asymptotic behaviour of bohmian trajectories in scattering situations we study the asymptotic behaviour of bohmian trajectories in a scattering situation with short range potential v and for wavefunctions with a scattering and a bound part it is shown that the set of possible trajectories splits into trajectories whose long time behaviour is governed by the scattering part of the wavefunction scattering trajectories and trajectories whose long time behaviour is governed by the bound part of the wavefunction bound trajectories furthermore the scattering trajectories behave like trajectories in classical mechanics in the limit t as an intermediate step we show that the asymptotic velocity exists almost surely and is randomly distributed with the density where is the outgoing asymptote of the scattering part of the wavefunction

sobolev embeddings in metric measure spaces with variable dimension in this article we study metric measure spaces with variable dimension we consider lebesgue spaces on these sets and embeddings of the riesz potential in these spaces we also investigate hajlasz type sobolev spaces and prove sobolev and trudinger inequalities with optimal exponents all of these questions lead naturally to function spaces with variable exponents

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

comparing the areas under two or more correlated receiver operating characteristic curves a nonparametric approach methods of evaluating and comparing the performance of diagnostic tests are of increasing importance as new tests are developed and marketed when a test is based on an observed variable that lies on a continuous or graded scale an assessment of the overall value of the test can be made through the use of a receiver operating characteristic roc curve the curve is constructed by varying the cutpoint used to determine which values of the observed variable will be considered abnormal and then plotting the resulting sensitivities against the corresponding false positive rates when two or more empirical curves are constructed based on tests performed on the same individuals statistical analysis on differences between curves must take into account the correlated nature of the data this paper presents a nonparametric approach to the analysis of areas under correlated roc curves by using the theory on generalized u statistics to generate an estimated covariance matrix

global weighted lorentz estimates to nonlinear parabolic equations over nonsmooth domains abstract an elaborate method is developed to establish a global calderon zygmund type theory in weighted lorentz spaces l q t for zero cauchy dirichlet problem of nonlinear parabolic equations of p laplacian type with p 2 d d 2 here we assume that the nonlinearity a a t x is merely measurable in the time variable t and has a mall bmo semi norm in the spatial variables x uniformly in variables while the boundary of bounded domain is flat in the sense of reifenberg our result not only develops nonlinear calderon zygmund theory under weak regularity assumptions on the datum but also extends the related framework from lebesgue spaces to refined weighted lorentz spaces

on the operator l f f log f abstract the present note deals with the operator l h 1 r n d r n which takes a given element f of the hardy space to the function f log f in general this function need not be locally integrable nevertheless due to peculiar cancellations of large positive and negative terms in the integral f log f with c 0 r n we are able to give meaning to f log f as a schwartz distribution we find several alternatives for this interpretation of f log f

regularity results for a class of functionals with non standard growth we consider the integral functional under non standard growth assumptions that we call p x type namely we assume that a relevant model case being the functional under sharp assumptions on the continuous function p x 1 we prove regularity of minimizers energies exhibiting this growth appear in several models from mathematical physics

existence and multiplicity results for a new p x kirchhoff problem abstract in this work we study the existence and multiplicity results for the following nonlocal p x kirchhoff problem 0 1 a b 1 p x u p x d x d i v u p x 2 u u p x 2 u g x u in u 0 on where a b 0 are constants r n is a bounded smooth domain p c with n p x 1 is a real parameter and g is a continuous function the analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties

the nested dirichlet process in multicenter studies subjects in different centers may have different outcome distributions this article is motivated by the problem of nonparametric modeling of these distributions borrowing information across centers while also allowing centers to be clustered starting with a stick breaking representation of the dirichlet process dp we replace the random atoms with random probability measures drawn from a dp this results in a nested dp prior which can be placed on the collection of distributions for the different centers with centers drawn from the same dp component automatically clustered together theoretical properties are discussed and an efficient markov chain monte carlo algorithm is developed for computation the methods are illustrated using a simulation study and an application to quality of care in u s hospitals

