bergman kernel from path integral we rederive the expansion of the bergman kernel on kahler manifolds developed by tian yau zelditch lu and catlin using path integral and perturbation theory and generalize it to supersymmetric quantum mechanics one physics interpretation of this result is as an expansion of the projector of wave functions on the lowest landau level in the special case that the magnetic field is proportional to the kahler form this is relevant for the quantum hall effect in curved space and for its higher dimensional generalizations other applications include the theory of coherent states the study of balanced metrics noncommutative field theory and a conjecture on metrics in black hole backgrounds discussed in 24 we give a short overview of these various topics from a conceptual point of view this expansion is noteworthy as it is a geometric expansion somewhat similar to the dewitt seeley gilkey et al short time expansion for the heat kernel but in this case describing the long time limit without depending on supersymmetry

elastoplastic truss design using a displacement based optimization abstract a displacement based optimization dbo method is applied to truss design problems with material nonlinearities to explore feasibility and verify efficiency of the method as compared to traditional structural optimization minimum weight truss sizing problems with various path independent elastoplastic laws including elastic perfectly plastic linear strain hardening and ramberg osgood models are investigated this type of material nonlinearity allows us to naturally extend the linear elastic truss sizing in the dbo setting to nonlinear problems to implement the methodology a computer program that uses the commercially available optimizer dot by vr d and imsl linear programming solver by visual numerics is developed several test problems are successfully solved using the dbo approach and solutions are compared to those available in the literature demonstrating significant reduction of computational time in comparison to the traditional structural optimization method in particular the dbo approach is found to be suitable for truss topology design since the method allows member areas to have cross sectional areas equal to zero exactly

coulomb gas ensembles and laplacian growth we consider weight functions q that are locally in a suitable sobolev space and impose a logarithmic growth condition from below we use q as a confining potential in the model of one component plasma 2 dimensional coulomb gas and study the configuration of the electron cloud as the number n of electrons tends to infinity while the confining potential is rescaled we use mq in place of q and let m tend to infinity as well we show that if m and n tend to infinity in a proportional fashion with n m t where 0 t is fixed then the electrons accumulate on a compact set st which we call the droplet the set s t can be obtained as the coincidence set of an obstacle problem if we remove a small set the shallow points moreover on the droplet st the density of electrons is asymptotically q the growth of the droplets st as t increases is known as the laplacian growth it is well known that laplacian growth is unstable to analyse this feature we introduce the notion of a local droplet which involves removing part of the obstacle away from the set s t the local droplets are no longer uniquely determined by the time parameter t but at least they may be partially ordered we show that the growth of the local droplets may be terminated in a maximal local droplet or by the droplets growing to infinity in some direction fingering

density of eigenvalues of random normal matrices the relation between random normal matrices and conformal mappings discovered by wiegmann and zabrodin is made rigorous by restricting normal matrices to have spectrum in a bounded set it is shown that for a suitable class of potentials the asymptotic density of eigenvalues is uniform with support in the interior domain of a simple smooth curve

asymptotic expansion of polyanalytic bergman kernels we consider the q analytic functions on a given planar domain omega square integrable with respect to a weight this gives us a q analytic bergman kernel which we use to extend the bergman metric

efficient monte carlo methods for conditional logistic regression abstract exact inference for the logistic regression model is based on generating the permutation distribution of the sufficient statistics for the regression parameters of interest conditional on the sufficient statistics for the remaining nuisance parameters despite the availability of fast numerical algorithms for the exact computations there are numerous instances where a data set is too large to be analyzed by the exact methods yet too sparse or unbalanced for the maximum likelihood approach to be reliable what is needed is a monte carlo alternative to the exact conditional approach which can bridge the gap between the exact and asymptotic methods of inference the problem is technically hard because conventional monte carlo methods lead to massive rejection of samples that do not satisfy the linear integer constraints of the conditional distribution we propose a network sampling approach to the monte carlo problem that eliminates rejection entirely its advantages over alternative saddlepoint

