integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity this article is devoted to the study of the asymptotic behavior of a class of energies defined on stochastic lattices under polynomial growth assumptions we prove that the energy functionals f varepsilon stored in the deformation of an varepsilon scaling of a stochastic lattice converge to a continuous energy functional when varepsilon goes to zero in particular the limiting energy functional is of integral type and deterministic if the lattice is ergodic we also generalize to systems and nonlinear settings well known results on stochastic homogenization of discrete elliptic equations as an application of the main result we prove the convergence of a discrete model for rubber towards the nonlinear theory of continuum mechanics we finally address some mechanical properties of the limiting models such as frame invariance isotropy and natural states

topology optimization using polytopes abstract meshing complex engineering domains is a challenging task arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains the geometric property of polyhedral meshes such as its unstructured nature and the connectivity of faces between elements makes them specially attractive for topology optimization applications numerical anomalies in designs such as the single node connections and checkerboard pattern can be naturally circumvented with polyhedrons in the current work we solve the governing three dimensional elasticity state equation using the virtual element method vem approach the main characteristic difference between vem and standard finite element methods fem is that in vem the canonical basis functions are not constructed explicitly rather the stiffness matrix is computed directly utilizing a projection map which extracts the linear component of the deformation such a construction guarantees the satisfaction of the patch test used by engineers as an indicator of optimal convergence of numerical solutions under mesh refinement finally the computations reduce to the evaluation of matrices which contain purely geometric surface facet quantities the present work focuses on the first order vem in which the degrees of freedom are associated with the vertices the features of the current optimization approach are demonstrated using numerical examples for compliance minimization and compliant mechanism problems

optimality of the triangular lattice for a particle system with wasserstein interaction we prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers the energy is defined on sets of points and their weights or equivalently on the set of atomic measures it consists of two terms the first term is the sum of the square root of the weights and the second is the quadratic optimal transport cost between the atomic measure and the lebesgue measure

harnack inequalities and discrete continuous error estimates for a chain of atoms with two body interactions we consider deformations in r 3 of an infinite linear chain of atoms where each atom interacts with all others through a two body potential we compute the effect of an external force applied to the chain at equilibrium the positions of the particles satisfy an euler lagrange equation for large classes of potentials we prove that every solution is well approximated by the solution of a continuous model we establish an error estimate between the discrete and the continuous solution based on a harnack lemma of indepen dent interest finally we apply our results to some lennard jones potentials

understanding unit rooters a helicopter tour skewed asymptotically while the likelihood and hence the posterior pdf remains symmetric we show that no single prior can rationalize treating p values as probabilities in these models and we display examples of the sample dependent priors that would do so we argue that these results imply at a minimum that the usual test statistics and covariance matrices for autoregressions which characterize the likelihood shape in dynamic models just as in static regression models should be reported without any corrections for the special unit root distribution theory even if the corrected classical p values are reported as well

bayesian vector autoregressions with stochastic volatility this paper proposes a bayesian approach to a vector autoregression with stochastic volatility where the multiplicative evolution of the precision matrix is driven by a multivariate beta variate exact updating formulas are given to the nonlinear filtering of the precision matrix estimation of the autoregressive parameters requires numerical methods an importance sampling based approach is explained here

higher dimensional coulomb gases and renormalized energy functionals we consider a classical system of n charged particles in an external confining potential in any dimension d larger than 2 the particles interact via pairwise repulsive coulomb forces and the coupling parameter scales like the inverse of n mean field scaling by a suitable splitting of the hamiltonian we extract the next to leading order term in the ground state energy beyond the mean field limit we show that this next order term which characterizes the fluctuations of the system is governed by a new renormalized energy functional providing a way to compute the total coulomb energy of a jellium i e an infinite set of point charges screened by a uniform neutralizing background in any dimension the renormalization that cuts out the infinite part of the energy is achieved by smearing out the point charges at a small scale as in onsager s lemma we obtain consequences for the statistical mechanics of the coulomb gas next to leading order asymptotic expansion of the free energy or partition function characterizations of the gibbs measures estimates on the local charge fluctuations and factorization estimates for reduced densities this extends results of sandier and serfaty to dimension higher than two by an alternative approach

tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing front delaunay triangulation a method of unstructured technical mesh generation for general three dimensional domains is presented a conventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology the geometry of the surfaces is represented either analytically or by piecewise polynominal interpolation a preliminary surface mesh is generated by an advancing front method with the nodes inserted by hard sphere packing in physical space in accordance with a prescribed mesh density interior nodes are inserted in a face centered cubic fcc crystal lattice arrangements coupled to octree spatial subdivision with the local lattice parameter determined by a prespecified nodal density function prior to triangulation of the volume the preliminary surface mesh is preprocessed by a combination of local transformations and subdivisions in order to guarantee that the surface triangulation be a subcomplex of the volume delaunay triangulation a joint delaunay triangulation of the interior and boundary nodes which preserves the modified surface mesh is then constructed via an advancing front approach the resulting mesh is finally improved upon by the application of local transformations the overall time complexity of the mesher is o n log n the robustness and versatility of the approach as well as the good quality of the resulting meshes is demostrated with the aid of selected examples

