Domino tilings and related models: space of configurations of domains with holes

We first prove that the set of domino tilings of a fixed finite figure is a distributive lattice, even in the case when the figure has holes. We then give a geometrical interpretation of the order given by this lattice, using (not necessarily local) transformations called {\em flips}. This study allows us to formulate an exhaustive generation algorithm and a uniform random sampling algorithm. We finally extend these results to other types of tilings (calisson tilings, tilings with bicolored Wang tiles).Comment: 17 pages, 11 figure

Average tree solutions for graph games

In this paper we consider cooperative graph games being TU-games in which players cooperate if they are connected in the communication graph. We focus our attention to the average tree solutions introduced by Herings, van der Laan and Talman [6] and Herings, van der Laan, Talman and Yang [7]. Each average tree solution is defined with re- spect to a set, say T , of admissible rooted spanning trees. Each average tree solution is characterized by efficiency, linearity and an axiom of T - hierarchy on the class of all graph games with a fixed communication graph. We also establish that the set of admissible rooted spanning trees introduced by Herings, van der Laan, Talman and Yang [7] is the largest set of rooted spanning trees such that the corresponding aver- age tree solution is a Harsanyi solution. One the other hand, we show that this set of rooted spanning trees cannot be constructed by a dis- tributed algorithm. Finally, we propose a larger set of spanning trees which coincides with the set of all rooted spanning trees in clique-free graphs and that can be computed by a distributed algorithm.

Average tree solutions for graph games

In this paper we consider cooperative graph games being TU-games in which players cooperate if they are connected in the communication graph. We focus our attention to the average tree solutions introduced by Herings, van der Laan and Talman [6] and Herings, van der Laan, Talman and Yang [7]. Each average tree solution is defined with re- spect to a set, say T , of admissible rooted spanning trees. Each average tree solution is characterized by efficiency, linearity and an axiom of T - hierarchy on the class of all graph games with a fixed communication graph. We also establish that the set of admissible rooted spanning trees introduced by Herings, van der Laan, Talman and Yang [7] is the largest set of rooted spanning trees such that the corresponding aver- age tree solution is a Harsanyi solution. One the other hand, we show that this set of rooted spanning trees cannot be constructed by a dis- tributed algorithm. Finally, we propose a larger set of spanning trees which coincides with the set of all rooted spanning trees in clique-free graphs and that can be computed by a distributed algorithm

Average tree solutions for graph games

In this paper we consider cooperative graph games being TU-games in which players cooperate if they are connected in the communication graph. We focus our attention to the average tree solutions introduced by Herings, van der Laan and Talman [6] and Herings, van der Laan, Talman and Yang [7]. Each average tree solution is defined with re- spect to a set, say T , of admissible rooted spanning trees. Each average tree solution is characterized by efficiency, linearity and an axiom of T - hierarchy on the class of all graph games with a fixed communication graph. We also establish that the set of admissible rooted spanning trees introduced by Herings, van der Laan, Talman and Yang [7] is the largest set of rooted spanning trees such that the corresponding aver- age tree solution is a Harsanyi solution. One the other hand, we show that this set of rooted spanning trees cannot be constructed by a dis- tributed algorithm. Finally, we propose a larger set of spanning trees which coincides with the set of all rooted spanning trees in clique-free graphs and that can be computed by a distributed algorithm

Pavage de figures par des barres et reconnaissance de graphes sous-jacents a un reseau d'automates

Available from INIST (FR), Document Supply Service, under shelf-number : T 82697 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc

Rhombus tilings:decomposition and space structure.

We study the spaces of rhombus tilings, i.e. the graphs whose vertices are tilings of a fixed zonotope, and two tilings are linked if one can pass from one to the other one by a local transformation, called flip.Nous étudions les espaces de pavages rhombiques, i.e. les graphes dont les sommets sont les pavages d’un zonotope fixé, et deux pavages sont liés si on peut passer de l’un`a l’autre par une série de transformations locales appelées flips.Nous utilisons une méthode de décomposition pour coder ces pavages,et donnons une caractérisation des séquences de bits codant effective-ment des pavages.En codimension 2, nous utilisons ce codage pour donner une représentation canonique des pavages, et une structure d’ordre sur l’espace des pavages. Cet ordre est gradué, ce qui nous permet d’en déduire la connexité de l’ensembl

