conditional intensity and gibbsianness of determinantal point processes the papangelou intensities of determinantal or fermion point processes are investigated these exhibit a monotonicity property expressing the repulsive nature of the interaction and satisfy a bound implying stochastic domination by a poisson point process we also show that determinantal point processes satisfy the so called condition which is a general form of gibbsianness under a continuity assumption the gibbsian conditional probabilities can be identified explicitly

on strong invariance principles under dependence assumptions on obtient des principes d invariance forts avec un ordre d approximation o t 1 2 k pour des suites de variables aleatoires dependantes

multivariate spatial central limit theorems with applications to percolation and spatial graphs suppose x x x x in z d is a family of i i d variables in some measurable space b 0 is a bounded set in r d and for t 1 h t is a measure on t b 0 determined by the restriction of x to lattice sites in or adjacent to t b 0 we prove convergence to a white noise process for the random measure on b 0 given by t d 2 h t ta eh t ta for subsets a of b 0 as t becomes large subject to h satisfying a stabilization condition whereby the effect of changing x at a single site x is local but with no assumptions on the rate of decay of correlations we also give a multivariate central limit theorem for the joint distributions of two or more such measures h t and adapt the result to measures based on poisson and binomial point processes applications given include a white noise limit for the measure which counts clusters of critical percolation a functional central limit theorem for the empirical process of the edge lengths of the minimal spanning tree on random points and central limit theorems for the on line nearest neighbor graph

tests of equal forecast accuracy and encompassing for nested models we examine the asymptotic and finite sample properties of tests for equal forecast accuracy and encompassing applied to 1 step ahead forecasts from nested linear models we first derive the asymptotic distributions of two standard tests and one new test of encompassing and provide tables of asymptotically valid critical values monte carlo methods are then used to evaluate the size and power of tests of equal forecast accuracy and encompassing the simulations indicate that post sample tests can be reasonably well sized of the post sample tests considered the encompassing test proposed in this paper is the most powerful we conclude with an empirical application regarding the predictive content of unemployment for inflation

discrete approximations of determinantal point processes on continuous spaces tree representations and tail triviality we prove tail triviality of determinantal point processes mu on continuous spaces tail triviality has been proved for such processes only on discrete spaces and hence we have generalized the result to continuous spaces to do this we construct tree representations that is discrete approximations of determinantal point processes enjoying a determinantal structure there are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic gaussian analytic function with bergman kernel and the thermodynamic limit of eigenvalues of gaussian random matrices for hbox sine 2 hbox airy 2 hbox bessel 2 and ginibre point processes our main theorem proves all these point processes are tail trivial

statistical tests for multiple forecast comparison abstract we consider a multivariate version of the diebold mariano test for equal predictive ability of three or more forecasting models the wald type test s which has a null distribution that is asymptotically chi squared is shown to be generally invariant with respect to the ordering of the models being compared finite sample corrections for the test are also developed monte carlo simulations indicate that s has reasonable size properties in large samples but tends to be oversized in moderate samples the finite sample correction succeeds in correcting for size but only partially for the size adjusted tests power increases with sample size as expected it is speculated that further finite sample improvements can be achieved using hotelling s t 2 or bootstrap critical values

predictive ability with cointegrated variables in this paper we outline conditions under which the diebold and mariano dm j bus econom statist 13 1995 253 test for predictive ability can be extended to the case of two forecasting models each of which may include cointegrating relations when allowing for parameter estimation error we show that in the cases where either the loss function is quadratic or the length of the prediction period p grows at a slower rate than the length of the regression period r the standard dm test can be used on the other hand in the case of a generic loss function if p r as t 0 then the asymptotic normality result of west econometrica 64 1996 1067 no longer holds we also extend the data snooping technique of white econometrica 68 2000 1097 for comparing the predictive ability of multiple forecasting models to the case of cointegrated variables in a series of monte carlo experiments we examine the impact of both short run and cointegrating vector parameter estimation error on dm data snooping and related tests our results suggest that size is reasonable for r and p greater than 50 and power improves with p as expected furthermore the additional cost in terms of size distortion due to the estimation of the cointegrating relations is not substantial we illustrate the use of the tests in a nonnested cointegration framework by forming prediction models for industrial production which include two interest rate variables prices and either m1 m2 or m3

non intersecting paths random tilings and random matrices we investigate certain measures induced by families of non intersecting paths in domino tilings of the aztec diamond rhombus tilings of an abc hexagon a dimer model on a cylindrical brick lattice and a growth model the measures obtained e g the krawtchouk and hahn ensembles have the same structure as the eigenvalue measures in random matrix theory like gue which can in fact can be obtained from non intersecting brownian motions the derivations of the measures are based on the karlin mcgregor or lindstrom gessel viennot method we use the measures to show some asymptotic results for the models

