on isospectral periodic potentials in rn ii on considere un reseau a n dimensions l dans r n et un potentiel q satisfaisant q x d q x pour d l on considere spec k q l ensemble des avec multiplicites telles que u qu u a une solution satisfaisant u x d u x exp 2i k d d l

an autoregressive growth model for longitudinal item analysis a first order autoregressive growth model is proposed for longitudinal binary item analysis where responses to the same items are conditionally dependent across time given the latent traits specifically the item response probability for a given item at a given time depends on the latent trait as well as the response to the same item at the previous time or the lagged response an initial conditions problem arises because there is no lagged response at the initial time period we handle this problem by adapting solutions proposed for dynamic models in panel data econometrics asymptotic and finite sample power for the autoregressive parameters are investigated the consequences of ignoring local dependence and the initial conditions problem are also examined for data simulated from a first order autoregressive growth model the proposed methods are applied to longitudinal data on korean students self esteem

on the period spectrum of a symplectic mapping let m be a compact riemannian manifold it has been known for a long time that the singularities of the wave trace trace cos t are located at the periods of the closed geodesics do these singularities also contain information about the geometry of m in the neighborhood of a closed geodesic we prove that the birkhoff canonical form of the poincare map can be determined from the singularities of the wave trace

mixed spectral boundary element embedding algorithms for the navier stokes equations in the vorticity stream function formulation an embedding approach based on fourier expansions and boundary integral equations is applied to the vorticity stream function formulation of the navier stokes equations the algorithm only requires efficient solvers of scalar elliptic equations and in an asymptotic version the boundary element method is only needed to solve the laplace equation the capabilities of this embedding method in both its full and asymptotic versions are pointed out by considering the classical problem of the flow between two eccentric cylinders

fourier integral operators on lie groupoids abstract as announced in 36 we develop a calculus of fourier integral g operators on any lie groupoid g for that purpose we study lagrangian conic submanifolds of the symplectic groupoid t g this includes their product transposition and inversion we also study the relationship between these lagrangian submanifolds and the equivariant families of lagrangian submanifolds of t g x t g x parametrized by the units x g 0 of g this allows us to select a subclass of lagrangian distributions on any lie groupoid g that deserve the name of fourier integral g operators g fios by construction the class of g fios contains the class of equivariant families of ordinary fourier integral operators on the manifolds g x x g 0 we then develop for g fios the first stages of the calculus in the spirit of hormander s work finally we illustrate this calculus in the case of manifolds with boundary

a comparison of numerical algorithms for fourier extension of the first second and third kinds the range of fourier methods can be significantly increased by extending a nonperiodic function f x to a periodic function f on a larger interval when f x is analytically known on the extended interval the extension is straightforward when f x is unknown outside the physical interval there is no standard recipe worse still like a radarless aircraft groping through fog the algorithm may wreck on the mountain in fog problem a function f x which is perfectly well behaved on the physical interval may very well have singularities in the extended domain in this article we compare several algorithms for successfully extending a function f x into the fog even when the analytic extension is singular the best third kind extension requires singular value decomposition with iterative refinement but achieves accuracy close to machine precision

birkhoff normal forms for fourier integral operators ii in this work we construct logarithms and birkhoff normal forms for elliptic fourier integral operators in the semi classical limit under more general assumptions than in a previous work by the first author the methods are similar but slightly different

rasch models for item bundles this paper discusses the application of a class of rasch models to situations where test items are grouped into subsets and the common attributes of items within these subsets brings into question the usual assumption of conditional independence the models are all expressed as particular cases of the random coefficients multinomial logit model developed by adams and wilson this formulation allows a very flexible approach to the specification of alternative models and makes model testing particularly straightforward the use of the models is illustrated using item bundles constructed in the framework of the solo taxonomy of biggs and collis

development of the mask method for incompressible unsteady flows abstract a new method is developed to solve 2 dimensional time dependent incompressible viscous flows in an arbitrary geometry the navier stokes equations are solved in primitive variables using a pseudospectral formulation the geometry is introduced by directly forcing the velocity field near the boundaries the method extends a similar computational technique introduced by basdevant and sadourny 1 some examples are shown to evaluate its efficiency and accuracy

