degenerate diffusion and the stefan problem on etudie le probleme i u t u xx f x u dans 0 1 r u 0 t 0 u 1 t 0 dans r u x 0 u 0 x dans 0 1 avec certaines hypotheses sur f et u 0 on etudie le caractere des solutions quand s annule sur un intervalle

linear filtering for bilinear stochastic differential systems with unknown inputs investigates the problem of state estimation for bilinear stochastic multivariable differential systems in the presence of an additional disturbance whose statistics are completely unknown a linear filter is proposed based on a suitable decomposition of the state of the bilinear system into two components the first one is a computable function of the observations while the second component is estimated via a suitable linear filtering algorithm no a priori information on the disturbance is required for the filter implementation the proposed filter is robust with respect to the unknown input in that the covariance of the estimation error is not affected by such input numerical simulations show the effectiveness of the proposed filter

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

dynamic 3d models with local and global deformations deformable superquadrics the authors present a physically based approach to fitting complex three dimensional shapes using a novel class of dynamic models that can deform both locally and globally they formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline the model s six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models the local deformation parameters reconstruct the details of complex shapes that the global abstraction misses the equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces the authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational rotational and deformational degrees of freedom of the models model fitting experiments involving 2d monocular image data and 3d range data are presented

on affine plane curve evolution abstract an affine invariant curve evolution process is presented in this work the evolution studied is the affine analogue of the euclidean curve shortening flow evolution equations for both affine and euclidean invariants are developed an affine version of the classical euclidean isoperimetric inequality is proved this inequality is used to show that in the case of affine evolution of convex plane curves the affine isoperimetric ratio is a non decreasing function of time convergence of this affine isoperimetric ratio to the ellipse s value 8 2 as well as convergence in the hausdorff metric of the evolving curve to an ellipse is also proved

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

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

continuity of solutions of a singular parabolic equation which is of parabolic divergence form since 3 0 a e however it is the solution u of 0 1 which will be continuous while the solution u of 0 2 need not be in certain physical applications u corresponds to temperature while u is the enthalpy the difficulty in the analysis of this equation written in the form 0 2 stems from the fact that c need not be bounded or bounded away from zero thus the equation may be of degenerate or singular parabolic type as particular cases of the equations covered by our results we mention the three model problems

parabolic equations for curves on surfaces 2 intersections blow up and generalized solutions we describe a theory for parabolic equations for immersed curves on surfaces which generalizes the curve shortening or flow by mean curvature problem as well as several models in the theory of phase transitions in two dimensions a class of equations is described for which the initial value problem is well posed for rough initial data for which one can give a description of the way a smooth solution becomes singular and for which one can define generalized solutions i e solutions which are smooth except at a discrete set of times the methods which are used in this paper are more geometrical than those of part i by comparing arbitrary solutions with certain special solutions and by considering the way they intersect we derive estimates for the curvature and the tangent which allow one to study the initial value problem and the way solutions become singular

local existence and regularity for a class of degenerate parabolic equations on etudie des equations paraboliques scalaires a une variable d espace de la forme u t f u u x uu xx ou f f u p s est une fonction lisse de u p s r 3 avec f s strictement positive

filtering of nonlinear stochastic feedback systems this paper concerns the filtering problem for a class of stochastic nonlinear systems where the drift term may depend either on some external function open loop system or on the system output closed loop system through a controller such systems are denoted feedback systems the following result is proven for feedback systems the optimal filter in the open loop case remains optimal when the feedback is closed the proof is obtained by showing equivalence of suitable expressions for the estimators of the open loop and closed loop systems obtained using the kallianpur striebel formula g kallianpur and c striebel ann math statist 39 1968 pp 785 801

a decoupled approach to filter design for stochastic systems abstractthis paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems this result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept two kinds of observers are treated the full order and reduced order cases

on rotationally symmetric mean curvature flow the evolutionary motion of surfaces by their mean curvature has been studied by several authors from different points of view a measure theoretic approach is studied by k a brakke b the classical parametric problem is studied by g huisken hl non parametric mean curvature evolution with boundary conditions is treated in h2 for a detailed discussion see h3 we restrict our attention to the case in which the initial surface has rotational symmetry we shall show that under suitable initial conditions the solution degenerates in the sense that its curvature develops a singularity at exactly one point this confirms numerical results of the first author d for general surfaces in r3 see also the work of m a grayson gl p 286 g2 the proofs rely on the parabolic maximum principle the second author is gratefully indebted to s angencnt for bringing the problem to his attention and for pointing out the resemblance to so called quenching problems this research was financially via sfb 256 and sfb 123

