Image Segmentation with Multidimensional Refinement Indicators

We transpose an optimal control technique to the image segmentation problem. The idea is to consider image segmentation as a parameter estimation problem. The parameter to estimate is the color of the pixels of the image. We use the adaptive parameterization technique which builds iteratively an optimal representation of the parameter into uniform regions that form a partition of the domain, hence corresponding to a segmentation of the image. We minimize an error function during the iterations, and the partition of the image into regions is optimally driven by the gradient of this error. The resulting segmentation algorithm inherits desirable properties from its optimal control origin: soundness, robustness, and flexibility

Trusting Computations: a Mechanized Proof from Partial Differential Equations to Actual Program

Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring specific accuracy issues due to their massive use of floating-point computations. Yet, it is uncommon to guarantee their correctness. Indeed, we had to extend existing methods and tools for proving the correct behavior of programs to verify an existing numerical analysis program. This C program implements the second-order centered finite difference explicit scheme for solving the 1D wave equation. In fact, we have gone much further as we have mechanically verified the convergence of the numerical scheme in order to get a complete formal proof covering all aspects from partial differential equations to actual numerical results. To the best of our knowledge, this is the first time such a comprehensive proof is achieved.Comment: N° RR-8197 (2012). arXiv admin note: text overlap with arXiv:1112.179

Interplay of anisotropy in shape and interactions in charged platelet suspensions

Motivated by the intriguing phase behavior of charged colloidal platelets, we investigate the structure and dynamics of charged repulsive disks by means of Monte-Carlo simulations. The electrostatic interactions are taken into account through an effective two-body potential, obtained within the non-linear Poisson-Boltzmann formalism, which has the form of anisotropic screened Coulomb potential. Recently, we showed that the original intrinsic anisotropy of the electrostatic potential in competition with excluded volume effects leads to a rich phase behavior that not only includes various liquid-crsytalline phases but also predicts the existence of novel structures composed of alternating nematic-antinematic sheets. Here, we examine the structural and dynamical signatures of each of the observed structures for both translational and rotational degrees of freedom. Finally, we discuss the influence of effective charge value and our results in relation to experimental findings on charged platelet suspensions.Comment: 22 pages, 17 figure

Format Unraveled

International audiencePretty-printing can be described as finding a good-looking solution to typeset data according to a set of formatting conventions. Oppen [6] pioneered the field with an algorithmic solution to pretty-printing, using the notions of boxes and break hints. The Format module is a direct descendant of this work: it is unfortunately often misunderstood or even misused. The first goal of this article is to enhance the available documentation about Format by explaining its basic and advanced features but also its relationship and differences with Oppen's seminal work. The second goal is to investigate the links that Format has with the document-based pretty-printing tradition fostered by the lazy programming community [3, 4, 9, 10]

Global Strong Solutions for a Class of Heterogeneous Catalysis Models

We consider a mathematical model for heterogeneous catalysis in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. The system under consideration consists of a diffusion-advection system inside the bulk phase and a reaction-diffusion-sorption system modeling the processes on the catalytic wall and the exchange between bulk and surface. We assume Fickian diffusion with constant coefficients, sorption kinetics with linear growth bound and a network of chemical reactions which possesses a certain triangular structure. Our main result gives sufficient conditions for the existence of a unique global strong $L^2$-solution to this model, thereby extending by now classical results on reaction-diffusion systems to the more complicated case of heterogeneous catalysis.Comment: 30 page

Couplage de codes numériques, parallélisme et langages de haut niveau

Le couplage de codes numériques associés à différents sous-domaines permet la mise en oeuvre de la modélisation de phénomènes physiques complexes. Les techniques de couplage s'apparentent à celles de parallélisation : les communications correspondent à des conditions de transmission aux interfaces entre les sous-domaines. Dans cette première évaluation du potentiel des langages de haut niveau pour le calcul scientifique, nous abordons la réalisation d'une maquette de couplage pour un cas simplifié en utilisant le langage fonctionnel Caml, et plus précisément à l'aide du système OCamlP3l dédié à la parallélisation

