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

a nonparametric test for spatial isotropy using subsampling a common requirement for spatial modeling is the development of an appropriate correlation structure although the assumption of isotropy is often made for this structure it is not always appropriate a conventional practice when checking for isotropy is to informally assess plots of direction specific sample semi variograms although a useful diagnostic these graphical techniques are difficult to assess and open to interpretation formal alternatives to graphical diagnostics are valuable but have been applied to a limited class of models in this article we propose a formal approach to test for isotropy that is both objective and valid for a wide class of models this approach which is based on the asymptotic joint normality of the sample variogram can be used to compare sample variograms in multiple directions an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample variogram is derived and used to construct a test statistic a subsampling approach and a limiting

an mrf model based approach to simultaneous recovery of depth and restoration from defocused images in this paper we propose a map markov random field mrf based scheme for recovering the depth and the focused image of a scene from two defocused images the space variant blur parameter and the focused image of the scene are both modeled as mrfs and their map estimates are obtained using simulated annealing the scheme is amenable to the incorporation of smoothness constraints on the spatial variations of the blur parameter as well as the scene intensity it also allows for inclusion of line fields to preserve discontinuities the performance of the proposed scheme is tested on synthetic as well as real data and the estimates of the depth are found to be better than that of the existing window based depth from defocus technique the quality of the space variant restored image of the scene is quite good even under severe space varying blurring conditions

quadratic operator relations and bethe equations for spin 1 2 richardson gaudin models in this work we demonstrate how one can in a generic approach derive a set of n simple quadratic bethe equations for integrable richardson gaudin rg models built out of n spins 1 2 these equations depend only on the n eigenvalues of the various conserved charges so that any solution of these equations defines indirectly through the corresponding set of eigenvalues one particular eigenstate the proposed construction covers the full class of integrable rg models of the xyz including the subclasses of xxz and xxx models type realised in terms of spins 1 2 coupled with one another through terms including as well magnetic field like terms linear in the pauli matrices the approach exclusively requires integrability defined here only by the requirement that n conserved charges r i with such that exist the result is therefore valid and equally simple for models with or without symmetry with or without a properly defined pseudo vacuum as well as for models with non skew symmetric couplings

performance analysis of maximum likelihood estimator for recovery of depth from defocused images and optimal selection ofcamera parameters the recovery of depth from defocused images involves calculating the depth of various points in a scene by modeling the effect that the focal parameters of the camera have on images acquired with a small depth of field in the existing methods on depth from defocus dfd two defocused images of a scene are obtained by capturing the scene with different sets of camera parameters although the dfd technique is computationally simple the accuracy is somewhat limited compared to the stereo algorithms further an arbitrary selection of the camera settings can result in observed images whose relative blurring is insufficient to yield a good estimate of the depth in this paper we address the dfd problem as a maximum likelihood ml based blur identification problem we carry out performance analysis of the ml estimator and study the effect of the degree of relative blurring on the accuracy of the estimate of the depth we propose a criterion for optimal selection of camera parameters to obtain an improved estimate of the depth the optimality criterion is based on the cramer rao bound of the variance of the error in the estimate of blur a number of simulations as well as experimental results on real images are presented to substantiate our claims

determinant permanent and macmahon s master theorem abstract as a unified extension of determinant and permanent a new matrix function with two extra parameters is introduced basic formulas are established which contain several known relations between determinants and permanents as special cases some expansions in terms of the matrix functions are investigated which yield macmahon s master theorem its dual version and their common generalization

fusing images with different focuses using support vector machines many vision related processing tasks such as edge detection image segmentation and stereo matching can be performed more easily when all objects in the scene are in good focus however in practice this may not be always feasible as optical lenses especially those with long focal lengths only have a limited depth of field one common approach to recover an everywhere in focus image is to use wavelet based image fusion first several source images with different focuses of the same scene are taken and processed with the discrete wavelet transform dwt among these wavelet decompositions the wavelet coefficient with the largest magnitude is selected at each pixel location finally the fused image can be recovered by performing the inverse dwt in this paper we improve this fusion procedure by applying the discrete wavelet frame transform dwft and the support vector machines svm unlike dwt dwft yields a translation invariant signal representation using features extracted from the dwft coefficients a svm is trained to select the source image that has the best focus at each pixel location and the corresponding dwft coefficients are then incorporated into the composite wavelet representation experimental results show that the proposed method outperforms the traditional approach both visually and quantitatively

solving the richardson equations close to the critical points we study the richardson equations close to the critical values of the pairing strength gc where the occurrence of divergences precludes numerical solutions we derive a set of equations for determining the critical g values and the non collapsing pair energies studying the behaviour of the solutions close to the critical points we develop a procedure to solve numerically the richardson equations for arbitrary coupling strength

periodic solutions of fokker planck equations abstract in this paper the existence of periodic solutions of fokker planck equations is obtained by discussing the existence of periodic solutions in distribution for some stochastic differential equations to prove the existence of periodic solutions in distribution for stochastic differential equations a new criterion analogous to halanay s criterion is given actually the criterion is similar to a law of large numbers based on this criterion the existence of periodic solutions in distribution for stochastic functional differential equations is established by lyapunov s method

