detecting the presence of mixing with multiscale maximum likelihood a test of homogeneity tries to decide whether observations come from a single distribution or from a mixture of several distributions a powerful theory has been developed for the case where the component distributions are members of an exponential family when no parametric assumptions are appropriate the standard approach is to test for bimodality which is known not to be very sensitive for detecting heterogeneity to develop a more sensitive procedure this article builds on an approach employed in sampling literature and models the component distributions as logarithmically concave densities it is shown how this leads to a special semiparametric model in which the homogeneity problem is equivalent to testing whether a parameter c equals zero versus the alternative that c 0 this setup leads naturally to a novel multiscale maximum likelihood procedure where the multiscale character reflects the desirable property of adaptivity to the unknown value of the parameter c under the alternative to en

the topology on the primitive ideal space of transformation group c algebras and c c r transformation group c algebras if g 8 is a second countable transformation group and the stability groups are amenable then c g 8 is c c r if and only if the orbits are closed and the stability groups are c c r in addition partial results relating closed orbits to c c r algebras are obtained in the nonseparable case in several cases the topology of the primitive ideal space is calculated explicitly in particular if the stability groups are all contained in a fixed abelian subgroup h then the topology is computed in terms of h and the orbit structure provided c g 8 and c h 8 are eh regular these conditions are automatically met if g is abelian and g 8 is second countable

classical limits of unbounded quantities by strict quantization this paper extends the tools of c algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories we introduce the approach first in the simple case of finite systems then we apply this approach to analyze the classical limits of unbounded quantities in bosonic quantum field theories with particular attention to number operators and hamiltonians the methods take classical limits in a representation independent manner and so allow one to compare quantities appearing in inequivalent fock space representations

moyal quantization of 2 1 dimensional galilean systems stratonovich weyl kernels are constructed for some of the coadjoint orbits of the two dimensional extended galilean group g 2 1 as an intermediate step the unitary irreducible representations associated with a given group orbit are obtained by using the kirillov mackey theory star products are defined in the sense of moyal for functions on each of these orbits the central extension of g 2 1 with parameter k is also analyzed which results from the commutator between the generators of boosts to conclude that it originates a sort of nonrelativistic remainder of the thomas precession

high order exactly well balanced numerical methods for shallow water systems abstract this paper is concerned with the development of high order methods for the shallow water system that preserve every stationary solution of the system and not only the water at rest ones the pursued strategy is based on the generalized hydrostatic reconstruction introduced in 10 and on the technique proposed in 8 to obtain high order well balanced reconstruction operators the more difficult step in the reconstruction procedure is the first one given a cell value a stationary solution of the system has to be found whose average at the cell equals the given value the implementation of this step is discussed in detail as well as the similarities and differences with some previous approaches to obtain well balanced methods for the shallow water system finally the well balanced properties of the developed numerical methods are checked in some test cases

equivariant deformations of homogeneous spaces abstract c algebraic deformations of homogeneous spaces g are constructed by completing dense subspaces of c 0 g in a different multiplication and c norm these deformations are equivariant in the sense that they still carry a natural action of g by left translation the motivating examples are the noncommutative heisenberg manifolds of rieffel but the construction given here is based on the authors twisted dual group algebras which are equivariant deformations of c 0 g the procedure is general enough to give other recently studied families of noncommutative spaces and some interesting new examples of simple c algebras

moment based oscillation properties of mixture models consider finite mixture models of the form g x q f f x dq where f is a parametric density and q is a discrete probability measure an important and difficult statistical problem concerns the determination of the number of support points usually known as components of q from a sample of observations from g for an important class of exponential family models we have the following result if p has more than p components and q is an appropriately chosen p component approximation of p then g x p g x q demonstrates a prescribed sign change behavior as does the corresponding difference in the distribution functions these strong structural properties have implications for diagnostic plots for the number of components in a finite mixture

equipartition of the eigenfunctions of quantized ergodic maps on the torus we give a simple proof of the equipartition of the eigenfunctions of a class of quantized ergodic area preserving maps on the torus examples are the irrational translations the skew translations the hyperbolic automorphisms and some of their perturbations

a godunov type method for the shallow water equations with discontinuous topography in the resonant regime abstract we investigate the riemann problem for the shallow water equations with variable and possibly discontinuous topography and provide a complete description of the properties of its solutions existence uniqueness in the non resonant regime multiple solutions in the resonant regime this analysis leads us to a numerical algorithm that provides one with a riemann solver next we introduce a godunov type scheme based on this riemann solver which is well balanced and of quasi conservative form finally we present numerical experiments which demonstrate the convergence of the proposed scheme even in the resonance regime except in the limiting situation when riemann data precisely belong to the resonance hypersurface

