minimum proper loss estimators for parametric models in this paper we propose a methodology for systematically deriving estimators minimizing proper loss functions defined on parametric statistical models by restricting ourselves to losses taking a functional form which allows for straightforward proofs of key properties proving propriety is tantamount to deriving a pairwise divergence quantity between probability measures admitting a natural interpretation of minimum proper loss estimators as divergence minimizers we show that proper losses of varying complexity can be readily constructed given propriety of losses taking a rudimentary form and that for many important models verifying desired properties in the rudimentary case is immediate as a special case we derive computationally tractable estimators requiring only the first and second moments verify strict propriety properties and empirically confirm their utility though parameter estimation tasks using both controlled simulations and real world meteorological network data sets comparisons against numerous standard estimators show that the proposed estimators are at least competitive with and often markedly superior to all standard references uniformly across tasks data sets and model classes suggesting a strong alternative to standard benchmarks in a wide variety of estimation problems

convolution generated motion and generalized huygens principles for interface motion a physical interface can often be modeled as a surface that moves with a velocity determined by the local geometry accordingly there is great interest in algorithms that generate such geometric interface motion in this paper we unify and generalize two simple algorithms for constant and mean curvature based interface motion the classical huygens principle and diffusion generated motion we show that the resulting generalization can be viewed both geometrically as a type of huygens principle and algebraically as a convolution generated motion using the geometric algebraic duality from the unification we construct specific convolution generated motion algorithms for a common class of anisotropic curvature dependent motionlaws we validate these algorithms with numerical experiments and show that they can be implemented accurately and efficiently with adaptive resolution and fast fourier transform techniques

fast sweeping algorithms for a class of hamilton jacobi equations we derive a godunov type numerical flux for the class of strictly convex homogeneous hamiltonians that includes h p q sqrt ap 2 bq 2 2cpq c 2 ab we combine our godunov numerical fluxes with simple gauss seidel type iterations for solving the corresponding hamilton jacobi hj equations the resulting algorithm is fast since it does not require a sorting strategy as found e g in the fast marching method in addition it providesa way to compute solutions to a class of hj equations for which the conventional fast marching method is not applicable our experiments indicate convergence after a few iterations even in rather difficult cases

euler s elastica and curvature based inpainting image inpainting is a special image restoration problem for which image prior models play a crucial role euler s elastica was first introduced to computer vision by mumford algebraic geometry and its applications springer verlag new york 1994 pp 491 506 as a curve prior model by functionalizing the elastica energy masnou and morel proceedings of the 5th ieee international conference image processing 3 1998 pp 259 263 proposed an elastica based variational inpainting model the current paper is intended to contribute to the development of its mathematical foundation and the study of its properties and connections to the earlier works of bertalmio sapiro caselles and ballester siggraph 2000 acm press new york 2000 and chan and shen j visual comm image rep 12 2001 pp 436 449 a computational scheme based on numerical pdes is presented which allows the automatic handling of topologically complex inpainting domains

a level set approach to 3d reconstruction from range data this paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3d objects from range data the strategy is to formulate 3d reconstruction as a statistical problem find that surface which is mostly likely given the data and some prior knowledge about the application domain the resulting optimization problem is solved by an incremental process of deformation we represent a deformable surface as the level set of a discretely sampled scalar function of three dimensions i e a volume such level set models have been shown to mimic conventional deformable surface models by encoding surface movements as changes in the greyscale values of the volume the result is a voxel based modeling technology that offers several advantages over conventional parametric models including flexible topology no need for reparameterization concise descriptions of differential structure and a natural scale space for hierarchical representations this paper builds on previous work in both 3d reconstruction and level set modeling it presents a fundamental result in surface estimation from range data an analytical characterization of the surface that maximizes the posterior probability it also presents a novel computational technique for level set modeling called the sparse field algorithm which combines the advantages of a level set approach with the computational efficiency and accuracy of a parametric representation the sparse field algorithm is more efficient than other approaches and because it assigns the level set to a specific set of grid points it positions the level set model more accurately than the grid itself these properties computational efficiency and subcell accuracy are essential when trying to reconstruct the shapes of 3d objects results are shown for the reconstruction objects from sets of noisy and overlapping range maps