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

weighted orlicz estimates for general nonlinear parabolic equations over nonsmooth domains we introduce a parabolic analogue of muckenhoupt weights to study optimal weighted regularity in orlicz spaces for a general nonlinear parabolic problem of p laplacian type in divergence form over a nonsmooth domain assuming that the nonlinearity is measurable with respect to the time variable and has a small bounded mean oscillation bmo with respect to the spatial variables that the lateral boundary of the parabolic cylinder is reifenberg flat and that the associated weight belongs to a suitable parabolic muckenhoupt class we obtain a global gradient estimate for such a nonlinear parabolic problem by essentially proving that the gradient of the weak solution is as globally integrable as the nonhomogeneous term in the weighted orlicz space our results extend the existing regularity estimates in lebesgue spaces to weighted orlicz spaces

scattering theory from microscopic first principles abstract we sketch a derivation of abstract scattering theory from the microscopic first principles defined by bohmian mechanics we emphasize the importance of the flux across surfaces theorem for the derivation and of randomness in the impact parameter of the initial wave function even for an inevitably inadequate orthodox derivation

regularity results for stationary electro rheological fluids we prove regularity results for weak solutions to systems modelling electro rheological fluids in the stationary case as proposed in 27 31 a particular case of the system we consider is

eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent in this paper we are concerned with a new class of anisotropic quasilinear elliptic equations with a power like variable reaction term one of the main features of our work is that the differential operator involves partial derivatives with different variable exponents so that the functional analytic framework relies upon anisotropic sobolev and lebesgue spaces existence and nonexistence results are deeply influenced by the competition between the growth rates of the anisotropic coefficients our main results point out some striking phenomena related to the existence of a continuous spectrum in several distinct situations

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

higher integrability for minimizers of integral functionals with p q growth abstract we prove higher integrability for minimizers u r n of integral functionals f du a x u dx where f satisfies a non standard growth condition of p q type z p f z l 1 z q p

an approach to the parameterization of structure for fast categorization a decomposition is described which parameterizes the geometry and appearance of contours and regions of gray scale images with the goal of fast categorization to express the contour geometry a contour is transformed into a local global space from which parameters are derived classifying its global geometry arc inflexion or alternating and describing its local aspects degree of curvature edginess symmetry regions are parameterized based on their symmetric axes which are evolved with a wave propagation process enabling to generate the distance map for fragmented contour images the methodology is evaluated on three image sets the caltech 101 set and two sets drawn from the corel collection the performance nearly reaches the one of other categorization systems for unsupervised learning

integral operators on the halfspace in generalized lebesgue spaces lp part ii in this paper we generalize a version of the classical calderon zygmund theorem on principle value integrals in generalized lebesgue spaces lp proved in j reine angew math 563 2003 197 220 to kernels which do not satisfy standard estimates on rd 1 this result will be used in part ii of this paper to prove the classical theorem on halfspace estimates of agmon douglis and nirenberg comm pure appl math 12 1959 623 727 for generalized lebesgue spaces lp

lp λ regularity for fully nonlinear elliptic equations abstract we establish the variable exponent morrey spaces l p estimate to the dirichlet problem for fully nonlinear elliptic equations on a c 1 1 bounded domain for variable exponents p and

an anova model for dependent random measures we consider dependent nonparametric models for related random probability distributions for example the random distributions might be indexed by a categorical covariate indicating the treatment levels in a clinical trial and might represent random effects distributions under the respective treatment combinations we propose a model that describes dependence across random distributions in an analysis of variance anova type fashion we define a probability model in such a way that marginally each random measure follows a dirichlet process dp and use the dependent dirichlet process to define the desired dependence across the related random measures the resulting probability model can alternatively be described as a mixture of anova models with a dp prior on the unknown mixing measure the main features of the proposed approach are ease of interpretation and computational simplicity because the model follows the standard anovastructure interpretation and inference parallels conventions for anova mode

