cartan integral invariants associated with the topology of the phase flow we compare the efficiency and accuracy of this method to that of existing integrators both symplectic and non symplectic by integrating the equations of motion corresponding to a nonlinear pendulum a particle in the field of a standing wave and a harmonic oscillator perturbed by a plane wave

improved conditioning of finite element matrices using new high order interpolatory bases the condition number of finite element matrices constructed from interpolatory bases will grow as the polynomial degree of the basis functions is increased the worst case scenario for this growth rate is exponential and in this paper we demonstrate through computational example that the traditional set of uniformly distributed interpolation points yields this behavior we propose a set of nonuniform interpolation points which yield a much improved polynomial growth rate of condition number these points can be used to construct several types of popular hexahedral basis functions including the 0 form standard lagrangian 1 form curl conforming and 2 form divergence conforming varieties we demonstrate through computational example the benefits of using these new interpolatory bases in finite element solutions to maxwell s equations in both the frequency and time domain

multidomain pseudospectral time domain algorithm using a symplectic integrator the novel multidomain pseudospectral time domain method based on a symplectic integrator scheme is presented in this paper a symplectic integrator scheme is a decomposition of the exponential operator or a general propagation technique the scheme is nondissipative and does not require additional memory for temporary storage of data for the internal stages the good performance of the scheme is demonstrated by numerical examples

conservative and provably stable fdtd subgridding the finite difference time domain fdtd method is a common robust simulation technique for transient electromagnetic interactions with complicated structures however the standard fdtd method is limited to cartesian grids everywhere in the computational grid many practitioners have extended fdtd to handle multiresolution problems by using finer grids near structures with small geometrical features abutted to coarse grids in regions of empty space unfortunately subgridding implementations based on interpolation or extrapolation of neighboring field values can exhibit late time instabilities herein a subgridding method based on multigrid finite element principles will be developed and its stability proven numerical results will assess its performance in 2 d and 3 d

a high order mixed vector finite element method for solving the time dependent maxwell equations on unstructured grids we present a mixed vector finite element method for solving the time dependent coupled ampere and faraday laws of maxwell s equations on unstructured hexahedral grids that employs high order discretization in both space and time the method is of arbitrary order accuracy in space and up to 4th order accurate in time making it well suited for electrically large problems where grid anisotropy and numerical dispersion have plagued other methods in addition the method correctly models both the jump discontinuities and the divergence free properties of the electric and magnetic fields is charge and energy conserving conditionally stable and free of spurious modes several computational experiments are performed to demonstrate the accuracy efficiency and benefits of the method

a new hybrid implicit explicit fdtd method for local subgridding in multiscale 2 d te scattering problems the conventional finite difference time domain fdtd method with staggered yee scheme does not easily allow including thin material layers especially so if these layers are highly conductive this paper proposes a novel subgridding technique for 2 d problems based on a hybrid implicit explicit scheme which efficiently copes with this problem in the subgrid the new method collocates field components such that the thin layer boundaries are defined unambiguously moreover aspect ratios of more than a million do not impair the stability of the method and allow for very accurate predictions of the skin effect the new method retains the courant limit of the coarse yee grid and is easily incorporated into existing fdtd codes a number of illustrative examples including scattering by a metal grating demonstrate the accuracy and stability of the new method

higher order hybrid implicit explicit fdtd time stepping both partially implicit fdtd methods and symplectic fdtd methods of high temporal accuracy 3rd or 4th order are well documented in the literature in this paper we combine them we construct a conservative fdtd method which is fourth order accurate in time and is partially implicit we show that the stability condition for this method depends exclusively on the explicit part which makes it suitable for use in e g modelling wave propagation in plasmas

the range of holomorphic maps at boundary points we prove a boundary version of the open mapping theorem for holomorphic maps between strongly pseudoconvex domains that is we prove that the local image of a holomorphic map f d rightarrow d close to a boundary regular contact point p in partial d where the jacobian is bounded away from zero along normal non tangential directions has to eventually contain every cone and more generally every region which is kobayashi asymptotic to a cone with vertex at f p