simultaneous structure and texture image inpainting an algorithm for the simultaneous filling in of texture and structure in regions of missing image information is presented in this paper the basic idea is to first decompose the image into the sum of two functions with different basic characteristics and then reconstruct each one of these functions separately with structure and texture filling in algorithms the first function used in the decomposition is of bounded variation representing the underlying image structure while the second function captures the texture and possible noise the region of missing information in the bounded variation image is reconstructed using image inpainting algorithms while the same region in the texture image is filled in with texture synthesis techniques the original image is then reconstructed adding back these two sub images the novel contribution of this paper is then in the combination of these three previously developed components image decomposition with inpainting and texture synthesis which permits the simultaneous use of filling in algorithms that are suited for different image characteristics examples on real images show the advantages of this proposed approach

efficient algorithms for diffusion generated motion by mean curvature the problem of simulating the motion of evolving surfaces with junctions according to some curvature dependent speed arises in a number of applications by alternately diffusing and sharpening characteristic functions for each region a variety of motions have been obtained which allow for topological mergings and breakings and produce no overlapping regions or vacuums however the usual finite difference discretization of these methods is often excessively slow when accurate solutions are sought even in two dimensions we propose a new spectral discretization of these diffusion generated methods which obtains greatly improved efficiency over the usual finite difference approach these efficiency gains are obtained in part through the use of a quadrature based refinement technique by integrating fourier modes exactly and by neglecting the contributions of rapidly decaying solution transients indeed numerical studies demonstrate that the new algorithm is often more than 1000 times faster than the usual finite difference discretization our findings are demonstrated on several examples

recent results on multiplicative noise recent developments in the analysis of langevin equations with multiplicative noise mn are reported in particular we i present numerical simulations in three dimensions showing that the mn equation exhibits like the kardar parisi zhang kpz equation both a weak coupling fixed point and a strong coupling phase supporting the proposed relation between mn and kpz ii present a dimensional and mean field analysis of the mn equation to compute critical exponents iii show that the phenomenon of the noise induced ordering transition associated with the mn equation appears only in the stratonovich representation and not in the ito one and iv report the presence of a first order like phase transition at zero spatial coupling supporting the fact that this is the minimum model for noise induced ordering transitions

dynamic mean field models h theorem for stochastic processes and basins of attraction of stationary processes abstract stochastic processes of dynamic mean field models are studied in terms of nonlinear fokker planck equations we show that h theorems for single time point distributions can be used to derive h theorems for hierarchies of joint distributions in doing so we prove the convergence of transient stochastic processes to stationary ones for multistable systems we furthermore determine the basins of attraction of these stationary processes our results are illustrated by means of a mean field model exhibiting bistability

rates of convergence for minimum contrast estimators we shall present here a general study of minimum contrast estimators in a nonparametric setting although our results are also valid in the classical parametric case for independent observations these estimators include many of the most popular estimators in various situations such as maximum likelihood estimators least squares and other estimators of the regression function estimators for mixture models or deconvolution the main theorem relates the rate of convergence of those estimators to the entropy structure of the space of parameters optimal rates depending on entropy conditions are already known at least for some of the models involved and they agree with what we get for minimum contrast estimators as long as the entropy counts are not too large but under some circumstances large entropies or changes in the entropy structure due to local perturbations the resulting the rates are only suboptimal counterexamples are constructed which show that the phenomenon is real for non parametric maximum likelihood or regression this proves that under purely metric assumptions our theorem is optimal and that minimum contrast estimators happen to be suboptimal

bayesian estimation and experimental design in linear regression models estimation and design as a bayesian decision problem choice of a prior distribution conjugate prior distributions bayes estimation of the regression parameter optimality and robustness of the bayes estimator bayesian interpretation of estimators using non bayesian prior knowledge bayes estimation in case of prior ignorance further problems the design problem for the linear bayes estimator characterization of optimal designs construction of optimal continuous designs construction of exact optimal designs