hierarchical dirichlet processes we consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups we assume that the number of mixture components is unknown a priori and is to be inferred from the data in this setting it is natural to consider sets of dirichlet processes one for each group where the well known clustering property of the dirichlet process provides a nonparametric prior for the number of mixture components within each group given our desire to tie the mixture models in the various groups we consider a hierarchical model specifically one in which the base measure for the child dirichlet processes is itself distributed according to a dirichlet process such a base measure being discrete the child dirichlet processes necessarily share atoms thus as desired the mixture models in the different groups necessarily share mixture components we discuss representations of hierarchical dirichlet processes

abstract hardy spaces with variable exponents abstract in this paper we introduce the definition of abstract hardy spaces with variable exponents via the atomic decomposition and molecular decomposition we prove the continuity from our variable hardy space h a t o p into l p where p r n 0 1 0 p p 1 moreover we investigate the bilinear theory finally we give an application of the abstract hardy spaces with variable exponents

describing visual scenes using transformed objects and parts we develop hierarchical probabilistic models for objects the parts composing them and the visual scenes surrounding them our approach couples topic models originally developed for text analysis with spatial transformations and thus consistently accounts for geometric constraints by building integrated scene models we may discover contextual relationships and better exploit partially labeled training images we first consider images of isolated objects and show that sharing parts among object categories improves detection accuracy when learning from few examples turning to multiple object scenes we propose nonparametric models which use dirichlet processes to automatically learn the number of parts underlying each object category and objects composing each scene the resulting transformed dirichlet process tdp leads to monte carlo algorithms which simultaneously segment and recognize objects in street and office scenes

geometric latent dirichlet allocation on a matching graph for large scale image datasets given a large scale collection of images our aim is to efficiently associate images which contain the same entity for example a building or object and to discover the significant entities to achieve this we introduce the geometric latent dirichlet allocation glda model for unsupervised discovery of particular objects in unordered image collections this explicitly represents images as mixtures of particular objects or facades and builds rich latent topic models which incorporate the identity and locations of visual words specific to the topic in a geometrically consistent way applying standard inference techniques to this model enables images likely to contain the same object to be probabilistically grouped and ranked additionally to reduce the computational cost of applying the glda model to large datasets we propose a scalable method that first computes a matching graph over all the images in a dataset this matching graph connects images that contain the same object and rough image groups can be mined from this graph using standard clustering techniques the glda model can then be applied to generate a more nuanced representation of the data we also discuss how hub images images representative of an object or landmark can easily be extracted from our matching graph representation we evaluate our techniques on the publicly available oxford buildings dataset 5k images and show examples of automatically mined objects the methods are evaluated quantitatively on this dataset using a ground truth labeling for a number of oxford landmarks to demonstrate the scalability of the matching graph method we show qualitative results on two larger datasets of images taken of the statue of liberty 37k images and rome 1m images

global gradient estimates for the parabolic p x t laplacian equation abstract in this paper we consider the global gradient estimates for weak solutions of the parabolic p x t laplacian type equation in a reifenberg flat domain

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

global regularity for higher order divergence elliptic and parabolic equations abstract in this paper we obtain the global regularity estimates of the weak solutions in sobolev spaces and orlicz spaces for higher order elliptic and parabolic equations of divergence form with small bmo coefficients in the whole space we only focus on the parabolic case while the corresponding result in the elliptic case can be obtained as a corollary

on w1 p estimates for elliptic equations in divergence form first we will apply the method to study w 1 p regularity for a nonlinear elliptic operator in divergence form we would like to point out that in the particular case of a linear elliptic equation this method gives an alternative proof to the classical one which uses the general theory of singular integrals the utility of the method that we describe below is that hypotheses a and b are obtained directly by studying the deviation of the coefficients of a from the coefficients of a0 and this is usually not a difficult task a more interesting application of this kind of approximation method is to elliptic homogenization problems for which we obtain results that give w 1 p estimates with a weak hypothesis of regularity in the coefficients for instance we are able to study the following cases