a central limit theorem for critical first passage percolation in two dimensions consider independent first passage percolation on the edges of 2 denote the passage time of the edge e in 2 by t e and assume that p t e 0 1 2 p 0 t e c 0 0 for some constant c 0 0 and that e t e 4 denote by b 0 n the passage time from 0 to the halfplane x y x n and by t 0 nu the passage time from 0 to the nearest lattice point to nu for u a unit vector we prove that there exist constants 0 c 1 c 2 and n such that c 1 log n 1 2 n c 2 log n 1 2 and such that n 1 b 0 n eb 0 n and 2 n 1 t 0 nu et 0 nu converge in distribution to a standard normal variable as n u fixed a similar result holds for the site version of first passage percolation on 2 when the common distribution of the passage times t v of the vertices satisfies p t v 0 1 p t v c 0 p c 2 site critical probability of site percolation on 2 and e t u 4

clump counts in a mosaic on decrit des proprietes de second ordre en utilisant la theorie limite et des methodes approchees

the stationary bootstrap abstract this article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations previously a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the m dimensional joint distribution of m consecutive observations where m is fixed this procedure has been generalized by constructing a blocks of blocks resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole i e infinite dimensional joint distribution of the stationary sequence of observations these methods share the construction of resampling blocks of observations to form a pseudo time series so that the statistic of interest may be recalculated based on the resampled data set but in the context of applying this method to stationary data it is natural

a variational principle in the dual pair of reproducing kernel hilbert spaces and an application given a positive definite bounded linear operator a on the hilbert space mathcal h 0 l2 e we consider a reproducing kernel hilbert space mathcal h with a reproducing kernel a x y here e is any countable set and a x y x y e is the representation of a w r t the usual basis of mathcal h 0 imposing further conditions on the operator a we also consider another reproducing kernel hilbert space mathcal h with a kernel function b x y which is the representation of the inverse of a in a sense so that mathcal h mathcal h 0 mathcal h becomes a rigged hilbert space we investigate the ratios of determinants of some partial matrices of a and b we also get a variational principle on the limit ratios of these values we apply this relation to show the gibbsianness of the determinantal point process or fermion point process defined by the operator a i a 1 on the set e

limit theorems for monolayer ballistic deposition in the continuum we consider a deposition model in which balls rain down at random towards a 2 dimensional surface roll downwards over existing adsorbed balls are adsorbed if they reach the surface and discarded if not we prove a spatial law of large numbers and central limit theorem for the ultimate number of balls adsorbed onto a large toroidal surface and also for the number of balls adsorbed on the restriction to a large region of an infinite surface

robust out of sample inference this paper presents analytical empirical and simulation results concerning inference about the moments of nondifferentiable functions of out of sample forecasts and forecast errors special attention is given to the measurement of a model s predictive ability using the test of equal mean absolute error tests for equal mean absolute error and mean square error are used to evaluate predictions of excess returns to the s p 500 composite simulations indicate that appropriately constructed tests for equal mean absolute error can provide more accurately sized and more powerful tests than inappropriately constructed tests for equal mean absolute error and mean square error

a note on the decay of correlations under δ pinning we prove that for a class of massless interface models on 2 introduction of an arbitrarily small pinning self potential leads to exponential decay of correlation or in other words to creation of mass

determining simplicity and computing topological change in strongly normal partial tilings of r2 or r3 abstract a convex polygon in r2 or a convex polyhedron in r3 will be called a tile a connected set p of tiles is called a partial tiling if the intersection of any two of the tiles is either empty or is a vertex or edge in r3 or face of both p is called strongly normal sn if for any partial tiling p p and any tile p p the neighborhood n p p of p the union of the tiles of p that intersect p is simply connected let p be sn and let n p p be the excluded neighborhood of p in p i e the union of the tiles of p other than p itself that intersect p we call p simple in p if n p p and n p p are topologically equivalent this paper presents methods of determining for an sn partial tiling p whether a tile p p is simple and if not of counting the numbers of components and holes in r3 components tunnels and cavities in n p p

on normal approximations of distributions in terms of dependency graphs l auteur interprete les bornes de l erreur introduites par stein dans l approximation normale de sommes de variables aleatoires dependantes en termes de graphes de dependance ceci mene a des ameliorations d un theoreme de limite centrale de petrovskaya et leontovich et de recentes applications de baldi et rinatt en particulier on obtient des bornes pour des taux de convergence on etudie ensuite l approximation normale du nombre de maximums locaux d une fonction aleatoire sur un graphe

refinements of stochastic domination in a recent paper by two of the authors the concepts of upwards and downwards epsilon movability were introduced mainly as a technical tool for studying dynamical percolation of interacting particle systems in this paper we further explore these concepts which can be seen as refinements or quantifications of stochastic domination and we relate them to previously studied concepts such as uniform insertion tolerance and extractability

asymptotics for out of sample tests of granger causality abstract this paper presents analytical monte carlo and empirical evidence concerning out of sample tests of granger causality the environment is one in which the relative predictive ability of two nested parametric regression models is of interest results are provided for three statistics a regression based statistic suggested by granger and newbold 1977 forecasting economic time series academic press inc london a t type statistic comparable to those suggested by diebold and mariano 1995 comparing predictive accuracy journal of business and economic statistics 13 253 263 and west 1996 asymptotic inference about predictive ability econometrica 64 1067 1084 and an f type statistic akin to theil s u since the asymptotic distributions under the null are nonstandard tables of asymptotically valid critical values are provided monte carlo evidence supports the theoretical results an empirical example evaluates the predictive content of the chicago fed national activity index for growth in industrial production and core pce based inflation

