Дисертації з теми "Graphes en rubans métriques"
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Yakovlev, Ivan. "Graphes en rubans métriques." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0143.
Повний текст джерелаThis thesis presents several contributions to the study of counting functions for metric ribbon graphs. Ribbon graphs, also known as combinatorial maps, are cellular embeddings of graphs in surfaces modulo homeomorphisms. They are combinatorial objects that can be represented as gluings of polygons or factorizations of permutations. Metric on a ribbon graph is an assignment of positive lengths to its edges. The counting functions give the number of integral metric ribbon graphs with fixed combinatorics (genus of the surface, degrees of vertices, number of boundaries) as a function of the perimeters of the boundaries. Our approach to their study is purely combinatorial and relies on bijections and surgeries for ribbon graphs. Firstly, we show that these functions are piecewise (quasi-)polynomials, specifying exactly the regions of (quasi-)polynomiality. We then study the cases when their top-degree terms are honest polynomials. Our interest in such cases comes from the fact that the corresponding polynomials can be used for refined enumeration of square-tiled surfaces, which correspond to integer points in the strata of (half-)translations surfaces (equivalently, strata of differentials on Riemann surfaces). Consequently, one can give refined/alternative formulas for Masur-Veech volumes of strata. One known example are the Kontsevich polynomials, counting trivalent metric ribbon graphs of given genus and perimeters of boundaries. They were recently used by Delecroix, Goujard, Zograf and Zorich to give a combinatorial formula for the volumes of principal strata of quadratic differentials. We concentrate on face-bipartite metric ribbon graphs, which appear in the study of Abelian differentials. We show that in the case of one-vertex graphs the top-degree terms of the counting functions on certain subspaces are in fact (explicit) polynomials. As a consequence, we deduce the generating function for the contributions of n-cylinder square-tiled surfaces to the volumes of minimal strata of Abelian differentials, refining a previous result of Sauvaget. We then present a similar polynomiality result for the two subfamilies of graphs corresponding to even/odd spin connected components of the minimal strata. This also gives a refinement of a formula for the corresponding volume differences previously obtained by Chen, Möller, Sauvaget and Zagier. Next we conjecture that the polynomiality phenomenon holds for families of graphs with several vertices, if each graph is weighted by the count of certain spanning trees. We prove the conjecture in the planar case. In the process, we construct families of plane trees which correspond to certain triangulations of the product of two simlpices, which are interesting from the point of view of the theory of polytopes. Finally, we present a contribution to a joint work with Duryev and Goujard, where the combinatorial formula of Delecroix, Goujard, Zograf and Zorich is generalized to all strata of quadratic differentials with odd singularities. The contribution is a combinatorial proof of the formula for coefficients counting certain degenerations of (non-face-bipartite) metric ribbon graphs
Ducoffe, Guillaume. "Propriétés métriques des grands graphes." Thesis, Université Côte d'Azur (ComUE), 2016. http://www.theses.fr/2016AZUR4134/document.
Повний текст джерелаLarge scale communication networks are everywhere, ranging from data centers withmillions of servers to social networks with billions of users. This thesis is devoted tothe fine-grained complexity analysis of combinatorial problems on these networks.In the first part, we focus on the embeddability of communication networks totree topologies. This property has been shown to be crucial in the understandingof some aspects of network traffic (such as congestion). More precisely, we studythe computational complexity of Gromov hyperbolicity and of tree decompositionparameters in graphs – including treelength and treebreadth. On the way, we givenew bounds on these parameters in several graph classes of interest, some of thembeing used in the design of data center interconnection networks. The main resultin this part is a relationship between treelength and treewidth: another well-studiedgraph parameter, that gives a unifying view of treelikeness in graphs and has algorithmicapplications. This part borrows from graph theory and recent techniques incomplexity theory. The second part of the thesis is on the modeling of two privacy concerns with social networking services. We aim at analysing information flows in these networks,represented as dynamical processes on graphs. First, a coloring game on graphs isstudied as a solution concept for the dynamic of online communities. We give afine-grained complexity analysis for computing Nash and strong Nash equilibria inthis game, thereby answering open questions from the literature. On the way, wepropose new directions in algorithmic game theory and parallel complexity, usingcoloring games as a case example
Turek, Ondrej. "Opérateurs de Schrödinger sur des graphes métriques." Phd thesis, Université du Sud Toulon Var, 2009. http://tel.archives-ouvertes.fr/tel-00527790.