white noise analysis for levy processes we construct a white noise theory for levy processes the starting point of this theory is a chaos expansion for square integrable random variables we use this approach to malliavin calculus to prove the following white noise generalization of the clark haussmann ocone formula for levy processes f e f m 1 0te dt m f ft y t m dt here e f is the generalized expectation the operators dt m f m 1 are generalized malliavin derivatives is the wick product and for all m 1y t m is the white noise of power jump processes yt m in particular y t 1 is the white noise of the levy process the formula holds for all f g l2 where g is a space of stochastic distributions and is a white noise probability measure finally we give an application of this formula to partial observation minimal variance hedging problems in financial markets driven by levy processes

asymptotics of plancherel measures for the infinite dimensional unitary group we study a two dimensional family of probability measures on infinite gelfand tsetlin schemes induced by a distinguished family of extreme characters of the infinite dimensional unitary group these measures are unitary group analogs of the well known plancherel measures for symmetric groups we show that any measure from our family defines a determinantal point process on z x z and we prove that in appropriate scaling limits such processes converge to two different extensions of the discrete sine process as well as to the extended airy and pearcey processes

optimality of the cusum procedure in continuous time the optimality of cusum under a lorden type criterion setting is considered we demonstrate the optimality of the cusum test for ito processes in a sense similar to lorden s but with a criterion that replaces expected delays by the corresponding kullback leibler divergence

the malliavin calculus for pure jump processes and applications to local time on obtient trois resultats une formule d integration par parties des conditions pour qu un processus de markov de saut pur ait une densite en lp et des conditions pour qu une martingale purement discontinue ait un temps local

the full infinite dimensional moment problem on semi algebraic sets of generalized functions we consider a generic basic semi algebraic subset s of the space of generalized functions that is a set given by not necessarily countably many polynomial constraints we derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on s namely to be the moment sequence of a finite measure concentrated on s our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi algebraic sets of rd in this way we determine realizability conditions that can be more easily verified than the well known haviland type conditions our result completely characterizes the support of the realizing measure in terms of its moments as concrete examples of semi algebraic sets of generalized functions we consider the set of all radon measures and the set of all the measures having bounded radon nikodym density w r t the lebesgue measure

marginal mark regression analysis of recurrent marked point process data summary longitudinal studies typically collect information on the timing of key clinical events and on specific characteristics that describe those events random variables that measure qualitative or quantitative aspects associated with the occurrence of an event are known as marks recurrent marked point process data consist of possibly recurrent events with the mark and possibly exposure measured if and only if an event occurs analysis choices depend on which aspect of the data is of primary scientific interest first factors that influence the occurrence or timing of the event may be characterized using recurrent event analysis methods second if there is more than one event per subject then the association between exposure and the mark may be quantified using repeated measures regression methods we detail assumptions required of any time dependent exposure process and the event time process to ensure that linear or generalized linear mixed models and generalized estimating equations provide valid estimates we provide theoretical and empirical evidence that if these conditions are not satisfied then an independence estimating equation should be used for consistent estimation of association we conclude with the recommendation that analysts carefully explore both the exposure and event time processes prior to implementing a repeated measures analysis of recurrent marked point process data

a moment preserving approach for depth from defocus abstract for range sensing using depth from defocus methods the distance d of a point object from the lens can be evaluated by the concise depth formula d p q d b where p and q are constants for a given camera setting and db is the diameter of the blur circle for the point object on the image detector plane the amount of defocus db is traditionally estimated from the spatial parameter of a gaussian point spread function using a complex iterative solution in this paper we use a straightforward and computationally fast method to estimate the amount of defocus from a single camera the observed gray level image is initially converted into a gradient image using the sobel edge operator for the edge point of interest the proportion of the blurred edge region pe in a small neighborhood window is then calculated using the moment preserving technique the value of pe increases as the amount of defocus increases and therefore is used as the description of degradation of the point spread function in addition to the use of the geometric depth formula for depth estimation artificial neural networks are also proposed in this study to compensate for the estimation errors from the depth formula experiments have shown promising results that the rms depth errors are within 5 for the depth formula and within 2 for the neural networks

the state of statistical process control as we proceed into the 21st century 2000 the state of statistical process control as we proceed into the 21st century journal of the american statistical association vol 95 no 451 pp 992 998

energy image density property and the lent particle method for poisson measures abstract we introduce a new approach to absolute continuity of laws of poisson functionals it is based on the energy image density property for dirichlet forms the associated gradient is a local operator and gives rise to a nice formula called the lent particle method which consists in adding a particle and taking it back after some calculation

nonparametric estimation of the moments of a general statistic computed from spatial data abstract a statistic s is computed on spatially indexed data x i i d where d is a finite subset of the integer lattice z2 we propose a simple nonparametric method for estimating the moments e g variance skewness of s d using only the observed data at hand the method uses replicates of s computed on smaller subsets of d no explicit knowledge of the underlying spatial dependence mechanism is needed and the marginal distribution of x i may also be unknown the shape of d can be quite irregular and s is allowed to be a general statistic the proposed estimator is shown to be consistent and asymptotically normal under mild conditions on s d and mixing conditions on the strength of spatial dependence as a numerical example the estimator is used in assessing the geographic clumping of cancer deaths in the united states

