gravity interpretation using the mellin transform the mellin transform of the gravity effect of a buried sphere and two dimensional horizontal circular cylinder and the first horizontal derivative of the gravity effect of a two dimensional thin fault layer are derived the transformed functions are bounded by two asymptotes they are analyzed and procedures are formulated excluding the asymptotic regions for the extraction of the body parameters the application of the mellin transform is tested on simulated models as well as on two field examples 1 the humble dome gravity anomaly near houston usa and 2 the louga gravity anomaly usa

how rare are multiple eigenvalues let a q be a differentiable family of self adjoint operators on a hilbert space h indexed by a parameter q that belongs to a separable banach manifold x assume that the spectrum of each operator a q is discrete of finite multiplicity and with no finite accumulation points we introduce a new concept of codimension in infinite dimensional space and then prove that under an appropriate transversality condition related to the strong arnold hypothesis the members of the family a q having multiple eigenvalues form a set of codimension at least 2 using this we show that a generic member of the family a q has a simple spectrum i e no repeated eigenvalues and that any two values q1 and q2 of the parameter can be connected by an analytic curve in x such that a q has a simple spectrum for all q in the interior of we then apply these results in two cases of physical interest to the laplace operator with the domain as parameter and to the schrodinger operator with a symmetric potential as parameter 1999 john wiley sons inc

exact controllability in projections of the bilinear schrodinger equation we consider the bilinear schrodinger equation with discrete spectrum drift we show for n n arbitrary exact controllability in projections on the first n given eigenstates the controllability result relies on a generic controllability hypothesis on some associated finite dimensional approximations the method is based on lie algebraic control techniques applied to the finite dimensional approximations coupled with classical topological arguments issuing from degree theory

inverse problems and chaotic dynamics of parabolic equations on arbitrary spatial domains let rnbe an arbitrary smooth bounded domain we prove the existence of a polynomial functiona x on rnsuch that an arbitrary and sufficiently small vector field on rn 1can be realized on the center manifold of the semilinear parabolic equation formula with an appropriate nonlinearityg x s w r rn g x s w r this extends earlier results of polacik and rybakowski and shows that arbitrary chaotic behavior is possible for semilinear scalar parabolic bvps on arbitrary bounded domains to prove this we establish some spectral perturbation and convergence results and solve an abstract inverse eigenvalue problem

optimal control in laser induced population transfer for two and three level quantum systems we apply the techniques of control theory and of sub riemannian geometry to laser induced population transfer in two and three level quantum systems the aim is to induce complete population transfer by one or two laser pulses minimizing the pulse fluences sub riemannian geometry and singular riemannian geometry provide a natural framework for this minimization where the optimal control is expressed in terms of geodesics we first show that in two level systems the well known technique of pulse transfer in the rotating wave approximation emerges naturally from this minimization in three level systems driven by two resonant fields we also find the counterpart of the pulse transfer this geometrical picture also allows one to analyze the population transfer by adiabatic passage

on the conicity of eigenvalues intersections for parameter dependent self adjoint operators motivated by recent controllability results for the bilinear schrodinger equation based on the existence of conical intersections in this paper we identify two physically interesting families of parameter dependent hamiltonians that admit residual and prevalent subfamilies for which all double eigenvalues are conical in order to obtain such a result we exploit a characterization of conical intersections in terms of a transversality condition which allows to apply a suitable transversality theorem

analysis of depth resolution in potential field inversion we study the inversion of potential fields and evaluate the degree of depth resolution achievable for a given problem to this end we introduce a powerful new tool the depth resolution plot drp the drp allows a theoretical study of how much the depth resolution in a potential field inversion is influenced by the way the problem is discretized and regularized the drp also allows a careful study of the influence of various kinds of ambiguities such as those from data errors or of a purely algebraic nature the achievable depth resolution is related to the given discretization regularization and data noise level we compute drp by means of singular value decomposition svd or its generalization gsvd depending on the particular regularization method chosen to illustrate the use of the drp we assume a source volume of specified depth and horizontal extent in which the solution is piecewise constant within a 3d grid of blocks we consider various linear regularization terms in a tikhonov damped least squares formulation some based on using higher order derivatives in the objective function drps are illustrated for both synthetic and real data our analysis shows that if the algebraic ambiguity is not too large and a suitable smoothing norm is used some depth resolution can be obtained without resorting to any subjective choice of depth weighting