asymptotic normality when regressors have a unit root under fairly general conditions ordinary least squares and linear instrumental variables estimators are asymptotically normal when a regression equation has nonstationary right hand side variables standard formulas may be used to calculate a consistent estimate of the asymptotic variance covariance matrix of the estimated parameter vector even if the disturbances are conditionally heteroskedastic and autocorrelated so inference may proceed in the usual way the key requirements are that the nonstationary variables share a common unit root and that the unconditional mean of their first differences is nonzero copyright 1988 by the econometric society

how to avoid spurious cluster validation a methodological investigation on simulated and fmri data abstract this paper presents an evaluation of a common approach that has been considered as a promising option for exploratory fmri data analyses the approach includes two stages creating from the data a sequence of partitions with increasing number of subsets clustering and selecting the one partition in this sequence that exhibits the clearest indications of an existing structure cluster validation in order to achieve that the selected partition is actually the best characterization of the data structure previous studies were directed to find the most appropriate validity function s in our analysis protocol we first optimize the sequence of partitions according to the given objective function our study showed that an insufficient optimization of the partition for one or more numbers of clusters can easily yield a spurious validation result which in turn may lead the analyst to a misleading interpretation of the fmri experiment however a sufficient optimization for each included number of clusters provided the basis for a reliable adequate characterization of the data furthermore it enabled an adequate evaluation of the validity functions these findings were obtained independently for three clustering algorithms representing the hard and fuzzy clustering variant and three up to date cluster validity functions the findings were derived from analyses of gaussian clusters simulated data sets that mimic typical fmri response signals and real fmri data based on our results we propose a number of options of how to configure improved clustering tools

negative association of random variables with applications random variables x 1 cdots x k are said to be negatively associated na if for every pair of disjoint subsets a 1 a 2 of 1 2 cdots k operatorname cov lbrack f x 1 i in a 1 g x j j in a 2 rbrack leq 0 for all nondecreasing functions f g the basic properties of negative association are derived especially useful is the property that nondecreasing functions of mutually exclusive subsets of na random variables are na this property is shown not to hold for several other types of negative dependence recently proposed one consequence is the inequality p x i leq x i i 1 cdots k leq prod k 1p x i leq x i for na random variables x 1 cdots x k and the dual inequality resulting from reversing the inequalities inside the square brackets in another application it is shown that negatively correlated normal random variables are na other na distributions are the a multinomial b convolution of unlike multinomials c multivariate hypergeometric d dirichlet and e dirichlet compound multinomial negative association is shown to arise in situations where the probability measure is permutation invariant applications of this are considered for sampling without replacement as well as for certain multiple ranking and selection procedures in a somewhat striking example na and positive association representing quite strong opposing types of dependence are shown to exist side by side in models of categorical data analysis

topology preservation in 3d digital space abstract in a 3d two tone digital space the conditions under which sequential transformation of an object point to a non object point or its inverse does not affect the image topology are investigated the concept of border connectivity is introduced and an efficient algorithm for checking a simple point is proposed in this connection some other interesting properties of 3d digital geometry are also discussed this investigation may be used in thinning and topology preserving morphological transformations in 3d digital space

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

towards a theory of negative dependence the fkg theorem says that the positive lattice condition an easily checkable hypothesis which holds for many natural families of events implies positive association a very useful property thus there is a natural and useful theory of positively dependent events there is as yet no corresponding theory of negatively dependent events there is however a need for such a theory this paper unfortunately contains no substantial theorems its purpose is to present examples that motivate a need for such a theory give plausibility arguments for the existence of such a theory outline a few possible directions such a theory might take and state a number of specific conjectures which pertain to the examples and to a wish list of theorems

the supercritical phase of percolation is well behaved we prove a general result concerning the critical probabilities of subsets of a lattice l it is a consequence of this result that the critical probability of a percolation process on l equals the limit of the critical probability of a slice of l as the thickness of the slice tends to infinity this verification of one of the standard hypotheses of the subject settles many questions concerning supercritical percolation

gibbsianness of fermion random point fields we consider fermion or determinantal random point fields on euclidean space d given a bounded translation invariant and positive definite integral operator j on l2 d we introduce a determinantal interaction for a system of particles moving on d as follows the n points located at x1 x n d have the potential energy given by where j x y is the integral kernel function of the operator j we show that the gibbsian specification for this interaction is well defined when j is of finite range in addition and for d 2 if the intensity is small enough we show that the fermion random point field corresponding to the operator j i j 1 is a gibbs measure admitted to the specification