Tiling a polygon with two kinds of rectangles

We fix two rectangles with integer dimensions. We give a quadratic time algorithm which, given a polygon F as input, produces a tiling of F with translated copies of our rectangles (or indicates that there is no tiling). Moreover, we prove that any pair of tilings can be linked by a sequence of local transformations of tilings, called flips. This study is based on the use of J. H. Conway's tiling groups and extends the results of C. Kenyon and R. Kenyon (limited to the case when each rectangle has a side of length $1$).Nous fixons deux rectangles aux dimensions entières. Nous produisons un algorithme en temps quadratique qui, étant donné un polygone F en entré, donne un pavage de F avec des copies traduites de nos rectangles (ou indique qu’il n’y a pas de pavage). De plus, nous prouvons que toute paire de pavages peut être relié par une suite de transformations locales élémentaires. Cette étude utilise les groupes de pavages de J. H. Conway et étend les résultats de C. Kenyon and R. Kenyon (limités au cas ou chaque rectangle a une dimension unitaire

Updating Automata Networks

Cette thèse s'intéresse aux évènements et aux ordonnancements d'évènements se produisant au sein de réseaux d'éléments conceptuels prédéterminés. Dans ces réseaux, les éléments, appelés plutôt "automates", s'incitent les uns les autres à changer d'état en accord avec des règles prédéfinies qui, précisément, définissent le (fonctionnement du) réseau. Lorsqu'un automate se conforme effectivement aux influences qu'il reçoit de la part des autres, on dit que son état est mis à jour. Les évènements élémentaires considérés sont les changements d'états des automates. Définir un mode de mise à jour pour l'ensemble des automates d'un réseau permet de sélectionner certains évènements parmi l'ensemble de ceux qui sont a priori possibles. Cela permet aussi d'organiser et d'ordonner les évènements les uns par rapport aux autres de façon, par exemple, à imposer que des évènements indépendants se produisent simultanément ou simplement, de manière assez rapprochée pour qu'aucun autre événement ne puisse se produire pendant leur occurrence. Informellement, les modes de mise à jour peuvent donc être interprétés comme l'expression d'influences extérieures au réseau interdisant certains changements, ou alors comme la formalisation d'une version relâchée et relative de l'écoulement de temps. Cette thèse propose d'étudier leur influence sur le comportement des réseaux. Et afin de distinguer cette influence de celle de la structure des réseaux, elle commence par mettre en évidence le rôle de certains motifs structurels. Après ça, elle s'intéresse en particulier à l'information "encodée" dans une séquence de mises à jour et à l'impact du synchronisme dans celles-ci.This thesis is concerned with the events and the organisation of events that take place within networks of abstract predetermined elements called "automata". In these networks, automata incite one another to switch states in agreement with predefined rules which, precisely, define the net-work. When an automaton effectively conforms to the influences it receives from others, its state is said to be updated. The elementary events that are considered here are thus automata state changes. To define an update mode for all the automata of a network allows to select some events among all those that are a priori possible. It also allows to organise and order the events relatively so as to impose, for example, that independent events occur simultaneously or so that simply, they happen close enough to disallow the occurrence of any other events in between. Informally, update modes can be interpreted as the expressions of influences incoming from outside the network, forbidding certain changes, or else, as the formalisation of a relaxed and relative version of time flow. This thesis proposes to study their influences on network behaviours. And to distinguish their influences from that of network structures, it starts by highlighting the role of certain structural motives. After that, it explores in particular the information that is "encoded" in a sequence of updates as well as the general impact of synchronism in updates.LYON-ENS Sciences (693872304) / SudocSudocFranceF

Contractions of octagonal tilings with rhombic tiles.

We prove that the space of rhombic tilings of a fixed octagon can be given a canonical order structure. We make a first study of this order, proving that it is a graded poset. As a consequence, we obtain the diameter of the space and a lower bound for the distance between tilings.Dans ce papier, nous prouvons que les pavages d’un octogone par des parallélogrammes peut être structuré de façon canonique. Une première étude de cette ordre est effectuée, et une preuve est faite de sa structure d’ordre gradué. Il en découle naturellement le diamètre de l’espace de pavages associé, ainsi qu’une borne inférieure pour la dis-tance de flips entre deux pavages