a note on a albert and j a anderson s conditions for the existence of maximum likelihood estimates in logistic regression models summary this note expands the paper by albert anderson 1984 on the existence and uniqueness of maximum likelihood estimates in logistic regression models their three possible mutually exclusive data pattems i overlap ii complete separation and iii quasiseparation are considered the maximum likelihood estimate exists only in i modifications of the statement and proofs of albert anderson s results are given for ii and iii the identifiability for a more general model arising in the study of iii is discussed together with the maximization of the corresponding likelihood a linear program is presented which determines whether data is of type i ii or iii and in the case of iii identifies albert anderson s minimal set qm

practical use of higher order asymptotics for multiparameter exponential families recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families especially in generalized linear models the aim here is to clarify and explore these attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family excellent approximations to exact conditional inferences are often available in terms of simple adjustments to the signed square root of the likelihood ratio statistic

displacement based optimization for truss structures subjected to static and dynamic constraints the use of displacements as design variables for truss structure optimization is considered as an alternative to the conventional finite element analysis based design approach a two level nested optimization has been developed in an inner level cross sectional areas of truss members are designed for a given displacement field and at an outer level optimal displacements corresponding to the minimum weight designs are searched through the use of sequential quadratic programming the computational efficiency of the method is demonstrated through three examples and the evolutions of the cross sectional areas and optimal weight as a function of the displacements are studied static dynamic and topology problems are considered it is shown that the method is highly efficient compared to the conventional design approaches it is also demonstrated that the weight is always continuous throughout the design history although areas might exhibit large discontinuities

computing distributions for exact logistic regression abstract logistic regression is a commonly used technique for the analysis of retrospective and prospective epidemiological and clinical studies with binary response variables usually this analysis is performed using large sample approximations when the sample size is small or the data structure sparse the accuracy of the asymptotic approximations is in question on other occasions singularity of the covariance matrix of parameter estimates precludes asymptotic analysis under these circumstances use of exact inferential procedures would seem to be a prudent alternative cox 1970 showed that exact inference on the parameters of a logistic model with binary response requires consideration of the distribution of sufficient statistics for these parameters to date however resorting to the exact method has not been computationally feasible except in a few special situations this article presents an efficient recursive algorithm that generates the joint and conditional distributions of the sufficient

on the lower order terms of the asymptotic expansion of tian yau zelditch we compute the first three coefficients of the asymptotic expansion of tian yau zelditch we also prove that in general the fcth coefficient is a polynomial of the curvature and its derivative of weight k

equivalence of palm measures for determinantal point processes governed by bergman kernels for a determinantal point process induced by the reproducing kernel of the weighted bergman space a 2 u omega over a domain u subset mathbb c d we establish the mutual absolute continuity of reduced palm measures of any order provided that the domain u contains a non constant bounded holomorphic function the result holds in all dimensions the argument uses the h infty u module structure of a 2 u omega a corollary is the quasi invariance of our determinantal point process under the natural action of the group of compactly supported diffeomorphisms of u

a new method for optimal truss topology design truss topology optimization formulated in terms of displacements and bar volumes results in a large nonconvex optimization problem for the case of maximization of stiffness for a prescribed volume this paper presents a new equivalent an unconstrained and convex minimization problem in displacements only where the function to be minimized is the sum of terms each of which is the maximum of two convex quadratic functions existence of solutions is proved as is the convergence of a nonsmooth steepest descent type algorithm for solving the topology optimization problem the algorithm is computationally attractive and has been tested on a large number of examples some of which are presented

on obtaining permutation distributions in polynomial time abstract polynomial time algorithms are presented for finding the permutation distribution of any statistic that is a linear combination of some function of either the original observations or the ranks this class of statistics includes the original fisher two sample location statistic and such common nonparametric statistics as the wilcoxon ansari bradley savage and many others the algorithms are presented for the two sample problem and it is shown how to extend them to the multisample problem for example to find the distribution of the kruskal wallis and other extensions of the wilcoxon and to the single sample situation stratification ties and censored observations are also easily handled by the algorithms the algorithms require polynomial time as opposed to complete enumeration algorithms which require exponential time this savings is effected by first calculating and then inverting the characteristic function of the statistic