on adding a list of numbers and other one dependent determinantal processes adding a column of numbers produces carries along the way we show that random digits produce a pattern of carries with a neat probabilistic description the carries form a one dependent determinantal point process this makes it easy to answer natural questions how many carries are typical where are they located we show that many further examples from combinatorics algebra and group theory have essentially the same neat formulae and that any one dependent point process on the integers is determinantal the examples give a gentle introduction to the emerging fields of one dependent and determinantal point processes

consistent ranking of volatility models abstract we show that the empirical ranking of volatility models can be inconsistent for the true ranking if the evaluation is based on a proxy for the population measure of volatility for example the substitution of a squared return for the conditional variance in the evaluation of arch type models can result in an inferior model being chosen as best with a probability that converges to one as the sample size increases we document the practical relevance of this problem in an empirical application and by simulation experiments our results provide an additional argument for using the realized variance in out of sample evaluations rather than the squared return we derive the theoretical results in a general framework that is not specific to the comparison of volatility models similar problems can arise in comparisons of forecasting models whenever the predicted variable is a latent variable

dirichlet forms and diffusion processes for fermion random point fields abstract we construct the dirichlet forms and the associated diffusion processes on the configuration space of particles moving on the euclidean space r d for which certain fermion random point fields are invariant

interpreting the evidence on money income causality abstract previous researchers have reached strikingly different conclusions about the usefulness of money for forecasting real output based on closely related regression based tests an examination of this and additional new evidence reveals that innovations in m1 have statistically significant marginal predictive value for industrial production both in a bivariate model and in a multivariate setting including a price index and an interest rate this conclusion follows from focusing on the trend properties of the data both stochastic and deterministic and from drawing inferences using asymptotic theory that explicitly addresses the implications of these trends for the distributions of the various test statistics

local characteristics entropy and limit theorems for spanning trees and domino tilings via transfer impedances let g be a finite graph or an infinite graph on which mathbb z d acts with finite fundamental domain if g is finite let mathbf t be a random spanning tree chosen uniformly from all spanning trees of g if g is infinite methods from pemantle show that this still makes sense producing a random essential spanning forest of g a method for calculating local characteristics i e finite dimensional marginals of mathbf t from the transfer impedance matrix is presented this differs from the classical matrix tree theorem in that only small pieces of the matrix n dimensional minors are needed to compute small n dimensional marginals calculation of the matrix entries relies on the calculation of the green s function for g which is not a local calculation however it is shown how the calculation of the green s function may be reduced to a finite computation in the case when g is an infinite graph admitting a z d action with finite quotient the same computation also gives the entropy of the law of mathbf t these results are applied to the problem of tiling certain lattices by dominos the so called dimer problem another application of these results is to prove modified versions of conjectures of aldous on the limiting distribution of degrees of a vertex and on the local structure near a vertex of a uniform random spanning tree in a lattice whose dimension is going to infinity included is a generalization of moments to tree valued random variables and criteria for these generalized moments to determine a distribution

digital topology and geometry in medical imaging a survey digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids such methods have been widely used in many medical imaging applications including image segmentation visualization manipulation interpolation registration surface tracking object representation correction quantitative morphometry etc digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability fidelity and efficiency this paper presents a comprehensive yet compact survey on results principles and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications specifically this paper reviews methods related to distance analysis and path propagation connectivity surface tracking image segmentation boundary and centerline detection topology preservation and local topological properties skeletonization and object representation correction and quantitative morphometry a common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity path propagation and neighborhood analysis

an efficient vector quantizer providing globally optimal solutions this paper presents a new approach in vector quantization that is designed for clustering or source coding it incorporates both the capability of fast convergence from a monotonically descending algorithm and provides a globally optimal solution by a random optimization technique thus it benefits from properties of deterministic and stochastic search comprehensive experiments demonstrate that the new algorithm actually assimilated the advantages of the both components it may be therefore regarded as an accelerated global optimization method whose convergence is theoretically proved according to the complexity of the quantization problem the convergence rate is shown numerically to approach that of a coordinate descent algorithm which is an iterative updating of a single codevector at a time generalized lloyd algorithm gla i e k means the new method is investigated and compared with gla and a globally operating stochastic relaxation technique the comparison was made with respect to quality reliability and efficiency and applied to four categories of data an easy to grasp example patterns derived from the eeg gauss markov and image sources

noncommutative analogs of probabilistic notions and results abstract considering a random variable as a multiplication operator by a measurable function a natural generalization consists in allowing noncommuting and unbounded operators defined on a common invariant domain with cyclic vector by multiplication and addition these operators generate a algebra which in turn can be considered as a representation of an abstract tensor algebra moments are replaced by m a 1 a n a 1 a n in analogy to the classical case the notions of cumulants addition of independent random variables and infinite divisibility are introduced as well as gaussianness as a generalization of normal random variables previous results are briefly reviewed including a characterization of infinite divisibility among the new results are noncommutative analogs of versions of the central limit theorem and of cramer s theorem all results have direct applications to representations of lie algebras to quantum field theory and to statistical mechanics