boundary behavior of infinitesimal generators in the unit ball we prove a julia wolff caratheodory type theorem for infinitesimal generators on the unit ball in n moreover we study jets expansions at the boundary and give necessary and sufficient conditions on such jets for an infinitesimal generator to generate a group of automorphisms of the ball

linear fractional maps of the unit ball a geometric study abstract we classify up to conjugation with automorphisms the linear fractional self maps of the unit ball of c n n 1 then we give some applications of these normal forms to the study of composition operators

boundary jets of holomorphic maps between strongly pseudoconvex domains abstract in this paper we consider jets taken at a fixed boundary point of germs of holomorphic diffeomorphisms which send one strongly pseudoconvex domain into another we completely describe possible first and second jets and conditions of extremality in terms of the chern moser normal forms of the domains

modeling microarray data using a threshold mixture model an important goal of microarray studies is the detection of genes that show significant changes in expression when two classes of biological samples are being compared we present an anova style mixed model with parameters for array normalization overall level of gene expression and change of expression between the classes for the latter we assume a mixing distribution with a probability mass concentrated at zero representing genes with no changes and a normal distribution representing the level of change for the other genes we estimate the parameters by optimizing the marginal likelihood to make this practical laplace approximations and a backfitting algorithm are used the performance of the model is studied by simulation and by application to publicly available data sets

a general maximum likelihood analysis of variance components in generalized linear models this paper describes an em algorithm for nonparametric maximum likelihood ml estimation in generalized linear models with variance component structure the algorithm provides an alternative analysis to approximate mql and pql analyses mcgilchrist and aisbett 1991 biometrical journal 33 131 141 breslow and clayton 1993 journal of the american statistical association 88 9 25 mcgilchrist 1994 journal of the royal statistical society series b 56 61 69 goldstein 1995 multilevel statistical models and to gee analyses liang and zeger 1986 biometrika 73 13 22 the algorithm first given by hinde and wood 1987 in longitudinal data analysis 110 126 is a generalization of that for random effect models for overdispersion in generalized linear models described in aitkin 1996 statistics and computing 6 251 262 the algorithm is initially derived as a form of gaussian quadrature assuming a normal mixing distribution but with only slight variation it can be used for a completely unknown mixing distribution giving a straightforward method for the fully nonparametric ml estimation of this distribution this is of value because the ml estimates of the glm parameters can be sensitive to the specification of a parametric form for the mixing distribution the nonparametric analysis can be extended straightforwardly to general random parameter models with full npml estimation of the joint distribution of the random parameters this can produce substantial computational saving compared with full numerical integration over a specified parametric distribution for the random parameters a simple method is described for obtaining correct standard errors for parameter estimates when using the em algorithm several examples are discussed involving simple variance component and longitudinal models and small area estimation

classification of semigroups of linear fractional maps in the unit ball we give a complete classiflcation up to conjugation of continuous semigroups of linear fractional self maps of the unit ball

iteration and the solution of functional equations for functions analytic in the unit disk this paper considers the classical functional equations of schroeder f o p xf and abel f o p f 1 and related problems of fractional iteration where 9p is an analytic mapping of the open unit disk into itself the main theorem states that under very general conditions there is a linear fractional transformation 4 and a function a analytic in the disk such that a oa p and that with suitable normalization 4 and a are unique in particular the hypotheses are satisfied if 4p is a probability generating function that does not have a double zero at 0 this intertwining relates solutions of functional equations for t to solutions of the corresponding equations for d for example it follows that if 4p has no fixed points in the open disk then the solution space of f o p xf is infinite dimensional for every nonzero x although the discrete semigroup of iterates of t usually cannot be embedded in a continuous semigroup of analytic functions mapping the disk into itself we find that for each z in the disk all sufficiently large fractional iterates of p can be defined at z this enables us to find a function meromorphic in the disk that deserves to be called the infinitesimal generator of the semigroup of iterates of p if the iterates of p can be embedded in a continuous semigroup we show that the semigroup must come from the corresponding semigroup for 4 and thus be real analytic in t the proof of the main theorem is not based on the well known limit technique introduced by koenigs 1884 but rather on the construction of a riemann surface on which an extension of 9p is a bijection much work is devoted to relating characteristics of p to the particular linear fractional transformation constructed in the theorem