an algorithm for calculating γ minimax decision rules under generalized moment conditions we present an algorithm for calculating a minimax decision rule when r is given by a finite number of generalized moment conditions such a decision rule minimizes the maximum of the integrals of the risk function with respect to all distributions in r the inner maximization problem is approximated by a sequence of linear programs this approximation is combined with an elimination technique which quickly reduces the domain of the variables of the outer minimization problem to test for convergence in a final step the inner maximization problem has to be completely solved once for the candidate of the r minimax rule found by the algorithm for an infinite compact parameter space this is done by semi infinite programming the algorithm is applied to calculate robustified bayesian designs in a logistic regression model and r minimax tests in monotone decision problems

a score regression approach to assess calibration of continuous probabilistic predictions calibration the statistical consistency of forecast distributions and the observations is a central requirement for probabilistic predictions calibration of continuous forecasts is typically assessed using the probability integral transform histogram in this article we propose significance tests based on scoring rules to assess calibration of continuous predictive distributions for an ideal normal forecast we derive the first two moments of two commonly used scoring rules the logarithmic and the continuous ranked probability score this naturally leads to the construction of two unconditional tests for normal predictions more generally we propose a novel score regression approach where the individual scores are regressed on suitable functions of the predictive variance this conditional approach is applicable even for certain nonnormal predictions based on the dawid sebastiani score two case studies illustrate that the score regression approach has typically more power in detecting miscalibrated forecasts than the other approaches considered including a recently proposed technique based on conditional exceedance probability curves

predictive model assessment for count data we discuss tools for the evaluation of probabilistic forecasts and the critique of statistical models for count data our proposals include a nonrandomized version of the probability integral transform marginal calibration diagrams and proper scoring rules such as the predictive deviance in case studies we critique count regression models for patent data and assess the predictive performance of bayesian age period cohort models for larynx cancer counts in germany the toolbox applies in bayesian or classical and parametric or nonparametric settings and to any type of ordered discrete outcomes

computational geometry for patient specific reconstruction and meshing of blood vessels from mr and ct angiography investigation of three dimensional 3 d geometry and fluid dynamics in human arteries is an important issue in vascular disease characterization and assessment thanks to recent advances in magnetic resonance mr and computed tomography ct it is now possible to address the problem of patient specific modeling of blood vessels in order to take into account interindividual anatomic variability of vasculature generation of models suitable for computational fluid dynamics is still commonly performed by semiautomatic procedures in general based on operator dependent tasks which cannot be easily extended to a significant number of clinical cases in this paper we overcome these limitations making use of computational geometry techniques in particular 3 d modeling was carried out by means of 3 d level sets approach model editing was also implemented ensuring harmonic mean curvature vectors distribution on the surface and model geometric analysis was performed with a novel approach based on solving eikonal equation on voronoi diagram this approach provides calculation of central paths maximum inscribed sphere estimation and geometric characterization of the surface generation of adaptive thickness boundary layer finite elements is finally presented the use of the techniques presented here makes it possible to introduce patient specific modeling of blood vessels at clinical level

chaos from nonlinear markov processes why the whole is different from the sum of its parts abstract nonlinear markov processes have been frequently used to address bifurcations and multistability in equilibrium and non equilibrium many body systems however our understanding of the range of phenomena produced by nonlinear markov processes is still in its infancy we demonstrate that in addition to bifurcations and multistability nonlinear markov processes can exhibit another key phenomena well known in the realm of nonlinear physics chaos it is argued that chaotically evolving process probabilities are a generic feature of many body systems exhibiting nonlinear markov processes even if the isolated subsystems do not exhibit chaos that is when considering a nonlinear markov process as an entity of its own type then the nonlinear markov process in general is qualitatively different from its constituent subprocesses which reflects that the many body system as a whole is different from the sum of its parts