pull backs of algebras and crossed products by certain diagonal actions let g be a locally compact group and p q t a principal g bundle if a is a c algebra with primitive ideal space t the pull back p a of a along p is the balanced tensor product co q c t a if 3 g aut a consists of c t module automorphisms and y g aut co q is the natural action then the automorphism group y 0x 3 of co q 0 a respects the balancing and induces the diagonal action p 3 of g on p a we discuss some examples of such actions and study the crossed product p a x p g we suggest a substitute d for the fixed point algebra prove p a x g is strongly morita equivalent to d and investigate the structure of d in various cases in particular we ask when d is strongly morita equivalent to a sometimes but by no means always and investigate the case where a has continuous trace let b be a c algebra and g a locally compact group acting on b as a strongly continuous automorphism group a our goal here is to study the crossed product c algebra b x g for two classes of diagonal actions for which the induced action of g on b is free the first class includes actions of the form y 0x3 on b co q 0 a where p q t is a principal g bundle y is the dual action of g on co q and 3 g aut a is an action of g on another c algebra a we also consider diagonal actions on algebras which are the pull backs of another algebra a along a principal bundle p q t if a is a c algebra with primitive ideal space t then the pull back p a is the balanced tensor product co q cb t a when 3 g aut a consists of c t module automorphisms the product action ty 0 3 preserves the balancing and the diagonal action p 3 is by definition the induced action on p a in general if f x y and q prima y are continuous then cb y acts on co x by composition with f and on a by composition with q and the daunshofmann theorem we can therefore define the pull back f a of a along f as the c algebraic tensor product co x cb y a the reason for the name is that when a is the algebra of sections of some c bundle e over y there is a natural isomorphism of f a onto the algebra of sections of the pull back f e in 1 we discuss this and other basic properties of pull backs and give some evidence to show they are likely to be of interest in particular we show that if g is abelian and a g aut a is locally unitary in the sense of 18 then the crossed product received by the editors october 20 1983 and in revised form february 15 1984 1980 mathematics subject classification primary 46l40 46l55

leaf preserving quantizations of poisson su 2 are not coalgebra homomorphisms although it has been found that some deformation quantizations of the poissonsu 2 preserve symplectic leaves and some preserve the group i e coalgebra operation this paper shows that a quantization ofsu 2 cannot be both leaf preserving and group preserving

tannaka krein duality for compact matrix pseudogroups twisted su n groups the notion of concrete monoidalw category is introduced and investigated a generalization of the tannaka krein duality theorem is proved it leads to new examples of compact matrix pseudogroups among them we have twistedsu n groups denoted bys u n it is shown that the representation theory fors u n is similar to that ofsu n irreducible representations are labeled by young diagrams and formulae for dimensions and multiplicity are the same as in the classical case

multiscale maximum likelihood analysis of a semiparametric model with applications a special semiparametric model for a univariate density is introduced that allows analyzing a number of problems via appropriate transformations two problems treated in some detail are testing for the presence of a mixture and detecting a wear out trend in a failure rate the analysis of the semiparametric model leads to an approach that advances the maximum likelihood theory of the grenander estimator to a multiscale analysis the construction of the corresponding test statistic rests on an extension of a result on a two sided brownian motion with quadratic drift to the simultaneous control of excursions under parabolas at various scales of a brownian bridge the resulting test is shown to be asymptotically optimal in the minimax sense regarding both rate and constant and adaptive with respect to the unknown parameter in the semiparametric model the performance of the method is illustrated with a simulation study for the failure rate problem and with data from a flow cytometry experiment for the mixture analysis

homogeneity tests against central mixture alternatives abstract a test of homogeneity is derived for a general sampling model the alternative hypothesis is a mixture over a parameter of the sampling model centered at the null hypothesis the test statistic is derived through a score test its functional form is independent of the particular mixing distribution suppose yi i 1 n are independent random variables with respective probability density or mass functions fi yi i under the null hypothesis suppose all i homogeneous and equal to the common value 0 under the alternative hypothesis suppose the i behave as random samples taken from a distribution with mean 0 and finite third moment the score statistic for testing these hypotheses rejects the null for large values of where is the maximum likelihood estimate of 0 under the null hypothesis and when the sample size n is large s is normally distributed under both the null hypothesis and a sequence of alternative hypotheses in which the variance of the mixing distribution tends

quantum mechanics on p adic numbers a quantum system with positions in and momenta in is studied displacement operators in the phase space of this system and the corresponding heisenberg weyl group are studied it is shown that such a system can be constructed from a semi infinite chain of spins which are coupled in a particular way

alternative em methods for nonparametric finite mixture models summary this research focuses on a general class of maximum likelihood problems in which it is desired to maximise a nonparametric mixture likelihood with finitely many known component densities over the set of unknown weight parameters convergence of the conventional em algorithm for this problem is extremely slow when the component densities are poorly separated and when the maximum likelihood estimator requires some of the weights to be zero as the algorithm can never reach such a boundary point alternative methods based on the principles of em are developed using a two stage approach first a new data augmentation scheme provides improved convergence rates in certain parameter directions secondly two cyclic versions of this data augmentation are created by changing the missing data formulation between the em steps these extend the acceleration directions to the whole parameter space giving another order of magnitude increase in convergence rate examples indicate that the new cyclic versions of the data augmentation schemes can converge up to 500 times faster than the conventional em algorithm for fitting nonparametric finite mixture models