lipschitz type smoothness of the fractional integral on variable exponent spaces fil ramseyer mauricio javier consejo nacional de investigaciones cientificas y tecnicas centro cientifico tecnologico conicet santa fe instituto de matematica aplicada del litoral universidad nacional del litoral instituto de matematica aplicada del litoral argentina

category level object segmentation by combining bag of words models with dirichlet processes and random fields this paper addresses the problem of accurately segmenting instances of object classes in images without any human interaction our model combines a bag of words recognition component with spatial regularization based on a random field and a dirichlet process mixture bag of words models successfully predict the presence of an object within an image however they can not accurately locate object boundaries random fields take into account the spatial layout of images and provide local spatial regularization yet as they use local coupling between image labels they fail to capture larger scale structures needed for object recognition these components are combined with a dirichlet process mixture it models images as a composition of regions each representing a single object instance gibbs sampling is used for parameter estimations and object segmentation our model successfully segments object category instances despite cluttered backgrounds and large variations in appearance and viewpoints the strengths and limitations of our model are shown through extensive experimental evaluations first we evaluate the result of two methods to build visual vocabularies second we show how to combine strong labeling segmented images with weak labeling images annotated with bounding boxes in order to limit the labeling effort needed to learn the model third we study the effect of different initializations we present results on four image databases including the challenging pascal voc 2007 data set on which we obtain state of the art results

an eigenvalue problem with variable exponents abstract a highly nonlinear eigenvalue problem is studied in a sobolev space with variable exponent the euler lagrange equation for the minimization of a rayleigh quotient of two luxemburg norms is derived the asymptotic case with a variable infinity is treated local uniqueness is proved for the viscosity solutions

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

detection localization and sex classification of faces from arbitrary viewpoints and under occlusion this paper presents a novel framework for detecting localizing and classifying faces in terms of visual traits e g sex or age from arbitrary viewpoints and in the presence of occlusion all three tasks are embedded in a general viewpoint invariant model of object class appearance derived from local scale invariant features where features are probabilistically quantified in terms of their occurrence appearance geometry and association with visual traits of interest an appearance model is first learned for the object class after which a bayesian classifier is trained to identify the model features indicative of visual traits the framework can be applied in realistic scenarios in the presence of viewpoint changes and partial occlusion unlike other techniques assuming data that are single viewpoint upright prealigned and cropped from background distraction experimentation establishes the first result for sex classification from arbitrary viewpoints an equal error rate of 16 3 percent based on the color feret database the method is also shown to work robustly on faces in cluttered imagery from the cmu profile database a comparison with the geometry free bag of words model shows that geometrical information provided by our framework improves classification a comparison with support vector machines demonstrates that bayesian classification results in superior performance

maximum principles for anisotropic elliptic inequalities we establish some maximum and comparison principles for weak distributional solutions of anisotropic elliptic inequalities in divergence form both in the homogeneous and non homogeneous case the main prototypes we have in mind are inequalities involving the p laplace operator and the generalized mean curvature operator

higher integrability for nonlinear elliptic equations with variable growth abstract in this paper based on the theory of variable exponent spaces we study the regularity for a class of nonlinear elliptic equation with p x laplacian under suitable assumptions we obtain a local gradient estimate in the orlicz space for weak solution

time of arrival from bohmian flow we develop a new conception for the quantum mechanical arrival time distribution from the perspective of bohmian mechanics a detection probability for detectors sensitive to quite arbitrary spacetime domains is formulated basic positivity and monotonicity properties are established we show that our detection probability improves and generalizes an earlier proposal by leavens and mckinnon the difference between the two notions is illustrated through application to a free wavepacket