analysis and geometry on configuration spaces the gibbsian case using a natural riemannian geometry like structure on the configuration space over rd we prove that for a large class of potentials the corresponding canonical gibbs measures on 1 can be completely characterized by an integration by parts formula that is if is the gradient of the riemannian structure on one can define a corresponding divergence div such that the canonical gibbs measures are exactly those measures for which and div are dual operators onl2 one consequence is that for such the corresponding dirichlet forms e are defined in addition each of them is shown to be associated with a conservative diffusion process on with invariant measure the corresponding generators are extensions of the operator div the diffusions can be characterized in terms of a martingale problem and they can be considered as a brownian motion on perturbed by a singular drift another main result of this paper is the following if is a canonical gibbs measure then it is extreme or a pure phase if and only if the corresponding weak sobolev spacew1 2 on is irreducible as a consequence we prove that for extreme canonical gibbs measures the above mentioned diffusions are time ergodic in particular this holds for tempered grand canonical gibbs measures ruelle measures provided that the activity constant is small enough we also include a complete discussion of the free case i e 0 where the underlying space rdis even replaced by a riemannian manifoldx

existence of periodic probability solutions to fokker planck equations with applications abstract in the present paper we consider a fokker planck equation associated to periodic stochastic differential equations with irregular coefficients we define periodic probability solutions to be periodic analogs of stationary measures for stationary fokker planck equations and study their existence in both non degenerate and degenerate cases in the non degenerate case a lyapunov condition is imposed to ensure the existence of periodic probability solutions to the fokker planck equation with sobolev coefficients in the degenerate case with slightly more regular coefficients the existence is established under the same lyapunov condition as applications of our results we construct periodic probability solutions to fokker planck equations associated to stochastic damping hamiltonian systems and stochastic differential inclusions

on the determinant representations of gaudin models scalar products and form factors we propose alternative determinant representations of certain form factors and scalar products of states in rational gaudin models realized in terms of compact spins we use alternative pseudo vacuums to write overlaps in terms of partition functions with domain wall boundary conditions contrarily to slavnov s determinant formulas this construction does not require that any of the involved states be solutions to the bethe equations a fact that could prove useful in certain non equilibrium problems moreover by using an atypical determinant representation of the partition functions we propose expressions for the local spin raising and lowering operators form factors which only depend on the eigenvalues of the conserved charges these eigenvalues define eigenstates via solutions of a system of quadratic equations instead of the usual bethe equations consequently the current work allows important simplifications to numerical procedures addressing decoherence in gaudin models

two body homogeneous rational gaudin models and the missing label problem for the n 2 rational gaudin hamiltonians based on it is shown that the spectral invariants of the lax matrix correspond to linear combinations of the labelling operators associated with the embedding of lie algebras the diagonalized spectral invariants are applied to the degeneracy separation in the clebsch gordan series of

optimal stopping times for detecting changes in distributions it is shown that page s stopping time is optimal for the detection of changes in distributions in a well defined sense this work is a generalization of an existing result where it was shown that page s stopping time is optimal asymptotically

non parametric blur map regression for depth of field extension real camera systems have a limited depth of field dof which may cause an image to be degraded due to visible misfocus or too shallow dof in this paper we present a blind deblurring pipeline able to restore such images by slightly extending their dof and recovering sharpness in regions slightly out of focus to address this severely ill posed problem our algorithm relies first on the estimation of the spatially varying defocus blur drawing on local frequency image features a machine learning approach based on the recently introduced regression tree fields is used to train a model able to regress a coherent defocus blur map of the image labeling each pixel by the scale of a defocus point spread function a non blind spatially varying deblurring algorithm is then used to properly extend the dof of the image the good performance of our algorithm is assessed both quantitatively using realistic ground truth data obtained with a novel approach based on a plenoptic camera and qualitatively with real images

multiresolution 3 d range segmentation using focus cues this paper describes a novel system for computing a three dimensional 3 d range segmentation of an arbitrary visible scene using focus information the process of range segmentation is divided into three steps an initial range classification a surface merging process and a 3 d multiresolution range segmentation first range classification is performed to obtain quantized range estimates the range classification is performed by analyzing focus cues within a bayesian estimation framework a combined energy functional measures the degree of focus and the gibbs distribution of the class field the range classification provides an initial range segmentation second a statistical merging process is performed to merge the initial surface segments this gives a range segmentation at a coarse resolution third 3 d multiresolution range segmentation 3 d mrs is performed to refine the range segmentation into finer resolutions the proposed range segmentation method does not require initial depth estimates it allows the analysis of scenes containing multiple objects and it provides a rich description of the 3 d structure of a scene

the full moment problem on subsets of probabilities and point configurations abstract the aim of this paper is to study the full k moment problem for measures supported on some particular non linear subsets k of an infinite dimensional vector space we focus on the case of random measures that is k is a subset of all non negative radon measures on r d we consider as k the space of sub probabilities probabilities and point configurations on r d for each of these spaces we provide at least one representation as a generalized basic closed semi algebraic set to apply the main result in infusino et al 2014 20 we demonstrate that this main result can be significantly improved by further considerations based on the particular chosen representation of k in the case when k is a space of point configurations the correlation functions also known as factorial moment functions are easier to handle than the ordinary moment functions hence we additionally express the main results in terms of correlation functions