quantization on the sphere when phase space is a sphere then conventional quantization is not available and the heisenberg algebra is most naturally replaced by so 3 quantization may be carried out in terms of invariant star products this leads to the study of an interesting family of polynomials that are defined in a natural and intrinsic way on the enveloping algebra of sl 2 these polynomials are related to legendre polynomials by a reordering rule that resembles the relation between hermite polynomials and normal ordered monomials they are identified as pasternack polynomials and related to jacobi polynomials new orthogonality properties are found and interpreted in terms of unitary representations of sl 2 r and so 3

a fast and stable well balanced scheme with hydrostatic reconstruction for shallow water flows we consider the saint venant system for shallow water flows with nonflat bottom it is a hyperbolic system of conservation laws that approximately describes various geophysical flows such as rivers coastal areas and oceans when completed with a coriolis term or granular flows when completed with friction numerical approximate solutions to this system may be generated using conservative finite volume methods which are known to properly handle shocks and contact discontinuities however in general these schemes are known to be quite inaccurate for near steady states as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions this difficulty can be overcome by using the so called well balanced schemes we describe a general strategy based on a local hydrostatic reconstruction that allows us to derive a well balanced scheme from any given numerical flux for the homogeneous problem whenever the initial solver satisfies some classical stability properties it yields a simple and fast well balanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality

the riemann problem for the one dimensional free surface shallow water equations with a bed step theoretical analysis and numerical simulations in this paper the solution of the riemann problem for the one dimensional free surface shallow water equations over a bed step is analyzed both from a theoretical and a numerical point of view particular attention has been paid to the wave that is generated at the location of the bed discontinuity starting from the classical shallow water equations considering the bed level as an additional variable and adding to the system an equation imposing its time invariance we show that this wave is a contact wave across which one of the riemann invariants namely the energy is not constant this is due to the fact that the relevant problem is nonconservative we demonstrate that in this type of system riemann invariants do not generally hold in contact waves furthermore we show that in this case the equations that link the flow variables across the contact wave are the generalized rankine hugoniot relations and we obtain these for the specific problem from the numerical point of view we present an accurate and efficient solver for the step riemann problem to be used in a finite volume godunov type framework through a two step predictor corrector procedure the solver is able to provide solutions with any desired accuracy the predictor step uses a well balanced generalized roe solver while the corrector step solves the exact nonlinear system of equations that consitutes the problem by means of an iterative procedure that starts from the predictor solution in order to show the effectiveness and the accuracy of the proposed approach we consider several step riemann problems and compare the exact solutions with the numerical results obtained by using a standard roe approach far from the step and the novel two step algorithm for the fluxes over the step achieving good results

exact solution of the riemann problem for the shallow water equations with discontinuous bottom geometry in this paper we present the exact solution of the riemann problem for the non linear shallow water equations with a step like bottom the solution has been obtained by solving an enlarged system that includes an additional equation for the bottom geometry and then using the principles of conservation of mass and momentum across the step the resulting solution is unique and satisfies the principle of dissipation of energy across the shock wave we provide examples of possible wave patterns numerical solution of a first order dissipative scheme as well as an implementation of our riemann solver in the second order upwind method are compared with the proposed exact riemann problem solution a practical implementation of the proposed exact riemann solver in the framework of a second order upwind tvd method is also illustrated

quantum symmetries and the weyl wigner product of group representations in the usual formulation of quantum mechanics groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex hilbert space in accordance with wigner s theorem in the phase space formulation they have real true unitary representations in the space of square integrable functions on phase space each such phase space representation is a weyl wigner product of the corresponding hilbert space representation with its contragredient and these can be recovered by factorizing the weyl wigner product however not every real unitary representation on phase space corresponds to a group of automorphisms so not every such representation is in the form of a weyl wigner product and can be factorized the conditions under which this is possible are examined examples are presented

quantization of the poisson su 2 and its poisson homogeneous space the 2 sphere we show that deformation quantizations of the poisson structures on the poisson lie groupsu 2 and its homogeneous space the 2 sphere are compatible with woronowicz s deformation quantization ofsu 2 s group structure and podles deformation quantization of 2 sphere s homogeneous structure respectively so in a certain sense the multiplicativity of the lie poisson structure onsu 2 at the classical level is preserved under quantization