trace expansions and the noncommutative residue for manifolds with boundary for a pseudodifferential boundary operator a of order 2 z and class 0 in the boutet de monvel calculus on a compact n dimensional manifold with boundary we consider the function tr ab s where b is an auxiliary system formed of the dirichlet realization of a second order strongly elliptic differential operator and an elliptic operator on the boundary we prove that tr ab s has a meromorphic extension to c with poles at the half integers s n j 2 j 2 n possibly double for s 0 and we prove that its residue at 0 equals the noncommutative residue of a as defined by fedosov golse leichtnam and schrohe by a different method to achieve this we establish a full asymptotic expansion of tr a b k in powersl 2 and log powersl 2 log where the noncommutative residue equals the coefficient of the highest order log power there is a related expansion of tr ae tb the paper will appear in journal reine angew math crelle s journal then is a holomorphic function of s for large re s we show that it extends to a mero morphic function on the whole complex plane with at most double poles moreover we prove that the noncommutative residue res a of a can be recovered as a residue in this

semiclassical spectral invariants for schrodinger operators in this article we show how to compute the semi classical spectral measure associated with the schrodinger operator on r n and by examining the rst few terms in the asymptotic expansion of this measure obtain inverse spectral results in one and two dimensions in particular we show that for the schrodinger operator on r 2 with a radially symmetric electric potential v and magnetic potential b both v and b are spectrally determined we also show that in one dimension there is a very simple explicit identity relating the spectral measure of the schrodinger operator with its birkho canonical form

recovering the hamiltonian from spectral data we show that the contributions to the gutzwiller formula with observable associated to the iterates of a given elliptic nondegenerate periodic trajectory gamma and to certain families of observables localized near gamma determine the quantum hamiltonian in a formal neighborhood of the trajectory gamma that is the full taylor expansion of its total symbol near gamma we also treat the bottom of a well case both for general and schrodinger operators

l 2 restriction bounds for eigenfunctions along curves in the quantum completely integrable case we show that for a quantum completely integrable system in two dimensions the l2 normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds of the form int gamma varphi j hbar 2 ds mathcal o log hbar for generic curves on the surface we also prove that the maximal restriction bounds of burq gerard tzvetkov bgt are generically attained for certain exceptional subsequences of eigenfunctions

a dynamic model for binary panel data with unobserved heterogeneity admitting a n consistent conditional estimator a model for binary panel data is introduced which allows for state dependence and unobserved heterogeneity beyond the effect of available covariates the model is of quadratic exponential type and its structure closely resembles that of the dynamic logit model however it has the advantage of being easily estimable via conditional likelihood with at least two observations further to an initial observation and even in the presence of time dummies among the regressors

quantum birkhoff gustavson normal form in some completely resonant cases abstract the goal of this paper is to present an explicit computation of the birkhoff gustavson normal form in the 1 1 1 2 and 1 3 resonances by using the concept of weyl quantization especially when it is about the first terms we use in particular the weyl symbolic calculus and the abstract theorem of the quantum birkhoff gustavson normal form in infinite dimension

spectral asymptotics via the semiclassical birkhoff normal form this article gives a simple treatment of the quantum birkhoff normal form for semiclassical pseudo differential operators with smooth coefficients the normal form is applied to describe the discrete spectrum in a generalised non degenerate potential well yielding uniform estimates in the energy e this permits a detailed study of the spectrum in various asymptotic regions of the parameters e h and gives improvements and new proofs for many of the results in the field in the completely resonant case we show that the pseudo differential operator can be reduced to a toeplitz operator on a reduced symplectic orbifold using this quantum reduction new spectral asymptotics concerning the fine structure of eigenvalue clusters are proved in the case of polynomial differential operators a combinatorial trace formula is obtained

power of the likelihood ratio test in covariance structure analysis a procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived the procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified using the noncentral chi square distribution the power of the test is approximated by the asymptotic one for a sequence of local alternatives the procedure is illustrated by an example a monte carlo experiment also shows how good the approximation is for a specific case

the canonical trace and the noncommutative residue on the noncommutative torus using a global symbol calculus for pseudodifferential operators on tori we build a canonical trace on classical pseudodifferential operators on noncommutative tori in terms of a canonical discrete sum on the underlying toroidal symbols we characterise the canonical trace on operators on the noncommutative torus as well as its underlying canonical discrete sum on symbols of fixed resp any non integer order on the grounds of this uniqueness result we prove that in the commutative setup this canonical trace on the noncommutative torus reduces to kontsevich and vishik s canonical trace which is thereby identified with a discrete sum a similar characterisation for the noncommutative residue on noncommutative tori as the unique trace which vanishes on trace class operators generalises fathizadeh and wong s characterisation in so far as it includes the case of operators of fixed integer order by means of the canonical trace we derive defect formulae for regularized traces the conformal invariance of the function at zero of the laplacian on the noncommutative torus is then a straightforward consequence