statistical inference for multiple choice tests finite sample inference procedures are considered for analyzing the observed scores on a multiple choice test with several items where for example the items are dissimilar or the item responses are correlated a discrete p parameter exponential family model leads to a generalized linear model framework and in a special case a convenient regression of true score upon observed score techniques based upon the likelihood function akaike s information criteria aic an approximate bayesian marginalization procedure based on conditional maximization bcm and simulations for exact posterior densities importance sampling are used to facilitate finite sample investigations of the average true score individual true scores and various probabilities of interest a simulation study suggests that when the examinees come from two different populations the exponential family can adequately generalize duncan s beta binomial model extensions to regression models the classical test theory model and empirical bayes estimation problems are mentioned the duncan keats and matsumura data sets are used to illustrate potential advantages and flexibility of the exponential family model and the bcm technique

bayesian kernel mixtures for counts although bayesian nonparametric mixture models for continuous data are well developed the literature on related approaches for count data is limited a common strategy is to use a mixture of poissons which unfortunately is quite restrictive in not accounting for distributions with variance less than the mean other approaches include mixing multinomials which requires finite support and using a dirichlet process prior with a poisson base measure which does not allow for smooth deviations from the poisson we propose broad class of alternative models nonparametric mixtures of rounded continuous kernels we develop an efficient gibbs sampler for posterior computation and perform a simulation study to assess performance focusing on the rounded gaussian case we generalize the modeling framework to account for multivariate count data joint modeling with continuous and categorical variables and other complications we illustrate our methods through applications to a developmental toxicity study and m

on structural equation modeling with data that are not missing completely at random a general latent variable model is given which includes the specification of a missing data mechanism this framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data here missing completely at random is not a prerequisite for unbiased estimation in large samples as when using the traditional listwise or pairwise present data approaches the theory is connected with old and new results in the area of selection and factorial invariance it is pointed out that in many applications maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software such as lisrel and liscomp several sets of artifical data are generated within the general model framework the proposed estimator is compared to the two traditional ones and found superior

newton s method and periodic solutions of nonlinear wave equations we prove the existence of periodic solutions of the nonlinear wave equation satisfying either dirichlet or periodic boundary conditions on the interval o the coefficients of the eigenfunction expansion of this equation satisfy a nonlinear functional equation using a version of newton s method we show that this equation has solutions provided the nonlinearity g x u satisfies certain generic conditions of nonresonance and genuine nonlinearity 1993 john wiley sons inc

complicated dynamics of scalar reaction diffusion equations with a nonlocal term we consider the dynamics of scalar equations ut uxx f x u c x u 0 x l where denotes some weighted spatial average and dinchlet boundary conditions are assumed prescribing f c appropriately it is shown that complicated dynamics can occur specifically linearisations at equilibria can have any number of purely imaginary eigenvalues moreover the higher order terms of the reduced vector field in an associated centre manifold can be prescribed arbitrarily up to any finite order these results are in marked contrast with the case 0 where bounded solutions are known to converge to equilibrium

finite controllability of infinite dimensional quantum systems quantum phenomena of interest in connection with applications to computation and communication often involve generating specific transfers between eigenstates and their linear superpositions for some quantum systems such as spin systems the quantum evolution equation the schrodinger equation is finite dimensional and old results on controllability of systems defined on on lie groups and quotient spaces provide most of what is needed insofar as controllability of non dissipative systems is concerned however in an infinite dimensional setting controlling the evolution of quantum systems often presents difficulties both conceptual and technical in this paper we present a systematic approach to a class of such problems for which it is possible to avoid some of the technical issues in particular we analyze controllability for infinite dimensional bilinear systems under assumptions that make controllability possible using trajectories lying in a nested family of pre defined subspaces this result which we call the finite controllability theorem provides a set of sufficient conditions for controllability in an infinite dimensional setting we consider specific physical systems that are of interest for quantum computing and provide insights into the types of quantum operations gates that may be developed

analysis of residuals for the multinomial item response model using the item response model as developed on the multinomial distribution asymptotic variances are obtained for residuals associated with response patterns and first and second order marginal frequencies of manifest variables when the model does not fit well an examination of these residuals may reveal the source of the poor fit finally a limited information test of fit for the model is developed by using residuals defined for the first and second order marginals model evaluation based on residuals for these marginals is particularly useful when the response pattern frequencies are sparse

a comparison of three simple test theory models in very simple test theory models such as the rasch model a single parameter is used to represent the ability of any examinee or the difficulty of any item simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available and are themselves of real practical value for small or even medium samples they can also serve a normative role in test design as an alternative to the rasch model or the rasch model with a correction for guessing a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference this model provides a natural account of guessing and has other useful things to contribute as well it also offers an alternative to the rasch model with the usual correction for guessing the three models are compared in terms of statistical properties and fits to actual data the goal of the paper is to widen the range of minimal models available to test analysts