a note on overdispersed exponential families abstract the issue of creating overdispersion in a given one parameter one dimensional exponential family by extending it to a two parameter exponential family with the same support is considered an easily verifiable sufficient condition for this is derived it is shown that a large class of families satisfy this condition and that this class includes efron s 1986 and lindsay s 1986 family as special cases this class is also closely related to jorgensen s 1988 exponential dispersion models ump unbiased tests for testing overdispersion are exhibited and it is shown that in this context cox s overdispersion test is a special case a graphical display is developed to select a family of the general class which should be used with a given set of data to overdisperse a given target one parameter family two real data illustrations are given kr

positive quantization in the presence of a variable magnetic field starting with a previously constructed family of coherent states we introduce the berezin quantization for a particle in a variable magnetic field and we show that it constitutes a strict quantization of a natural poisson algebra the phase space reinterpretation involves a magnetic version of the bargmann space and leads naturally to berezin toeplitz operators

nonparametric mle under two closed capture recapture models with heterogeneity we conduct nonparametric maximum likelihood estimation under two common heterogeneous closed population capture recapture models our models specify mixture models as did previous researchers models which have a common generating distribution say f for the capture probabilities using lindsay and roeder s 1992 journal of the american statistical association 87 785 794 mixture model results and the em algorithm a nonparametric maximum likelihood estimator mle of f for any specified population size n is obtained then the nonparametric mle of the n f pair and thus for n is determined perhaps most importantly since our mle pair maximizes the likelihood under the entire nonparametric probability model it provides an excellent foundation for estimating properties of estimators conducting a goodness of fit test and performing a likelihood ratio test these are illustrated in the paper

a general theory of phase space quasiprobability distributions we present a general theory of quasiprobability distributions on phase spaces of quantum systems whose dynamical symmetry groups are finite dimensional lie groups the family of distributions on a phase space is postulated to satisfy the stratonovich weyl correspondence with a generalized traciality condition the corresponding family of the stratonovich weyl kernels is constructed explicitly in the presented theory we use the concept of generalized coherent states that brings physical insight into the mathematical formalism

minimum hellinger distance estimation for finite mixtures of poisson regression models and its applications il a ete montre que l estimation au minimum de la distance de hellinger mhde reduit des points irreguliers par effet de lissage avec une efficacite du premier ordre pour un modele correctement specifie on propose une approche d estimation adaptee aux melanges finis de modeles de regression de poisson basee sur la mhde les simulations de monte carlo montrent a l evidence que la mhde est une alternative viable a l estimation au maximum de vraisemblance lorsque les composants du melange ne sont pas bien separes ou lorsque les parametres du modele sont proches de zero des applications de biometrie illustrent egalement l utilite pratique de la methode mhde

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

metric aspects of noncommutative homogeneous spaces for a closed cocompact subgroup of a locally compact group g given a compact abelian subgroup k of g and a homomorphism k g satisfying certain conditions landstad and raeburn constructed equivariant noncommutative deformations c g of the homogeneous space g generalizing rieffel s construction of quantum heisenberg manifolds we show that when g is a lie group and g is connected given any norm on the lie algebra of g the seminorm on c g induced by the derivation map of the canonical g action defines a compact quantum metric furthermore it is shown that this compact quantum metric space depends on continuously with respect to quantum gromov hausdorff distances

deformations of momentum maps and g systems in this note we give an explicit formula for a family of deformation quantizations for the momentum map associated with the cotangent lift of a lie group action on rd this family of deformations is parametrized by the formal g systems introduced in b dherin and i mencattini g systems and deformations of g actions on rd j math phys 55 011702 2014 see also b dherin and i mencattini quantization of volume preserving actions on rd e print arxiv 1202 0886 and allows us to obtain classical invariant hamiltonians that quantize without anomalies with respect to the quantizations of the action prescribed by the formal g systems

the yang mills functional and laplace s equation on quantum heisenberg manifolds in this paper we discuss the yang mills functional and a certain family of its critical points on quantum heisenberg manifolds using noncommutative geometrical methods developed by a connes and m rieffel in our main result we construct a certain family of connections on a projective module over a quantum heisenberg manifold that gives rise to critical points of the yang mills functional moreover we show that there is a relationship between this particular family of critical points of the yang mills functional and laplace s equation on multiplication type skew symmetric elements of quantum heisenberg manifolds recall that laplacian is the leading term for the coupled set of equations making up the yang mills equation

semiparametric estimation in the rasch model and related exponential response models including a simple latent class model for item analysis abstract the rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects leading to the failure of the usual likelihood methodology both conditional likelihood methods and mixture model techniques have been used to circumvent these problems in this article we show that these seemingly unrelated analyses are in fact closely linked to each other despite dramatic structural differences between the classes of models implied by each approach we show that the finite mixture model for j dichotomous items having t latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if t j 1 2 unconditional maximum likelihood estimators for the finite mixture model can be viewed as keifer wolfowitz estimators for the random effects version of the rasch model latent class versions of the model are especially attractive when t is