some current cfd issues relevant to the incompressible navier stokes equations abstract the goals of this paper are to carefully define a particular class of well set incompressible navier stokes problems in the continuum partial differential equation pde setting and to discuss some relevant and sometimes poorly understood issues related to these well posed pde problems both in the continuum world and in its computer counterpart emphasized are three common formulations used to generate computer codes the primitive variable velocity pressure formulation and two derived variable formulations pressure poisson equation and vorticity transport equation

estimating latent correlations between repeated testings a model for longitudinal latent structure analysis is proposed we assume that test scores for a given mental or attitudinal test are observed for the same individuals at two different points in time the purpose of the analysis is to fit a model that combines the values of the latent variable at the two time points in a two dimensional latent density the correlation coefficient between the two values of the latent variable can then be estimated the theory and methods are illustrated by a danish dataset concerning psychic vulnerability

parallel algorithms with local fourier basis abstract we present a nonoverlapping domain decomposition method with local fourier basis applied to a model problem in liquid flames the introduction of domain decomposition techniques in this paper is for numerical and parallel efficiency purposes when one requires a large number of grid points to catch complex structures we obtain then a high order accurate domain decomposition method that allows us to generalize our previous work on the use of local fourier basis to solve combustion problems with nonperiodic boundary conditions m garbey and d tromeur dervout j comput phys 145 316 1998 local fourier basis methodology fully uses the superposition principle to split the searched solution in a numerically computed part and an analytically computed part our present methodology generalizes the israeli et al 1993 j sci comput 8 135 method which applies domain decomposition with local fourier basis to the helmholtz s problem in the present work several new difficulties occur first the problem is unsteady and nonlinear which makes the periodic extension delicate to construct in terms of stability and accuracy second we use a streamfunction biharmonic formulation of the incompressible navier stokes equation in two space dimensions the application of domain decomposition with local fourier basis to a fourth order operator is more difficult to achieve than for a second order operator a systematic investigation of the influence of the method s parameters on the accuracy is done a detail parallel mimd implementation is given we give an a priori estimate that allows the relaxation of the communication between processors for the interface problem treatment results on nonquasi planar complex frontal polymerization illustrate the capability of the method

expansion functions for two dimensional incompressible fluid flow in arbitrary domains expansion functions are presented for two dimensional incompressible fluid flow in arbitrary domains that optimally conserve the 2d structure of vortex dynamics this is obtained by conformal mapping of the domain onto a circle and by constructing orthogonal radial polynomials and angular harmonics on the new domain such that the kinetic energy is diagonal and the separate components satisfy all of the required physical boundary conditions

a spectral embedding method applied to the advection diffusion equation in order to solve partial differential equations in complex geometries with a spectral type method one describes an embedding approach which essentially makes use of fourier expansions and boundary integral equations for the advection diffusion equation the method is based on an efficient helmholtz solver the accuracy of which is tested by considering 1d and 2d helmholtz like problems finally the capabilities of the method are pointed out by considering a 2d advection diffusion problem in a hexagonal geometry

noncommutative residue for heisenberg manifolds applications in cr and contact geometry abstract this paper has four main parts in the first part we construct a noncommutative residue for the hypoelliptic calculus on heisenberg manifolds that is for the class of h do operators introduced by beals greiner and taylor this noncommutative residue appears as the residual trace on integer order h dos induced by the analytic extension of the usual trace to non integer order h dos moreover it agrees with the integral of the density defined by the logarithmic singularity of the schwartz kernel of the corresponding h do in addition we show that this noncommutative residue provides us with the unique trace up to constant multiple on the algebra of integer order h dos in the second part we give some analytic applications of this construction concerning zeta functions of hypoelliptic operators logarithmic metric estimates for green kernels of hypoelliptic operators and the extension of the dixmier trace to the whole algebra of integer order h dos in the third part we present examples of computations of noncommutative residues of some powers of the horizontal sublaplacian and the contact laplacian on contact manifolds in the fourth part we present two applications in cr geometry first we give some examples of geometric computations of noncommutative residues of some powers of the horizontal sublaplacian and of the kohn laplacian second we make use of the framework of noncommutative geometry and of our noncommutative residue to define lower dimensional volumes in pseudohermitian geometry e g we can give sense to the area of any 3 dimensional cr manifold endowed with a pseudohermitian structure on the way we obtain a spectral interpretation of the einstein hilbert action in pseudohermitian geometry