subsample instability and asymmetries in money income causality abstract one puzzle in the money income causality literature is the variability in results across sample periods particularly with regard to the 1980 s this paper shows that the p values of money income causality tests across sample periods are highly correlated with the level of real activity when real activity declines money income causalitybecomes stronger and when real activity increases the relationship becomes weaker the investigation proceeds in three stages first rolling regressions are used to document the subsample instability and the correlation with real activity as well as the variability of the results across model specifications trend specifications and over the business cycle the second stage uses bootstrap simulations to show that the variability across sample periods and the correlation with real activity is significant and the third stage builds a combination dummy variable and varying coefficients var model that captures the asymmetries in the relationship between money and income

a topological characterization of thinning abstract a large number of skeletonization algorithms for binary images use the method of thinning successive layers of pixels are deleted from the figure until it becomes one pixel thick in this paper we analyze the topological properties of the set d of pixels to be deleted from a figure f in order to get a skeleton we characterize them by the concept of strong k deletability k 4 or 8 for individual pixels strong k deletability is equivalent to a more general property that we call k deletability which is well known connectivity requirement assumed at least implicity in all existing thinning algorithms we show then that a strongly k deletable subset d of a figure f can be deleted by a succession of deletions of individual pixels p 1 p t where each p i is k deletable from f p j j i this justifies our definition of strong deletability and shows that any topologically valid skeleton can be obtained by some thinning process

surface order large deviations for ising potts and percolation models we derive uniform surface order large deviation estimates for the block magnetization in finite volume ising or potts models with plus or free or a combination of both boundary conditions in the phase coexistence regime ford 3 the results are valid up to a limit of slab thresholds conjectured to agree with the critical temperature our arguments are based on the renormalization of the random cluster model withq 1 andd 3 and on corresponding large deviation estimates for the occurrence in a box of a largest cluster with density close to the percolation probability the results are new even for the case of independent percolation q 1 as a byproduct of our methods we obtain further results in the fk model concerning semicontinuity inp andq of the percolation probability the second largest cluster in a box and the tail of the finite cluster size distribution

central limit theorem for exponentially quasi local statistics of spin models on cayley graphs central limit theorems for linear statistics of lattice random fields including spin models are usually proven under suitable mixing conditions or quasi associativity many interesting examples of spin models do not satisfy mixing conditions and on the other hand it does not seem easy to show central limit theorem for local statistics via quasi associativity in this work we prove general central limit theorems for local statistics and exponentially quasi local statistics of spin models on discrete cayley graphs with polynomial growth further we supplement these results by proving similar central limit theorems for random fields on discrete cayley graphs taking values in a countable space but under the stronger assumptions of alpha mixing for local statistics and exponential alpha mixing for exponentially quasi local statistics all our central limit theorems assume a suitable variance lower bound like many others in the literature we illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology statistical physics and random networks examples of clustering spin models include quasi associated spin models with fast decaying covariances like the off critical ising model level sets of gaussian random fields with fast decaying covariances like the massive gaussian free field and determinantal point processes with fast decaying kernels examples of local statistics include intrinsic volumes face counts component counts of random cubical complexes while exponentially quasi local statistics include nearest neighbour distances in spin models and betti numbers of sub critical random cubical complexes

automatic detection of optic disc based on pca and mathematical morphology the algorithm proposed in this paper allows to automatically segment the optic disc from a fundus image the goal is to facilitate the early detection of certain pathologies and to fully automate the process so as to avoid specialist intervention the method proposed for the extraction of the optic disc contour is mainly based on mathematical morphology along with principal component analysis pca it makes use of different operations such as generalized distance function gdf a variant of the watershed transformation the stochastic watershed and geodesic transformations the input of the segmentation method is obtained through pca the purpose of using pca is to achieve the grey scale image that better represents the original rgb image the implemented algorithm has been validated on five public databases obtaining promising results the average values obtained a jaccard s and dice s coefficients of 0 8200 and 0 8932 respectively an accuracy of 0 9947 and a true positive and false positive fractions of 0 9275 and 0 0036 demonstrate that this method is a robust tool for the automatic segmentation of the optic disc moreover it is fairly reliable since it works properly on databases with a large degree of variability and improves the results of other state of the art methods

choosing a spanning tree for the integer lattice uniformly consider the nearest neighbor graph for the integer lattice zd in d dimensions for a large finite piece of it consider choosing a spanning tree for that piece uniformly among all possible subgraphs that are spanning trees as the piece gets larger this approaches a limiting measure on the set of spanning graphs for zd this is shown to be a tree if and only if d 4 in this case the tree has only one topological end that is there are no doubly infinite paths when d 2 5 the spanning forest has infinitely many components almost surely with each component having one or two topological ends