a generalized mass lumping technique for vector finite element solutions of the time dependent maxwell equations time domain finite element solutions of maxwell s equations require the solution of a sparse linear system involving the mass matrix at every time step this process represents the bulk of the computational effort in time dependent simulations as such mass lumping techniques in which the mass matrix is reduced to a diagonal or block diagonal matrix are very desirable in this paper we present a special set of high order 1 form also known as curl conforming basis functions and reduced order integration rules that together allow for a dramatic reduction in the number of nonzero entries in a vector finite element mass matrix the method is derived from the nedelec curl conforming polynomial spaces and is valid for arbitrary order hexahedral basis functions for finite element solutions to the second order wave equation for the electric or magnetic field intensity we present a numerical eigenvalue convergence analysis of the method and quantify its accuracy and performance via a series of computational experiments

empirical bayes analysis of a microarray experiment microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels a typical microarray experiment can produce millions of data points raising serious problems of data reduction and simultaneous inference we consider one such experiment in which oligonucleotide arrays were employed to assess the genetic effects of ionizing radiation on seven thousand human genes a simple nonparametric empirical bayes model is introduced which is used to guide the efficient reduction of the data to a single summary statistic per gene and also to make simultaneous inferences concerning which genes were affected by the radiation although our focus is on one specific experiment the proposed methods can be applied quite generally the empirical bayes inferences are closely related to the frequentist false discovery rate fdr criterion

island coalescence using parallel first order system least squares on incompressible resistive magnetohydrodynamics this paper investigates the performance of a parallel newton first order system least squares fosls finite element method with local adaptive refinement and algebraic multigrid amg applied to incompressible resistive magnetohydrodynamics in particular an island coalescence test problem is studied that models magnetic reconnection using a reduced two dimensional 2d model of a tokamak fusion reactor the results show that using an appropriate temporal and spatial resolution these methods are capable of resolving the physical instabilities accurately at small computational cost the time dependent nonlinear system of pdes is solved using work equivalent to about 50 60 simple relaxation sweeps gauss seidel iterations per time step experiments show that unless the time step is sufficiently small nonphysical numerical instabilities may occur further decreasing the time step size does not proportionally increase the cost of the computation because amg convergence is improved in addition

parabolic composition operators on the ball abstract we give a classification up to automorphisms of parabolic linear fractional maps of the ball we then show that this classification is very convenient to study the geometric properties of these maps as well as the associated composition operators

fourth order symplectic integration abstract in this paper we present an explicit fourth order method for the integration of hamilton s equations this method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state that is the integration step is an explicit symplectic map although the result is first derived for a specific type of hamiltonian it is shown to be quite general in particular the results can be applied to any lie group

numerical stability of nonorthogonal fdtd methods in this paper a sufficient test for the numerical stability of generalized grid finite difference time domain fdtd schemes is presented it is shown that the projection operators of such schemes must be symmetric positive definite without this property such schemes can exhibit late time instabilities the origin and the characteristics of these late time instabilities are also uncovered based on this study nonorthogonal grid fdtd schemes nfdtd and the generalized yee gy methods are proposed that are numerically stable in the late time for quadrilateral prism elements allowing these methods to be extended to problems requiring very long time simulations the study of numerical stability that is presented is very general and can be applied to most solutions of maxwell s equations based on explicit time domain schemes