on the misuse of manifest variables in the detection of measurement bias measurement invariance lack of bias of a manifest variabley with respect to a latent variablew is defined as invariance of the conditional distribution ofy givenw over selected subpopulations invariance is commonly assessed by studying subpopulation differences in the conditional distribution ofy given a manifest variablez chosen to substitute forw a unified treatment of conditions that may allow the detection of measurement bias using statistical procedures involving only observed or manifest variables is presented theorems are provided that give conditions for measurement invariance and for invariance of the conditional distribution ofy givenz additional theorems and examples explore the bayes sufficiency ofz stochastic ordering inw local independence ofy andz exponential families and the reliability ofz it is shown that when bayes sufficiency ofz fails the two forms of invariance will often not be equivalent in practice bayes sufficiency holds under rasch model assumptions and in long tests under certain conditions it is concluded that bias detection procedures that rely strictly on observed variables are not in general diagnostic of measurement bias or the lack of bias

connections of berry and hannay type for moving lagrangian submanifolds abstract berry s phase is the holonomy of the natural connection on the canonical circle bundle over projectivized quantum hilbert space given a symplectic manifold p a classical limit of this phase is constructed as the holonomy of a berry connection over a finite codimensional isodrastic foliation defined by constancy of action integrals on the space of lagrangian submanifolds in p equipped with smooth densities of total measure 1 if the densities are determined by a kahler metric compatible with the symplectic structure the curvature of the berry connection at the lagrangian submanifold l is given by a simple formula involving curvature of l in particular the berry connection defines a homotopy invariant for isodrastic loops of minimal lagrangian submanifolds in a simply connected kahler manifold a similar invariant constructed by the author for loops of symplectomorphisms is also a special case of the classical berry phase a classical analogue of berry s phase was discovered by hannay for moving families of completely integrable systems following berry and hannay we interpret hannay s angles as the holonomy of a hannay connection on a bundle of tori over the isodrastic foliation on the space of lagrangian toral layers consisting of lagrangian tori with a flat affine structure and an extension of this structure to the first infinitesimal neighborhood finally we show that the hannay angles are the derivatives with respect to action variables of the classical berry phase

spectral domain embedding for elliptic pdes in complex domains spectral methods are a class of methods for solving partial differential equations pdes when the solution of the pde is analytic it is known that the spectral solutions converge exponentially as a function of the number of modes used the basic spectral method works only for regular domains such as rectangles or disks domain decomposition methods spectral element methods extend the applicability of spectral methods to more complex geometries an alternative is to embed the irregular domain into a regular one this paper uses the spectral method with domain embedding to solve pdes on complex geometry the running time of the new algorithm has the same order as that for the usual spectral collocation method for pdes on regular geometry the algorithm is extremely simple and can handle dirichlet neumann boundary conditions as well as nonlinear equations

misspecified maximum likelihood estimates and generalised linear mixed models summary we investigate the impact of model violations on the estimate of a regression coefficient in a generalised linear mixed model specifically we evaluate the asymptotic relative bias that results from incorrect assumptions regarding the random effects we compare the impact of model violation for two parameterisations of the regression model substantial bias in the conditionally specified regression point estimators can result from using a simple random intercepts model when either the random effects distribution depends on measured covariates or there are autoregressive random effects a marginally specified regression structure that is estimated using maximum likelihood is much less susceptible to bias resulting from random effects model misspecification

fourier embedded domain methods extending a function defined on an irregular region to a rectangle so that the extension is spatially periodic and c a simple way to solve a partial differential equation in a non rectangular domain w is to embed the domain in a rectangle b and solve the problem more easily in the rectangle to apply a fourier spectral method on the rectangle it is necessary to extend the inhomogeneous term in the pde f x y to b in such a way that the extended function g x y is periodic and infinitely differentiable and yet is equal to f x y everywhere in the irregular domain w if the boundary of w email protected is defined as the zero isoline of a function f x y then a suitable extension is g x y f x y h email protected x y constant where h is a smoothed approximation to the step function which is defined in the main text