boundary recovery for three dimensional conforming delaunay triangulation we present an efficient boundary recovery method for conforming delaunay triangulation of three dimensional domains our method combines local transformations like edges faces swappings and modified constrained delaunay refinement like edges faces splittings to recover the missing boundary edges and faces its convergence is theoretically proved its effectiveness is also demonstrated through some meshing examples

nonparametric identification in nonseparable panel data models with generalized fixed effects abstract this paper extends the familiar notion of fixed effects to nonlinear structures with infinite dimensional unobservables like preferences the main result is that a generalized version of differencing identifies local average responses lars in nonseparable structures in contrast to existing results this does not require either substantial restrictions on functional form or independence between the persistent unobservables and the explanatory variables of interest and it requires only two time periods on the other hand the results are confined to the subpopulation of stayers chamberlain 1982 i e the population for which the explanatory variables do not change over time we extend the basic framework to include time trends and dynamics in the explanatory variables and we show how distributional effects as well as average partial effects are identified our approach also allows endogeneity in the transitory unobservables furthermore we show that this new identification principle can be applied to well known objects like the slope coefficient in the semiparametric panel data binary choice model with fixed effects finally we suggest estimators for the local average response and average partial effect and we analyze their large and finite sample behavior

regularity of local minimizers of the interaction energy via obstacle problems the repulsion strength at the origin for repulsive attractive potentials determines the regularity of local minimizers of the interaction energy in this paper we show that if this repulsion is like newtonian or more singular than newtonian but still locally integrable then the local minimizers must be locally bounded densities and even continuous for more singular than newtonian repulsion we prove this and some other regularity results by first showing that the potential function associated to a local minimizer solves an obstacle problem and then by using classical regularity results for such problems

sieve m inference on irregular parameters abstract this paper presents sieve inferences on possibly irregular i e slower than root n estimable functionals of semi nonparametric models with i i d data we provide a simple consistent variance estimator of the plug in sieve m estimator of a possibly irregular functional and the asymptotic standard normality of the sieve t statistic we show that for hypothesis testing of irregular functionals the sieve likelihood ratio statistic is asymptotically chi square distributed these results are useful in inference on structural parameters that may have singular semiparametric efficiency bounds a simulation study and an empirical application of heckman and singer 1984 duration model are presented

binary response models for panel data identification and information this paper considers a panel data model for predicting a binary outcome the conditional probability of a positive response is obtained by evaluating a given distribution function f at a linear combination of the predictor variables one of the predictor variables is unobserved it is a random effect that varies across individuals but is constant over time the semiparametric aspect is that the conditional distribution of the random effect given the predictor variables is unrestricted this paper has two results if the support of the observed predictor variables is bounded then identification is possible only in the logistic case even if the support is unbounded so that from manski 1987 identification holds quite generally the information bound is zero unless f is logistic hence consistent estimation at the standard pn rate is possible only in the logistic case

the energy of some microscopic stochastic lattices we introduce a notion of energy for some microscopic stochastic lattices such lattices are broad generalizations of simple periodic lattices for which the question of the definition of an energy was examined in a series of previous works 14 18 note that slightly more general deterministic geometries were also considered in 6 these lattices are involved in the modelling of materials whose microscopic structure is a perturbation in a sense made precise in the article of the periodic structure of a perfect crystal the modelling considered here is either a classical modelling where the sites of the lattice are occupied by ball like atomic systems that interact by pair potentials or a quantum modelling where the sites are occupied by nuclei equipped with an electronic structure spread all over the ambient space the corresponding energies for the infinite stochastic lattices are derived consistently with truncated systems of finite size by application of a thermodynamic limit process subsequent works 7 8 will be devoted to the macroscopic limits of the energies of such microscopic lattices thereby extending to a stochastic context the results of 4 5 such convergences in a stochastic setting in dimension 1 have been studied in 21 22 we will also study in 8 some variants and extensions of the stationary setting presented here

testing identifying assumptions in nonseparable panel data models abstract recent work on nonparametric identification of average partial effects apes from panel data require restrictions on individual or time heterogeneity identifying assumptions under the generalized first differencing category such as time homogeneity chernozhukov et al 2013 have testable equality restrictions on the distribution of the outcome variable this paper proposes specification tests based on these restrictions the bootstrap critical values for the resulting kolmogorov smirnov and cramer von mises statistics are shown to be asymptotically valid and deliver good finite sample properties in monte carlo simulations an empirical application illustrates the merits of testing nonparametric identification from an empiricist s perspective

uniform energy distribution for an isoperimetric problem with long range interactions we study minimizers of a nonlocal variational problem the problem is a mathematical paradigm for the ubiquitous phenomenon of energy driven pattern formation induced by competing short and long range interactions the short range interaction is attractive and comes from an interfacial energy and the long range interaction is repulsive and comes from a nonlocal energy contribution in particular the problem is the sharp interface version of a problem used to model microphase separation of diblock copolymers a natural conjecture is that in all space dimensions minimizers are essentially periodic on an intrinsic scale however proving any periodicity result turns out to be a formidable task in dimensions larger than one in this paper we address a weaker statement concerning the distribution of energy for minimizers we prove in any space dimension that each component of the energy interfacial and nonlocal of any minimizer is uniformly distributed on cubes which are suciently large with respect to the intrinsic length scale moreover we also prove an l 1 bound on the optimal potential associated with the long range interactions this bound allows for an interesting interpretation note that the average volume fraction of the optimal pattern in a subsystem of size r fluctuates around the system average m the bound on the potential yields a rate of decay of these fluctuations as r tends to 1 this rate of decay is stronger than the one for a random checkerboard pattern in this sense the optimal pattern has less large scale variations of the average volume fraction than a pattern with a finite correlation