performance analysis of sequential tests between poisson processes the problem of performance computation for sequential tests between poisson processes is considered the average sample numbers and error probabilities of the sequential probability ratio test sprt between two homogeneous poisson processes are known to solve certain delay differential equations ddes exact numerically stable solutions to these ddes are developed here and their asymptotic properties are explored these solutions are seen to be superior to earlier solutions of dvoretsky kiefer and wolfowitz 1953 which suffer from severe numerical instability in some ranges of parameters of interest in applications the application of these results is illustrated in the problem of performance approximation for the cumulative sum cusum quickest detection procedure

tests for independence between marks and points of a marked point process a convenient assumption while modeling a marked point process is that the observations i e marks and the locations i e points are independent we propose new graphical and formal testing approaches to test for this assumption the proposed graphical procedures are easy to obtain and can be used to diagnose the nature and range of dependence between marks and points the formal testing procedures require only minimal conditions on marks and thus can be applied to a variety of settings we illustrate these procedures through a simulation study and an application to some real data

testing separability in spatial temporal marked point processes nonparametric tests for investigating the separability of a spatial temporal marked point process are described and compared it is shown that a cramer von mises type test is very powerful at detecting gradual departures from separability and that a residual test based on randomly rescaling the process is powerful at detecting nonseparable clustering or inhibition of the marks an application to los angeles county wildfire data is given in which it is shown that the separability hypothesis is invalidated largely due to clustering of fires of similar sizes within periods of up to 3 9 years

random periodic solutions of random dynamical systems abstract in this paper we give the definition of the random periodic solutions of random dynamical systems we prove the existence of such periodic solutions for a c 1 perfect cocycle on a cylinder using a random invariant set the lyapunov exponents and the pullback of the cocycle

moment estimation for statistics from marked point processes in spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations in other words the data form a realization of a marked point process in this paper we formulate subsampling estimators of the moments of general statistics computed from marked point process data and we establish their l 2 consistency the variance estimator in particular can be used for the construction of confidence intervals for estimated parameters a practical data based method for choosing a subsampling parameter is given and illustrated on a data set finite sample simulation examples are also presented

edge and depth from focus this paper proposes a novel method to obtain the reliable edge and depth information by integrating a set of multi focus images i e a sequence of images taken by systematically varying a camera parameter focus in previous work on depth measurement using focusing or defocusing the accuracy depends upon the size and location of local windows where the amount of blur is measured in contrast no windowing is needed in our method the blur is evaluated from the intensity change along corresponding pixels in the multi focus images such a blur analysis enables us not only to detect the edge points without using spatial differentiation but also to estimate the depth with high accuracy in addition the analysis result is stable because the proposed method involves integral computations such as summation and least square model fitting this paper first discusses the fundamental properties of multi focus images based on a step edge model then two algorithms are presented edge detection using an accumulated defocus image which represents the spatial distribution of blur and depth estimation using a spatio focal image which represents the intensity distribution along focus axis the experimental results demonstrate that the highly precise measurement has been achieved 0 5 pixel position fluctuation in edge detection and 0 2 error at 2 4 m in depth estimation

a transfer principle from wiener to poisson space and applications the aim of this work is to construct the stochastic calculus of variations on poisson space and some of its applications via the stochastic analysis on wiener space we define a new gradient operator on wiener space whose adjoint extends the poisson stochastic integral this yields a new decomposition of the ornstein uhlenbeck operator and a substructure of the standard dirichlet structure on wiener space with applications to stochastic analysis on poisson space and infinite dimensional analysis for the exponential density

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

an investigation of methods for determining depth from focus the concept of depth from focus involves calculating distances to points in an observed scene by modeling the effect that the camera s focal parameters have on images acquired with a small depth of field this technique is passive and requires only a single camera the most difficult segment of calculating depth from focus is deconvolving the defocus operator from the scene and modeling it most current methods for determining the defocus operator employ inverse filtering the authors reveal some fundamental problems with inverse filtering inaccuracies in finding the frequency domain representation windowing effects and border effects a general matrix based method using regularization is presented which eliminates these problems the new method is confirmed experimentally with the results showing an rms error of 1 3

is lebesgue measure the only σ finite invariant borel measure abstract s saks and recently r d mauldin asked if every translation invariant finite borel measure on r d is a constant multiple of lebesgue measure the aim of this paper is to investigate the versions of this question since surprisingly the answer is yes and no depending on what we mean by borel measure and by constant according to a folklore result if the measure is only defined for borel sets then the answer is affirmative we show that if the measure is defined on a algebra containing the borel sets then the answer is negative however if we allow the multiplicative constant to be infinity then the answer is affirmative in this case as well moreover our construction also shows that an isometry invariant finite borel measure in the wider sense on r d can be non finite when we restrict it to the borel sets

analysis of photometric properties of occluding edges by the reversed projection blurring model this paper analyzes photometric properties of occluding edges and proves that an object surface behind a nearer object is partially observable beyond the occluding edges we first discuss a limitation of the image blurring model using the convolution and then present an optical flux based blurring model named the reversed projection blurring rpb model unlike the multicomponent blurring model proposed by nguyen et al the rpb model enables us to explore the optical phenomena caused by a shift variant point spread function that appears at a depth discontinuity using the rpb model theoretical analysis of occluding edge properties are given and two characteristic phenomena are shown 1 a blurred occluding edge produces the same brightness profiles as would be predicted for a surface edge on the occluding object when the occluded surface radiance is uniform and 2 a nonmonotonic brightness transition would be observed in blurred occluding edge profiles when the occluded object has a surface edge experimental results using real images have demonstrated the validity of the rpb model as well as the observability of the characteristic phenomena of blurred occluding edges