Повний текст джерелаTurek, Ondřej. "Opérateurs de Schrödinger sur des graphes métriques." Toulon, 2009. http://tel.archives-ouvertes.fr/tel-00527790/fr/.
Повний текст джерелаThis thesis is devoted to investigation of quantum graphs, in other words, quantum systems in which a nonrelativistic particle is confined to a graph. We propose a new way to represent the boundary conditions, and with the help of this result we solve the longstanding open problemof approximating by regular graphs all singular vertex couplings in quantum graph vertices. We present a construction in which the edges are disjunct and the pairs of the so obtained endpoints are joined by additional connecting edges of lengths 2d. Each connecting edge carries a delta potential and a vector potential. It is shown that when the lengths 2d of the connecting edges shrink to zero and the added potentials properly depend on d, the limit can yield any requested singular vertex coupling. This type of boundary conditions is used to examine scattering properties of singular vertices of degrees 2 and 3. We show thar the couplings between each pair of the outgoing edges are individually tunable, which could enable the design of quantum spectral junctions filters. We also study Schrödinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by delta-couplings. If the graph is periodic, the Hamiltonian has a band spectrum. We consid a "bending" deformation of the chain consisting in changing the position of the point of contact between two rings. We show that this deformation gives rive to eigenvalues and analyze their dependence on the "bending angle"
Sénizergues, Delphin. "Structures arborescentes aléatoires : recollements d’espaces métriques et graphes stables." Thesis, Sorbonne Paris Cité, 2019. http://www.theses.fr/2019USPCD013.
Повний текст джерелаThe subject of this thesis is the study of some random metric spaces with a tree-like structure. We first study a construction in which we glue a sequence of metric spaces onto each other in a sequential manner. Under some conditions on the spaces that we aggregate, we compute the Hausdorff dimension of the obtained structure and it has a surprising expression ! We then investigate some asymptotic properties (degrees, height,profile) of two models of growing discrete trees, the weighted recursive trees and the preferential attachment trees with additive fitnesses. The former encodes the underlying discrete structure in the construction described above and the latter have a similar interpretation for some models of discrete growing graphs. We make use of this connection in order to prove scaling limit results for these random discrete graphs towards continuous metric space constructed by a gluing procedure. Last, in a joint work with Christina Goldschmidt and Bénédicte Haas, we investigate the behaviour of the alphastable component with fixed surplus. This random metric space appears as the scaling limit of large connected components of the configuration model with heavy-tailed degrees. This abject is almost a tree except for a finite number of cycles. We compute the distribution of the cyclic structure and give a description of the whole space as trees glued along this structure
Saidane, Faouzi. "Graphes et langages : une approche métrique." Lyon 1, 1991. http://www.theses.fr/1991LYO10206.
Повний текст джерелаMarcus, Karina. "Multiflots, métriques et graphes h-parfaits : les cycles impairs dans l'optimisation combinatoire." Phd thesis, Université Joseph Fourier (Grenoble), 1996. http://tel.archives-ouvertes.fr/tel-00005002.
Повний текст джерелаChepoi, Victor. "Métriques et convexité dans les graphes et espaces discrèts : propriétés et algorithmes." Aix-Marseille 2, 1997. http://www.theses.fr/1997AIX22124.
Повний текст джерелаBeaudou, Laurent. "Autour de problèmes de plongements de graphes." Phd thesis, Grenoble 1, 2009. http://www.theses.fr/2009GRE10089.
Повний текст джерелаThis Ph. D. Manuscript is built around the notion of graph embedding. An embedding of a graph G is an application mapping the vertices of G to elements of another structure, and preserving some properties of G. There are two types of embeddings. The combinatorial embeddings map the vertices of a graph G to the vertices of a graph H. The usual property that is preserved is the adjacency between vertices. In this thesis, we consider the isometric embeddings, preserving in addition the distances between vertices. We give some structural characterizations for families of graphs isometrically embeddable in hypercubes or Hamming graphs. The topological embeddings aim at drawing a graph G on some surface. Vertices are mapped to distinct points of the surface and the edges are represented by continuous curves linking these points. Is it possible to draw a graph G so that the edges do not cross eachother ? If not, what is the minimum number of crossings of a drawing of G ? We deal with these questions on different surfaces, or in relation with some graph operations as direct product or zip product
Beaudou, Laurent. "Autour de problèmes de plongements de graphes." Phd thesis, Université Joseph Fourier (Grenoble), 2009. http://tel.archives-ouvertes.fr/tel-00401226.