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

the strength of evidence for unit autoregressive roots and structural breaks a bayesian perspective economic time series may be generated by a process with a unit autoregressive root and the generating process may exhibit an abrupt break in trend it is well known that the outcomes of classical tests for either one of these phenomena can be seriously influenced when the presence of the other is ignored therefore care is required in disentangling evidence in the data supporting the two phenomena and there is some question as to the extent to which such disentanglement is feasible we approach this question from a bayesian perspective assessing the impact on the strength of evidence for each of the phenomena in the presence of the other

froth like minimizers of a non local free energy functional with competing interactions we investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions in particular the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one the competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction in this sense the optimal or quasi optimal profiles are froth like if seen on the scale of the antiferromagnetic potential they look neutral but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other in this paper we prove the validity of this picture we compute the oscillation scale of the quasi optimal profiles and we quantify their distance in norm from a reference periodic profile the proof consists of two main steps we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale in this way we reduce the original functional to an effective sharp interface one next we study the latter by reflection positivity methods which require as a key ingredient the exact locality of the short range term our proof has the conceptual interest of combining coarse graining with reflection positivity methods an idea that is presumably useful in much more general contexts than the one studied here

using a likelihood perspective to sharpen econometric discourse three examples this paper discusses a number of areas of inference where dissatisfaction by applied workers with the prescriptions of econometric high theory is strong and where a likelihood approach diverges strongly from the mainstream approach in its practical prescriptions two of the applied areas are related and have in common that they involve nonstationarity macroeconomic time series modeling and analysis of panel data in the presence of potential nonstationarity the third area is nonparametric kernel regression methods the conclusion is that in these areas a likelihood perspective leads to more useful honest and objective reporting of results and characterization of uncertainty it also leads to insights not as easily available from the usual perspective on inference

geometric self assembly of rigid shapes self assembly of shapes from spheres to nonsmooth and possibly nonconvex shapes is pervasive throughout the sciences these arrangements arise in biology for animal flocking and herding in condensed matter physics with molecular and nano self assembly and in control theory for coordinated motion problems while idealizing these often nonconvex objects as points or spheres aids in analysis the effects of shape curvature and convexity are often dramatic especially for short range interactions in this paper we develop a general purpose model for arranging rigid shapes in euclidean domains and on flat tori the shapes are arranged optimally with respect to minimization of a geometric voronoi based cost function which generalizes the notion of a centroidal voronoi tessellation from point sources to general rigid shapes building upon our previous work in l j larsson r choksi and j c nave siam j sci comput 36 2014 pp a792 a827 we present an efficient and fast algorithm for the minimization of this nonlocal albeit finite dimensional variational problem the algorithm applies in any space dimension and can be used to generate self assemblies of any collection of nonconvex piecewise smooth shapes we also provide a result which supports the intuition that self assembled shapes should be centered in and aligned with their voronoi regions

the optimal centroidal voronoi tessellations and the gersho s conjecture in the three dimensional space optimal centroidal voronoi tessellations have important applications in many different areas such as vector quantization data and image processing clustering analysis and resource management in the three dimensional euclidean space they are also useful to the mesh generation and optimization in this paper we conduct extensive numerical simulations to investigate the asymptotic structures of optimal centroidal voronoi tessellations for a given domain such a problem is intimately related to the famous gersho s conjecture for which a full proof is still not available we provide abundant evidence to substantiate the claim of the conjecture the body centered cubic lattice or par6 based centroidal voronoi tessellation has the lowest cost or energy per unit volume and is the most likely congruent cell predicted by the three dimensional gersho conjecture more importantly we probe the various properties of this optimal configuration including its dual triangulations which bear significant consequences in applications to three dimensional high quality meshing

a proof of crystallization in two dimensions many materials have a crystalline phase at low temperatures the simplest example where this fundamental phenomenon can be studied are pair interaction energies of the type where y x 2 is the position of particle x and v r is the pair interaction energy of two particles which are placed at distance r due to the mermin wagner theorem it can t be expected that at finite temperature this system exhibits long range ordering we focus on the zero temperature case and show rigorously that under suitable assumptions on the potential v which are compatible with the growth behavior of the lennard jones potential the ground state energy per particle converges to an explicit constant e where e is the minimum of a simple function on 0 furthermore if suitable dirichlet or periodic boundary conditions are used then the minimizers form a triangular lattice to the best knowledge of the author this is the first result in the literature where periodicity of ground states is established for a physically relevant model which is invariant under the euclidean symmetry group consisting of rotations and translations