image restoration via the adaptive tvp regularization abstract to keep structures in the restoration problem is very important via coupling the local information of the image with the proposed model in this paper we propose a local self adaptive l p regularization model for p 0 2 based on the total variation scheme where the choice of p depends on the local structures described by the eigenvalues of the structure tensor since the proposed model as the classic l p problem unifies two classes of optimization problems such as the nonconvex and nonsmooth problem when p 0 1 and the convex and smooth problem when p 1 2 it is generally challenging to find a ready algorithmic framework to solve it here we propose a new and robust numerical method via coupling with the half quadratic scheme and the alternating direction method of multipliers admm the convergence of the proposed algorithm is established and the numerical experiments illustrate the possible advantages of the proposed model and numerical methods over some existing variational based models and methods

high dimensional maximum marginal likelihood item factor analysis by adaptive quadrature although the bock aitkin likelihood based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations a serious limitation of the method is its reliance on fixed point gauss hermite g h quadrature in the solution of the likelihood equations and likelihood ratio tests when the number of latent dimensions is large computational considerations require that the number of quadrature points per dimension be few but with large numbers of items the dispersion of the likelihood given the response pattern becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space in this paper we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data in particular we show that adaptive g h quadrature combined with mean and covariance adjustments at each iteration of an em algorithm produces an accurate fast converging solution with as few as two points per dimension evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions unlike an earlier application of adaptive gibbs sampling to this problem by meng and schilling the simulations also confirm the validity of the present method in calculating likelihood ratio chi square statistics for determining the number of factors required in the model finally we apply the method to a sample of real data from a test of teacher qualifications

controllability of a quantum particle in a moving potential well we consider a nonrelativistic charged particle in a 1d moving potential well this quantum system is subject to a control which is the acceleration of the well it is represented by a wave function solution of a schrodinger equation the position of the well together with its velocity we prove the following controllability result for this bilinear control system given 0 close enough to an eigenstate and f close enough to another eigenstate the wave function can be moved exactly from 0 to f in finite time moreover we can control the position and the velocity of the well our proof uses moment theory a nash moser implicit function theorem the return method and expansion to the second order

compact gravity inversion we present a new criterion for the inversion of gravity data the principle employed is to minimize the volume of the causative body which is equivalent to maximizing its compactness the anomalous density distribution is obtained using an iterative technique which is numerically stable and rapidly convergent the principle can also be adapted to include modeling of gravity anomalies by single density sources the advantage of this approach is that desirable geologic characteristics are automatically incorporated into the model with a minimum of subjective judgments on the part of the interpreter the treatment of noise in the data fits naturally into the formulation of the inversion procedure the method is illustrated by the inversion of noise free and noisy data generated from a two dimensional model consisting of a regular array of identical rectangular blocks whose densities can be individually specified in every case the algorithm successfully recovers the correct density distribution from the dat

periodic and quasi periodic solutions of nonlinear wave equations via kam theory in this paper the nonlinear wave equation u u u xx v x u x t varepsilon u 3 x t 0 is studied it is shown that for a large class of potentials v x one can use kam methods to construct periodic and quasi periodic solutions in time for this equation

on the uniqueness of the inverse potential problem for homogeneous polyhedrons the uniqueness of a homogeneous polyhedron as determined from its exterior newtonian potential has been studied as a result of the special apparatus developed in this paper the two dimensional research methods could be applied to study three dimensional cases

robust steering of n level quantum systems robust open loop steering of a finite dimensional quantum system is a central problem in a growing number of applications of information engineering in this note we reformulate the problem in the classical control theoretic setting and provide a precise definition of robustness of the control strategy we then discuss and compare some significant problems from nuclear magnetic resonance in the light of the given definition we obtain quantitative results that are consistent with the qualitative ones available in the physics literature

a spillover phenomenon in the optimal location of actuators in this paper we are interested in finding the optimal location and shape of the actuators in a stabilization problem namely we consider the one dimensional wave equation damped by an internal feedback supported on a subdomain omega of given length the criterion we want to optimize represents the rate of decay of the total energy of the system it theoretically involves all the eigenmodes of the operator from an engineering point of view it seems more realistic to consider only a finite number of modes say the n first ones in that context we are able to prove existence and uniqueness of an optimal domain omega n it is the better possible location for the actuators we characterize this optimal domain and we point out the following strange phenomenon at least for small lengths the optimal domain omega n which is the better one for the n first modes is actually the worse one for the n 1th mode this looks like the well known spillover phenomenon in control theory at last we will give some possible extension and open problems in higher dimension