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

discrete polynuclear growth and determinantal processes we consider a discrete polynuclear growth png process and prove a functional limit theorem for its convergence to the airy process this generalizes previous results by prahofer and spohn the result enables us to express the f1 goe tracy widom distribution in terms of the airy process we also show some results and give a conjecture about the transversal fluctuations in a point to line last passage percolation problem furthermore we discuss a rather general class of measures given by products of determinants and show that these measures have determinantal correlation functions

determinant representation of the domain wall boundary condition partition function of a richardson gaudin model containing one arbitrary spin in this work we present a determinant expression for the domain wall boundary condition partition function of rational xxx richardson gaudin models which in addition to spins contains one arbitrarily large spin s the proposed determinant representation is written in terms of a set of variables which from previous work are known to define eigenstates of the quantum integrable models belonging to this class as solutions to quadratic bethe equations such a determinant can be useful numerically since systems of quadratic equations are much simpler to solve than the usual highly nonlinear bethe equations it can therefore offer significant gains in stability and computation speed

existence and uniqueness of martingale solutions for sdes with rough or degenerate coefficients abstract in this paper we extend recent results on the existence and uniqueness of solutions of odes with non smooth vector fields to the case of martingale solutions in the stroock varadhan sense of sdes with non smooth coefficients in the first part we develop a general theory which roughly speaking allows to deduce existence uniqueness and stability of martingale solutions for l d almost every initial condition x whenever existence and uniqueness is known at the pde level in the l setting and conversely if existence and uniqueness of martingale solutions is known for l d a e initial condition then existence and uniqueness for the pde holds in the second part of the paper we consider situations where on the one hand no pointwise uniqueness result for the martingale problem is known and on the other hand well posedness for the fokker planck equation can be proved thus the theory developed in the first part of the paper is applicable in particular we will study the fokker planck equation in two somehow extreme situations in the first one assuming uniform ellipticity of the diffusion coefficients and lipschitz regularity in time we are able to prove existence and uniqueness in the l 2 setting in the second one we consider an additive noise and assuming the drift b to have bv regularity and allowing the diffusion matrix a to be degenerate also identically 0 we prove existence and uniqueness in the l setting therefore in these two situations our theory yields existence uniqueness and stability results for martingale solutions

some properties of set valued stochastic integrals abstract the present paper is devoted to properties of set valued stochastic integrals defined as some special type of set valued random variables in particular it is shown that if the probability base is separable or probability measure is nonatomic then defined set valued stochastic integrals can be represented by a sequence of ito s integrals of nonanticipative selectors of integrated set valued processes immediately from michael s continuous selection theorem it follows that the indefinite set valued stochastic integrals possess some continuous selections the problem of integrably boundedness of set valued stochastic integrals is considered some remarks dealing with stochastic differential inclusions are also given

the moment problem on compact semi algebraic sets in this chapter we begin the study of the multidimensional moment problem the passage to dimensions d 2 brings new difficulties and unexpected phenomena in sect 3 2 we derived solvability criteria of the moment problem on intervals in terms of positivity conditions it seems to be natural to look for similar characterizations in higher dimensions as well this leads us immediately into the realm of real algebraic geometry and to descriptions of positive polynomials on semi algebraic sets in this chapter we treat this approach for basic closed compact semi algebraic subsets of mathbb r d it turns out that for such sets there is a close interaction between the moment problem and positivstellensatze for strictly positive polynomials

pathwise random periodic solutions of stochastic differential equations abstract in this paper we study the existence of random periodic solutions for semilinear stochastic differential equations we identify these as the solutions of coupled forward backward infinite horizon stochastic integral equations in general cases we then use the argument of the relative compactness of wiener sobolev spaces in c 0 0 t l 2 and generalized schauder s fixed point theorem to prove the existence of a solution of the coupled stochastic forward backward infinite horizon integral equations the condition on f is then further weakened by applying the coupling method of forward and backward gronwall inequalities the results are also valid for stationary solutions as a special case when the period can be an arbitrary number

depth from motion and optical blur with an unscented kalman filter space variantly blurred images of a scene contain valuable depth information in this paper our objective is to recover the 3 d structure of a scene from motion blur optical defocus in the proposed approach the difference of blur between two observations is used as a cue for recovering depth within a recursive state estimation framework for motion blur we use an unblurred blurred image pair since the relationship between the observation and the scale factor of the point spread function associated with the depth at a point is nonlinear we propose and develop a formulation of unscented kalman filter for depth estimation there are no restrictions on the shape of the blur kernel furthermore within the same formulation we address a special and challenging scenario of depth from defocus with translational jitter the effectiveness of our approach is evaluated on synthetic as well as real data and its performance is also compared with contemporary techniques