the riemann problem for the shallow water equations with discontinuous topography the wet dry case abstract in this paper we consider riemann problems for the shallow water equations with discontinuous topography whose initial conditions correspond to a wet dry front at time t 0 there is vacuum on the right or on the left of the step besides the theoretical interest of this analysis the results may be useful to design numerical methods and or to produce reference solutions to compare different schemes we show that depending on the state at the wet side 0 1 or 2 self similar solutions can be constructed by composing simple waves in problems with 0 solutions the step acts as an obstacle for the fluid and physically meaningful solutions can be constructed by interpreting the problem as a partial riemann problems for the homogeneous shallow water system some numerical results are shown where different numerical methods are compared in particular it is shown that in the non uniqueness cases the numerical solutions can converge to one or to the other solution what is the reason that explains the huge differences observed when different numerical methods are applied to the shallow water system with abrupt changes in the bottom moreover problems with zero solutions will be reinterpreted as partial riemann problems for the homogeneous system what will allow us to build a physically solution when one side of the step is wet and the other one is dry we will specify the regions where we can find zero one or two solutions giving the form of the solution when it is possible and giving an alternative when it is not possible

the geometry of mixture likelihoods a general theory in this paper certain fundamental properties of the maximum likelihood estimator of a mixing distribution are shown to be geometric properties of the likelihood set the existence support size likelihood equations and uniqueness of the estimator are revealed to be directly related to the properties of the convex hull of the likelihood set and the support hyperplanes of that hull it is shown using geometric techniques that the estimator exists under quite general conditions with a support size no larger than the number of distinct observations analysis of the convex dual of the likelihood set leads to a dual maximization problem a convergent algorithm is described the defining equations for the estimator are compared with the usual parametric likelihood equations for finite mixtures sufficient conditions for uniqueness are given part ii will deal with a special theory for exponential family mixtures

continuous fields of c algebras coming from group cocycles and actions recently i have been attempting to formulate a suitable c algebraic framework for the subject of deformation quantization 3 19 continuous fields of c algebras provide one of the key elements for this framework the main examples of deformation quantizations which i have constructed up to now in this c algebra framework come from letting either cocycles on groups or actions of groups vary it has thus become necessary to show that one obtains in this way fields of c aigebras that are indeed continuous since this material is of a general nature and can be useful in other situations 4 6 11 13 it has seemed appropriate to give a separate exposition of it in the present article section 1 of this article contains a review of the published results on continuous fields which we will need as well as a discussion of the fact that the approach which we will take involves treating upper and lower semi continuity separately in sect 2 we discuss the continuity of fields of c algebras which arise from varying cocycles on groups while in sect 3 we do the same for actions which vary

ergodic actions of compact groups on operator algebras iii classification for su 2 we prove that the only ergodic actions ofsu 2 are on type i von neumann algebras using the theory developed in 8

poisson geometry of the principal series and nonlinearizable structures si g est une algebre de lie sur r alors l espace dual g porte une structure de poisson lineaire o appelee la structure de lie poisson on etudie le probleme de la linearisation

the stratonovich weyl correspondence for one dimensional kinematical groups the stratonovich weyl correspondence is a restatement of the moyal quantization where the phase space is a manifold and where a group of transformations acts on it transitively the first and most important step is to define a mapping from the manifold into the set of self adjoint operators on a hilbert space under suitable conditions this mapping is called a stratonovich weyl kernel the construction of this mapping is discussed on coadjoint orbits of the one dimensional galilei poincare and newton hooke groups as well as the two dimensional euclidean group

residual diagnostics for growth mixture models examining the impact of a preventive intervention on multiple trajectories of aggressive behavior growth mixture modeling has become a prominent tool for studying the heterogeneity of developmental trajectories within a population in this article we develop graphical diagnostics to detect misspecification in growth mixture models regarding the number of growth classes growth trajectory means and covariance structures for each model misspecification we propose a different type of empirical bayes residual to quantify the departure our procedure begins by imputing multiple independent sets of growth classes for the sample then from these so called pseudoclass draws we form diagnostic plots to examine the averaged empirical distributions of residuals in each such class our proposals draw on the property that each single set of pseudoclass adjusted residuals is asymptotically normal with known mean and co variance when the underlying model is correct these methods are justified in simulation studies involving two classes of linear growth curves that also differ by their covariance structures

reliability of first order numerical schemes for solving shallow water system over abrupt topography we compare some first order well balanced numerical schemes for shallow water system with special interest in applications where there are abrupt variations of the topography we show that the space step required to obtain a prescribed error depends on the method moreover the solutions given by the numerical scheme can be significantly different if not enough space resolution is used we shall pay special attention to the well known hydrostatic reconstruction technique where it is shown that the effect of large bottom discontinuities might be missed and a modification is proposed to avoid this problem

a groenewold van hove theorem for s 2 we prove that there does not exist a nontrivial quantization of the poisson algebra of the symplectic manifold s2 which is irreducible on the su 2 subalgebra generated by the components s1 s2 s3 of the spin vector in fact there does not exist such a quantization of the poisson subalgebra p consisting of polynomials in s1 s2 s3 furthermore we show that the maximal poisson subalgebra of p containing 1 s1 s2 s3 that can be so quantized is just that generated by 1 s1 s2 s3