computing exact distributions for polytomous response data abstract this article presents an efficient method for computing exact conditional distributions of the sufficient statistics for the parameters of four polytomous response models for nominal response two baseline category logit models and for ordinal response two adjacent categories logit models are considered the method consists of recursive generation of the joint distribution of the sufficient statistics augmented by a technique to slice off portions of the evolving sample space so as to eventually yield the required conditional distribution two actual data sets are analyzed to illustrate the method

on the solution of a minimum weight elastoplastic problem involving displacement and complementarity constraints this paper deals with a special class of minimum weight design problem involving discretized structures holonomic reversible plasticity and constraints on displacements a key feature of the optimization problem is the presence of complementarity conditions involving the orthogonality of two sign constrained vectors this problem falls within the important class of so called mathematical programs with equilibrium constraints mpecs two simple algorithms are proposed to solve our synthesis problem and application is illustrated by some examples concerning truss like structures

bulk asymptotics for polyanalytic correlation kernels for a weight function q c r and a positive scaling parameter m we study reproducing kernels kq mq n of the polynomial spaces aq mq n2 spanc z rzj 0 r q 1 0 j n 1 equipped with the inner product from the space l2 e mq z da z here da denotes a suitably normalized area measure on c for a point z0 belonging to the interior of certain compact set s and satisfying q z0 0 we define the rescaled coordinates z z0 m q z0 w z0 m q z0 the following universality result is proved in the case q 2 1m q z0 kq mq n z w e 12mq z 12mq w lq 11 2 e 12 2 as m n while n m m for any fixed m 0 uniformly for in compact subsets of c2 the notation lq 11 stands for the associated laguerre polynomial with parameter 1 and degree q 1 this generalizes a result of ameur hedenmalm and makarov concerning analytic polynomials to bianalytic polynomials we also discuss how to generalize the result to q 2 our methods include a simplification of a bergman kernel expansion algorithm of berman berndtsson and sjostrand in the one compex variable setting and extension to the context of polyanalytic functions we also study off diagonal behaviour of the kernels kq mq n

random normal matrices and ward identities we consider the random normal matrix ensemble associated with a potential in the plane of sufficient growth near infinity it is known that asymptotically as the order of the random matrix increases indefinitely the eigenvalues approach a certain equilibrium density given in terms of frostman s solution to the minimum energy problem of weighted logarithmic potential theory at a finer scale we may consider fluctuations of eigenvalues about the equilibrium in the present paper we give the correction to the expectation of the fluctuations and we show that the potential field of the corrected fluctuations converge on smooth test functions to a gaussian free field with free boundary conditions on the droplet associated with the potential

harmonic analysis in phase space and finite weyl heisenberg ensembles weyl heisenberg ensembles are translation invariant determinantal point processes on mathbb r 2d associated with the schrodinger representation of the heisenberg group and include as examples the ginibre ensemble and the polyanalytic ensembles which model the higher landau levels in physics we introduce finite versions of the weyl heisenberg ensembles and show that they behave analogously to the finite ginibre ensembles more specifically guided by the observation that the ginibre ensemble with n points is asymptotically close to the restriction of the infinite ginibre ensemble to the disk of area n we define finite wh ensembles as adequate finite approximations of the restriction of infinite wh ensembles to a given domain omega we provide a precise rate for the convergence of the corresponding one point intensities to the indicator function of omega as omega is dilated and the process is rescaled proportionally thermodynamic regime the construction and analysis rely neither on explicit formulas nor on the asymptotics for orthogonal polynomials but rather on phase space methods second we apply our construction to study the pure finite ginibre type polyanalytic ensembles which model finite particle systems in a single landau level and are defined in terms of complex hermite polynomials on a technical level we show that finite wh ensembles provide an approximate model for finite polyanalytic ginibre ensembles and we quantify the corresponding deviation by means of this asymptotic description we derive estimates for the rate of convergence of the one point intensity of polyanalytic ginibre ensembles in the thermodynamic limit