a variational approach to recovering depth from defocused images in this paper we propose a regularized solution to the depth from defocus dfd problem using the space frequency representation sfr framework a smoothness constraint is imposed on the estimates of the blur parameter and a variational approach to the dfd problem is developed among the numerous sfrs we study the applicability of the complex spectrogram and the wigner distribution in particular for depth recovery the performance of the proposed variational method is tested on both synthetic and real images the method yields good results and the quality of the estimates is significantly better than that obtained without the smoothness constraint on the blur parameter

rational filter design for depth from defocus the paper describes a new simple procedure to determine the rational filters that are used in the depth from defocus dfd procedure previously researched by watanabe and nayar 1998 4 their dfd uses two differently defocused images and the filters accurately model the relative defocus in the images and provide a fast calculation of distance this paper presents a simple method to determine the filter coefficients by separating the m p ratio into a linear and a cubic error correction model the method avoids the previous iterative minimisation technique and computes efficiently the model has been verified by comparison with the theoretical m p ratio the proposed filters have been compared with the previous for frequency response closeness of fit to m p rotational symmetry and measurement accuracy experiments were performed for several defocus conditions it was observed that the new filters were largely insensitive to object texture and modelled the blur more precisely than the previous experiments with real planar images demonstrated a maximum rms depth error of 1 18 for the proposed compared to 1 54 for the previous filters complicated objects were also accurately measured

traces of semigroups associated with interacting particle systems abstract witten laplacians associated with interacting particle systems on infinite coverings of compact manifolds are considered the probabilistic representations of the corresponding heat kernels are given von neumann traces of the corresponding semigroups are computed

multidimensional residual analysis of point process models for earthquake occurrences residual analysis methods for examining the fit of multidimensional point process models are applied to point process models for the space time magnitude distribution of earthquake occurrences using in particular the multidimensional version of ogata s epidemic type aftershock sequence etas model and a 30 year catalog of 580 earthquakes occurring in bear valley california one method involves rescaled residuals obtained by transforming points along one coordinate to form a homogeneous poisson process inside a random irregular boundary another method involves thinning the point process according to the conditional intensity to form a homogeneous poisson process on the original untransformed space the thinned residuals suggest that the fit of the model may be significantly improved by using an anisotropic spatial distance function in the estimation of the spatially varying background rate using rescaled residuals it is shown that the temporal magnitude distribution of aftershock activity is not

risk adjusted monitoring of time to event recently there has been interest in risk adjusted cumulative sum charts cusums to monitor the performance of e g hospitals taking into account the heterogeneity of patients even though many outcomes involve time only conventional regression models are commonly used in this article we investigate how time to event models may be used for monitoring purposes we consider monitoring using cusums based on the partial likelihood ratio between an out of control state and an in control state we consider both proportional and nonproportional alternatives as well as a head start against proportional alternatives we present an analytic method of computing the expected number of observed events before stopping or the probability of stopping before a given observed number of events in a stationary set up the former is roughly proportional to the average run length in calendar time adding a head start changes the threshold only slightly if the expected number of events until hitting is used as a criterion however it changes the threshold substantially if a false alarm probability is used in simulation studies charts based on survival analysis perform better than simpler monitoring schemes we present one example from retail finance and one medical application

algebraic bethe ansatze and eigenvalue based determinants for dicke jaynes cummings gaudin quantum integrable models in this work we construct an alternative formulation to the traditional algebraic bethe ans tze for quantum integrable models derived from a generalized rational gaudin algebra realized in terms of a collection of spins 1 2 coupled to a single bosonic mode the ensemble of resulting models which we call dicke jaynes cummings gaudin models are particularly relevant for the description of light matter interaction in the context of quantum optics having two distinct ways to write any eigenstate of these models we then combine them in order to write overlaps and form factors of local operators in terms of partition functions with domain wall boundary conditions we also demonstrate that they can all be written in terms of determinants of matrices whose entries only depend on the eigenvalues of the conserved charges since these eigenvalues obey a much simpler set of quadratic bethe equations the resulting expressions could then offer important simplifications for the numerical treatment of these models

detecting dependence between marks and locations of marked point processes two characteristics for stationary and isotropic marked point processes e r and v r are introduced that allow for investigating mark point interactions these quantities are functions of the inter point distance rand denote the conditional expectation and the conditional variance of a mark respectively given there is a further point of the process a distance rapart tests based on eand vare presented that help to decide whether the values of the marks can be modelled by random field that is independent of the unmarked point process we demonstrate the use of our approach for three data sets in forestry

blind identification of multichannel fir blurs and perfect image restoration despite its practical importance in image processing and computer vision blind blur identification and blind image restoration have so far been addressed under restrictive assumptions such as all pole stationary image models blurred by zero or minimum phase point spread functions relying upon diversity availability of a sufficient number of multiple blurred images we develop blind fir blur identification and order determination schemes apart from a minimal persistence of the excitation condition also present with nonblind setups the inaccessible input image is allowed to be deterministic or random and of unknown color of distribution with the blurs satisfying a certain co primeness condition in addition we establish existence and uniqueness results which guarantee that single input multiple output fir blurred images can be restored blindly though perfectly in the absence of noise using linear fir filters results of simulations employing the blind order determination blind blur identification and blind image restoration algorithms are presented when the snr is high direct image restoration is found to yield better results than indirect image restoration which employs the estimated blurs in low snr indirect image restoration performs well while the direct restoration results vary with the delay but improve with larger equalizer orders