symplectic discretization for spectral element solution of maxwell s equations applying the spectral element method sem based on the gauss lobatto legendre gll polynomial to discretize maxwell s equations we obtain a poisson system or a poisson system with at most a perturbation for the system we prove that any symplectic partitioned runge kutta prk method preserves the poisson structure and its implied symplectic structure numerical examples show the high accuracy of sem and the benefit of conserving energy due to the use of symplectic methods

cyclic behavior of linear fractional composition operators in the unit ball of c n we characterize the cyclicity and hypercyclicity of composition operators induced by linear fractional self maps of b n on the hardy space h 2 b n based on the classification of linear fractional maps given by bisi and bracci c 2007 elsevier inc all rights reserved

stability of explicit implicit hybrid time stepping schemes for maxwell s equations an improved version of the stable fem fdtd hybrid method t rylander and a bondeson comput phys commun 125 75 2000 for maxwell s equations is presented the new formulation has a modified time stepping scheme and is rigorously proven to be stable for time steps up to the stability limit for the fdtd the new scheme gives less reflection at the boundary between the structured and unstructured grids than the original formulation the hybrid method is compared to the fdtd with staircasing for scattering from a conducting sphere the discretization errors of the hybrid show quadratic dependence on mesh size while the scaling is less clear for the fdtd the fdtd gives errors that are 5 60 times higher than that of the hybrid depending on resolution and staircasing strategy

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

standard errors for em estimates in generalized linear models with random effects a procedure is derived for computing standard errors of em estimates in generalized linear models with random effects quadrature formulas are used to approximate the integrals in the em algorithm where two different approaches are pursued i e gauss hermite quadrature in the case of gaussian random effects and nonparametric maximum likelihood estimation for an unspecified random effect distribution an approximation of the expected fisher information matrix is derived from an expansion of the em estimating equations this allows for inferential arguments based on em estimates as demonstrated by an example and simulations

an efficient vector finite element method for nonlinear electromagnetic modeling we have developed a mixed vector finite element method vfem for maxwell s equations with a nonlinear polarization term the method allows for discretization of complicated geometries with arbitrary order representations of the b and e fields in this paper we will describe the method and a series of optimizations that significantly reduce the computational cost additionally a series of test simulations will be presented to validate the method finally a nonlinear waveguide mode mixing example is presented and discussed

lattice electromagnetic theory from a topological viewpoint the language of differential forms and topological concepts are applied to study classical electromagnetic theory on a lattice it is shown that differential forms and their discrete counterparts cochains provide a natural bridge between the continuum and the lattice versions of the theory allowing for a natural factorization of the field equations into topological field equations i e invariant under homeomorphisms and metric field equations the various potential sources of inconsistency in the discretization process are identified distinguished and discussed a rationale for a consistent extension of the lattice theory to more general situations such as to irregular lattices is considered

explicit and provably stable spatiotemporal fdtd refinement abstract in this paper we introduce an explicit and provably conditionally stable finite difference time domain fdtd algorithm for maxwell s equations with local refinement in both the spatial discretization length and in the time step spatiotemporal refinement this enables local spatial refinement with a locally reduced time step

a class of linear fractional maps of the ball and their composition operators abstract we study a class of linear fractional self maps of the ball which seems to be a good generalization of parabolic non automorphisms of the unit disk we give a normal form of these maps and use it to compute the spectrum of the composition operators induced by them we also show that these composition operators are never hypercyclic applications are given to the study of more general linear fractional transformations

a time discontinuous implicit variational integrator for stress wave propagation analysis in solids this paper proposes a time discontinuous and space continuous variational integration tdsc vi method for accurate elastic stress wave propagation computations in one dimensional bar the algorithm employs a limiter akin to classical artificial viscosity treatment to mitigate the deleterious gibbs jumps across the stress discontinuities and a parametrized consistent mass to alleviate dispersion error when the stepsizes are different from the courant stability limit which becomes necessary for elastic unloading and internal reflections in plastic deformation problems stability and accuracy analyses of the proposed tdsc vi method are carried out and compared with several well known traditional integration algorithms numerical experiments are carried out with the proposed implicit and explicit methods which show that the proposed methods perform favorably compared to the trapezoidal rule and the central difference method