flow by mean curvature of convex surfaces into spheres the motion of surfaces by their mean curvature has been studied by brakke 1 from the viewpoint of geometric measure theory other authors investigated the corresponding nonparametric problem 2 5 9 a reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal in this paper we take a more classical point of view consider a compact uniformly convex w dimensional surface m mo without boundary which is smoothly imbedded in r let mo be represented locally by a diffeomorphism

inferring surface trace and differential structure from 3 d images early image understanding seeks to derive analytic representations from image intensities the authors present steps towards this goal by considering the inference of surfaces from three dimensional images only smooth surfaces are considered and the focus is on the coupled problems of inferring the trace points the points through which the surface passes and estimating the associated differential structure given by the principal curvature and direction fields over the estimated smooth surfaces computation of these fields is based on determining an atlas of local charts or parameterizations at estimated surface points algorithm robustness and the stability of results are essential for analyzing real images to this end the authors present a functional minimization algorithm utilizing overlapping local charts to refine surface points and curvature estimates and develop an implementation as an iterative constraint satisfaction procedure based on local surface smoothness properties examples of the recovery of local structure are presented for synthetic images degraded by noise and for clinical magnetic resonance images

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

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

nonstationary filtration in partially saturated porous media from the mathematical formulation of a one dimensional flow through a partially saturated porous medium we arrive at a nonlinear free boundary problem the boundary being between the saturated and the unsaturated regions in the medium in particular we obtain an equation which is parabolic in the unsaturated part of the domain and elliptic in the saturated part

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

state estimation and control of conditionally linear systems the filtering problem for a partially observable stochastic system with linear in unobservable state dynamics and non gaussian initial conditions is studied here it is shown that the conditional expected value of the unobservable states given the past and present observations can be expressed in terms of a finite dimensional set of statistics this result which generalizes the conditionally gaussian filter is used to derive a separation principle for a linear quadratic control problem

what is the best causal scale space for three dimensional images we study the unique affine invariant morphological scale space in three dimensions we discuss its properties and show that it improves the dynamic shape model we explain the algorithms and display the first numerical experiments

bounds on the dimension of ext for finite groups of lie type abstract let g be a finite group of lie type defined in characteristic p and let k be an algebraically closed field of characteristic r 0 we will assume that r p so we are in the non defining characteristic case let v be a finite dimensional irreducible left kg module in 2011 guralnick and tiep found bounds on the dimension of h 1 g v in non defining characteristic which are independent of v the aim of this paper is to generalize the work of gurlanick and tiep we assume that g is split and use methods of modular harish chandra theory to find bounds on the dimension of ext k g 1 y v where y and v are irreducible kg modules we then use dipper and du s algorithms to illustrate our bounds in a series of examples

optimal filter approximations in conditionally gaussian pairwise markov switching models we consider a general triplet markov gaussian linear system bf x bf r bf y where bf x is an hidden continuous random sequence bf r is an hidden discrete markov chain bf y is an observed continuous random sequence when the triplet bf x bf r bf y is a classical conditionally gaussian linear state space model cglssm the mean square error optimal filter is not workable with a reasonable complexity and different approximate methods e g based on particle filters are used we propose two contributions the first one is to extend the cglssm to a new more general model called the conditionally gaussian pairwise markov switching model cgpmsm in which bf x is not necessarily markov given bf r the second contribution is to consider a particular case of cgpmsm in which bf r bf y is markov and in which an exact filter optimal in the sense of mean square error can be performed with linear time complexity some experiments show that the proposed method and the suited particle filter have comparable efficiency while the second one is much faster

finite dimensional filters part i the wei norman technique this two part paper deals with necessary or sufficient conditions for the existence of finite dimensional filters in this first part we set the problem and propose a construction of such filters by the wei norman technique after having formulated the problem of finite dimensional filters in terms of finite dimensional realizations of input output mappings we specify the dependence with respect to the initial measure we show how different notions of dependence imply different properties of the so called estimation algebra cal e cal e is homomorphic to a lie algebra of vector fields cal e contains only operators of order less than or equal to two cal e is finite dimensional and contains only operators of order less than or equal to two these results depend on a precise definition of a finite dimensional realization especially on what concerns the domain of the output function the last and most stringent condition on cal e will be shown to be almost sufficient to recover a family of finite dimensional realizations thanks to the proof of a baker campbell hausdorff formula which allows us to apply the wei norman technique in a quite general setting