bayesian depth from defocus with shading constraints we present a method that enhances the performance of depth from defocus dfd through the use of shading information dfd suffers from important limitations namely coarse shape reconstruction and poor accuracy on textureless surfaces that can be overcome with the help of shading we integrate both forms of data within a bayesian framework that capitalizes on their relative strengths shading data however is challenging to accurately recover from surfaces that contain texture to address this issue we propose an iterative technique that utilizes depth information to improve shading estimation which in turn is used to elevate depth estimation in the presence of textures the shading estimation can be performed in general scenes with unknown illumination using an approximate estimate of scene lighting with this approach we demonstrate improvements over existing dfd techniques as well as effective shape reconstruction of textureless surfaces

shape from defocus via diffusion defocus can be modeled as a diffusion process and represented mathematically using the heat equation where image blur corresponds to the diffusion of heat this analogy can be extended to nonplanar scenes by allowing a space varying diffusion coefficient the inverse problem of reconstructing 3d structure from blurred images corresponds to an inverse diffusion that is notoriously ill posed we show how to bypass this problem by using the notion of relative blur given two images within each neighborhood the amount of diffusion necessary to transform the sharper image into the blurrier one depends on the depth of the scene this can be used to devise a global algorithm to estimate the depth profile of the scene without recovering the deblurred image using only forward diffusion

stochastic differential equations with coefficients in sobolev spaces abstract we consider the ito stochastic differential equation d x t j 1 m a j x t d w t j a 0 x t d t on r d the diffusion coefficients a 1 a m are supposed to be in the sobolev space w loc 1 p r d with p d and to have linear growth for the drift coefficient a 0 we distinguish two cases i a 0 is a continuous vector field whose distributional divergence a 0 with respect to the gaussian measure d exists ii a 0 has sobolev regularity w loc 1 p for some p 1 assume r d exp 0 a 0 j 1 m a j 2 a j 2 d d for some 0 0 in case i if the pathwise uniqueness of solutions holds then the push forward x t d admits a density with respect to d in particular if the coefficients are bounded lipschitz continuous then x t leaves the lebesgue measure leb d quasi invariant in case ii we develop a method used by g crippa and c de lellis for ode and implemented by x zhang for sde to establish existence and uniqueness of stochastic flow of maps

quasi symmetries of determinantal point processes the main result of this paper is that determinantal point processes on mathbb r corresponding to projection operators with integrable kernels are quasi invariant in the continuous case under the group of diffeomorphisms with compact support theorem 1 4 in the discrete case under the group of all finite permutations of the phase space theorem 1 6 the radon nikodym derivative is computed explicitly and is given by a regularized multiplicative functional theorem 1 4 applies in particular to the sine process as well as to determinantal point processes with the bessel and the airy kernels theorem 1 6 to the discrete sine process and the gamma kernel process the paper answers a question of grigori olshanski

gibbs cluster measures on configuration spaces the probability distribution gcl of a gibbs cluster point process in x rd with i i d random clusters attached to points of a gibbs configuration with distribution g is studied via the projection of an auxiliary gibbs measure g in the space of configurations x y x x where x x indicates a cluster center and y x nxn represents a corresponding cluster relative to x we show that the measure gcl is quasi invariant with respect to the group diff0 x of compactly supported diffeomorphisms of x and prove an integration by parts formula for gcl the associated equilibrium stochastic dynamics is then constructed using the method of dirichlet forms

poisson cluster measures quasi invariance integration by parts and equilibrium stochastic dynamics the distribution cl of a poisson cluster process in x r d with i i d clusters is studied via an auxiliary poisson measure on the space of configurations in x f n x n with intensity measure defined as a convolution of the background intensity of cluster centres and the probability distribution of a generic cluster we show that the measure cl is quasiinvariant with respect to the group of compactly supported diffeomorphisms ofx and prove an integration by parts formula for cl the corresponding equilibrium stochastic dynamics is then constructed using the method of dirichlet forms

bias corrected variance estimation and hypothesis testing for spatial point and marked point processes using subsampling summary we introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes for variance estimation our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval we show that they can achieve better rates in mean squared error than the usual subsampling variance estimator in particular for n n observation windows the optimal rate of n 2 can be achieved if the data have a finite dependence range for hypothesis testing we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics we assess the numerical performance of the proposed methods through simulation and apply them to analyze a tropical forest data set

analysis and geometry on configuration spaces abstract in this paper foundations are presented to a new systematic approach to analysis and geometry for an important class of infinite dimensional manifolds namely configuration spaces more precisely a differential geometry is introduced on the configuration space x over a riemannian manifold x this geometry is non flat even if x r d it is obtained as a natural lifting of the riemannian structure on x in particular a corresponding gradient divergence div and laplace beltrami operator h div gamma are constructed the associated volume elements i e all measures on x w r t which and div gamma become dual operators on l 2 x are identified as exactly the mixed poisson measures with mean measure equal to a multiple of the volume element dx on x in particular all these measures obey an integration by parts formula w r t vector fields on x the corresponding dirichlet forms e on l 2 x are therefore defined each is shown to be associated with a diffusion process which is thus the brownian motion on x and which is sub sequently identified as the usual independent infinite particle process on x the associated heat semigroup t t t 0 is calculated explicitly it is also proved that the diffusion process when started with is time ergodic or equivalently e gamma is irreducible or equivalently t t t 0 is ergodic if and only if is poisson measure z dx with intensity z dx for some z 0 furthermore it is shown that the laplace beltrami operator h div gamma gamma on l 2 x z dx is unitary equivalent to the second quantization of the laplacian x on x on the corresponding fock space n 0 l 2 x z dx n as another direct consequence of our results we obtain a representation of the lie algebra of compactly supported vector fields on x on poisson space finally generalizations to the case where dx is replaced by an absolutely continuous measure and also to interacting particle systems on x are described in particular the case where the mixed poisson measures are replaced by gibbs measures of ruelle type on x