shuffle relations for regularised integrals of symbols we prove shuffle relations which relate a product of regularised integrals of classical symbols int reg sigma i d xi i i 1 ldots k to regularised nested iterated integrals prod i 1 k int reg sigma i d xi i sum tau in sigma k int reg d xi 1 int vert xi 2 vert leq vert xi 1 vert d xi 2 cdots int vert xi l vert leq vert xi k 1 vert d xi k otimes i 1 k sigma tau i where k is the group of permutations over k elements we show that these shuffle relations hold if all the symbols i have vanishing residue this is true of non integer order symbols on which the regularised integrals have all the expected properties such as stokes property mmp in general the shuffle relations hold up to finite parts of corrective terms arising from a renormalisation on tensor products of classical symbols a procedure adapted from renormalisation methods to compute feynman diagrams familiar to physicists we relate the shuffle relations for regularised integrals of symbols with shuffle relations for multiple zeta functions adapting the above constructions to the case of a symbol on the unit circle

extremals of determinants of laplacians on etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand la metrique est bien restreinte

non singular boundary integral representation of potential field gradients in this paper we derive the non singular boundary integral representation of the field gradients for two dimensional problems of classical potential field theory numerical implementation of this representation is developed too the proposed method eliminates the most inaccurate influence coefficients which arise when singular integral representations are used and the internal point approaches the boundary since the integrands in this new method are finite at any internal point accurate numerical results are achieved even in that portion of a solid which is very close to a discretized boundary two test problems are analysed in which the numerical results computed by strongly singular weakly singular and non singular integral representations are compared mutually and with exact solutions

fourier embedded domain methods periodic and c extension of a function defined on an irregular region to a rectangle via convolution with gaussian kernels abstract one possible way to solve a partial differential equation in an irregular region is the use of the so called domain embedding methods in where the domain of interest is embedded within a rectangle in order to apply a fourier spectral method on the rectangle the inhomogeneous term f x y has to be extended to a new function g x y that is periodic and infinitely differentiable and equal to f x y everywhere within some authors have given explicit methods to compute extensions with infinite order convergence for the cases in where the boundary of can be defined as the zero isoline of a function x y for the cases in where this is not possible we suggest a new method to build these extensions via convolution with gaussian kernels

dynamic latent trait models for multidimensional longitudinal data this article presents a new approach for analysis of multidimensional longitudinal data motivated by studies using an item response battery to measure traits of an individual repeatedly over time a general modeling framework is proposed that allows mixtures of count categorical and continuous response variables each response is related to age specific latent traits through a generalized linear model that accommodates item specific measurement errors a transition model allows the latent traits at a given age to depend on observed predictors and on previous latent traits for that individual following a bayesian approach to inference a markov chain monte carlo algorithm is proposed for posterior computation the methods are applied to data from a neurotoxicity study of the pesticide methoxychlor and evidence of a dose dependent increase in motor activity is presented

a bayesian random effects model for testlets standard item response theory irt models fit to dichotomous examination responses ignore the fact that sets of items testlets often come from a single common stimuli e g a reading comprehension passage in this setting all items given to an examinee are unlikely to be conditionally independent given examinee proficiency models that assume conditional independence will overestimate the precision with which examinee proficiency is measured overstatement of precision may lead to inaccurate inferences such as prematurely ending an examination in which the stopping rule is based on the estimated standard error of examinee proficiency e g an adaptive test to model examinations that may be a mixture of independent items and testlets we modified one standard irt model to include an additional random effect for items nested within the same testlet we use a bayesian framework to facilitate posterior inference via a data augmented gibbs sampler dags tanner wong 1987 the modified and standard irt models are both applied to a data set from a disclosed form of the sat we also provide simulation results that indicates that the degree of precision bias is a function of the variability of the testlet effects as well as the testlet design