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

approximate controllability exact controllability and conical eigenvalue intersections for quantum mechanical systems we study the controllability of a closed control affine quantum system driven by two or more external fields we provide a sufficient condition for controllability in terms of existence of conical intersections between eigenvalues of the hamiltonian in dependence of the controls seen as parameters such spectral condition is structurally stable in the case of three controls or in the case of two controls when the hamiltonian is real the spectral condition appears naturally in the adiabatic control framework and yields approximate controllability in the infinite dimensional case in the finite dimensional case it implies that the system is lie bracket generating when lifted to the group of unitary transformations and in particular that it is exactly controllable hence lie algebraic conditions are deduced from purely spectral properties

on the essential spectrum of schrodinger operators abstract an extension of the theorem of hunziker van winter zhislin on the location of the essential spectrum of many body hamiltonians

prevalence a translation invariant almost every on infinite dimensional spaces we present a measure theoretic condition for a property to hold almost everywhere on an infinite dimensional vector space with particularemphasis on function spaces such as c k and l p like the concept of lebesgue almost every on an infinite dimensional spaces our notion of prevalence is translation invariant instead of using a specific measure on the entire space we define prevalence in terms of the class of all probability measures with compact support prevalence is a more appropriate condition than the topological concepts of open and dense or generic when one desires a probabilistic result on the likelihood of a given property on a function space

a model for evaluating sensitivity and specificity for correlated diagnostic tests in efficacy studies with an imperfect reference test abstract the purpose of a diagnostic efficacy study is to evaluate and compare the sensitivities and specificities of several diagnostic tests usually the diagnostic tests are correlated conditional on disease status and the reference test is subject to error in the chlamydia trachomatis study five screening tests for detecting chlamydia in endocervical specimens were compared the five tests are correlated and the reference test the cell culture test has less than 100 sensitivity the conventional method ignores both the correlations between the tests and the misclassification of the reference test and thus cannot provide a valid analysis we propose a model to evaluate and compare the sensitivities and specificities of correlated diagnostic tests when there is either an imperfect reference test or even no reference test the model also can estimate the effects of covariates it is a generalized linear mixed model with two unobserved variables one continuous and one dichotomous we use a hybrid

gravity inversion using open reject and shape of anomaly fill criteria a gravity inversion method is developed by iteratively applying open reject and fill o r f criteria within a model space comprising a great many rectangular prisms each prism is assigned a density contrast the modeling procedure consists of filling some prisms while leaving others empty only one element is filled for each pass generally elements are added only to the periphery of the growing model models can be allowed to grow in any combination of directions or in all directions by application of a shape of anomaly fill criterion the model rapidly attains a form which yields gravity approximating the given gravity scaled down by some constant factor as the model continues to grow this scale factor approaches unity the method readily yields inverse models comprising several thousand individual prisms examples presented here give applications to 2 d problems the method is readily applicable to 212 d and 3 d problems as well overhanging elements are obtained by appropriate use of model

the dutch identity a new tool for the study of item response models the dutch identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions irfs and the latent trait distribution the identity may be exploited in several ways for example a to suggest how item response models behave for large numbers of items they are approximate submodels of second order loglinear models for 2 j tables b to suggest new ways to assess the dimensionality of the latent trait principle components analysis of matrices composed of second order interactions from loglinear models c to give insight into the structure of latent class models and d to illuminate the problem of identifying the irfs and the latent trait distribution from sample data

sensitivity analysis for problems of dynamic stability abstract in mechanics as well as in physics the most general and important thing is to study the dependence of the characteristics of a physical process on problem parameters problems of dynamic stability for non conservative systems involve determination of eigenvalues and eigenvectors for these problems it is shown in general how the different sensitivity analyses can be performed without any new eigenvalue analyses the main question relates to the change in flutter load as a function of change in stiffness mass boundary conditions or load distribution discretized as well as non discretized examples are presented in details

existence of quasiperiodic solutions of elliptic equations on rn 1 via center manifold and kam theorems abstract we consider elliptic equations on r n 1 of the form 1 x u u y y g x u 0 x y r n r where g x u is a sufficiently regular function with g 0 0 we give sufficient conditions for the existence of solutions of 1 which are quasiperiodic in y and decaying as x uniformly in y such solutions are found using a center manifold reduction and results from the kam theory we discuss several classes of nonlinearities g to which our results apply

v i arnold s conjecture on avoidance of intersection hausdorff codimension and a structure theorem for finite index maps abstract the functional analytic approach taken in this work gives a geometric description of the image of a smooth finite index map between hilbert spaces and solves avoidance of intersection problems an application of this work extends from finite to infinite dimensions the results of von neumann and wigner in finite dimensions on the avoidance of intersection problems in physics the present work solves v i arnold s conjecture on avoidance of intersection the solution depends on determining the size of the image of a finite index map between infinite dimensional separable hilbert spaces we define the hausdorff codimension of subsets of infinite dimensional linear space hausdorff codimension measures the metric size of subsets of an infinite dimensional linear space and includes previous descriptions by b white and others on the size of sets we apply hausdorff codimension to finite index maps and establish a structure theorem for these maps that includes smale s extension of sard s theorem an application of the structure theorem to the avoidance of intersection problem determines the metric size of a set of functions whose images intersect a given countable union of smooth submanifolds each with codimension at least two