Повний текст джерелаKabil, Mustapha. "Enveloppe injective de graphes et de systèmes de transitions et idéaux de mots." Lyon 1, 1992. http://www.theses.fr/1992LYO10149.
Повний текст джерелаLehbab, Imène. "Problèmes métriques dans les espaces de Grassmann." Electronic Thesis or Diss., Mulhouse, 2023. http://www.theses.fr/2023MULH6508.
Повний текст джерелаThis work contributes to the field of metric geometry of the complex projective plane CP2 and the real Grassmannian manifold of the planes in R6. More specifically, we study all p-tuples, p ≥ 3, of equiangular lines in C3 or equidistant points in CP2, and p-tuples of equi-isoclinic planes in R6. Knowing that 9 is the maximum number of equiangular lines that can be constructed in C3, we develop a method to obtain all p-tuples of equiangular lines for all p ϵ [3,9]. In particular, we construct in C3 five congruence classes of quadruples of equiangular lines, one of which depends on a real parameter ɣ, which we extend to an infinite family of sextuples of equiangular lines depending on the same real parameter ɣ. In addition, we give the angles for which our sextuples extend beyond and up to 9-tuples. We know that there exists a p-tuple, p ≥ 3, of equi-isoclinic planes generating Rr, r ≥ 4, with parameter c, 0< c <1, if and only if there exists a square symmetric matrix, called Seidel matrix, of p × p square blocks of order 2, whose diagonal blocks are all zero and the others are orthogonal matrices in O(2) and whose smallest eigenvalue is equal to - 1/c and has multiplicity 2p-r. In this thesis, we investigate the case r=6 and we also show that we can explicitly determine the spectrum of all Seidel matrices of order 2p, p ≥ 3 whose off-diagonal blocks are in {R0, S0} where R0 and S0 are respectively the zero-angle rotation and the zero-angle symmetry. We thus show an unexpected link between some p-tuples of equi-isoclinic planes in Rr and simple graphs of order p
Bénéteau, Laurine. "Médians de graphes : algorithmes, connexité et axiomatique." Electronic Thesis or Diss., Aix-Marseille, 2022. http://www.theses.fr/2022AIXM0512.
Повний текст джерелаThe median problem is one of the most investigated problem in metric graph theory. We will start by studying this problem in median graphs. We present a linear time algorithm based on the majority rule which characterize the median in median graphs and on a fast computation of the parallelism classes of the edges (the \Theta-classes) via LexBFS which is a particular breadth first search algorithm.We also provide linear time algorithms to compute the median set in the l_1-cube complexes of median graphs and in event structures. Then, we provide a characterization of the graphs with connected medians in the pth power of the graph and provide a polynomial method to check if a graph is a G^p-connected median graph, extending a result of Bandelt and Chepoi (case p=1). We use this characterization to prove that some important graph classes in metric graph theory have G2-connected medians, such as bipartite Helly graphs and bridged graphs. We will also studied the axiomatic aspect of the median function by investigating the ABC-problem, which determine the graphs (named ABC-graphs) in which the median function is the only consensus function verifying three simples axioms (A) Anonymat, (B) Betweeness and (C) Consistency. We show that modular graphs with G2-connected medians are ABC-graphs and define new axioms allowing us to characterize the median function on some graph classes. For example the graphs with connected medians (including Helly graphs). We also show that a known class of ABC-graphs (graphs satisfying the pairing property) is a proper subclass of bipartite Helly graphs and we investigate their recognition
Kozhevnikov, Artem. "Propriétés métriques des ensembles de niveau des applications différentiables sur les groupes de Carnot." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112073/document.
