Relevant bibliographies by topics / Graphons de probabilités

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Graphons de probabilités'

Author: Grafiati
Published: 14 December 2024

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Journal articles on the topic "Graphons de probabilités"

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McMillan, Audra, and Adam Smith. "When is non-trivial estimation possible for graphons and stochastic block models?‡." Information and Inference: A Journal of the IMA 7, no. 2 (August 23, 2017): 169–81. http://dx.doi.org/10.1093/imaiai/iax010.

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Abstract Block graphons (also called stochastic block models) are an important and widely studied class of models for random networks. We provide a lower bound on the accuracy of estimators for block graphons with a large number of blocks. We show that, given only the number $k$ of blocks and an upper bound $\rho$ on the values (connection probabilities) of the graphon, every estimator incurs error ${\it{\Omega}}\left(\min\left(\rho, \sqrt{\frac{\rho k^2}{n^2}}\right)\right)$ in the $\delta_2$ metric with constant probability for at least some graphons. In particular, our bound rules out any non-trivial estimation (that is, with $\delta_2$ error substantially less than $\rho$) when $k\geq n\sqrt{\rho}$. Combined with previous upper and lower bounds, our results characterize, up to logarithmic terms, the accuracy of graphon estimation in the $\delta_2$ metric. A similar lower bound to ours was obtained independently by Klopp et al.
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HATAMI, HAMED, and SERGUEI NORINE. "The Entropy of Random-Free Graphons and Properties." Combinatorics, Probability and Computing 22, no. 4 (May 16, 2013): 517–26. http://dx.doi.org/10.1017/s0963548313000175.

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Every graphon defines a random graph on any given number n of vertices. It was known that the graphon is random-free if and only if the entropy of this random graph is subquadratic. We prove that for random-free graphons, this entropy can grow as fast as any subquadratic function. However, if the graphon belongs to the closure of a random-free hereditary graph property, then the entropy is O(n log n). We also give a simple construction of a non-step-function random-free graphon for which this entropy is linear, refuting a conjecture of Janson.
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Backhausz, Ágnes, and Dávid Kunszenti-Kovács. "On the dense preferential attachment graph models and their graphon induced counterpart." Journal of Applied Probability 56, no. 2 (June 2019): 590–601. http://dx.doi.org/10.1017/jpr.2019.34.

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AbstractLetting ℳ denote the space of finite measures on ℕ, and μλ ∊ ℳ denote the Poisson distribution with parameter λ, the function W : [0, 1]2 → ℳ given by W(x, y) = μc log x log y is called the PAG graphon with density c. It is known that this is the limit, in the multigraph homomorphism sense, of the dense preferential attachment graph (PAG) model with edge density c. This graphon can then in turn be used to generate the so-called W-random graphs in a natural way, and similar constructions also work in the slightly more general context of the so-called PAGκ models. The aim of this paper is to compare these dense PAGκ models with the W-random graph models obtained from the corresponding graphons. Motivated by the multigraph limit theory, we investigate the expected jumble-norm distance of the two models in terms of the number of vertices n. We present a coupling for which the expectation can be bounded from above by O(log3/2n · n−1/2), and provide a universal lower bound that is coupling-independent, but without the logarithmic term.
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Kalampakas, Antonios. "Graph Automata and Graph Colorability." European Journal of Pure and Applied Mathematics 16, no. 1 (January 29, 2023): 112–20. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4629.

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Automata recognizing graphs can be constructed by employing the algebraic structure of graphoids. For the construction of a graph automaton, the relations over the Kleene star of the state set must constitute a graphoid. Hence different kinds of graphoids produce graph automata with diverse operation and recognition capacity. In this paper we show that graph colorability is recognized by automata operating over the simplest possible abelian graphoid.
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Zhang, Yuan, Elizaveta Levina, and Ji Zhu. "Estimating network edge probabilities by neighbourhood smoothing." Biometrika 104, no. 4 (September 15, 2017): 771–83. http://dx.doi.org/10.1093/biomet/asx042.