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

uniform spanning forests we study uniform spanning forest measures on infinite graphs which are weak limits of uniform spanning tree measures from finite subgraphs these limits can be taken with free fsf or wired wsf boundary conditions pemantle proved that the free and wired spanning forests coincide in z d and that they give a single tree iff d 4 in the present work we extend pemantle s alternative to general graphs and exhibit further connections of uniform spanning forests to random walks potential theory invariant percolation and amenability the uniform spanning forest model is related to random cluster models in statistical physics but because of the preceding connections its analysis can be carried further among our results are the following the fsf and wsf in a graph g coincide iff all harmonic dirichlet functions on g are constant the tail fields of the wsf and the fsf are trivial on any graph on any cayley graph that is not a finite extension of z all component trees of the wsf have one end this is new in z d for d 5 on any tree as well as on any graph with spectral radius less than 1 a s all components of the wsf are recurrent the basic topology of the free and the wired uniform spanning forest measures on lattices in hyperbolic space h d is analyzed a cayley graph is amenable iff for all e 0 the union of the wsf and bernoulli percolation with parameter e is connected harmonic measure from infinity is shown to exist on any recurrent proper planar graph with finite codegrees we also present numerous open problems and conjectures

bayesian model selection and prediction with empirical applications abstract this paper builds on some recent work by the author and werner ploberger 1991 1994 on the development of bayes models for time series and on the authors model selection criterion pic the pic criterion is used in this paper to determine the lag order the trend degree and the presence or absence of a unit root in an autoregression with deterministic trend a new forecast encompassing test for bayes models is developed which allows one bayes model to be compared with another on the basis of their respective forecasting performance the paper reports an extended empirical application of the methodology to the nelson plosser 1982 and schotman van dijk 1991 data it is shown that parsimonious evolving format bayes models forecastencompass fixed bayes models of the ar 3 linear trend variety for most of these series in some cases the forecast performance of the parsimonious bayes models is substantially superior the results cast some doubts on the value of working with fixedformat time series models in empirical research and demonstrate the practical advantages of evolving format models the paper makes a new suggestion for modelling interest rates in terms of reciprocals of levels rather than levels which display more volatility and shows that the best data determined model for this transformed series is a martingale

a central limit theorem with applications to percolation epidemics and boolean models suppose x x x x zd is a white noise process and h b defined for finite subsets b of z d is determined in a stationary way by the restriction of x to b using a martingale approach we prove a central limit theorem clt for h as b becomes large subject to h satisfying a stabilization condition the effect of changing x x at a single site needs to be local this clt is then applied to component counts for percolation and boolean models to the size of the big cluster for percolation on a box and to the final size of a spatial epidemic

bootstrap conditional distribution tests in the presence of dynamic misspecification abstract in this paper we show the first order validity of the block bootstrap for kolmogorov type conditional distribution tests under dynamic misspecification and parameter estimation error our approach is unique because we construct statistics that allow for dynamic misspecification under both hypotheses we consider two tests the ck test of andrews 1997 a conditional kolmogorov test econometrica 65 1097 1128 and a version of the dgt test of diebold gunther and tay 1998a evaluating density forecasts with applications to finance and management international economic review 39 863 883 test limiting distributions are gaussian processes with covariance kernels that reflect dynamic misspecification and parameter estimation error critical values are based on an extension of the empirical process version of the block bootstrap to the case of nonvanishing parameter estimation error monte carlo experiments are also carried out

a width independent fast thinning algorithm the skeleton of a digital figure can often be regarded as a convenient alternative to the figure itself it is useful both to diminish drastically the amount of data to be handled and to simplify the computational procedures required for description and classification purposes thinning a digital figure down to its skeleton is a time consuming process when conventional sequential computers are employed the procedure we propose allows one to speed up the thinning transformation and to get a well shaped skeleton after cleaning of the input picture has been performed the pixels of the figure are labeled according to their distance from the background and a set whose pixels are symmetrically placed with respect to distinct contour parts of the figure is found this set is then given a linear structure by applying topology preserving removal operations finally a pruning step regarding branches not relevant in the framework of the problem domain completes the process the resulting skeleton is a labeled set of pixels which is shown to possess all the required properties particularly those concerning connectedness topology and shape moreover the original figure can almost completely be recovered by means of a reverse distance transformation only a fixed and small number of sequential passes through the picture is necessary to achieve the goal the computational effort is rather modest and the use of the proposed algorithm turns out to be more advantageous the greater the width of the figure to be thinned

determinantal processes and completeness of random exponentials the critical case for a locally finite point set lambda subset mathbb r consider the collection of exponential functions given by mathcal e lambda e i lambda x lambda in lambda we examine the question whether mathcal e lambda spans the hilbert space l 2 pi pi when lambda is random for several point processes of interest this belongs to a certain critical case of the corresponding question for deterministic lambda about which little is known for lambda the continuum sine kernel process obtained as the bulk limit of gue eigenvalues we establish that mathcal e lambda is indeed complete almost surely we also answer an analogous question on mathbb c for the ginibre ensemble arising as weak limits of the spectra of certain non hermitian gaussian random matrices in fact we establish completeness for any rigid determinantal point process in a general setting in addition we partially answer two questions of lyons and steif about stationary determinantal processes on mathbb z d