constrained centroidal voronoi tessellations for surfaces centroidal voronoi tessellations are useful for subdividing a region in euclidean space into voronoi regions whose generators are also the centers of mass with respect to a prescribed density function of the regions their extensions to general spaces and sets are also available for example tessellations of surfaces in a euclidean space may be considered in this paper a precise definition of such constrained centroidal voronoi tessellations ccvts is given and a number of their properties are derived including their characterization as minimizers of an energy deterministic and probabilistic algorithms for the construction of ccvts are presented and some analytical results for one of the algorithms are given computational examples are provided which serve to illustrate the high quality of ccvt point sets finally ccvt point sets are applied to polynomial interpolation and numerical integration on the sphere

bayesian and frequentist inference in partially identified models a large sample approximation of the posterior distribution of partially identified structural parameters is derived for models that can be indexed by a finite dimensional reduced form parameter vector it is used to analyze the dierences between frequentist confidence sets and bayesian credible sets in partially identified models a key dierence is that frequentist set estimates extend beyond the boundaries of the identified set conditional on the estimated reduced form parameter whereas bayesian credible sets can asymptotically be located in the interior of the identified set our asymptotic approximations are illustrated in the context of simple moment inequality models and a numerical illustration for a two player entry game is provided

constrained boundary recovery for three dimensional delaunay triangulations summary a new constrained boundary recovery method for three dimensional delaunay triangulations is presented it successfully resolves the difficulties related to the minimal addition of steiner points and their good placement applications to full mesh generation are discussed and numerical examples are provided to illustrate the effectiveness of guaranteed recovery procedure copyright 2004 john wiley sons ltd

ground states of the 2d sticky disc model fine properties and n 3 4 law for the deviation from the asymptotic wulff shape we investigate ground state configurations for a general finite number n of parti cles of the heitmann radin sticky disc pair potential model in two dimensions exact energy minimizers are shown to exhibit large microscopic fluctuations about the asymptotic wulff shape which is a regular hexagon there are arbitrarily large n with ground state configura tions deviating from the nearest regular hexagon by a number of n 3 4 particles we also prove that for any n and any ground state configuration this deviation is bounded above by n 3 4 as a consequence we obtain an exact scaling law for the fluctuations about the asymptotic wulff shape in particular our results give a sharp rate of convergence to the limiting wulff shape

binary response correlated random coefficient panel data models abstract in this paper we consider binary response correlated random coefficient crc panel data models which are frequently used in the analysis of treatment effects and demand of products we focus on the nonparametric identification and estimation of panel data models under unobserved heterogeneity which is captured by random coefficients and when these random coefficients are correlated with regressors our identification conditions and estimation are based on the framework of the model with a special regressor which is a novel approach proposed by lewbel 1998 lewbel 2000 to solve the heterogeneity and endogeneity problem in the binary response models with the help of the additional information on the special regressor we can transform a binary response crc model to a linear moment relation we also construct a semiparametric estimator for the average slopes and derive the n normality result further we propose a nonparametric method to test the correlations between random coefficients and regressors simulations are given to show the finite sample performance of our estimators and test statistics

a theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity the energy functional of nonlinear plate theory is a curvature functional for surfaces rst proposed on physical grounds by g kirchhoff in 1850 we show that it arises as a 0 limit of three dimensional nonlinear elasticity theory as the thickness of a plate goes to zero a key ingredient in the proof is a sharp rigidity estimate for maps v v u r n u r n we show that the l 2 distance of rv from a single rotation matrix is bounded by a multiple of the l 2 distance from

individual and time effects in nonlinear panel models with large n t fixed eects estimators of nonlinear panel data models can be severely biased because of the well known incidental parameter problem we develop analytical and jackknife bias corrections for nonlinear models with both individual and time eects under asymptotic sequences where the time dimension t grows with the cross sectional dimension n the time eects introduce additional incidental parameter bias as the existing bias corrections apply to models with only individual eects we derive the appropriate corrections the basis for the corrections are general asymptotic expansions of xed eects estimators with incidental parameters in multiple dimensions we apply the expansions to m estimators with concave objective functions in parameters for panel models with additive individual and time eects these estimators cover xed eects estimators of the most popular limited dependent variable models such as logit probit ordered probit tobit and poisson models our analysis therefore extends the use of large t bias adjustments to an important class of models we also develop bias corrections for functions of the data parameters and individual and time eects including average partial eects in this case the incidental parameter bias is asymptotically of second order in general but the corrections improve nite sample properties

comparing dynamic equilibrium models to data a bayesian approach abstract this paper studies the properties of the bayesian approach to estimation and comparison of dynamic equilibrium economies both tasks can be performed even if the models are nonnested misspecified and nonlinear first we show that bayesian methods have a classical interpretation asymptotically the parameter point estimates converge to their pseudotrue values and the best model under the kullback leibler distance will have the highest posterior probability second we illustrate the strong small sample behavior of the approach using a well known application the u s cattle cycle bayesian estimates outperform maximum likelihood results and the proposed model is easily compared with a set of bvars

error bands for impulse responses we show how correctly to extend known methods for generating error bands in reduced form var s to overidentified models we argue that the conventional pointwise bands common in the literature should be supplemented with measures of shape uncertainty and we show how to generate such measures we focus on bands that characterize the shape of the likelihood such bands are not classical confidence regions we explain that classical confidence regions mix information about parameter location with information about model fit and hence can be misleading as summaries of the implications of the data for the location of parameters because classical confidence regions also present conceptual and computational problems in multivariate time series models we suggest that likelihood based bands rather than approximate confidence bands based on asymptotic theory be standard in reporting results for this type of model