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

making and evaluating point forecasts typically point forecasting methods are compared and assessed by means of an error measure or scoring function with the absolute error and the squared error being key examples the individual scores are averaged over forecast cases to result in a summary measure of the predictive performance such as the mean absolute error or the mean squared error i demonstrate that this common practice can lead to grossly misguided inferences unless the scoring function and the forecasting task are carefully matched effective point forecasting requires that the scoring function be specified ex ante or that the forecaster receives a directive in the form of a statistical functional such as the mean or a quantile of the predictive distribution if the scoring function is specified ex ante the forecaster can issue the optimal point forecast namely the bayes rule if the forecaster receives a directive in the form of a functional it is critical that the scoring function be consistent for it in the sense that t

nonequilibrium wetting transitions with short range forces we analyze within mean field theory as well as numerically a kardar parisi zhang equation that describes nonequilibrium wetting both complete and critical wettitng transitions were found and characterized in detail for one dimensional substrates the critical weting temperature is depressed by fluctuations in addition we have investigated a region in the space of parameters temperature and chemical potential where the wet and nonwet phases coexist finite size scaling analysis of the interfacial detaching times indicates that the finite coexistence region survives in the thermodynamic limit within this region we have observed stable or very long lived structures related to spatiotemporal intermittency in other systems in the interfacial representation these structures exhibit perfect triangular pyramidal patterns in one dimension two dimensions which are characterized by their slope and size distribution

two approximations of solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of application including the calculus of variations control theory and differential games the associated initial value problems almost never have global time classical solutions and one must deal with suitable generalized solutions the correct class of generalized solutions has only recently been established by the authors this article establishes the convergence of a class of difference approximations to these solutions by obtaining explicit error estimates analogous results are proved by similar means for the method of vanishing viscosity author

on the optimality of conditional expectation as a bregman predictor we consider the problem of predicting a random variable x from observations denoted by a random variable z it is well known that the conditional expectation e x z is the optimal l sup 2 predictor also known as the least mean square error predictor of x among all borel measurable functions of z in this orrespondence we provide necessary and sufficient conditions for the general loss functions under which the conditional expectation is the unique optimal predictor we show that e x z is the optimal predictor for all bregman loss functions blfs of which the l sup 2 loss function is a special case moreover under mild conditions we show that the blfs are exhaustive i e if for every random variable x the infimum of e f x y over all constants y is attained by the expectation e x then f is a blf

motion of multiple junctions a level set approach abstract a coupled level set method for the motion of multiple junctions is proposed the new method extends the hamilton jacobi level set formulation of osher and sethian it retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front the diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature dependent speed systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature dependent motion

a wavelet laplace variational technique for image deconvolution and inpainting we construct a new variational method for blind deconvolution of images and inpainting motivated by recent pde based techniques involving the ginzburg landau functional but using more localized wavelet based methods we present results for both binary and grayscale images comparable speeds are achieved with better sharpness of edges in the reconstruction

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

convolution generated motion as a link between cellular automata and continuum pattern dynamics cellular automata have been used to model the formation and dynamics of patterns in a variety of chemical biological and ecological systems however for patterns in which sharp interfaces form and propagate automata simulations can exhibit undesirable properties including spurious anisotropy and poor representation of interface curvature effects these simulations are also prohibitively slow when high accuracy is required even in two dimensions also the highly discrete nature of automata models makes theoretical analysis difficult in this paper we present a method for generating interface motions that is similar to the threshold dynamics type cellular automata but based on continuous convolutions rather than discrete sums these convolution generated motions naturally achieve the fine grid limit of the corresponding automata and they are also well suited to numerical and theoretical analysis because of this the desired pattern dynamics can be computed accurately and efficiently using adaptive resolution and fast fourier transform techniques and for a large class of convolutions the limiting interface motion laws can be derived analytically thus convolution generated motion provides a numerically and analytically tractable link between cellular automata models and the smooth features of pattern dynamics this is useful both as a means of describing the continuum limits of automata and as an independent foundation for expressing models for pattern dynamics in this latter role it also has a number of benefits over the traditional reaction diffusion ginzburg landau continuum pde models of pattern formation which yield true moving interfaces only as singular limits we illustrate the power of this approach with convolution generated motion models for pattern dynamics in developmental biology and excitable media