complicated dynamics of parabolic equations with simple gradient dependence let q c jr2 be a smooth bounded domain given positive integers n k and ql 0 x y y u 01 1 1 t o x s c 9q where a x y and al x y are smooth functions by refining and extending previous results of polaik we show that arbitrary k jets of vector fields in rn can be realized in equations of the form e in particular taking ql 1 we see that very complicated chaotic behavior is possible for reaction diffusionconvection equations with linear dependence on vu introduction let q c r2 be a smooth bounded domain we consider the semilinear parabolic equation ut uxx uyy 4a x y u f x y u uy t o x y e q u 0 t 0 x y e where a 1r2 r is continuous and f r4 r x y s w f x y s w is a smooth function more precisely f is continuous together with all its partial derivatives with respect to s w set x lp q p 2 and let a w2p q nwo p q x be the linear operator defined as au uxx uyy a x y u being a sectorial operator a generates the family x a 0 of fractional power spaces choosing a with 2 p a 1 we have that x c c01 q with continuous p inclusion define the nemitski operator f x x by f u x y f x y 2 x y uy x y received by the editors may 16 1996 1991 mathematics subject classification primary 35k20 secondary 35b40

asymptotic standard errors of irt observed score equating methods a method of the irt observed score equating using chain equating through a third test without equating coefficients is presented with the assumption of the three parameter logistic model the asymptotic standard errors of the equated scores by this method are obtained using the results given by m liou and p e cheng the asymptotic standard errors of the irt observed score equating method using a synthetic examinee group with equating coefficients which is a currently used method are also provided numerical examples show that the standard errors by these observed score equating methods are similar to those by the corresponding true score equating methods except in the range of low scores

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

the turnpike property in finite dimensional nonlinear optimal control turnpike properties have been established long time ago in finite dimensional optimal control problems arising in econometry they refer to the fact that under quite general assumptions the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces the first and the last of which being transient short time arcs and the middle piece being a long time arc staying exponentially close to the optimal steady state solution of an associated static optimal control problem we provide in this paper a general version of a turnpike theorem valuable for nonlinear dynamics without any specific assumption and for very general terminal conditions not only the optimal trajectory is shown to remain exponentially close to a steady state but also the corresponding adjoint vector of the pontryagin maximum principle the exponential closedness is quantified with the use of appropriate normal forms of riccati equations we show then how the property on the adjoint vector can be adequately used in order to initialize successfully a numerical direct method or a shooting method in particular we provide an appropriate variant of the usual shooting method in which we initialize the adjoint vector not at the initial time but at the middle of the trajectory

bayesian estimation of a multilevel irt model using gibbs sampling in this article a two level regression model is imposed on the ability parameters in an item response theory irt model the advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error another advantage is that contrary to observed scores latent scores are test independent which offers the possibility of using results from different tests in one analysis where the parameters of the irt model and the multilevel model can be concurrently estimated the two parameter normal ogive model is used for the irt measurement model it will be shown that the parameters of the two parameter normal ogive model and the multilevel model can be estimated in a bayesian framework using gibbs sampling examples using simulated and real data are given

weighted likelihood estimation of ability in item response theory applications of item response theory which depend upon its parameter invariance property require that parameter estimates be unbiased a new method weighted likelihood estimation wle is derived and proved to be less biased than maximum likelihood estimation mle with the same asymptotic variance and normal distribution wle removes the first order bias term from mle two monte carlo studies compare wle with mle and bayesian modal estimation bme of ability in conventional tests and tailored tests assuming the item parameters are known constants the monte carlo studies favor wle over mle and bme on several criteria over a wide range of the ability scale

practical applications of uniqueness theorems in gravimetry part i constructing sound interpretation methods to obtain a unique and stable solution to the gravity inverse problem a priori information reflecting geological attributes of the gravity source must be used mathematical conditions to obtain stable solutions are established in tikhonov s regularization method where the a priori information is introduced via a stabilizing functional which may be suitably designed to incorporate some relevant geological information however there is no unifying approach establishing general uniqueness conditions for a gravity inverse problem rather there are many theorems usually establishing just abstract mathematical conditions and making it difficult to devise the type of geological information needed to guarantee a unique solution in part i of these companion papers we show that translating the mathematical uniqueness conditions into geological constraints is an important step not only in establishing the type of geological setting where a particular method may be applied but also in designing new gravity inv