priors for unit root models abstract a method of assessing an economist s subjective prior for a unit root model is given and applied the methods extend previous work by allowing a family of piecewise conjugate prior distribution that permit different opinions when 1 this larger family is still closed under sampling so it retains the simplicity that is the principal advantage of conjugate analysis

large sample properties of posterior densities bayesian information criterion and the likelihood principle in nonstationary time series models asymptotic normality of the posterior is a well understood result for dynamic as well as nondynamic models based on sets of abstract conditions whose actual applicability is hardly known especially for the case of nonstationarity in this paper we provide a set of conditions by which we can relatively easily prove the asymptotic posterior normality under quite general situations of possible nonstationarity this result reinforces and generalizes the point of sims and uhlig 1991 that inference based on the likelihood principle explained by berger and wolpert 1988 will be unchanged regardless of whether the data are generated by a stationary process or by a unit root process on the other hand our conditions allow us to generalize the bayesian information criterion known as the schwarz criterion to the case of possible nonstationarity in addition we have shown that consistency of the maximum likelihood estimator not the asymptotic normality of the estimator with some minor additional assumptions is sufficient for asymptotic posterior normality

phase transitions for dilute particle systems with lennard jones potential we consider a classical dilute particle system in a large box with pair interaction given by a lennard jones type potential the inverse temperature is picked proportionally to the logarithm of the particle density we identify the free energy per particle in terms of a variational formula and show that this formula exhibits a cascade of phase transitions as the temperature parameter ranges from zero to infinity loosely speaking the particle system separates into spatially distant components in such a way that within each phase all components are of the same size which is the larger the lower the temperature the main tool in our proof is a new large deviation principle for sparse point configurations

multiplicative error models with sample selection this paper presents a simple approach to deal with sample selection in models with multiplicative errors models for non negative limited dependent variables such as counts fit this framework the approach builds on a specification of the conditional mean of the outcome only and is therefore semiparametric in nature gmm estimators are constructed for both cross section data and for panel data we derive distribution theory and present monte carlo evidence on the finite sample performance of the estimators

a physics motivated centroidal voronoi particle domain decomposition method in this paper we propose a novel domain decomposition method for large scale simulations in continuum mechanics by merging the concepts of centroidal voronoi tessellation cvt and voronoi particle dynamics vp the cvt is introduced to achieve a high level compactness of the partitioning subdomains by the lloyd algorithm which monotonically decreases the cvt energy the number of computational elements between neighboring partitioning subdomains which scales the communication effort for parallel simulations is optimized implicitly as the generated partitioning subdomains are convex and simply connected with small aspect ratios moreover voronoi particle dynamics employing physical analogy with a tailored equation of state is developed which relaxes the particle system towards the target partition with good load balance since the equilibrium is computed by an iterative approach the partitioning subdomains exhibit locality and the incremental property numerical experiments reveal that the proposed centroidal voronoi particle cvp based algorithm produces high quality partitioning with high efficiency independently of computational element types thus it can be used for a wide range of applications in computational science and engineering

average and quantile effects in nonseparable panel models nonseparable panel models are important in a variety of economic settings including discrete choice this paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like time is randomly assigned or time is an instrument partial identification results for average and quantile effects are given for discrete regressors under static or dynamic conditions in fully nonparametric and in semiparametric models with time effects it is shown that the usual linear fixed effects estimator is not a consistent estimator of the identified average effect and a consistent estimator is given a simple estimator of identified quantile treatment effects is given providing a solution to the important problem of estimating quantile treatment effects from panel data bounds for overall effects in static and dynamic models are given the dynamic bounds provide a partial identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity the impact of t the number of time periods is shown by deriving shrinkage rates for the identified set as t grows we also consider semiparametric discrete choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds computationally convenient methods for semiparametric models are presented we propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples we give empirical illustrations

a zador like formula for quantizers based on periodic tilings we consider zador s 1963 1966 1982 asymptotic formula for the distortion rate function for a variable rate vector quantizer in the high rate case this formula involves the differential entropy of the source the rate of the quantizer in bits per sample and a coefficient g which depends on the geometry of the quantizer but is independent of the source we give an explicit formula for g in the case when the quantizing regions form a periodic tiling of n dimensional space in terms of the volumes and second moments of the voronoi cells as an application we show extending earlier work of kashyap and neuhoff see ibid vol 47 p 2538 2383 2001 that even a variable rate three dimensional quantizer based on the a15 structure is still inferior to a quantizer based on the body centered cubic lattice we also determine the smallest covering radius of such a structure

centroidal voronoi tessellation based finite element superconvergence in this article a finding on finite element superconvergence is reported the laplacian operator with dirichlet boundary condition is considered the linear finite element solutions have an o h2 0 5 superconvergence in l2 norm at nodes on an almost equilateral triangular mesh generated based on centroidal voronoi tessellation for an arbitrary 2d bounded domain extensive numerical examples are presented to demonstrate the superconvergence property copyright 2008 john wiley sons ltd