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

mathematics of random growing interfaces we establish a thermodynamic limit and gaussian fluctuations for the height and surface width of the random interface formed by the deposition of particles on surfaces the results hold for the standard ballistic deposition model as well as the surface relaxation model in the off lattice setting the results are proved with the aid of general limit theorems for stabilizing functionals of marked poisson point processes

asymptotics of plancherel measures for symmetric groups 1 1 plancherel measures given a finite group g by the corresponding plancherel measure we mean the probability measure on the set g of irreducible representations of g which assigns to a representation g the weight dim g for the symmetric group s n the set s n is the set of partitions of the number n which we shall identify with young diagrams with n squares throughout this paper the plancherel measure on partitions arises naturally in representation theoretic combinatorial and probabilistic problems for example the plancherel distribution of the first part of a partition coincides with the distribution of the longest increasing subsequence of a uniformly distributed random permutation 31 we denote the plancherel measure on partitions of n by mn

homotopy in two dimensional digital images we recall the basic definitions concerning homotopy in 2d digital topology and we set and prove several results concerning homotopy of subsets then we introduce an explicit isomorphism between the fundamental group and a free group as a consequence we provide an algorithm for deciding whether two closed path are homotopic

negative dependence and the geometry of polynomials we introduce the class of strongly rayleigh probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter this class covers important models such as determinantal measures e g product measures and uniform random spanning tree measures and distributions for symmetric exclusion processes we show that strongly rayleigh measures enjoy all virtues of negative dependence and we also prove a series of conjectures due to liggett pemantle and wagner respectively moreover we extend lyons recent results on determinantal measures and we construct counterexamples to several conjectures of pemantle and wagner on negative dependence and ultra log concave rank sequences

a bayesian approach to dynamic macroeconomics abstract we propose and implement a coherent statistical framework for combining theoretical and empirical models of macroeconomic activity the framework is bayesian and enables the formal yet probabilistic incorporation of uncertainty regarding the parameterization of theoretical models the approach is illustrated using a neoclassical business cycle model that builds on the greenwood et al 1988 american economic review 78 402 417 variable utilization framework to study out of sample forecasting of output and investment the forecasts so produced are comparable with those from a bayesian vector autoregression

testing structural stability with endogenous breakpoint a size comparison of analytic and bootstrap procedures abstract we compare the performance of two alternative approximations to the finite sample distributions of test statistics for structural change one based on asymptotics and one based on the bootstrap we focus on tests acknowledging that the breakpoint is selected endogenously in particular the supremum tests of andrews 1993 we explore a variety of issues of interest in applied work focusing particularly on smaller samples and persistent dynamics the bootstrap approximation to the finite sample distribution appears consistently accurate in contrast to the asymptotic approximation the results are of interest not only from the perspective of testing for structural change but also from the broader perspective of compiling evidence on the adequacy of bootstrap approximations to finite sample distributions in econometrics

minimization by random search techniques we give two general convergence proofs for random search algorithms we review the literature and show how our results extend those available for specific variants of the conceptual algorithm studied here we then exploit the convergence results to examine convergence rates and to actually design implementable methods finally we report on some computational experience

two symmetrical thinning algorithms for 3d binary images based on p simple points in this paper we propose two 3d symmetrical thinning algorithms based on the parallel deletion of p simple points the first one permits surface skeletons to be obtained the second one permits curve skeletons to be extracted and as far as we know this is the only symmetrical curve thinning algorithm which preserves topology these algorithms have been conceived in order to obtain precise results on simple specific objects parallelepipeds consequently we can predict the number of deletion iterations the number of deleted points and the skeleton of these objects obtained by the two algorithms which is hardly ever possible to assess with other algorithms even on these simple objects

alignment and integration of complex networks by hypergraph based spectral clustering complex networks possess a rich multiscale structure reflecting the dynamical and functional organization of the systems they model often there is a need to analyze multiple networks simultaneously to model a system by more than one type of interaction or to go beyond simple pairwise interactions but currently there is a lack of theoretical and computational methods to address these problems here we introduce a framework for clustering and community detection in such systems using hypergraph representations our main result is a generalization of the perron frobenius theorem from which we derive spectral clustering algorithms for directed and undirected hypergraphs we illustrate our approach with applications for local and global alignment of protein protein interaction networks between multiple species for tripartite community detection in folksonomies and for detecting clusters of overlapping regulatory pathways in directed networks