implementation of neumann boundary condition with influence matrix method for viscous annular flow using pseudospectral collocation the flowfield of an annular couette flow is predicted numerically from an unsteady initial condition using the chebyshev fourier collocation method the numerical solution is obtained from the vorticity velocity formulation of the unsteady navier stokes equations in this formulation the velocity boundary conditions are overspecified while vorticity boundary conditions are unspecified this difficulty is resolved by a matrix influence method to convert the overspecified velocity boundary conditions to sufficiently specified dirichlet boundary conditions for both velocity and vorticity these boundary conditions are implemented by considering three methods the traditional row replacement method fornberg s fictitious points method and driscoll and hale s rectangular collocation method the solution is advanced in time using the third order adams bashforth semi implicit backward differentiation scheme the accuracy of the numerical solutions are assessed in two ways in one case the accuracy of the converged steady state solution is compared to the analytical solution in the second case the residual of the continuity equation for the vorticity velocity method is assessed in comparison to the vorticity streamfunction formulation that inherently satisfies the continuity equation all methods demonstrate high accuracy for the continuity equation residual at the domain interior however the row replacement and fictitious points methods exhibit poor accuracy at the boundaries during the transient the rectangular projection method exhibits excellent accuracy throughout the domain and boundaries at all times using the resampling points on the other hand for evaluating secondary quantities such as the wall shear stress the rectangular projection method demonstrates several orders of magnitude less accuracy when evaluated using the resampling points but high accuracy when evaluated directly at the original collocation points

some remarks about semiclassical trace invariants and quantum normal forms in this paper we explore the connection between semi classical and quantum birkhoff canonical forms bcf for schrodinger operators in particular we give a non symbolic operator theoretic derivation of the quantum birkhoff canonical form and provide an explicit recipe for expressing the quantum bcf in terms of the semi classical bcf

a small scale density of states formula let m g be a c compact riemann manifold with classical hamiltonian h c t m assume that the corresponding quantization p1 op h is quantum completely integrable we establish an microlocal weyl law on short spectral intervals of size 2 e e 0 for various families of operators p1u u i containing p1 both in the mean and pointwise a e for u i the microlocalization refers to a small tubular neighbourhood of a non degenerate stable periodic bicharacteristic t m 0

a composite likelihood inference in latent variable models for ordinal longitudinal responses the paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model the model considers time dependent latent variables and item specific random effects to be accountable for the interdependencies of the multivariate ordinal items time dependent latent variables are linked with an autoregressive model simulation results have shown composite likelihood estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood model selection criteria developed for composite likelihood estimation are used in the applications furthermore lower order residuals are used as measures of fit for the selected models

semiclassical non concentration near hyperbolic orbits for a large class of semiclassical pseudodifferential operators including schrodinger operators p h h2 g v x on compact riemannian manifolds we give logarithmic lower bounds on the mass of eigenfunctions outside neighbourhoods of generic closed hyperbolic orbits more precisely we show that if a is a pseudodifferential operator which is microlocally equal to the identity near the hyperbolic orbit and microlocally zero away from the orbit then u c log 1 h h p h u clog 1 h i a u this generalizes earlier estimates of colin de verdiere and parisse y colin de verdiere b parisse equilibre instable en regime semi classique i concentration microlocale comm partial differential equations 19 1994 1535 1563 equilibre instable en regime semi classique ii conditions de bohr sommerfeld ann inst h poincare phys theor 61 1994 347 367 obtained for a special case and of burq and zworski n burq m zworski geometric control in the presence of a black box j amer math soc 17 2004 443 471 for real hyperbolic orbits

a note on the bias of estimators with missing data it is well known that many standard analyses including maximum likelihood estimation and the generalized estimating equation approach liang and zeger 1986 biometrika 73 13 22 can result in biased estimation when there are missing observations in such cases it is of interest to calculate the magnitude of the bias incurred under specific assumptions about the process generating the full data and the nonresponse mechanism in this paper we give a condition that identifies the limit in probability of estimators that are solutions of estimating equations computed from the incomplete data with discrete data this condition suggests a simple algorithm to compute the asymptotic bias of these estimators that can be easily implemented with existing statistical software we illustrate our approach with asthma prevalence data in children

regularizing feynman path integrals using the generalized kontsevich vishik trace a fully regulated definition of feynman s path integral is presented here the proposed re formulation of the path integral coincides with the familiar formulation whenever the path integral is well defined in particular it is consistent with respect to lattice formulations and wick rotations i e it can be used in euclidean and minkowski space time the path integral regularization is introduced through the generalized kontsevich vishik trace that is the extension of the classical trace to fourier integral operators physically we are replacing the time evolution semi group by a holomorphic family of operators such that the corresponding path integrals are well defined in some half space of c the regularized path integral is thus defined through analytic continuation this regularization can be performed by means of stationary phase approximation or computed analytically depending only on the hamiltonian and the observable i e known a priori in either case the computational effort to eval