survey on symplectic finite difference time domain schemes for maxwell s equations to discretize maxwell s equations a variety of high order symplectic finite difference time domain schemes which use th order symplectic integration time stepping and th order staggered space differencing are surveyed first the order conditions for the symplectic integrators are derived second the comparisons of numerical stability dispersion and energy conservation are provided between the high order symplectic schemes and other high order time approaches finally these symplectic schemes are studied by using different space and time strategies according to our survey high order time schemes for matching high order space schemes are required for optimum electromagnetic simulation numerical experiments have been conducted on radiation of electric dipole and wideband s parameter extraction of dielectric filled waveguide the results demonstrate that the high order symplectic scheme can obtain satisfying numerical solutions under high courant friedrichs levy number and coarse grid conditions

time integration methods for finite element discretisations of the second order maxwell equation this article deals with time integration for the second order maxwell equations with possibly non zero conductivity in the context of the discontinuous galerkin finite element method dg fem and the h curl conforming fem for the spatial discretisation hierarchic h curl conforming basis functions are used up to polynomial order p 3 over tetrahedral meshes meaning fourth order convergence rate a high order polynomial basis often warrants the use of high order time integration schemes but many well known high order schemes may suffer from a severe time step stability restriction owing to the conductivity term we investigate several possible time integration methods from the point of view of accuracy stability and computational work we also carry out a numerical fourier analysis to study the dispersion and dissipation properties of the semi discrete dg fem scheme as well as the fully discrete schemes with several of the time integration methods the dispersion and dissipation properties of the spatial discretisation and those of the time integration methods are investigated separately providing additional insight into the two discretisation steps

norms and spectral radii of linear fractional composition operators on the ball abstract we give a new proof that every linear fractional map of the unit ball induces a bounded composition operator on the standard scale of hilbert function spaces on the ball and obtain new norm bounds analogous to the standard one variable estimates we also show that cowen s one variable spectral radius formula extends to these operators the key observation underlying these results is that every linear fractional map of the ball belongs to the schur agler class

valiron s theorem in the unit ball and spectra of composition operators abstract we prove a version of valiron s conjugacy theorem for schur class mappings of the unit ball of c n as an application we obtain a formula for the spectral radius of composition operators on the ball with schur class symbols

a proof of the muir suffridge conjecture for convex maps of the unit ball in mathbb c n c n we prove and improve the muir suffridge conjecture for holomorphic convex maps namely let f mathbb b n rightarrow mathbb c n be a univalent map from the unit ball whose image d is convex let mathcal s subset partial mathbb b n be the set of points xi such that lim z rightarrow xi vert f z vert infty then we prove that mathcal s is either empty or contains one or two points and f extends as a homeomorphism tilde f overline mathbb b n setminus mathcal s rightarrow overline d moreover mathcal s emptyset if d is bounded mathcal s has one point if d has one connected component at infty and mathcal s has two points if d has two connected components at infty and up to composition with an automorphism of the ball and renormalization f is an extension of the strip map in the plane to higher dimension

the lobatto cell robust explicit higher order fdtd that handles inhomogeneous media to improve numerical dispersion and second order convergence behavior of the traditional yee finite difference time domain fdtd algorithm various higher order finite difference implementations have been proposed many have difficulty handling interfaces between distinct dielectric media or metallic sheets because the high order taylor expansions on which these codes are based are invalidated by field or derivative discontinuities one sided extensions extrapolations are a common approach to remedy interface discontinuities here another approach based upon whitney form mass lumped finite elements is pursued to develop the ldquolobatto cell rdquo a high order replacement for the yee cell with appropriate continuity behavior at contrasting media interfaces the lobatto cell retains many robust features of the yee method discrete conservation laws a guarantee of conditional stability and straightforward explicit updating but provides higher order interpolation and dispersion error convergence a notable drawback of the method is larger modeling granularity staircasing which is managed here by combining the lobatto cell method with preexisting robust subgridding techniques