Повний текст джерелаMetric properties of level sets of differentiable maps on Carnot groupsAbstract.We investigate the local metric properties of level sets of mappings defined between Carnot groups that are horizontally differentiable, i.e.with respect to the intrinsic sub-Riemannian structure. We focus on level sets of mapping having a surjective differential,thus, our study can be seen as an extension of implicit function theorem for Carnot groups.First, we present two notions of tangency in Carnot groups: one based on Reifenberg's flatness condition and another coming from classical convex analysis.We show that for both notions, the tangents to level sets coincide with the kernels of horizontal differentials.Furthermore, we show that this kind of tangency characterizes the level sets called ``co-abelian'', i.e.for which the target space is abelian andthat such a characterization may fail in general.This tangency result has several remarkable consequences.The most important one is that the Hausdorff dimension of the level sets is the expected one. We also show the local connectivity of level sets and, the fact that level sets of dimension one are topologically simple arcs.Again for dimension one level set, we find an area formula that enables us to compute the Hausdorff measurein terms of generalized Stieltjes integrals.Next, we study deeply a particular case of level sets in Heisenberg groups. We show that the level sets in this case are topologically equivalent to their tangents.It turns out that the Hausdorff measure of high-codimensional level sets behaves wildly, for instance, it may be zero or infinite.We provide a simple sufficient extra regularity condition on mappings that insures Ahlfors regularity of level sets.Among other results, we obtain a new general characterization of Lipschitz graphs associated witha semi-direct splitting of a Carnot group of arbitrary step.We use this characterization to derive a new characterization of co-ablian level sets that can be represented as graphs
Badr, Nadine. "Interpolation réelle des espaces de Sobolev sur les espaces métriques mesurés et applications aux inégalités fonctionnelles." Phd thesis, Université Paris Sud - Paris XI, 2007. http://tel.archives-ouvertes.fr/tel-00736066.
Повний текст джерелаCledel, Thomas. "Cyber-résilience des infrastructures critiques : analyse préventive des défaillances d’origine malveillante." Thesis, Ecole nationale supérieure Mines-Télécom Atlantique Bretagne Pays de la Loire, 2020. http://www.theses.fr/2020IMTA0180.
Повний текст джерелаThe property of resilience began to be studied in the fields of ecology and psychology before becoming of interest to researchers in economics, anthropology, civil infrastructure and more recently in computer science and information technology. Resilience is originally concerned with the survival and adaptation of a population to changes, but the case of infrastructures is different as survival may not be considered as an end goal but rather as a mean to another end: providing goods or services. Nevertheless, the protection of such infrastructures remains necessary and has long been accomplished in accordance with the paradigms of safety and dependability. However, these approaches require a detailed knowledge of the feared events that may affect the systems. Several events such as the accident at the Fukushima nuclear power plant or cyber-attacks such as StuxNet and BlackEnergy have highlighted several weaknesses in these paradigms.Research is therefore being conducted on the resilience of systems to address these weaknesses. The work presented in this thesis proposes a new model for assessing the resilience of a system by only having to detail its components and their relationships, whereas previous evaluation models focused on describing the threats and their impacts on the system
Souche, Estelle. "Quasi-isométries et quasi-plans dans l'étude des groupes discrets." Aix-Marseille 1, 2001. http://www.theses.fr/2001AIX11048.
Повний текст джерелаMoustrou, Philippe. "Geometric distance graphs, lattices and polytopes." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0802/document.
Повний текст джерелаA distance graph G(X;D) is a graph whose set of vertices is the set of points X of a metric space (X; d), and whose edges connect the pairs fx; yg such that d(x; y) 2 D. In this thesis, we consider two problems that may be interpreted in terms of distance graphs in Rn. First, we study the famous sphere packing problem, in relation with thedistance graph G(Rn; (0; 2r)) for a given sphere radius r. Recently, Venkatesh improved the best known lower bound for lattice sphere packings by a factor log log n for infinitely many dimensions n. We prove an effective version of this result, in the sense that we exhibit, for the same set of dimensions, finite families of lattices containing a lattice reaching this bound. Our construction uses codes over cyclotomic fields, lifted to lattices via Construction A. We also prove a similar result for families of symplectic lattices. Second, we consider the unit distance graph G associated with a norm k _ k. The number m1 (Rn; k _ k) is defined as the supremum of the densities achieved by independent sets in G. If the unit ball corresponding with k _ k tiles Rn by translation, then it is easy to see that m1 (Rn; k _ k) > 1 2n . C. Bachoc and S. Robins conjectured that the equality always holds. We show that this conjecture is true for n = 2 and for several Voronoï cells of lattices in higher dimensions, by solving packing problems in discrete graphs
Girardet, Xavier. "Paysage & [et] infrastructures de transport : modélisation des impacts des infrastructures sur les réseaux écologiques." Phd thesis, Université de Franche-Comté, 2013. http://tel.archives-ouvertes.fr/tel-01069242.