adiabatic control of the schrodinger equation via conical intersections of the eigenvalues in this paper we present a constructive method to control the bilinear schrodinger equation via two controls the method is based on adiabatic techniques and works if the spectrum of the hamiltonian admits eigenvalue intersections and if the latter are conical as it happens generically in this framework we are able to spread on several levels connected by conical intersections a state initially concentrated in a single energy level we provide sharp estimates on the dependence of the error with respect to the controllability time moreover we identify some special curves in the space of controls that improve the precision of the adiabatic approximation when passing through conical intersections with respect to classical adiabatic theory

probability matrix decomposition models in this paper we consider a class of models for two way matrices with binary entries of 0 and 1 first we considerboolean matrix decomposition conceptualize it as alatent response model lrm and by making use of this conceptualization generalize it to a larger class of matrix decomposition models second probability matrix decomposition pmd models are introduced as a probabilistic version of this larger class of deterministic matrix decomposition models third an algorithm for the computation of the maximum likelihood ml and the maximum a posteriori map estimates of the parameters of pmd models is presented this algorithm is an em algorithm and is a special case of a more general algorithm that can be used for the whole class of lrms and fourth as an example a pmd model is applied to data on decision making in psychiatric diagnosis

practical applications of uniqueness theorems in gravimetry part ii pragmatic incorporation of concrete geologic information we illustrate the importance of establishing solution uniqueness through mathematical restrictions reflecting a source attribute we also illustrate the validity and utility of a guideline derived in an accompanying paper for constructing sound gravity inversion methods for the class of sources presenting either homogeneous or depth independent density distributions the two part guideline is 1 to introduce a priori information favoring uniqueness either by assuming that a nonnull density distribution depending only on x and y is confined to the interior of a horizontal slab with known position or by limiting the class of possible solutions to homogeneous simply connected polygons or polyhedra with known density displaying no fancy shapes and no curling apophyses at their borders and 2 to introduce information favoring solution stability by estimating only the features of the source which may be resolved by the data following the guideline we apply different methods to gravity data using interp

multi input schrodinger equation controllability tracking and application to the quantum angular momentum abstract we present a sufficient condition for approximate controllability of the bilinear discrete spectrum schrodinger equation in the multi input case the controllability result extends to simultaneous controllability approximate controllability in h s and tracking in modulus the sufficient condition is more general than those present in the literature even in the single input case and allows the spectrum of the uncontrolled operator to be very degenerate e g to have multiple eigenvalues or equal gaps among different pairs of eigenvalues we apply the general result to a rotating polar linear molecule driven by three orthogonal external fields a remarkable property of this model is the presence of infinitely many degeneracies and resonances in the spectrum

collapse of the keldysh chains and stability of continuous nonconservative systems in the present paper eigenvalue problems for non self adjoint linear differential operators smoothly dependent on a vector of real parameters are considered bifurcation of eigenvalues along smooth curves in the parameter space is studied the case of a multiple eigenvalue with the keldysh chain of arbitrary length is investigated explicit expressions describing bifurcation of eigenvalues are found the obtained formulas use eigenfunctions and associated functions of the adjoint eigenvalue problems as well as the derivatives of the differential operator taken at the initial point of the parameter space these results are important for the stability problems and sensitivity analysis of nonconservative systems as a mechanical application the extended beck problem of stability of an elastic column subjected to a partially tangential follower force is considered and discussed in detail

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

some generic properties of schrodinger operators with radial potentials we consider a class of schrodinger operators on with radial potentials viewing them as self adjoint operators on the space of radially symmetric functions in we show that the following properties are generic with respect to the potential p1 the eigenvalues below the essential spectrum are nonresonant i e rationally independent and so are the square roots of the moduli of these eigenvalues p2 the eigenfunctions corresponding to the eigenvalues below the essential spectrum are algebraically independent on any nonempty open set the genericity means that in suitable topologies the potentials having the above properties form a residual set as we explain p1 p2 are prerequisites for some applications of kam type results to nonlinear elliptic equations similar properties also play a role in optimal control and other problems in linear and nonlinear partial differential equations

semiparametric bayesian inference in autoregressive panel data models this paper develops bayesian methods for inference in dynamic panel data models with individual effects and applies them to study longitudinal data on earnings from the panel study of income dynamics psid we study semiparametric versions of commonly used random effects autoregressive models in which the distribution of the disturbances is not restricted to fall in a parametric class to model the unknown distributions without resorting to strong parametric assumptions we draw upon recent advances in the theory and computation of nonparametric bayesian models using dirichlet process priors the overall approach can be viewed as an application of the general semiparametric bayesian approach of west muller and escobar 1994 which in turn makes use of results on bayesian density estimation by escobar 1994 and escobar and west 1995 most conventional panel data methods e g anderson and hsiao 1981 macurdy