explicit local time stepping methods for maxwell s equations explicit local time stepping methods are derived for time dependent maxwell equations in conducting and non conducting media by using smaller time steps precisely where smaller elements in the mesh are located these methods overcome the bottleneck caused by local mesh refinement in explicit time integrators when combined with a finite element discretisation in space with an essentially diagonal mass matrix the resulting discrete time marching schemes are fully explicit and thus inherently parallel in a non conducting source free medium they also conserve a discrete energy which provides a rigorous criterion for stability starting from the standard leap frog scheme local time stepping methods of arbitrarily high accuracy are derived for non conducting media numerical experiments with a discontinuous galerkin discretisation in space validate the theory and illustrate the usefulness of the proposed time integration schemes

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

a general approach for the stability analysis of the time domain finite element method for electromagnetic simulations this paper presents a general approach for the stability analysis of the time domain finite element method tdfem for electromagnetic simulations derived from the discrete system analysis the approach determines the stability by analyzing the root locus map of a characteristic equation and evaluating the spectral radius of the finite element system matrix the approach is applicable to the tdfem simulation involving dispersive media and to various temporal discretization schemes such as the central difference forward difference backward difference and newmark methods it is shown that the stability of the tdfem is determined by the material property and by the temporal and spatial discretization schemes the proposed approach is applied to a variety of tdfem schemes which include 1 time domain finite element modeling of dispersive media 2 time domain finite element boundary integral method 3 higher order tdfem and 4 orthogonal tdfem numerical results demonstrate the validity of the proposed approach for stability analysis

wavelet thresholding via a bayesian approach we discuss a bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression a prior distribution is imposed on the wavelet coefficients of the unknown response function designed to capture the sparseness of wavelet expansion that is common to most applications for the prior specified the posterior median yields a thresholding procedure our prior model for the underlying function can be adjusted to give functions falling in any specific besov space we establish a relationship between the hyperparameters of the prior model and the parameters of those besov spaces within which realizations from the prior will fall such a relationship gives insight into the meaning of the besov space parameters moreover the relationship established makes it possible in principle to incorporate prior knowledge about the function s regularity properties into the prior model for its wavelet coefficients however prior knowledge about a function s regularity properties might be difficult to elicit with this in mind we propose a standard choice of prior hyperparameters that works well in our examples several simulated examples are used to illustrate our method and comparisons are made with other thresholding methods we also present an application to a data set that was collected in an anaesthesiological study

unification of leapfrog and crank nicolson finite difference time domain methods in this paper we present a unified theory of explicit leapfrog and implicit crank nicolson finite difference time domain fdtd time stepping schemes this enables us to interface leapfrog fdtd with crank nicolson fdtd and we will prove that the result is stable at the courant limit of the leapfrog part it also enables us to construct explicit fdtd like algorithms whose stability condition is less restrictive than that of leapfrog fdtd and a remarkable explicit 1 2 fdtd refinement scheme which is stable up to the courant limit of the coarse part

hyperbolic composition operators on the ball we give a classification up to automorphisms of hyperbolic linear fractional maps of the ball we then show that this classification is very convenient to study the geometric properties of these maps as well as the spectrum and the dynamics of the associated composition operators we conclude by showing how these properties can be tranfered to composition operators associated to hyperbolic self maps of the ball which are not linearfractional maps

a schwarz lemma at the boundary using the julia wolff caratheodory type condition on finite dimensional irreducible bounded symmetric domains abstract in this paper we prove a schwarz lemma at the boundary for holomorphic self mappings f of finite dimensional irreducible bounded symmetric domains without assuming the boundary regularity of f our result generalizes the previous results obtained for holomorphic self mappings f of the euclidean unit ball or of the classical cartan domains of type i and of type ii which are smooth up to the boundary