bayesian nonparametric spatial modeling with dirichlet process mixing customary modeling for continuous point referenced data assumes a gaussian process that is often taken to be stationary when such models are fitted within a bayesian framework the unknown parameters of the process are assumed to be random so a random gaussian process results here we propose a novel spatial dirichlet process mixture model to produce a random spatial process that is neither gaussian nor stationary we first develop a spatial dirichlet process model for spatial data and discuss its properties because of familiar limitations associated with direct use of dirichlet process models we introduce mixing by convolving this process with a pure error process we then examine properties of models created through such dirichlet process mixing in the bayesian framework we implement posterior inference using gibbs sampling spatial prediction raises interesting questions but these can be handled finally we illustrate the approach using simulated data as well as a dataset involving precipitati

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

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

mappings of bmo bounded distortion this paper can be viewed as a sequel to the work 9 where the theory of mappings of bmo bounded distortion is developed largely in even dimensions using singular integral operators and recent developments in the theory of higher integrability of jacobians in hardy orlicz spaces in this paper we continue this theme refining and extending some of our earlier work as well as obtaining results in new directions the planar case was studied earlier by g david 4 in particular he obtained existence theorems modulus of continuity estimates and bounds on area distortion for mappings of bmo distortion in fact in slightly more generality we obtain similar results in all even dimensions one of our main new results here is the extension of the classical theorem of painleve concerning removable singularties for bounded analytic functions to the class of mappings of bmo bounded distortion the setting of the plane is of particular interest and somewhat more can be said here because of the existence theorem or the measurable riemann mapping theorem which is not available in higher dimensions we give a construction to show our results are qualitatively optimal another surprising fact is that there are domains which support no bounded quasiregular mappings but admit

the flux across surfaces theorem for short range potentials and wave functions without energy cutoffs the quantum probability flux of a particle integrated over time and a distant surface gives the probability for the particle crossing that surface at some time the relation between these crossing probabilities and the usual formula for the scattering cross section is provided by the flux across surfaces theorem which was conjectured by combes newton and shtokhamer phys rev d 11 366 372 1975 we prove the flux across surfaces theorem for short range potentials and wave functions without energy cutoffs the proof is based on the free flux across surfaces theorem daumer et al lett math phys 38 103 116 1996 and on smoothness properties of generalized eigenfunctions it is shown that if the potential v x decays like x at infinity with n n then the generalized eigenfunctions of the corresponding hamiltonian 1 2 v are n 2 times continuously differentiable with respect to the momentum variable

interior a priori estimates for solutions of fully non linear equations on etend une theorie de perturbations aux solutions d equations uniformement elliptiques d ordre 2 totalement non lineaires

learning pairwise image similarities for multi classification using kernel regression trees we are often faced with the problem of distinguishing between visually similar objects that share the same general appearance characteristics as opposed to object categorization this task is focused on capturing fine image differences in a pose dependent fashion our research addresses this particular family of problems and is centered around the concept of learning from example pairs formally we construct a parameterized visual similarity function optimally separating the pairs of images that depict the objects of the same class or identity from the pairs representing different object classes identities it combines various image distances that are quantified by comparing local descriptor responses at the corresponding locations in both paired images to find the best combinations we train ensembles of so called kernel regression trees which model the desired similarity function as a hierarchy of fuzzy decision stumps the obtained function is then used within a k nn like framework to address complex multi classification problems through the experiments with several image datasets we demonstrate the numerous advantages of the proposed approach high classification accuracy scalability ease of interpretation and the independence of the feature representation

generalized eigenfunctions for dirac operators near criticality critical dirac operators are those which have eigenfunctions and or resonances for e m we estimate the behavior of the generalized eigenfunctions of critical dirac operators under small perturbations of the potential the estimates are done in the l norm we show that for small k the generalized eigenfunctions are in leading order multiples of the respective eigenfunctions and or resonances we also estimate the k derivatives which are important for estimating decay the method also applies for other differential operators for example schrodinger operators