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

an algorithm for exact logistic regression abstract an efficient algorithm is given for the exact logistic analysis of a single parameter hypothesis tests and confidence intervals for a logistic regression parameter are obtained the method provides for the control of the effect of a stratification factor when making inferences concerning the regression parameter

semi analytical static nonlinear structural sensitivity analysis the paper discusses two uses of the semi analytical method for nonlinear sensitivity analysis first the application to noncritical response is analyzed it is shown that the semi analytical method is equivalent to a particular form of the overall finite difference approach it is concluded that the difference between overall finite differences and the semi analytical approach is blurred for the case of nonlinear static response next the application of the semi analytical method to calculating sensitivities of limit loads is discussed a formulation that is easy to implement in general purpose finite element programs is derived three examples are used to demonstrate the application of the formulation and to explore its accuracy

approximate conditional inference in generalized linear models on developpe des approximations precises et facilement calculables pour les densites conditionnelles et les distributions des statistiques exhaustives dans les modeles lineaires generalises avec des fonctions de liaison canoniques

berezin transform in polynomial bergman spaces fix a smooth weight function q in the plane subject to a growth condition from below let k m n denote the reproducing kernel for the hilbert space of analytic polynomials of degree at most n 1 of finite l 2 norm with respect to the measure e mq da here da is normalized area measure and m is a positive real scaling parameter the polynomial berezin measure db m n z k m n z 0 z 0 1 k m n z z 0 2e mq z da z for the point z 0 is a probability measure that defines the polynomial berezin transform b m n f z 0 c f db m n for continuous f l c we analyze the semiclassical limit of the berezin measure and transform as m while n m o 1 where is fixed positive and real we find that the berezin measure for z 0 converges weak star to the unit point mass at the point z 0 provided that q z 0 0 and that z 0 is contained in the interior of a compact set s defined as the coincidence set for an obstacle problem as a refinement we show that the appropriate local blowup of the berezin measure converges to the standardized gaussian measure in the plane for points z 0 c s the berezin measure cannot converge to the point mass at z 0 in the model case q z z 2 when s is a closed disk we find that the berezin measure instead converges to harmonic measure at z 0 relative to c s our results have applications to the study of the eigenvalues of random normal matrices the auxiliary results include weighted l 2 estimates for the equation overscore u f when f is a suitable test function and the solution u is restricted by a polynomial growth bound at

on the existence of maximum likelihood estimators for the binomial response models summary necessary and sufficient conditions are given for the existence of maximum likelihood estimators of the linear regression parameter in binomial response this includes logit and probit models the question of existence of maximum likelihood estimators mle for logit models arose in an analysis of the relationship of psychiatric caseness to scores on a psychiatric screening questionnaire tennant 1977 administered the ghq general health questionnaire goldberg 1972 to 120 patients attending a general practitioner s surgery and also gave each one a standardized psychiatric interview from the interview patients were classified as psychiatric case non case in a secondary analysis of tennant s data duncan jones and henderson 1978 fitted a logit regression of caseness on ghq score and obtained a good fit with the model

equivalence between conditional and mixture approaches to the rasch model and matched case control studies with applications analyses of data using rasch models including the special case of matched case control studies are common applications of conditional likelihood in which the usual inferential procedures are applied only after conditioning on an approximately ancillary statistic another common approach to the analysis of rasch models is to integrate the nuisance parameters over a mixing distribution using the marginal likelihood obtained as the basis for inference we show that the full conditional likelihood can always be obtained exactly via the marginal approach given a particular choice of mixing distribution and derive necessary and sufficient conditions for the two approaches to agree previous work has shown that with sufficient flexibility in the mixing distribution the maxima of the marginal and conditional likelihoods will be equivalent under concordance criteria our argument requires no such criteria and for any dataset guarantees the equivalence of the whole of the two likelihoods not just their maxi