hexagonal patterns in a simplified model for block copolymers in this paper we study a new model for patterns in two dimensions inspired by diblock copolymer melts with a dominant phase the model is simple enough to be amenable not only to numerics but also to analysis yet sophisticated enough to reproduce hexagonally packed structures that resemble the cylinder patterns observed in block copolymer experiments starting from a sharp interface continuum model a nonlocal energy functional involving a wasserstein cost we derive the new model using gamma convergence in a limit where the volume fraction of one phase tends to zero the limit energy is defined on atomic measures in three dimensions the atoms represent small spherical blobs of the minority phase and in two dimensions they represent thin cylinders of the minority phase we then study local minimizers of the limit energy numerical minimization is performed in two dimensions by recasting the problem as a computational geometry problem involving power diagrams the numerical results suggest that the sma

a model of fractional cointegration and tests for cointegration using the bootstrap abstract the paper proposes a framework for modelling cointegration in fractionally integrated processes and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap in these procedures arfima models are fitted to the data and the estimates used to simulate the null hypothesis of non cointegration in a vector autoregressive modelling framework the simulations are used to estimate p values for alternative regression based test statistics including the f goodness of fit statistic the durbin watson statistic and estimates of the residual d the bootstrap distributions are economical to compute being conditioned on the actual sample values of all but the dependent variable in the regression the procedures are easily adapted to test stronger null hypotheses such as statistical independence the tests are not in general asymptotically pivotal but implemented by the bootstrap are shown to be consistent against alternatives with both stationary and nonstationary cointegrating residuals as an example the tests are applied to the series for uk consumption and disposable income the power properties of the tests are studied by simulations of artificial cointegrating relationships based on the sample data the f test performs better in these experiments than the residual based tests although the durbin watson in turn dominates the test based on the residual d

voronoi regions of lattices second moments of polytopes and quantization if a point is picked at random inside a regular simplex octahedron 600 cell or other polytope what is its average squared distance from the centroid in n dimensional space what is the average squared distance of a random point from the closest point of the lattice a n or d n e n a n ast or d n ast the answers are given here together with a description of the voronoi or nearest neighbor regions of these lattices the results have applications to quantization and to the design of signals for the gaussian channel for example a quantizer based on the eight dimensional lattice e8 has a mean squared error per symbol of 0 0717 cdots when applied to uniformly distributed data compared with 0 08333 cdots for the best one dimensional quantizer

identification and n consistent estimation of a nonlinear panel data model with correlated unobserved effects abstract this paper investigates identification and root n consistent estimation of a class of single index panel data models in which the link function is unknown the unobserved individual effects may be correlated with all the explanatory variables and all the explanatory variables may be predetermined we propose two sets of sufficient conditions one in which link function is assumed to be strictly increasing and the other in which it is not we propose simple kernel based estimators for the models and derive consistency and asymptotic normality results for the proposed estimators finally we present results of two monte carlo studies of the estimators

bounds on the geometric complexity of optimal centroidal voronoi tesselations in 3d gersho s conjecture in 3d asserts the asymptotic periodicity and structure of the optimal centroidal voronoi tessellation this relatively simple crystallization problem remains to date open we prove bounds on the geometric complexity of optimal centroidal voronoi tessellations as the number of generators tends to infinity combined with an approach of gruber in 2d these bounds reduce the resolution of the 3d gersho s conjecture to a finite albeit very large computation of an explicit convex problem in finitely many variables

droplet minimizers of an isoperimetric problem with long range interactions we give a detailed description of the geometry of single droplet patterns in a non local isoperimetric problem in particular we focus on the sharp interface limit of the ohta kawasaki free energy for diblock copolymers regarded as a paradigm for those energies modeling physical systems characterized by a competition between short and a long range interactions exploiting fine properties of the regularity theory for minimal surfaces we extend previous partial results in different directions and give robust tools for the geometric analysis of more complex patterns where u is the order parameter of a two phases system confined in r n and and m are two nonnegative numerical parameters the two terms in the energy mimic attractive short range and repulsive long range energies between the phases more precisely the first term is local it favors minimal interface area and drives the system toward a partition into few pure phases while the second term involving a coulomb like kernel g is non local and favor a fine mixing of the phases a detailed description of the energy is given in 1 the competition between these two terms is expected to induce the formation of highly regular mesoscopic patterns whose geometry strongly depends on the choice of the parameters and m e g spherical spots cylinders gyroids and lamellae 0 1 the ohta kawasaki functional for diblock copolymers the model we consider arises as a simplification of a ginzburg landau functional proposed by ohta and kawasaki in their pioneering paper 41 as a possible description of a diblock copolymers dbc system even though it is questionable whether such an energy actually describes dbcs see choksi and ren 15 muratov 39 and niethammer and oshita 40 nevertheless it is a first and mathematically non trivial attempt to capture some of the main features of these systems for such a reason it deserved over the last twenty years great attention from both the mathematical and the physical

the hexagon theorem we wish to int s z f z 2 s the unit square over all choices of f z which take just n values for large n it is shown that f z approaches that function which on each face of a hexagonal mesh has the value of the centroid of that face this problem in the design of quantizers for a pulse code modulation pcm system arose in which pairs of adjacent samples are quantized in an effort to capitalize on the correlation between samples and on the geometry of the plane