Повний текст джерелаChen, Li. "Quasi transformées de Riesz, espaces de Hardy et estimations sous-gaussiennes du noyau de la chaleur." Phd thesis, Université Paris Sud - Paris XI, 2014. http://tel.archives-ouvertes.fr/tel-01001868.
Повний текст джерелаBarazer, Simon. "Geometric recursion and volumes of moduli spaces : Oriented ribbon graphs, acyclic decomposion, “Cut-and-Join” operators." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM003.
Повний текст джерелаIn this thesis we study the relations between topological and geometric recursions and Masur Veech volumes of moduli spaces of quadratic and Abelian differentials. We chose to study ribbon graphs because they can be used to compute these volumes. In the case of trivalent ribbon graphs we give a geometric recursion formula that was also independently found in "On the Kontsevich geometry of the combinatorial Teichmüller space". We also study oriented ribbon graphs, in this case we found decomposition of graphs that we call "The acyclic decomposition''. This decomposition allow to decompose general oriented ribbon graphs into graphs with only one vertex. Using this we are able to compute volumes of their moduli spaces. We relate the acyclic decomposition to cut and joins operators. At the end of the memoir we study degenerations of ribbon graphs and show that volumes of moduli spaces of oriented ribbon graphs admit continuous extensions
Labbé, Cyril. "Flots stochastiques et représentation lookdown." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2013. http://tel.archives-ouvertes.fr/tel-00874551.
Повний текст джерелаZaidi, Faraz. "Analysis, structure and organization of complex networks." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14112/document.
Повний текст джерелаNetwork science has emerged as a fundamental field of study to model many physicaland real world systems around us. The discovery of small world and scale free propertiesof these real world networks has revolutionized the way we study, analyze, model andprocess these networks. In this thesis, we are interested in the study of networks havingthese properties often termed as complex networks. In our opinion, research conducted inthis field can be grouped into four categories, Analysis, Structure, Processes-Organizationand Visualization. We address problems pertaining to each of these categories throughoutthis thesis. (...)
Zaidi, Faraz. "Analyse, Structure et Organisation des Réseaux Complexes." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2010. http://tel.archives-ouvertes.fr/tel-00542703.
Повний текст джерелаSahraoui, Yohan. "Le paysage, entre esthétique & écologie : modélisation rétrospective à partir de changements d'occupation du sol." Thesis, Besançon, 2016. http://www.theses.fr/2016BESA1022/document.
Повний текст джерелаLandscape is both a backdrop to the lives of human populations and a medium for the life cycle of animal species. Landscape changes induced by land-use and land-cover dynamics affect both these dimensions, the one aesthetic, and the other ecological. Because these rationales areusually studied within different disciplines, little research has been done into how the two clashor combine as and when landscape structures change. This work seeks therefore to model the spatial co-evolution of the aesthetic and ecological functions of landscape retrospectively usingspatial metrics based on land-cover data. It focuses on changes in the urban fringes of two French cities (Paris and Besançon) over the last 30 years. The approach attempts first to use land-cover data to model (1) the landscape preferences of a set of individuals and (2) the ecological connectivity of a set of animal species. Drawing on both multivariate statistical analysis and spatial analysis, the core of this work consists in investigating how the two functions have evolved in convergent or divergent ways over time. The results provide fresh insight into the relationship between landscape aesthetics and landscape ecology and raise questions about the value of spatial modelling for a landscape management approach that endeavours to reconcile the preservation of residents’ living environments and the conservationof biodiversity
Bettinelli, Jérémie. "Limite d'échelle de cartes aléatoires en genre quelconque." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00638065.
Повний текст джерелаTriestino, Michele. "La dynamique des difféomorphismes du cercle selon le point de vue de la mesure." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2014. http://tel.archives-ouvertes.fr/tel-01065468.
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