the polyanalytic ginibre ensembles for integers n q 1 2 3 let pol n q denote the mathbb c linear space of polynomials in z and bar z of degree n 1 in z and of degree q 1 in bar z we supply pol n q with the inner product structure of begin aligned l 2 bigl mathbb c mathrm e m z 2 mathrm d a bigr quad mbox where mathrm d a z pi 1 mathrm d x mathrm d y z x mathrm i y end aligned the resulting hilbert space is denoted by pol m n q here it is assumed that m is a positive real we let k m n q denote the reproducing kernel of pol m n q and study the associated determinantal process in the limit as m n while n m o 1 the number q the degree of polyanalyticity is kept fixed we call these processes polyanalytic ginibre ensembles because they generalize the ginibre ensemble the eigenvalue process of random normal matrices with gaussian weight there is a physical interpretation in terms of a system of free fermions in a uniform magnetic field so that a fixed number of the first landau levels have been filled we consider local blow ups of the polyanalytic ginibre ensembles around points in the spectral droplet which is here the closed unit disk bar mathbb d z in mathbb c z le1 we obtain asymptotics for the blow up process using a blow up to characteristic distance m 1 2 the typical distance is the same both for interior and for boundary points of bar mathbb d this amounts to obtaining the asymptotical behavior of the generating kernel k m n q following ameur et al in commun pure appl math 63 12 1533 1584 2010 the asymptotics of the k m n q are rather conveniently expressed in terms of the berezin measure and density open image in new window for interior points z 1 in contrast for exterior points z 1 we have instead that mathrm d b langle z rangle m n q w to mathrm d omega w z mathbb d e where mathrm d omega w z mathbb d e is the harmonic measure at z with respect to the exterior disk mathbb d e w in mathbb c w 1 for boundary points z 1 the berezin measure mathrm d b langle z rangle m n q converges to the unit point mass at z as with interior points but the blow up to the scale m 1 2 exhibits quite different behavior at boundary points compared with interior points we also obtain the asymptotic boundary behavior of the 1 point function at the coarser local scale q 1 2 m 1 2

a closed formula for the asymptotic expansion of the bergman kernel we prove a graph theoretic closed formula for coefficients in the tian yau zelditch asymptotic expansion of the bergman kernel the formula is expressed in terms of the characteristic polynomial of the directed graphs representing weyl invariants the proof relies on a combinatorial interpretation of a recursive formula due to m englis and a loi

large n expansion for the 2d dyson gas we discuss the 1 n expansion of the free energy of n logarithmically interacting charges in the plane in an external field for some particular values of the inverse temperature this system is equivalent to the eigenvalue version of certain random matrix models where it is referred to as the dyson gas of eigenvalues to find the free energy at large n and the structure of 1 n corrections we first use the effective action approach and then confirm the results by solving the loop equation the results obtained give some new representations of the mathematical objects related to the dirichlet boundary value problem complex analysis and spectral geometry of exterior domains they also suggest interesting links with bosonic field theory on riemann surfaces gravitational anomalies and topological field theories

large scale correlations in normal non hermitian matrix ensembles we compute the large scale macroscopic correlations in ensembles of normal random matrices with a general non gaussian measure and in ensembles of general non hermitian matrices with a class of non gaussian measures in both cases the eigenvalues are complex and in the large n limit they occupy a domain in the complex plane for the case when the support of eigenvalues is a connected compact domain we compute two three and four point connected correlation functions in the first non vanishing order in 1 n in a manner that the algorithm of computing higher correlations becomes clear the correlation functions are expressed through the solution of the dirichlet boundary problem in the domain complementary to the support of eigenvalues

polyharmonic bergman spaces and bargmann type transforms abstract in the main result of the paper we prove the decomposition of polyharmonic bergman spaces over the upper half plane into spaces of polyanalytic functions then we introduce the decomposition of polyharmonic bergman spaces into the orthogonal sum of its true polyharmonic bergman subspaces and we state isometric isomorphisms between the different true polyharmonic bergman spaces this allows us to define the k th harmonic hilbert component of a polyharmonic bergman function and to prove closed formulas for the reproducing kernel functions of the true polyharmonic and the polyharmonic bergman spaces the harmonic complex fourier transform is introduced in order to give an explicit description of the cartesian and the laguerre harmonic components of the images of a bargmann type transform for the true polyharmonic bergman spaces finally it is proved that the polyharmonic bergman space of order j is isometric isomorphic to 2j copies of the corresponding hardy space