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Summary The estimation of probabilities of network edges from the observed adjacency matrix has important applications to the prediction of missing links and to network denoising. It is usually addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighbourhood smoothing, to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires. The neighbourhood smoothing method requires little tuning, has a competitive mean squared error rate and outperforms many benchmark methods for link prediction in simulated and real networks.
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Shi, Tan, Qing Peng, Zhitong Bai, Fei Gao, and Igor Jovanovic. "Proton irradiation of graphene: insights from atomistic modeling." Nanoscale 11, no. 43 (2019): 20754–65. http://dx.doi.org/10.1039/c9nr06502d.

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Peng, Songang, Zhi Jin, Dayong Zhang, Jingyuan Shi, Yanhui Zhang, and Guanghui Yu. "Evidence of electric field-tunable tunneling probability in graphene and metal contact." Nanoscale 9, no. 27 (2017): 9520–28. http://dx.doi.org/10.1039/c7nr02502e.

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Yoder, J. W., E. Littell, and B. T. Williams. "Probability Graphics Support for Medical Reasoning." Methods of Information in Medicine 32, no. 03 (1993): 229–32. http://dx.doi.org/10.1055/s-0038-1634928.

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Abstract:Graphic displays of data from clinical observations and laboratory testing provide important support to the health practitioner in managing an increasing amount of complex information. A graphic display program is described that preserves much of the context of data that is important to their evaluation, and that maintains a sense of the strength of the signal when aberrant data are encountered.
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VANTAGGI, BARBARA. "CONDITIONAL INDEPENDENCE STRUCTURES AND GRAPHICAL MODELS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11, no. 05 (October 2003): 545–71. http://dx.doi.org/10.1142/s0218488503002326.

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In this paper we study conditional independence structures arising from conditional probabilities and lower conditional probabilities. Such models are based on notions of stochastic independence apt to manage also those situations where zero evaluations on possible events are present: this is particularly crucial for lower probability. The "graphoid" properties of such models are investigated, and the representation problem of conditional independence structures is dealt with by generalizing the wellknown classic separation criteria for undirected and directed acyclic graphs. Our graphical models describe the independence statements and the possible logical dependencies among the random variables.
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Raturi, Ashish, and Sudhanshu Choudhary. "Simulation Study on Understanding the Spin Transport in MgO Adsorbed Graphene Based Magnetic Tunnel Junction." SPIN 06, no. 03 (September 2016): 1650011. http://dx.doi.org/10.1142/s2010324716500119.

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First principles calculations of spin-dependent electronic transport properties of magnetic tunnel junction (MTJ) consisting of MgO adsorbed graphene nanosheet sandwiched between two CrO2 half-metallic ferromagnetic (HMF) electrodes is reported. MgO adsorption on graphene opens bandgap in graphene nanosheet which makes it more suitable for use as a tunnel barrier in MTJs. It was found that MgO adsorption suppresses transmission probabilities for spin-down channel in case of parallel configuration (PC) and also suppresses transmission in antiparallel configuration (APC) for both spin-up and spin-down channel. Tunnel magneto-resistance (TMR) of 100% is obtained at all bias voltages in MgO adsorbed graphene-based MTJ which is higher than that reported in pristine graphene-based MTJ. HMF electrodes were found suitable to achieve perfect spin filtration effect and high TMR. I–V characteristics for both parallel and antiparallel magnetization states of junction are calculated. High TMR suggests its usefulness in spin valves and other spintronics-based applications.
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Dissertations / Theses on the topic "Graphons de probabilités"

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Weibel, Julien. "Graphons de probabilités, limites de graphes pondérés aléatoires et chaînes de Markov branchantes cachées." Electronic Thesis or Diss., Orléans, 2024. http://www.theses.fr/2024ORLE1031.