parameter neutral optimum design for non linear models some bayesian approaches to d optimum design of experiments are considered from the viewpoint of invariance under reparameterization of the underlying statistical model an invariant criterion is proposed which does not require the detailed specification of a prior and which is shown to be equivalent to g optimality under a jeffreys prior the methods are applied and discussed in the contexts of exponential decay and quantal response models

parametric solution method for self consistency equations and order parameter equations derived from nonlinear fokker planck equations abstract we propose a parametric approach to solve self consistency equations that naturally arise in many body systems described by nonlinear fokker planck equations in general and nonlinear vlasov fokker planck equations of haissinski type in particular we demonstrate for the hess doi edwards model and the mcmillan model of nematic and smectic liquid crystals that the parametric approach can be used to compute bifurcation diagrams and critical order parameters for systems exhibiting one or more than one order parameters in addition we show that in the context of the parametric approach solutions of the haissinski model can be studied from the perspective of a pseudo order parameter

systems with multiplicative noise critical behavior from kpz equation and numerics we show that certain critical exponents of systems with multiplicative noise can be obtained from exponents of the kpz equation numerical simulations in 1d confirm this prediction and yield other exponents of the multiplicative noise problem the numerics also verify an earlier prediction of the divergence of the susceptibility over an entire range of control parameter values and show that the exponent governing the divergence in this range varies continuously with control parameter

a new multiscale representation for shapes and its application to blood vessel recovery in this paper we will first introduce a novel multiscale representation msr for shapes via level set motions and pdes based on the msr we will then design a surface inpainting algorithm to recover three dimensional geometry of blood vessels because of the nature of irregular morphology in vessels and organs both phantom and real inpainting scenarios were tested using our new algorithm successful vessel recoveries are demonstrated with numerical estimation of the degree of arteriosclerosis and vessel occlusion

robust and efficient estimation by minimising a density power divergence a minimum divergence estimation method is developed for robust parameter estimation the proposed approach uses new density based divergences which unlike existing methods of this type such as minimum hellinger distance estimation avoid the use of nonparametric density estimation and associated complications such as bandwidth selection the proposed class of density power divergences is indexed by a single parameter which controls the trade off between robustness and efficiency the methodology affords a robust extension of maximum likelihood estimation for which 0 choices of near zero afford considerable robustness while retaining efficiency close to that of maximum likelihood

a predictive approach to the bayesian design problem with application to normal regression models a predictive decision theoretic approach is developed for the bayesian design problem the loss functions used are fair bayes or proper scoring rules and are quadratic measures of distance between probability measures optimal bayesian designs are those which minimise the preposterior risk for the decision problem such designs typically depend on both the prior distribution and the loss function the results are applied to certain normal regression models where explicit optimal designs are constructed

game theory maximum entropy minimum discrepancy and robust bayesian decision theory we describe and develop a close relationship between two problems that have customarily been regarded as distinct that of maximizing entropy and that of minimizing worst case expected loss using a formulation grounded in the equilibrium theory of zero sum games between decision maker and nature these two problems are shown to be dual to each other the solution to each providing that to the other although topsoe described this connection for the shannon entropy over 20 years ago it does not appear to be widely known even in that important special case we here generalize this theory to apply to arbitrary decision problems and loss functions we indicate how an appropriate generalized definition of entropy can be associated with such a problem and we show that subject to certain regularity conditions the above mentioned duality continues to apply in this extended context this simultaneously provides a possible rationale for maximizing entropy and a tool for finding robust bayes acts we also describe the essential identity between the problem of maximizing entropy and that of minimizing a related discrepancy or divergence between distributions this leads to an extension to arbitrary discrepancies of a well known minimax theorem for the case of kullback leibler divergence the redundancy capacity theorem of information theory for the important case of families of distributions having certain mean values specified we develop simple sufficient conditions and methods for identifying the desired solutions we use this theory to introduce a new concept of generalized exponential family linked to the specific decision problem under consideration and we demonstrate that this shares many of the properties of standard exponential families finally we show that the existence of an equilibrium in our game can be rephrased in terms of a pythagorean property of the related divergence thus generalizing previously announced results for kullback leibler and bregman divergences