sieve wald and qlr inferences on semi nonparametric conditional moment models this paper considers inference on functionals of semi nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals which include all of the nonlinear nonparametric instrumental variables iv as special cases these models are often ill posed and hence it is difficult to verify whether a possibly nonlinear functional is root n estimable or not we provide computationally simple unified inference procedures that are asymptotically valid regardless of whether a functional is root n estimable or not we establish the following new useful results 1 the asymptotic normality of a plug in penalized sieve minimum distance psmd estimator of a possibly nonlinear functional 2 the consistency of simple sieve variance estimators for the plug in psmd estimator and hence the asymptotic chi square distribution of the sieve wald statistic 3 the asymptotic chi square distribution of an optimally weighted sieve quasi likelihood ratio qlr test under the null hypothesis 4 the asymptotic tight distribution of a non optimally weighted sieve qlr statistic under the null 5 the consistency of generalized residual bootstrap sieve wald and qlr tests 6 local power properties of sieve wald and qlr tests and of their bootstrap versions 7 asymptotic properties of sieve wald and sqlr for functionals of increasing dimension simulation studies and an empirical illustration of a nonparametric quantile iv regression are presented

existence of compactly supported global minimisers for the interaction energy the existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses the main assumption on the potential is that it is catastrophic or not h stable which is the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics the proof is based on a uniform control on the local mass around each point of the support of a global minimiser together with an estimate on the size of the gaps it may have the class of potentials for which we prove the existence of global minimisers includes power law potentials and for some range of parameters morse potentials widely used in applications we also show that the support of local minimisers is compact under suitable assumptions

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments

new integral estimates for deformations in terms of their nonlinear strains if u is a bi lipschitzian deformation of a bounded lipschitz domain in ln n 2 we show that the lp norm p 1 p n of a certain nonlinear strain function e u associated with u dominates the distance in lq q np n p if p n from u to a suitably chosen rigid motion of n this work extends that of f john who proved corresponding estimates for p 1 under the hypothesis that u has uniformly small strain we also obtain a bound for the oscillation of du in l2 these estimates are apparently the first to apply with no a priori pointwise hypotheses upon the strain of u in 3 the integral int limits omega e u 2d 3 is dominated by typical hyperelastic energy functionals proposed in the literature for modeling the behavior of rubber thus the case n 3 p 2 gives the first general bound for the deformations of such materials in terms of the associated nonlinear elastic work

grid generation and optimization based on centroidal voronoi tessellations centroidal voronoi tessellations cvts are voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding voronoi regions such tessellations are of use in very diverse applications including data compression clustering analysis cell biology territorial behavior of animals and optimal allocation of resources in this paper we explore the use of cvts in grid generation in connection with finite element approximations of partial differential equations we being by describing these tessellations and methods for their determination we then discuss their application to mesh generation and finish with some examples of their use for the solution of partial differential equations

deciding between i 1 and i 0 abstract a class of procedures that consistently classify the stochastic component of a time series as being integrated either of order zero i 1 or one i 1 are proposed for general i 0 or i 1 processes and polynomial or piecewise linear detrending large sample bayesian inference is free of nuisance parameters describing short run dynamics and requires specifying priors only on the point hypotheses i 1 and i 1 thereby avoiding problematic choices of parametric priors over roots and nuisance parameters applied to the nelson plosser 1982 data with linear detrending these procedures largely support nelson and plosser s original inferences with piecewise linear detrending these data are typically uninformative producing bayes ratios close to one

superconvergence analysis for the explicit polynomial recovery method a new recovery technique explicit polynomial recovery epr is analyzed for finite element methods epr reconstructs the value at edge centers by solving a local problem in combination with the finite element solution at the vertex a quadratic approximation is constructed besides improving the accuracy it can also be applied in building the epr based error estimator for the poisson equation the element center is a superconvergent point of the gradient of the epr recovered function on an equilateral triangulation numerical examples are presented to verify the theoretical results and to show the performance of the epr in the adaptive finite element method

heterogeneity and selection in dynamic panel data abstract the data generating process dgp for generic dynamic panel data consists of a law of state dynamics g a selection or attrition rule h and an initial condition f i study nonparametric identifiability of this complete dgp g h f using short unbalanced panel data allowing for nonseparability between observed states and unobserved heterogeneity in each of g h and f for t 3 the dgp is identified by using a proxy variable for t 6 the three additional periods construct a proxy and thus the dgp is identified without an auxiliary variable

convergence of the lloyd algorithm for computing centroidal voronoi tessellations centroidal voronoi tessellations cvts are voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids mass centers of the corresponding voronoi regions with respect to a given density function centroidal voronoi tessellations may also be defined in more abstract and more general settings due to the natural optimization properties enjoyed by cvts they have many applications in diverse fields the lloyd algorithm is one of the most popular iterative schemes for computing the cvts but its theoretical analysis is far from complete in this paper some new analytical results on the local and global convergence of the lloyd algorithm are presented these results are derived through careful utilization of the optimization properties shared by cvts numerical experiments are also provided to substantiate the theoretical analysis