reconstructing arbitrarily focused images from two differently focused images using linear filters we present a novel filtering method for reconstructing an all in focus image or an arbitrarily focused image from two images that are focused differently the method can arbitrarily manipulate the degree of blur of the objects using linear filters without segmentation the filters are uniquely determined from a linear imaging model in the fourier domain an effective and accurate blur estimation method is developed the simulation results show that the accuracy and computational time of the proposed method are improved compared with the previous iterative method and that the effects of blur estimation error on the quality of the reconstructed image are very small the method performs well for real images acquired without visible artifacts

quasi invariance and integration by parts for determinantal and permanental processes abstract determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent their atoms exhibit mutual attraction of repulsion thus these processes are very far from the uncorrelated situation encountered in poisson models we establish a quasi invariance result we show that if atom locations are perturbed along a vector field the resulting process is still a determinantal respectively permanental process the law of which is absolutely continuous with respect to the original distribution based on this formula following bismut approach of malliavin calculus we then give an integration by parts formula

kernel estimation of hazard functions when observations have dependent and common covariates abstract we propose a hazard model where dependence between events is achieved by assuming dependence between covariates this model allows for correlated variables specific to observations as well as macro variables which all observations share this setup better fits many economic and financial applications where events are not independent nonparametric estimation of the hazard function is then studied kernel estimators proposed in nielsen and linton 1995 and linton et al 2003 are shown to have similar asymptotic properties compared with the i i d case mixing conditions ensure the asymptotic results follow these results depend on adjustments to bandwidth conditions simulations are conducted which verify the impact of dependence on estimators bandwidth selection accounting for dependence is shown to improve performance in an empirical application trade intensity in high frequency financial data is estimated

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

holomorphic bogoliubov functionals for interacting particle systems in continuum combinatorial harmonic analysis techniques are used to develop new analytical methods for the study of interacting particle systems in continuum based on a bogoliubov functional approach concrete applications of the methods are presented namely conditions for the existence of bogoliubov functionals a uniqueness result for gibbs measures in the high temperature regime we also propose a new approach to the study of non equilibrium stochastic dynamics in terms of evolution equations for bogoliubov functionals

a geometric approach to shape from defocus we introduce a novel approach to shape from defocus i e the problem of inferring the three dimensional 3d geometry of a scene from a collection of defocused images typically in shape from defocus the task of extracting geometry also requires deblurring the given images a common approach to bypass this task relies on approximating the scene locally by a plane parallel to the image the so called equifocal assumption we show that this approximation is indeed not necessary as one can estimate 3d geometry while avoiding deblurring without strong assumptions on the scene solving the problem of shape from defocus requires modeling how light interacts with the optics before reaching the imaging surface this interaction is described by the so called point spread function psf when the form of the psf is known we propose an optimal method to infer 3d geometry from defocused images that involves computing orthogonal operators which are regularized via functional singular value decomposition when the form of the psf is unknown we propose a simple and efficient method that first learns a set of projection operators from blurred images and then uses these operators to estimate the 3d geometry of the scene from novel blurred images our experiments on both real and synthetic images show that the performance of the algorithm is relatively insensitive to the form of the psf our general approach is to minimize the euclidean norm of the difference between the estimated images and the observed images the method is geometric in that we reduce the minimization to performing projections onto linear subspaces by using inner product structures on both infinite and finite dimensional hilbert spaces both proposed algorithms involve only simple matrix vector multiplications which can be implemented in real time

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

existence of periodic solutions in distribution for stochastic newtonian systems periodic phenomena such as oscillation have been studied for many years in this paper we verify the stochastic version of levinson s conjecture which confirmed the existence of stochastic periodic solutions for second order newtonian systems with dissipativeness first we provide a stochastic duffing s equation to display our result then we apply wong zakai approximation method and lyapunov s method to stochastic second order newtonian systems driven by brownian motions with the help of horn s fixed point theorem we prove that this kind of systems is stochastic dissipative and admits periodic solutions in distribution

determinant formula for the six vertex model the partition function of a six vertex model with domain wall boundary conditions is considered on the finite lattice the authors show that the partition function satisfies a recursive relation they solve the recursion relation by a determinant formula this gives a determinant representation for the partition function they use the quantum inverse scattering method qism

moment formulae for general point processes abstract the goal of this paper is to generalize most of the moment formulae obtained in 12 more precisely we consider a general point process and show that the quantities relevant to our problem are the so called papangelou intensities when the papangelou intensities of are well defined we show some general formulae to recover the moment of order n of the stochastic integral of the point process we will use these extended results to introduce a divergence operator and study a random transformation of the point process