variational problems and partial differential equations on implicit surfaces a novel framework for solving variational problems and partial differential equations for scalar and vector valued data defined on surfaces is introduced in this paper the key idea is to implicitly represent the surface as the level set of a higher dimensional function and to solve the surface equations in a fixed cartesian coordinate system using this new embedding function the equations are then both intrinsic to the surface and defined in the embedding space this approach thereby eliminates the need for performing complicated and inaccurate computations on triangulated surfaces as is commonly done in the literature we describe the framework and present examples in computer graphics and image processing applications including texture synthesis flow field visualization and image and vector field intrinsic regularization for data defined on 3d surfaces

higher order elicitability and osband s principle a statistical functional such as the mean or the median is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score such scoring functions are called strictly consistent for the functional the elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores in this paper we explore the notion of elicitability for multi dimensional functionals and give both necessary and sufficient conditions for strictly consistent scoring functions we cover the case of functionals with elicitable components but we also show that one dimensional functionals that are not elicitable can be a component of a higher order elicitable functional in the case of the variance this is a known result however an important result of this paper is that spectral risk measures with a spectral measure with finite support are jointly elicitable if one adds the correct quantiles a direct consequence of applied interest is that the pair value at risk expected shortfall is jointly elicitable under mild conditions that are usually fulfilled in risk management applications

motion of level sets by mean curvature i we continue our investigation of the level set technique for describing the generalized evolution of hypersurfaces moving according to their mean curvature the principal assertion of this paper is a kind of reconciliation with the geometric measure theoretic approach pioneered by k brakke we prove that almost every level set of the solution to the mean curvature evolution pde is in fact aunit density varifold moving according to its mean curvature in particular a e level set is endowed with a kind of geometric structure the proof utilizes compensated compactness methods to pass to limits in various geometric expressions

blind separation of mixture of independent sources through a quasi maximum likelihood approach we propose two methods for separating mixture of independent sources without any precise knowledge of their probability distribution they are obtained by considering a maximum likelihood ml solution corresponding to some given distributions of the sources and relaxing this assumption afterward the first method is specially adapted to temporally independent non gaussian sources and is based on the use of nonlinear separating functions the second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters a theoretical analysis of the performance of the methods has been made a simple procedure for optimally choosing the separating functions is proposed further in the second method a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided finally some numerical and simulation results are given illustrating the performance of the method and the good agreement between the experiments and the theory

inpainting of binary images using the cahn hilliard equation image inpainting is the filling in of missing or damaged regions of images using information from surrounding areas we outline here the use of a model for binary inpainting based on the cahn hilliard equation which allows for fast efficient inpainting of degraded text as well as super resolution of high contrast images

roughness of two nonintersecting one dimensional interfaces the dynamics of two spatially discrete one dimensional single step model interfaces with a noncrossing constraint is studied in both nonsymmetric propagating and symmetric relaxing cases we consider possible scaling scenarios and study a few special cases by using continuous time monte carlo simulations the roughness of the interfaces is observed to be nonmonotonic as a function of time and in the stationary state it is nonmonotonic also as a function of the strength of the effective force driving the interfaces against each other this is related on the one hand to the reduction of the available configuration space and on the other hand to the ability of the interfaces to conform to each other