The multi-dimensional refinement indicators algorithm for optimal parameterization

International audienceThe estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori information by reducing the number of unknowns according to the physics of the problem. The refinement indicators algorithm provides a fruitful adaptive parameterization technique that parsimoniously opens the degrees of freedom in an iterative way. We present a new general form of the refinement indicators algorithm that is applicable to the estimation of multi-dimensional parameters in any PDE. In the linear case, we state the relationship between the refinement indicator and the decrease of the usual least-squares data misfit objective function. We give numerical results in the simple case of the identity model, and this application reveals the refinement indicators algorithm as an image segmentation technique.L'estimation de paramètres distribués dans des équations aux dérivées partielles (EDP) à partir de mesures de la solution de l'EDP peut mener à des problèmes de sous-détermination. Le choix d'une paramétrisation est un moyen usuel pour ajouter de l'information a priori en réduisant le nombre d'inconnues en relation avec la physique du problème. L'algorithme des indicateurs de raffinement fourni une technique de paramétrisation adaptative fructueuse qui ouvre parcimonieusement les degrés de liberté de façon itérative. Nous présentons une nouvelle forme générale de l'algorithme des indicateurs de raffinement qui s'applique à l'estimation des paramètres multi-dimensionnels dans toute EDP. Dans le cas linéaire, nous établissons le lien entre l'indicateur de raffinement et la décroissance de la fonction objectif des moindres carrés quantifiant l'erreur aux données. Nous donnons des résultats numériques pour le cas simple du modèle identité, et cette application permet de voir l'algorithme des indicateurs de raffinement comme une technique de segmentation d'image

The CAML reference manual

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Parallel Programming with the System Applications to Numerical Code Coupling

Writing parallel programs is not easy, and debugging them is usually a nightmare. To cope with these difficulties, a structured approach to parallel programming using skeletons and templates based compilation techniques has been developed over the past years by several researchers, including the P3L group in Pisa. The system marries the functional programming language with the skeletons, yielding a powerful parallel programming system and methodology: allows the programmer to write and debug a sequential version of his program (which, if not easy, could be considered as routine), and then the parallel version is automatically deduced by recompilation of the source program. The invaluable advantage of this approach is stagging: the programmer has just to concentrate on the easy part, the sequential programming, relieving on the system to obtain the hard part, the parallel version. As an additional benefit, the semantics adequacy of the sequential and parallel versions of the program is no more the programmer's concern: it is now the entire responsability of the compiler. In this paper, we report on the successful application of in the field of scientific computing, where the system has been used to solve a problem of numerical code coupling, obtaining parallelization for free. The interaction has been quite successful, as, in the process of solving the coupling problem, a wealth of new ideas have emerged on the design of the system, which are now incorporated in the current version of : coloring of virtual and physical computing network nodes to specify their relative mapping, and the new notion of parfuns or parallel computing sub-networks reified as functions at the programmer's level. Those two notions both increase efficiency and ease the writing of programs, being a step to smoother integration of parallel computing into the functional programming paradigm

An Improved Search for the Neutron Electric Dipole Moment

A permanent electric dipole moment of fundamental spin-1/2 particles violates both parity (P) and time re- versal (T) symmetry, and hence, also charge-parity (CP) symmetry since there is no sign of CPT-violation. The search for a neutron electric dipole moment (nEDM) probes CP violation within and beyond the Stan- dard Model. The experiment, set up at the Paul Scherrer Institute (PSI), an improved, upgraded version of the apparatus which provided the current best experimental limit, dn < 2.9E-26 ecm (90% C.L.), by the RAL/Sussex/ILL collaboration: Baker et al., Phys. Rev. Lett. 97, 131801 (2006). In the next two years we aim to improve the sensitivity of the apparatus to sigma(dn) = 2.6E-27 ecm corresponding to an upper limit of dn < 5E-27 ecm (95% C.L.), in case for a null result. In parallel the collaboration works on the design of a new apparatus to further increase the sensitivity to sigma(dn) = 2.6E-28 ecm.Comment: APS Division for particles and fields, Conference Proceedings, Two figure