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

decay of correlations under dobrushin s uniqueness condition and its applications an estimate on the correlation of functionals of gibbs fields satisfying dobrushin s uniqueness condition is given as a consequence a result of gross saying that the truncated pair correlation function decays in the same weighted summability sense as the potential can be extended to the whole dobrushin uniqueness region applications to the central limit theorem and the second derivative of the pressure are also given

distribution of size structure and number of vacant regions in a high intensity mosaic a mosaic is formed by centring independent and identically distributed random sets at points of a poisson process in euclidean space we derive high intensity approximations to the distributions of size structure and number of uncovered regions in a mosaic a limit theorem is proved for vacancy and leads to a general approximation to the probability that a given region is completely covered by random shapes

random point fields associated with certain fredholm determinants i fermion poisson and boson point processes we introduce certain classes of random point fields including fermion and boson point processes which are associated with fredholm determinants of certain integral operators and study some of their basic properties limit theorems correlation functions palm measures etc also we propose a conjecture on an analogue of the determinant and permanent

a consistent test for nonlinear out of sample predictive accuracy abstract in this paper we draw on both the consistent specification testing and the predictive ability testing literatures and propose an integrated conditional moment type predictive accuracy test that is similar in spirit to that developed by bierens j econometr 20 1982 105 econometrica 58 1990 1443 and bierens and ploberger econometrica 65 1997 1129 the test is consistent against generic nonlinear alternatives and is designed for comparing nested models one important feature of our approach is that the same loss function is used for in sample estimation and out of sample prediction in this way we rule out the possibility that the null model can outperform the nesting generic alternative model it turns out that the limiting distribution of the icm type test statistic that we propose is a functional of a gaussian process with a covariance kernel that reflects both the time series structure of the data as well as the contribution of parameter estimation error as a consequence critical values that are data dependent and cannot be directly tabulated one approach in this case is to obtain critical value upper bounds using the approach of bierens and ploberger econometrica 65 1997 1129 here we establish the validity of a conditional p value method for constructing critical values the method is similar in spirit to that proposed by hansen econometrica 64 1996 413 and inoue econometric theory 17 2001 156 although we additionally account for parameter estimation error in a series of monte carlo experiments the finite sample properties of three variants of the predictive accuracy test are examined our findings suggest that all three variants of the test have good finite sample properties when quadratic loss is specified even for samples as small as 600 observations however non quadratic loss functions such as linex loss require larger sample sizes of 1000 observations or more in order to ensure reasonable finite sample performance

a new shape preserving parallel thinning algorithm for 3d digital images this paper is concerned with a new parallel thinning algorithm for three dimensional digital images that preserves the topology and maintains their shape we introduce an approach of selecting shape points and outer layer used for erosion during each iteration the approach produces good skeleton for different types of corners the concept of using two image versions in thinning is introduced and its necessity in parallel thinning is justified the robustness of the algorithm under pseudo random noise as well as rotation with respect to shape properties is studied and the results are found to be satisfactory

the central limit theorem for supercritical oriented percolation in two dimensions we consider the cardinality of supercritical oriented bond percolation in two dimensions we show that whenever the the origin is conditioned to percolate the process appropriately normalized converges asymptotically in distribution to the standard normal law this resolves a longstanding open problem pointed out to in several instances in the literature the result applies also to the continuous time analog of the process viz the basic one dimensional contact process we also derive general random indices central limit theorems for associated random variables as byproducts of our proof

percolation of poisson sticks on the plane we consider a percolation model on the plane which consists of 1 dimensional sticks placed at points of a poisson process onr 2 each stick having a random but bounded length and a random direction the critical probabilities are defined with respect to the occupied clusters and vacant clusters and they are shown to be equal the equality is shown through a pivotal cell argument using a version of the russo seymour welsh theorem which we obtain for this model

random point fields associated with certain fredholm determinants ii fermion shifts and their ergodic and gibbs properties we construct and study a family of probability measures on the configuration space over countable discrete space associated with nonnegative definite symmetric operators via determinants under a mild condition they turn out unique gibbs measures also some ergodic properties including the entropy positivity are discussed in the lattice case

correlation functions for random complex zeroes strong clustering and local universality we prove strong clustering of k point correlation functions of zeroes of gaussian entire functions in the course of the proof we also obtain universal local bounds for k point functions of zeroes of arbitrary nondegenerate gaussian analytic functions in the second part of the paper we show that strong clustering yields the asymptotic normality of fluctuations of some linear statistics of zeroes of gaussian entire functions in particular of the number of zeroes in measurable domains of large area this complements our recent results from the paper fluctuations in random complex zeroes

a new algorithm for three dimensional voronoi tessellation abstract a new efficient algorithm for computing the voronoi tessellation in three dimensions is presented the voronoi tessellation is obtained by constructing delaunay tetrahedra the complete set of these tetrahedra corresponds to that of a single voronoi polyhedron

geodesic methods in quantitative image analysis abstract let x be a part of an image to be analysed given two arbitrary points x and y of x let us define the number d x x y as follows d x x y is the lower bound of the lengths of the arcs in x ending at points x and y if such arcs exist and if not the function d x is an x intrinsic distance function called geodesic distance note that if x and y belong to two disjoint connected components of x d x x y in other words d x seems to be an appropriate distance function to deal with connectivity problems in the metric space x d x all the classical morphological transformations dilation erosion skeletonization etc can be defined the geodesic distance d x also provides rigorous definitions of topological transformations which can be performed by automatic image analysers with the help of parallel iterative algorithms all these notions are illustrated by several examples definition of the length of a fibre and of an effective length factor automatic detection of cells having at least one nucleus or having one single nucleus definitions of the geodesic center and of the ends of an object without a hole etc the corresponding algorithms are described