local calderon zygmund estimates for parabolic minimizers abstract we establish local calderon zygmund estimates for parabolic minimizers u to certain variational inequalities the formal corresponding parabolic partial differential equation would be t u div f z u d u u f z u d u div f p 2 f h with p 2 n n 2 however since we do not impose any condition on the existence of the derivative u f the pde above may not have any meaning at all for proving the calderon zygmund estimates we thus remain solely on the level of parabolic minimizers precisely for q p we prove that d u l loc q if u is locally holder continuous and f l loc q and h l loc q for a q depending on q

rao blackwellisation of sampling schemes summary this paper proposes a post simulation improvement for two common monte carlo methods the accept reject and metropolis algorithms the improvement is based on a rao blackwellisation method that integrates over the uniform random variables involved in the algorithms and thus post processes the standard estimators we show how the rao blackwellised versions of these algorithms can be implemented and through examples illustrate the improvement in variance brought by these new procedures we also compare the improved version of the metropolis algorithm with ordinary and rao blackwellised importance sampling procedures for independent and general metropolis set ups

on the asymptotic behaviour of a quantum two body system in the small mass ratio limit we consider a quantum system of two particles in dimension three interacting via a smooth potential we characterize the asymptotic dynamics in the limit of small mass ratio for an initial state given in product form with an explicit control of the error an application to the decoherence effect produced on the heavy particle is also discussed

transformation invariant clustering using the em algorithm clustering is a simple effective way to derive useful representations of data such as images and videos clustering explains the input as one of several prototypes plus noise in situations where each input has been randomly transformed e g by translation rotation and shearing in images and videos clustering techniques tend to extract cluster centers that account for variations in the input due to transformations instead of more interesting and potentially useful structure for example if images from a video sequence of a person walking across a cluttered background are clustered it would be more useful for the different clusters to represent different poses and expressions instead of different positions of the person and different configurations of the background clutter we describe a way to add transformation invariance to mixture models by approximating the nonlinear transformation manifold by a discrete set of points we show how the expectation maximization algorithm can be used to jointly learn clusters while at the same time inferring the transformation associated with each input we compare this technique with other methods for filtering noisy images obtained from a scanning electron microscope clustering images from videos of faces into different categories of identification and pose and removing foreground obstructions from video we also demonstrate that the new technique is quite insensitive to initial conditions and works better than standard techniques even when the standard techniques are provided with extra data

spatial random tree grammars for modeling hierarchal structure in images with regions of arbitrary shape we present a novel probabilistic model for the hierarchical structure of an image and its regions we call this model spatial random tree grammars srtgs we develop algorithms for the exact computation of likelihood and maximum a posteriori map estimates and the exact expectation maximization em updates for model parameter estimation we collectively call these algorithms the center surround algorithm we use the center surround algorithm to automatically estimate the maximum likelihood ml parameters of srtgs and classify images based on their likelihood and based on the map estimate of the associated hierarchical structure we apply our method to the task of classifying natural images and demonstrate that the addition of hierarchical structure significantly improves upon the performance of a baseline model that lacks such structure

gradient estimates for the p x laplacean system we prove calderon and zygmund type estimates for a class of elliptic problems whose model is the non homogeneous p x laplacean system div jduj p x 2 du div jf j p x 2 f

on dynamical justification of quantum scattering cross section abstract we suggest a dynamical justification of quantum differential cross section in the context of long time transition to stationary regime for the schrodinger equation the problem has been stated by reed and simon our approach is based on spherical incident waves produced by a harmonic source and the long range asymptotics for the corresponding spherical limiting amplitudes the main results are as follows i the convergence of spherical limiting amplitudes to the limit as the source goes away to infinity and ii the proof of the coincidence of the corresponding limit scattering cross section with the universally recognized formula the main technical ingredients are the agmon jensen kato s analytical theory of the green function ikebe s uniqueness theorem for the lippmann schwinger equation and some refinement of classical long range asymptotics for the coulomb potentials