a dynamic generalization of the rasch model in the present paper a model for describing dynamic processes is constructed by combining the common rasch model with the concept of structurally incomplete designs this is accomplished by mapping each item on a collection of virtual items one of which is assumed to be presented to the respondent dependent on the preceding responses and or the feedback obtained it is shown that in the case of subject control no unique conditional maximum likelihood cml estimates exist whereas marginal maximum likelihood mml proves a suitable estimation procedure a hierarchical family of dynamic models is presented and it is shown how to test special cases against more general ones furthermore it is shown that the model presented is a generalization of a class of mathematical learning models known as luce s beta model

invariants for smooth conjugacy of hyperbolic dynamical systems ii we show that the eigenvalues of the derivatives at periodic points form a complete set of invariants for smooth local conjugacy of anosov diffeomorphisms oft2

riemannian nilmanifolds and the trace formula this paper examines the clean intersection hypothesis required for the expression of the wave invariants computed from the asymptotic expansion of the classical wave trace by duistermaat and guillemin the main result of this paper is the calculation of a necessary and sufficient condition for an arbitrary riemannian two step nilmanifold to satisfy the clean intersection hypothesis this condition is stated in terms of metric lie algebra data we use the calculation to show that generic two step nilmanifolds satisfy the clean intersection hypothesis in contrast we also show that the family of two step nilmanifolds that fail the clean intersection hypothesis are dense in the family of two step nilmanifolds finally we give examples of nilmanifolds that fail the clean intersection hypothesis

a multidimensional latent trait model for measuring learning and change a latent trait model is presented for the repeated measurement of ability based on a multidimensional conceptualization of the change process a simplex structure is postulated to link item performance under a given measurement condition or occasion to initial ability and to one or more modifiabilities that represent individual differences in change since item discriminations are constrained to be equal within a measurement condition the model belongs to the family of multidimensional rasch models maximum likelihood estimators of the item parameters and abilities are derived and an example provided that shows good recovery of both item and ability parameters properties of the model are explored particularly for several classical issues in measuring change

a fictitious domain method for external incompressible viscous flow modeled by navier stokes equations abstract in this article we discuss a fictitious domain method for the numerical solutions of three dimensional elliptic problems with dirichlet boundary conditions and also of the navier stokes equations modeling incompressible viscous flow the methodology for the navier stokes equations described here takes a systematic advantage of time discretization by operator splitting in order to treat separately advection imbedding and incompressibility due to the decoupling fast elliptic solvers can be used to treat the incompressibility condition even if the original problem is taking place on a nonregular geometry the resulting methodology is applied to two dimensional unsteady external incompressible viscous flow problems and three dimensional stokes problems

weighted trace formula near a hyperbolic trajectory and complex orbits in this paper we consider a weighted trace formula for schrodinger operators more precisely let j and ej denote the eigenfunctions and eigenvalues of a schrodinger type operator h with a discrete spectrum let x be a coherent state centered at a point x of a hyperbolic closed orbit we show that as 0 the leading term of j ej e x j 2 can be expressed in terms of the analytic continuation on the upper and lower half planes of the positive and negative frequencies part of the result is also related to complex trajectories surrounding

copula functions for residual dependency most item response theory models are not robust to violations of conditional independence however several modeling approaches e g conditioning on other responses additional random effects exist that try to incorporate local item dependencies but they have some drawbacks such as the nonreproducibility of marginal probabilities and resulting interpretation problems in this paper a new class of models making use of copulas to deal with local item dependencies is introduced these models belong to the bigger class of marginal models in which margins and association structure are modeled separately it is shown how this approach overcomes some of the problems associated with other local item dependency models

inverse spectral problem for analytic domains ii ℤ2 symmetric domains this paper develops and implements a new algorithm for calculating wave trace invariants of a bounded plane domain around a periodic billiard orbit the algorithm is based on a new expression for the localized wave trace as a special multiple oscillatory integral over the boundary and on a feynman diagrammatic analysis of the stationary phase expansion of the oscillatory integral the algorithm is particularly effective for euclidean plane domains possessing a 2 symmetry which reverses the orientation of a bouncing ball orbit it is also very effective for domains with dihedral symmetries for simply connected analytic euclidean plane domains in either symmetry class we prove that the domain is determined within the class by either its dirichlet or neumann spectrum this improves and generalizes the best prior inverse result that simply connected analytic plane domains with two symmetries are spectrally determined within that class