on quantization with the weaire phelan partition until recently the solution to the kelvin problem of finding a partition of r sup 3 into equal volume cells with the least surface area was believed to be tessellation by the truncated octahedron in 1994 d weaire and r phelan described a partition that outperformed the truncated octahedron partition in this respect this raises the question of whether the weaire phelan wp partition can outperform the truncated octahedron partition in terms of normalized moment of inertia nmi thus providing a counterexample to gersho s conjecture that the truncated octahedron partition has the least nmi among all partitions of r sup 3 in this correspondence we show that the effective nmi of the wp partition is larger than that of the truncated octahedron partition we also show that if the wp partition is used as the partition of a three dimensional 3 d vector quantizer vq with the corresponding codebook consisting of the centroids of the cells then the resulting quantization error is white we then show that the effective nmi of the wp partition cannot he reduced by passing it through an invertible linear transformation another contribution of this correspondence is a proof of the fact that the quantization error corresponding to an optimal periodic partition is white which generalizes a result of zamir and feder 1996

tetrahedral mesh generation and optimization based on centroidal voronoi tessellations the centroidal voronoi tessellation based delaunay triangulation cvdt provides an optimal distribution of generating points with respect to a given density function and accordingly generates a high quality mesh in this paper we discuss algorithms for the construction of the constrained cvdt from an initial delaunay tetrahedral mesh of a three dimensional domain by establishing an appropriate relationship between the density function and the specified sizing field and applying the lloyd s iteration the constrained cvdt mesh is obtained as a natural global optimization of the initial mesh simple local operations such as edges faces flippings are also used to further improve the cvdt mesh several complex meshing examples and their element quality statistics are presented to demonstrate the effectiveness and efficiency of the proposed mesh generation and optimization method copyright 2003 john wiley sons ltd

centroidal power diagrams lloyd s algorithm and applications to optimal location problems in this paper we develop a numerical method for solving a class of optimization problems known as optimal location or quantization problems the target energy can be written either in terms of atomic measures and the wasserstein distance or in terms of weighted points and power diagrams generalized voronoi diagrams the latter formulation is more suitable for computation we show that critical points of the energy are centroidal power diagrams which are generalizations of centroidal voronoi tessellations and that they can be approximated by a generalization of lloyd s algorithm lloyd s algorithm is a common method for finding centroidal voronoi tessellations we prove that the algorithm is energy decreasing and prove a convergence theorem numerical experiments suggest that the algorithm converges linearly we illustrate the algorithm in two and three dimensions using simple models of optimal location and crystallization see online supplementary material

nonparametric identification of discrete choice models with lagged dependent variables abstract variation in covariates can be used to nonparametrically identify a discrete choice model with a lagged dependent variable and discrete unobserved heterogeneity kasahara and shimotsu 2009 browning and carro 2014 in some cases the number of support points of the unobserved heterogeneity distribution is restricted only by the number of points of support in the distribution of the covariates this paper provides conditions under which these models can be identified with continuous heterogeneity using continuous variation in the covariates the identification argument is related to that of honore and lewbel 2002 in that it requires a special regressor lewbel 1998 but it does not assume an additively separable latent index identification requires only 3 time periods neither stationarity nor time homogeneity is imposed and the distribution of the initial condition is not restricted apart from conditions required for the special regressor i demonstrate the result through a monte carlo simulation

existence of ground states of nonlocal interaction energies we investigate which nonlocal interaction energies have a ground state global minimizer we consider this question over the space of probability measures and establish a sharp condition for the existence of ground states we show that this condition is closely related to the notion of stability i e h stability of pairwise interaction potentials our approach uses the direct method of the calculus of variations

on the phase diagram for microphase separation of diblock copolymers an approach via a nonlocal cahn hilliard functional we consider analytical and numerical aspects of the phase diagram for microphase separation of diblock copolymers our approach is variational and is based upon a density functional theory which entails minimization of a nonlocal cahn hilliard functional based upon two parameters which characterize the phase diagram we give a preliminary analysis of the phase plane that is we divide the plane into regions wherein a combination of analysis and numerics is used to describe minimizers in particular we identify a regime wherein the uniform disordered state is the unique global minimizer a regime wherein the constant state is linearly unstable and where numerical simulations are currently the only tool for characterizing the phase geometry and a regime of small volume fraction wherein we conjecture that small well separated approximately spherical objects are the unique global minimizer for this last regime we present an asymptotic analysis from the point of view of the energetics which will be comp

meshfree probabilistic determination of point sets and support regions for meshless computing new algorithms are presented for the determination of point sets and associated support regions that can then be used in meshless computing methods the algorithms are probabilistic in nature so that they are totally meshfree i e they do not require at any stage the use of any coarse or fine boundary conforming or superimposed meshes computational examples are provided that show for both uniform and non uniform point distributions that the algorithms result in high quality point sets and high quality support regions furthermore the algorithms lend themselves well to parallelization

eqsm an efficient high quality surface grid generation method based on remeshing the eqsm method for the generation of unstructured triangular surface grids is presented the method is based on remeshing techniques and avoids the need for traditional mesh triangulation approaches such as the advancing front and the delaunay methods normalized edge lengths based on a metric derived from curvature or from a user specified spacing are employed as the remeshing criterion it is assumed that the geometry is input in the form of composite parametric surfaces with analytic definition or ferguson or nurbs type multiple patch representation examples based upon typical aircraft geometries are included to demonstrate how high quality grids can be efficiently generated on surfaces that exhibit a high degree of geometric complexity