non parametric identification and estimation of the number of components in multivariate mixtures this article analyzes the identiability of the number of components in k variate mcomponent nite mixture models in which each component distribution has independent marginals including models in latent class analysis without making parametric assumptions on the component distributions we investigate how one can identify the number of components from the distribution function of the observed data when k 2 a lower bound on the number of components m is nonparametrically identiable from the rank of a matrix constructed from the distribution function of the observed variables building on this identication condition we develop a procedure to consistently estimate a lower bound on the number of components

on the moduli space of a quantum heisenberg manifold we investigate the yang mills problem on a quantum heisenberg manifold d c in the setting of the non commutative differential geometry this problem was already studied by kang 2010 in 6 for a specific module over d c and kang obtained a family of connections which are critical points of the yang mills functional on but it turned out that they are neither minima nor maxima in this article we construct a connection 0 on and show that it is a minimum of the yang mills functional on the module moreover we give a certain family of minima including 0 and show that the moduli space for is non trivial

convergence of the wick star product we construct a frechet space as a subspace of c omega mathbb c n where the wick star product converges and is continuous the resulting frechet algebra mathcal a is studied in detail including a representation of mathcal a in the bargmann fock space and a discussion of star exponentials and coherent states

semiparametric maximum likelihood for measurement error model regression this paper presents an em algorithm for semiparametric likelihood analysis of linear generalized linear and nonlinear regression models with measurement errors in explanatory variables a structural model is used in which probability distributions are specified for a the response and b the measurement error a distribution is also assumed for the true explanatory variable but is left unspecified and is estimated by nonparametric maximum likelihood for various types of extra information about the measurement error distribution the proposed algorithm makes use of available routines that would be appropriate for likelihood analysis of a and b if the true x were available simulations suggest that the semiparametric maximum likelihood estimator retains a high degree of efficiency relative to the structural maximum likelihood estimator based on correct distributional assumptions and can outperform maximum likelihood based on an incorrect distributional assumption the approach is illustrated on three examples with a variety of structures and types of extra information about the measurement error distribution

deformation quantization and the baum connes conjecture alternative titles of this paper would have been index theory without index or the baum connes conjecture without baum

residual diagnostics for mixture models abstract a sample is commonly modeled by a mixture distribution if the observations follow a common distribution but the parameter of interest differs between observations for example we observe the lengths but not the ages of a sample offish it may be reasonable to assume that length is normally distributed about an unknown mean that depends on the age of the fish provided there is more than one age class in the sample then the data are distributed as a mixture of normals in this article we assume that the data are a random sample from a mixture of exponential family distributions and that for each observation the parameter of interest is sampled independently from an unknown mixing distribution q the adequacy of a fitted mixture model can be assessed by examining residuals based on the ratio of the observed to expected fit residuals based on the homogeneity model in which q is a one point distribution display a convexity property when the data follow a mixture model this becomes the basis fo

deformation quantization of the heisenberg group a product compatible with the comultiplication of the hopf algebra of the functions on the heisenberg group is determined by deforming a coboundary lie poisson structure defined by a classicalr matrix satisfying the modified yang baxter equation the corresponding quantum group is studied and itsr matrix is explicitly calculated

quantum systems with finite hilbert space galois fields in quantum mechanics a galois quantum system in which the position and momentum take values in the galois field gf pl is considered it is comprised of l component systems which are coupled in a particular way and is described by a certain class of hamiltonians displacements in the gf pl gf pl phase space and the corresponding heisenberg weyl group are studied symplectic transformations are shown to form the sp 2 gf pl group wigner and weyl functions are defined and their properties are studied frobenius symmetries which are based on frobenius automorphisms in the theory of galois fields are a unique feature of these systems for l 2 if they commute with the hamiltonian there are constants of motion which are discussed an analytic representation in the l sheeted complex plane provides an elegant formalism that embodies the properties of frobenius transformations the difference between a galois quantum system and other finite quantum systems where the position and momentum take values in the ring is discussed

transformation group c algebras with continuous trace we obtain several results characterizing when transformation group c algebras have continuous trace these results can be stated most succinctly when g l is second countable and the stability groups are contained in a fixed abelian subgroup in this case c g q has continuous trace if and only if the stability groups vary continuously on r and compact subsets of q are wandering in an appropriate sense in general we must assume that the stability groups vary continuously and if g j is not second countable that the natural maps of g s onto g x are homeomorphisms for each x then c g 0 has continuous trace if and only if compact subsets of 0 are wandering and an additionai c algebra constructed from the stability groups and 0 has continuous trace