the ginibre ensemble of real random matrices and its scaling limits we give a closed form for the correlation functions of ensembles of a class of asymmetric real matrices in terms of the pfaffian of an antisymmetric matrix formed from a 2 2 matrix kernel associated to the ensemble we apply this result to the real ginibre ensemble and compute the bulk and edge scaling limits of its correlation functions as the size of the matrices becomes large

computational tools for exact conditional logistic regression logistic regression analyses are often challenged by the inability of unconditional likelihood based approximations to yield consistent valid estimates and p values for model parameters this can be due to sparseness or separability in the data conditional logistic regression though useful in such situations can also be computationally unfeasible when the sample size or number of explanatory covariates is large we review recent developments that allow efficient approximate conditional inference including monte carlo sampling and saddlepoint approximations we demonstrate through real examples that these methods enable the analysis of significantly larger and more complex data sets we find in this investigation that for these moderately large data sets monte carlo seems a better alternative as it provides unbiased estimates of the exact results and can be executed in less cpu time than can the single saddlepoint approximation moreover the double saddlepoint approximation while computationally the easiest to obtain offers little practical advantage it produces unreliable results and cannot be computed when a maximum likelihood solution does not exist

optimization of structures with nonlinear behavior using equivalent loads abstract nonlinear response optimization using the equivalent loads nroel method algorithm is proposed to perform optimization of non linear response structures the conventional method spends most of the design time on nonlinear analysis the nroel algorithm makes the equivalent load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions the equivalent loads are defined as the loads in linear analysis which generate the same response fields as those in nonlinear analysis the algorithm is validated for convergence and optimality the proposed algorithm is applied to a simple mathematical problem to verify the convergence and the optimality the nroel algorithm is applied to several structural problems with geometric and or material nonlinearity conventional optimization with sensitivity analysis using the finite difference method is also applied to the same examples the results of the optimizations are compared the proposed nroel method is found to be very efficient and good solutions are derived

fluctuations of eigenvalues of random normal matrices in this article we consider a fairly general potential in the plane and the corresponding boltzmann gibbs distribution of eigenvalues of random normal matrices as the order of the matrices tends to infinity the eigenvalues condensate on a certain compact subset of the plane the droplet we prove that fluctuations of linear statistics of eigenvalues of random normal matrices converge on compact subsets of the interior of the droplet to a gaussian field and we discuss various ramifications of this result

new approximation method for stress constraints in structural synthesis a new approximation method for dealing with stress constraints in structural synthesis is presented in previous methods it has been common to create an approximation of the actual constraints with respect to the design variables and then use this with optimization to produce a new candidate design in the present method the finite element nodal forces are instead approximated and these are used to create an explicit but often nonlinear approximation to the original problem the principal motivation is to create the best approximation possible in order to reduce the number of detailed finite element analyses needed to reach the optimum the method is shown to be quite simple while providing significant efficiency gains in the overall optimization task also the method produces such high quality approximations to the original problem that the need for move limits during the approximate optimization stage is greatly reduced examples are offered and compared with published results to demonstrate the efficiency and reliability of the proposed method it is concluded that there are considerable gains yet to be achieved through continued careful investigation of approximation techniques

an empirical assessment of saddlepoint approximations for testing a logistic regression parameter saddlepoint methods provide quick and easy approximations to significance levels for conditional tests of logistic regression parameters we evaluate the accuracies of saddlepoint approximations for three well known conditional tests bartlett s test for no three factor interaction in a 2 x 2 x 2 table the test for trend in a series of probabilities and the exact test of no association in stratified 2 x 2 tables with a common odds ratio general recommendations are suggested regarding the use of saddlepoint approximations for exact conditional significance levels

integrated nonlinear structural analysis and design proposition d une approche integree de l optimisation de structures mecaniques necessitant une analyse non lineaire le processus d optimisation part d une reponse linearisee de la structure les non linearites etant introduites au fur et a mesure de la convergence verification de la reduction du cout de l analyse par cette methode traitement de deux exemples de structure en treillis