a boundary mixture approach to violations of conditional independence conditional independence is a fundamental principle in latent variable modeling and item response theory violations of this principle commonly known as local item dependencies are put in a test information perspective and sharp bounds on these violations are defined a modeling approach is proposed that makes use of a mixture representation of these boundaries to account for the local dependence problem by finding a balance between independence on the one side and absolute dependence on the other side in contrast to alternative approaches the nature of the proposed boundary mixture model does not necessitate a change in formulation of the typical item characteristic curves used in item response theory this has attractive interpretational advantages and may be useful for general test construction purposes

full information item bi factor analysis a plausibles factor solution for many types of psychological and educational tests is one that exhibits a general factor ands 1 group or method related factors the bi factor solution results from the constraint that each item has a nonzero loading on the primary dimension and at most one of thes 1 group factors this paper derives a bi factor item response model for binary response data in marginal maximum likelihood estimation of item parameters the bi factor restriction leads to a major simplification of likelihood equations and a permits analysis of models with large numbers of group factors b permits conditional dependence within identified subsets of items and c provides more parsimonious factor solutions than an unrestricted full information item factor analysis in some cases

prolate spheroidal wavefunctions as an alternative to chebyshev and legendre polynomials for spectral element and pseudospectral algorithms prolate spheroidal functions of order zero are generalizations of legendre polynomials which when the bandwidth parameter c 0 oscillate more uniformly on x 1 1 than either chebyshev or legendre polynomials this suggests that compared to these polynomials prolate functions give more uniform spatial resolution further when used as the spatial discretization for time dependent partial differential equations in combination with explicit time marching prolate functions allow a longer stable timestep than legendre polynomials we show that these advantages are real and further that it is almost trivial to modify existing pseudospectral and spectral element codes to use the prolate basis however improvements in spatial resolution are at most a factor of 2 approached slowly as n the timestep can be lengthened by several times but not by a factor that grows rapidly with n the prolate basis is not likely to radically expand the range of problems that can be done on a workstation however for production runs on the bleeding edge edge of arithmurgy such as numerical weather prediction the rewards for switching to a prolate basis may be considerable

the local and global parts of the basic zeta coefficient for operators on manifolds with boundary for operators on a compact manifold x with boundary x the basic zeta coefficient c0 b p1 t is the regular value at s 0 of the zeta function tr b p 1 t s where b p g is a pseudodifferential boundary operator in the boutet de monvel calculus for example the solution operator of a classical elliptic problem and p1 t is a realization of an elliptic differential operator p1 having a ray free of eigenvalues relative formulas e g for the difference between the constants with two different choices of p1 t have been known for some time and are local we here determine c0 b p1 t itself with even order p1 showing how it is put together of local residue type integrals generalizing the noncommutative residues of wodzicki guillemin fedosov golse leichtnam schrohe and global canonical trace type integrals generalizing the canonical trace of kontsevich and vishik formed of hadamard finite parts our formula generalizes a formula shown recently by paycha and scott for manifolds without boundary it leads in particular to new definitions of noncommutative residues of expressions involving log p1 t since the complex powers of p1 t lie far outside the boutet de monvel calculus the standard consideration of holomorphic families is not really useful here instead we have developed a resolvent parametric method where results from our calculus of parameter dependent boundary operators can be used

a fast solver for navier stokes equations in the lamina regime using mortar finite element and boundary element methods a multistep method is used to solve the navier stokes equations formulated with vorticity and stream function each time step is decomposed into three stages a convection step using the character

maximum likelihood estimation of limited and discrete dependent variable models with nested random effects abstract gauss hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models unfortunately the estimates are biased for large cluster sizes and or intraclass correlations we show that adaptive quadrature largely overcomes these problems we then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables the models can include several nested random effects intercepts and coefficients representing unobserved heterogeneity at different levels of a hierarchical dataset the required multivariate integrals are evaluated efficiently using spherical quadrature rules simulations show that adaptive quadrature performs well in a wide range of situations