on the approximation of the quadratic exponential distribution in a latent variable context summary following cox wermuth 1994 2002 we show that the distribution of a set of binary observable variables induced by a certain discrete latent variable model may be approximated by a quadratic exponential distribution this discrete latent variable model is equivalent to the latent class version of the two parameter logistic model of birnbaum 1968 which may be seen as a generalized version of the rasch model rasch 1960 1961 on the basis of this result we develop an approximate maximum likelihood estimator of the item parameters of the two parameter logistic model which is very simply implemented the proposed approach is illustrated through an example based on a dataset on educational assessment

gravity and magnetic inversion with minimization of a specific functional the nonuniqueness of gravity or magnetic data inversion is well known in order to remove ambiguity some authors have sought solutions minimizing a functional describing geometrical or physical properties last and kubik 1983 in particular developed a method explaining the observed anomaly by structures of minimum volume in this method the domain where anomalous sources are searched is divided into elementary prisms of a constant density or susceptibility contrast each elementary contrast is allowed to vary individually thus a contrast distribution is computed the search for this kind of solution leads in general to geologically more appropriate bodies but exceptions do occur in this paper the technique is broadened to include the search for solutions minimizing the moment of inertia with respect to the center of gravity or with respect to a given dip line passing through it the resulting structures are both deeper and more compact precisely as is required in specific cases theoretical and

controllability for distributed bilinear systems this paper studies controllability of systems of the form dw dt mathcal a w p t mathcal b w where mathcal a is the infinitesimal generator of a c 0 semigroup of bounded linear operators e mathcal a t on a banach space x mathcal b x to x is a c 1 map and p in l 1 0 t mathbb r is a control the paper i gives conditions for elements of x to be accessible from a given initial state w 0 and ii shows that controllability to a full neighborhood in x of w 0 is impossible for dim x infty examples of hyperbolic partial differential equations are provided

projective hilbert space structures at exceptional points a non hermitian complex symmetric 2 2 matrix toy model is used to study projective hilbert space structures in the vicinity of exceptional points eps the bi orthogonal eigenvectors of a diagonalizable matrix are puiseuxexpanded in terms of the root vectors at the ep it is shown that the apparent contradiction between the two incompatible normalization conditions with finite and singular behaviour in the ep limit can be resolved by projectively extending the original hilbert space the complementary normalization conditions correspond then to two different affine charts of this enlarged projective hilbert space geometric phase and phase jump behaviour are analysed and the usefulness of the phase rigidity as measure for the distance to ep configurations is demonstrated finally ep related aspects of pt symmetrically extended quantum mechanics are discussed and a conjecture concerning the quantum brachistochrone problem is formulated

on the number of mather measures of lagrangian systems in 1996 ricardo ricardo mane discovered that mather measures are in fact the minimizers of a universal infinite dimensional linear programming problem this fundamental result has many applications of which one of the most important is to the estimates of the generic number of mather measures mane obtained the first estimation of that sort by using finite dimensional approximations recently we were able with gonzalo contreras to use this method of finite dimensional approximation in order to solve a conjecture of john mather concerning the generic number of mather measures for families of lagrangian systems in the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem we use a notion of countably rectifiable sets of finite codimension in banach and frechet spaces which may deserve independent interest

binary programming and test design an algorithmic approach to test design using information functions is presented the approach uses a special branch of linear programming i e binary programming in addition results of some benchmark problems are presented within the same framework it is also possible to formulate the problem of individualized testing

propagation through conical crossings an asymptotic semigroup we consider the standard model problem for a conical intersection of electronic surfaces in molecular dynamics our main result is the construction of a semi group in order to approximate the wigner function associated with the solution of the schrodinger equation at leading order in the semiclassical parameter the semigroup stems from an underlying markov process that combines deterministic transport along classical trajectories within the electronic surfaces and random jumps between the surfaces near the crossing our semigroup can be viewed as a rigorous mathematical counterpart of so called trajectory surface hopping algorithms which are of major importance in molecular simulations in chemical physics the key point of our analysis the incorporation of the nonadiabatic transitions is based on the landau zener type formula of fermanian kammerer and gerard10 for the propagation of two scale wigner measures through conical crossings 2005 wiley periodicals inc

hermitian matrices depending on three parameters coalescing eigenvalues abstract we consider hermitian matrix valued functions depending on three parameters that vary in a bounded surface of r 3 we study how to detect when such functions have coalescing eigenvalues inside this surface our criterion to locate these singularities is based on a construction suggested by stone 20 for generic coalescings any such singularity is related to a particular accumulation of a certain phase or lack thereof as we cover the surface