strictly proper scoring rules prediction and estimation scoring rules assess the quality of probabilistic forecasts by assigning a numerical score based on the predictive distribution and on the event or value that materializes a scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionf if he or she issues the probabilistic forecast f rather than g f it is strictly proper if the maximum is unique in prediction problems proper scoring rules encourage the forecaster to make careful assessments and to be honest in estimation problems strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand this article reviews and develops the theory of proper scoring rules on general probability spaces and proposes and discusses examples thereof proper scoring rules derive from convex functions and relate to information measures entropy functions and bregman divergences in the case of categorical variables we prove a rigorous version of the

coherent dispersion criteria for optimal experimental design we characterize those coherent design criteria which depend only on the dispersion matrix assumed proper and nonsingular of the state of nature which may be a parameter vector or a set of future observables and describe the associated decision problems connections are established with the classical approach to optimal design theory for the normal linear model based on concave functions of the information matrix implications of the theory for more general models are also considered

second order efficiency of minimum contrast estimators in a curved exponential family this paper presents a sufficient condition for second order efficiency of an estimator the condition is easily checked in the case of minimum contrast estimators the a minimum contrast estimator is defined and proved to be second order efficient for every a 0 a 1 the fisher scoring method is also considered in the light of second order efficiency it is shown that a contrast function is associated with the second order tensor and the affine connection this fact leads us to prove the above assertions in the differential geometric framework due to amari

wavelet frame based algorithm for 3d reconstruction in electron microscopy in electron microscopy three dimensional 3d reconstruction is one key component in many computerized techniques for solving 3d structures of large protein assemblies using electron microscopy images of particles main challenges in 3d reconstruction include very low signal to noise ratio and very large scale of data sets involved in the computation motivated by the recent advances of sparsity based regularization in the wavelet frame domain for solving various linear inverse problems in imaging science we proposed a wavelet tight frame based 3d reconstruction approach that exploits the sparsity of the 3d density map in a wavelet tight frame system the proposed approach not only runs efficiently in terms of cpu time but also requires a much lower memory footprint than existing framelet based regularization methods the convergence of the proposed iterative scheme and the functional it minimizes is also examined together with the connection to existing wavelet frame based regularizations the numeric

maximum entropy reconstruction using derivative information part 1 fisher information and convex duality maximum entropy spectral density estimation is a technique for reconstructing an unknown density function from some known measurements by maximizing a given measure of entropy of the estimate here we present a variety of new entropy measures which attempt to control derivative values of the densities our models apply among others to the inference problem based on the averaged fisher information measure the duality theory we develop resembles models used in convex optimal control problems we present a variety of examples including relaxed moment matching with fisher information and best interpolation on a strip

motion of level sets by mean curvature ii we give a new proof of short time existence for the classical motion by mean curvature of a smooth hypersurface our method consists in studying a fully nonlinear uniformly parabolic equation satisfied by the signed distance function to the surface

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

first order phase transition in a nonequilibrium growth process we introduce a simple continuous model for nonequilibrium surface growth the dynamics of the system is defined by the kardar parisi zhang equation with a morse like potential representing a short range interaction between the surface and the substrate the mean field solution displays a nontrivial phase diagram with a first order transition between a growing and a bound surface associated with a region of coexisting phases and a tricritical point where the transition becomes second order numerical simulations in three dimensions show quantitative agreement with mean field results and the features of the phase space are preserved even in two dimensions

on bayesian d optimum design criteria and the equivalence theorem in non linear models the concavity of some bayesian d optimality criteria is investigated and is found in some cases to depend on the prior distribution in the case of a non concave criterion the standard equivalence theorem may fail but a local version continues to apply

genus zero surface conformal mapping and its application to brain surface mapping we developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one forms for surfaces with or without boundaries gu and yau 2002 gu and yau 2003 for genus zero surfaces our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map in this paper we apply the algorithm to the cortical surface matching problem we use a mesh structure to represent the brain surface further constraints are added to ensure that the conformal map is unique empirical tests on magnetic resonance imaging mri data show that the mappings preserve angular relationships are stable in mris acquired at different times and are robust to differences in data triangulation and resolution compared with other brain surface conformal mapping algorithms our algorithm is more stable and has good extensibility