moyal quantization with compact symmetry groups and noncommutative harmonic analysis the phase space approach to quantization of systems whose symmetry group is compact and semisimple is developed from two basic principles covariance and traciality this generalizes results and methods already implemented for spin systems j c varilly and j m gracia bondia ann phys 190 107 1989 the twisted product of phase space functions is shown to be the image of group convolution in the context of a novel fourier theory on the coadjoint orbits

the noncommutative lorentzian cylinder as an isospectral deformation we present a new example of a finite dimensional noncommutative manifold namely the noncommutative cylinder it is obtained by isospectral deformation of the canonical triple associated with the euclidean cylinder we discuss connes character formula for the cylinder in the second part we discuss noncommutative lorentzian manifolds here the definition of spectral triples involves krein spaces and operators on krein spaces a central role is played by the admissible fundamental symmetries on the krein space of square integrable sections of a spin bundle over a lorentzian manifold finally we discuss isospectral deformation of the lorentzian cylinder and determine all admissible fundamental symmetries of the noncommutative cylinder

categorical perspective on quantization of poisson algebra we propose a generalization of quantization using a categorical approach for a fixed poisson algebra quantization categories are defined as subcategories of the r module category equipped with the structure of classical limits we then construct the generalized quantization categories including matrix regularization strict deformation quantization prequantization and poisson enveloping algebra it is shown that the categories of strict deformation quantization prequantization and matrix regularization with certain conditions are equivalent categories on the other hand the categories of poisson enveloping algebra are not equivalent to the other categories

the a polynomial from the noncommutative viewpoint the paper introduces a noncommutative generalization of the a polynomial of a knot this is done using the kauffman bracket skein module of the knot complement and is based on the relationship between skein modules and character varieties the construction is possible because the kauffman bracket skein algebra of the cylinder over the torus is a subalgebra of the noncommutative torus the generalized version of the a polynomial called the noncommutative a ideal consists of a finitely generated ideal of polynomials in the quantum plane some properties of the noncommutative a ideal and its relationships with the a polynomial and the jones polynomial are discussed the paper concludes with the description of the examples of the unknot and the right and left handed trefoil knots

toeplitz quantization on fock space for toeplitz operators t f t acting on the weighted fock space h t 2 we consider the semi commutator t f t t g t t fg t where t 0 is a certain weight parameter that may be interpreted as planck s constant hbar in rieffel s deformation quantization in particular we are interested in the semi classical limit begin equation tag lim limits t to 0 t f t t g t t fg t t end equation it is well known that t f t t g t t fg t t tends to 0 under certain smoothness assumptions imposed on f and g this result was recently extended to f g in textup buc c n by bauer and coburn we now further generalize to not necessarily bounded uniformly continuous functions and symbols in the algebra textup vmo cap l infty of bounded functions having vanishing mean oscillation on mathbb c n our approach is based on the algebraic identity t f t t g t t fg t h bar f t h g t where h g t denotes the hankel operator corresponding to the symbol g and norm estimates in terms of the weighted heat transform as a consequence only f or likewise only g has to be contained in one of the above classes for to vanish for g we only have to impose limsup t to 0 h g t t infty e g g in l infty c n we prove that the set of all symbols f in l infty mathbb c n with the property that lim t rightarrow 0 t t ft t g t t fg t lim t rightarrow 0 t g t t f t t gf t t 0 for all g in l infty mathbb c n coincides with textup vmo cap l infty additionally we show that lim limits t to 0 t f t t f infty holds for all f in l infty c n finally we present new examples including bounded smooth functions where does not vanish

the characteristic classes of morita equivalent star products on symplectic manifolds in this paper we give a complete characterization of morita equivalent star products on symplectic manifolds in terms of their characteristic classes two star products and on m are morita equivalent if and only if there exists a symplectomorphism colon m m such that the relative class t is 2 i integral for star products on cotangent bundles we show that this integrality condition is related to dirac s quantization condition for magnetic charges

testing the number of components in normal mixture regression models testing the number of components in finite normal mixture models is a long standing challenge because of its nonregularity this article studies likelihood based testing of the number of components in normal mixture regression models with heteroscedastic components we construct a likelihood based test of the null hypothesis of m0 components against the alternative hypothesis of m0 1 components for any m0 the null asymptotic distribution of the proposed modified em test statistic is the maximum of m0 random variables that can be easily simulated the simulations show that the proposed test has very good finite sample size and power properties supplementary materials for this article are available online

on the efficiency of score tests for homogeneity in two component parametric models for discrete data in many applications of two component mixture models for discrete data such as zero inflated models it is often of interest to conduct inferences for the mixing weights score tests derived from the marginal model that allows for negative mixing weights have been particularly useful for this purpose but the existing testing procedures often rely on restrictive assumptions such as the constancy of the mixing weights and typically ignore the structural constraints of the marginal model in this article we develop a score test of homogeneity that overcomes the limitations of existing procedures the technique is based on a decomposition of the mixing weights into terms that have an obvious statistical interpretation we exploit this decomposition to lay the foundation of the test simulation results show that the proposed covariate adjusted test statistic can greatly improve the efficiency over test statistics based on constant mixing weights a real life example in dental caries research is used to illustrate the methodology

