Enumeration of polyominoes using Macsyma

AbstractThis paper shows the use of a symbolic language, Macsyma, to obtain new exact or asymptotic results in combinatorics. The examples are taken among polyominoes objects. The main purpose is to show how easy it is to bring some methods into operation in order to obtain new results in enumerative combinatorics

Etat de l'art de la segmentation de maillage 3D par patchs surfaciques

National audienceLa segmentation de maillage 3D est une composante essentielle de nombreuses applications. Elle se décline en deux familles : la segmentation en patchs surfaciques et la segmentation en parties significatives. Dans cet article, nous traitons principalement de la segmentation de maillages 3D en patchs surfaciques et en proposons un état de l'art. Nous positionnons le contexte de ce type de segmentation et discutons des contributions les plus pertinentes

Modeling and Evaluating of Human 3d+t Activities in Virtual Environment

International audienceThis paper studies the problem of evaluation of human 3d+t activities in Virtual Environments (VE) for Learning (VEL). Current evaluation methods focus mostly on: (i) the automatic identification of an ordered sequence of actions and/or (ii), an empirical analysis made by experts through the VE. In many cases, the learner's activity can be represented by some specific time series made of geometrical data of 3D artefacts. For the extraction and analysis of such Motions Of Interest (MOI), one can manually segment them among the traces, and/or use automatic approaches requiring a database of annotated examples. Both cases usually require too many resources to design such environments. Consequently, this work presents a method allowing teachers to quickly build, compare and evaluate a 3d+t learning activity in VE. This method is based on a semi-automatic approach combining the Dynamic Time Warping algorithm, with 3D reference shapes and few expert's demonstrations of the task to learn

Solving multivariate functional equations

This paper presents a new method to solve functional equations of multivariate generating functions, such as $$F(r,s)=e(r,s)+xf(r,s)F(1,1)+xg(r,s)F(qr,1)+xh(r,s)F(qr,qs),$$ giving a formula for $F(r,s)$ in terms of a sum over finite sequences. We use this method to show how one would calculate the coefficients of the generating function for parallelogram polyominoes, which is impractical using other methods. We also apply this method to answer a question from fully commutative affine permutations.Comment: 11 pages, 1 figure. v3: Main theorems and writing style revised for greater clarity. Updated to final version, to appear in Discrete Mathematic

Enumeration of Directed Column-Convex Animals with a Given Perimeter and Area

We give exact formulae for the number of directed column-convex animals with a given bond perimeter and area. The proof is based upon bijections and combinatorics related to the algebraic language theory

Segmentation hiérarchique de maillage 3D à partir des dynamiques de contour

La segmentation de maillage 3D est un problème fondamental en synthèse d'image et est devenu un enjeu important pour de nombreuses applications. Cet article introduit une nouvelle méthode de segmentation hiérarchique basée sur la ligne de partage des eaux (LPE), les cascades et les dynamiques de contour. La LPE génère une première partition composée de petits patchs surfaciques ; les dynamiques de contour offrent une bonne caractérisation des frontières et les cascades mettent à disposition plusieurs niveaux de segmentation pour l'utilisateur. Le procédé de fusion hiérarchique basé sur les cascades génère un arbre qui contient plusieurs schémas de segmentation ; l'utilisateur a ainsi la possibilité de parcourir facilement chacun des niveaux de segmentation contenus dans cet arbre pour sélectionner le plus adapté à son application

A New Coding for Parallelogram Animals

We describe a new coding for parallelogram animals and Motzkin words. From this new coding, we deduce a relation between the Catalan numbers, Motzkin words and parallelogram animals

pH-Dependent behaviour of soluble protein aggregates formed during heat-treatment of milk at pH 6.5 or 7.2

Soluble (SA) and micelle-bound (MA) protein aggregatesformed during the heat-treatment of milk are thought toincrease the gelation pH and gel strength of acid milk gels.The ratio SA/MA increases as heat-treatment pH is increased and the resulting gels are stronger. The objective was to study the pH-dependent behaviour of SA produced by heattreatment at pH 6.5 (SA6.5) and 7.2 (SA7.2) in order to get a better understanding of their role in acid gelation of heated skim milk

A heuristic for the retrieval of objects in low resolution video

International audienceIn this paper, we tackle the problem of matching of objects in video in the context of the rough indexing paradigm. In this context, the video data are of very low resolution and segmentation is consequently inaccurate. The region features (texture, color, shape) are not strongly relevant due to the resolution. The structure of the objects must be considered in order to improve the robustness of the matching of regions. Indeed, the problem of object matching can be expressed in terms of directed acyclic graph (DAG) matching. Here, we propose a method based on a heuristic in order to approach object matching. The results are compared with those of a method based on relaxation matching

Recherche de motifs quasi-similaires dans des graphes

National audienceNous décrivons un algorithme basé sur des métriques intrinsèques de graphes permettant de découvrir des motifs communs et similaires entre plu- sieurs graphes. Nous montrons des applications à la recherche d?image dans une collection et à l?interprétation de données géographique