supersonic flutter analysis of composite plates and shells a high precision doubly curved quadrilateral thin shell finite element is used the composite material property is included using classical lamination theory and the supersonic aerodynamic effect is included using linearized piston theory the normal modes approach is adopted results are presented for composite plates and curved panels and composite cylindrical and conical shells parametric studies concerning the effects of boundary conditions fiber orientation degree of orthotropy and flow angle on the flutter characteristics are presented

nonparametric priors for ordinal bayesian social science models specification and estimation a generalized linear mixed model ordered probit is used to estimate levels of stress in presidential political appointees as a means of understanding their surprisingly short tenures a bayesian approach is developed where the random effects are modeled with a dirichlet process mixture prior allowing for useful incorporation of prior information but retaining some vagueness in the form of the prior applications of bayesian models in the social sciences are typically done with uninformative priors although some use of informed versions exists there has been disagreement over this and our approach may be a step in the direction of satisfying both camps we give a detailed description of the data show how to implement the model and describe some interesting conclusions the model utilizing a nonparametric prior fits better and reveals more information in the data than standard approaches

on the controllability of quantum transport in an electronic nanostructure we investigate the controllability of quantum electrons trapped in a two dimensional device typically a metal oxide semiconductor mos field effect transistor the problem is modeled by the schrodinger equation in a bounded domain coupled to the poisson equation for the electrical potential the controller acts on the system through the boundary condition on the potential on a part of the boundary modeling the gate we prove that generically with respect to the shape of the domain and boundary conditions on the gate the device is controllable we also consider control properties of a more realistic nonlinear version of the device taking into account the self consistent electrostatic poisson potential

semiparametric bayesian estimation for marginal parametric potential outcome modeling application to causal inference we propose a new semiparametric bayesian model for causal inference in which assignment to treatment depends on potential outcomes the model uses the probit stick breaking process mixture proposed by chung and dunson 2009 a variant of the dirichlet process mixture modeling in contrast to previous bayesian models the proposed model directly estimates the parameters of the marginal parametric model of potential outcomes while it relaxes the strong ignorability assumption and requires no parametric model assumption for the assignment model and conditional distribution of the covariate vector the proposed estimation method is more robust than maximum likelihood estimation in that it does not require knowledge of the full joint distribution of potential outcomes covariates and assignments in addition the method is more efficient than fully nonparametric bayes methods we apply this model to infer the differential effects of cognitive and noncognitive skills on the wages of production and nonprodu

high dimensional multivariate probit analysis a computationally practical form of probit analysis for multiple response variables based on an assumed common factor model for the latent tolerances is proposed numerical integration over the factor space provides maximum likelihood estimation of the probit regression parameters and of the probabilities of response combinations under the model the procedure is applied to five variables from the pneumoconiosis field trial two variables of which were previously analyzed by ashford and sowden 1970 biometrics 26 535 546

coupling of eigenvalues of complex matrices at diabolic and exceptional points the paper presents a general theory of coupling of eigenvalues of complex matrices of an arbitrary dimension depending on real parameters the cases of weak and strong coupling are distinguished and their geometric interpretation in two and three dimensional spaces is given general asymptotic formulae for eigenvalue surfaces near diabolic and exceptional points are presented demonstrating crossing and avoided crossing scenarios two physical examples illustrate effectiveness and accuracy of the presented theory

linear inversion of gravity data for 3 d density distributions we have developed an improved levenburg marquart technique to rapidly invert bouguer gravity data for a 3 d density distribution as a source of the observed field this technique is designed to replace tedious forward modeling with an automatic solver that determines density models constrained by geologic information supplied by the user where such information is not available objective models are generated the technique estimates the density distribution within the source volume using a least squares inverse solution that is obtained iteratively by singular value decomposition using orthogonal decomposition of matrices with sequential householder transformations the source volume is subdivided into a series of right rectangular prisms of specified size but of unknown density this discretization allows the construction of a system of linear equations relating the observed gravity field to the unknown density distribution convergence of the solution to the system is tightly controlled by a damping pa

birkhoff normal form for partial differential equations with tame modulus we prove an abstract birkhoff normal form theorem for hamiltonian partial differential equations pdes the theorem applies to semilinear equations with nonlinearity satisfying a property that we call tame modulus such a property is related to the classical tame inequality by moser in the nonresonant case we deduce that any small amplitude solution remains very close to a torus for very long times we also develop a general scheme to apply the abstract theory to pdes in one space dimensions and we use it to study some concrete equations nonlinear wave nlw equation nonlinear schrodinger nls equation with different boundary conditions an application to an nls equation on the d dimensional torus is also given in all cases we deduce bounds on the growth of high sobolev norms in particular we get lower bounds on the existence time of solutions