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

overdispersion diagnostics for generalized linear models abstract generalized linear models glm s are simple convenient models for count data but they assume that the variance is a specified function of the mean although overdispersed glm s allow more flexible mean variance relationships they are often not as simple to interpret nor as easy to fit as standard glm s this article introduces a convexity plot or c plot for short that detects overdispersion and relative variance curves and relative variance tests that help to understand the nature of the overdispersion convexity plots sometimes detect overdispersion better than score tests and relative variance curves and tests sometimes distinguish the source of the overdispersion better than score tests

analytic representations in quantum mechanics various euclidean hyperbolic and elliptic analytic representations are introduced and relations among them are discussed the bargmann analytic representation in the complex plane is considered and its relation to other phase space methods for the harmonic oscillator is reviewed the general theory that relates the growth of analytic functions with the density of their zeros is applied to bargmann functions and it leads to theorems on the completeness of sequences of glauber coherent states two hyperbolic analytic representations in the unit disc based on su 1 1 coherent states and also on phase states are introduced a third analytic representation in the complex plane based on barut girardello states is also considered and transformations which relate it to the other ones are studied in the case of systems with finite dimensional hilbert space an elliptic analytic representation in the extended complex plane and also another analytic representation based on theta functions are introduced the berezin formalism in the euclidean hyperbolic and elliptic cases is discussed contour analytic representations in these three cases are also presented

a new hydrostatic reconstruction scheme based on subcell reconstructions a key difficulty in the analysis and numerical approximation of the shallow water equations is the nonconservative product of measures due to the gravitational force acting on a sloped bottom solu

on the uniqueness of the moyal structure of phase space functions uniqueness up to isomorphism of the moyal product and bracket of functions on as associative and lie deformations of the ordinary product and poisson bracket is known to follow under additional hypotheses using an integral formalism we show here that this result holds without these hypotheses

deformation quantization of heisenberg manifolds form a smooth manifold equipped with a poisson bracket we formulate ac algebra framework for deformation quantization including the possibility of invariance under a lie group of diffeomorphisms preserving the poisson bracket we then show that the much studied non commutative tori give examples of such deformation quantizations invariant under the usual action of ordinary tori going beyond this the main results of the paper provide a construction of invariant deformation quantizations for those poisson brackets on heisenberg manifolds which are invariant under the action of the heisenberg lie group and for various generalizations suggested by this class of examples interesting examples are obtained of simplec algebras on which the heisenberg group acts ergodically

unified maximum likelihood estimates for closed capture recapture models using mixtures summary agresti 1994 biometrics50 494 500 and norris and pollock 1996a biometrics52 639 649 suggested using methods of finite mixtures to partition the animals in a closed capture recapture experiment into two or more groups with relatively homogeneous capture probabilities this enabled them to fit the models mh mbh norris and pollock and mth agresti of otis et al 1978 wildlife monographs62 1 135 in this article finite mixture partitions of animals and or samples are used to give a unified linear logistic framework for fitting all eight models of otis et al by maximum likelihood likelihood ratio tests are available for model comparisons for many data sets a simple dichotomy of animals is enough to substantially correct for heterogeneity induced bias in the estimation of population size although there is the option of fitting more than two groups if the data warrant it

a penalized nonparametric maximum likelihood approach to species richness estimation we propose a class of penalized nonparametric maximum likelihood estimators npmles for the species richness problem we use a penalty term on the likelihood because likelihood estimators that lack it have an extreme instability problem the estimators are constructed using a conditional likelihood that is simpler than the full likelihood we show that the full likelihood npmle solution given by norris and pollock can be found with great accuracy by using an appropriate penalty term on the conditional likelihood so it is an element of our class of estimators a simple and fast algorithm for the penalized npmle is developed it can be used to greatly speed up computation of the unconditional npmle it can also be used to find profile mixture likelihoods based on our goal of attaining high stability while retaining sensitivity we propose an adaptive quadratic penalty function a systematic simulation study using a wide range of scenarios establishes the success of this method relative to its competi

quantization and the resolvent algebra abstract we introduce a novel commutative c algebra c r x of functions on a symplectic vector space x admitting a complex structure along with a strict deformation quantization that maps a dense subalgebra of c r x to the resolvent algebra introduced by buchholz and grundling 2 the associated quantization map is a field theoretical weyl quantization compatible with the work of binz honegger and rieckers 1 we also define a berezin type quantization map on all of c r x which continuously and bijectively maps it onto the resolvent algebra the commutative resolvent algebra c r x generally defined on a real inner product space x intimately depends on the finite dimensional subspaces of x we thoroughly analyze the structure of this algebra in the finite dimensional case by giving a characterization of its elements and by computing its gelfand spectrum