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Les graphes sont des objets mathématiques qui servent à modéliser tout type de réseaux, comme les réseaux électriques, les réseaux de communications et les réseaux sociaux. Formellement un graphe est composé d'un ensemble de sommets et d'un ensemble d'arêtes reliant des paires de sommets. Les sommets représentent par exemple des individus, tandis que les arêtes représentent les interactions entre ces individus. Dans le cas d'un graphe pondéré, chaque arête possède un poids ou une décoration pouvant modéliser une distance, une intensité d'interaction, une résistance. La modélisation de réseaux réels fait souvent intervenir de grands graphes qui ont un grand nombre de sommets et d'arêtes.La première partie de cette thèse est consacrée à l'introduction et à l'étude des propriétés des objets limites des grands graphes pondérés : les graphons de probabilités. Ces objets sont une généralisation des graphons introduits et étudiés par Lovász et ses co-auteurs dans le cas des graphes sans poids sur les arêtes. À partir d'une distance induisant la topologie faible sur les mesures, nous définissons une distance de coupe sur les graphons de probabilités. Nous exhibons un critère de tension pour les graphons de probabilités lié à la compacité relative dans la distance de coupe. Enfin, nous prouvons que cette topologie coïncide avec la topologie induite par la convergence en distribution des sous-graphes échantillonnés. Dans la deuxième partie de cette thèse, nous nous intéressons aux modèles markoviens cachés indexés par des arbres. Nous montrons la consistance forte et la normalité asymptotique de l'estimateur de maximum de vraisemblance pour ces modèles sous des hypothèses standards. Nous montrons un théorème ergodique pour des chaînes de Markov branchantes indexés par des arbres avec des formes générales. Enfin, nous montrons que pour une chaîne stationnaire et réversible, le graphe ligne est la forme d'arbre induisant une variance minimale pour l'estimateur de moyenne empirique parmi les arbres avec un nombre donné de sommets
Graphs are mathematical objects used to model all kinds of networks, such as electrical networks, communication networks, and social networks. Formally, a graph consists of a set of vertices and a set of edges connecting pairs of vertices. The vertices represent, for example, individuals, while the edges represent the interactions between these individuals. In the case of a weighted graph, each edge has a weight or a decoration that can model a distance, an interaction intensity, or a resistance. Modeling real-world networks often involves large graphs with a large number of vertices and edges.The first part of this thesis is dedicated to introducing and studying the properties of the limit objects of large weighted graphs : probability-graphons. These objects are a generalization of graphons introduced and studied by Lovász and his co-authors in the case of unweighted graphs. Starting from a distance that induces the weak topology on measures, we define a cut distance on probability-graphons. We exhibit a tightness criterion for probability-graphons related to relative compactness in the cut distance. Finally, we prove that this topology coincides with the topology induced by the convergence in distribution of the sampled subgraphs. In the second part of this thesis, we focus on hidden Markov models indexed by trees. We show the strong consistency and asymptotic normality of the maximum likelihood estimator for these models under standard assumptions. We prove an ergodic theorem for branching Markov chains indexed by trees with general shapes. Finally, we show that for a stationary and reversible chain, the line graph is the tree shape that induces the minimal variance for the empirical mean estimator among trees with a given number of vertices
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Selig, Thomas. "Convergence de cartes et tas de sable." Thesis, Bordeaux, 2014. http://www.theses.fr/2014BORD0286/document.

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Cette thèse est dédiée à l'étude de divers problèmes se situant à la frontière entre combinatoire et théorie des probabilités. Elle se compose de deux parties indépendantes : la première concerne l'étude asymptotique de certaines familles de \cartes" (en un sens non traditionnel), la seconde concerne l'étude d'une extension stochastique naturelle d'un processus dynamique classique sur un graphe appelé modèle du tas de sable. Même si ces deux parties sont a priori indépendantes, elles exploitent la même idée directrice, à savoir les interactions entre les probabilités et la combinatoire, et comment ces domaines sont amenés à se rendreservice mutuellement. Le Chapitre introductif 1 donne un bref aperçu des interactions possibles entre combinatoire et théorie des probabilités, et annonce les principaux résultats de la thèse. Le Chapitres 2 donne une introduction au domaine de la convergence des cartes. Les contributions principales de cette thèse se situent dans les Chapitres 3, 4 (pour les convergences de cartes) et 5 (pour le modèle stochastique du tas de sable)
This Thesis studies various problems located at the boundary between Combinatorics and Probability Theory. It is formed of two independent parts. In the first part, we study the asymptotic properties of some families of \maps" (from a non traditional viewpoint). In thesecond part, we introduce and study a natural stochastic extension of the so-called Sandpile Model, which is a dynamic process on a graph. While these parts are independent, they exploit the same thrust, which is the many interactions between Combinatorics and Discrete Probability, with these two areas being of mutual benefit to each other. Chapter 1 is a general introduction to such interactions, and states the main results of this Thesis. Chapter 2 is an introduction to the convergence of random maps. The main contributions of this Thesis can be found in Chapters 3, 4 (for the convergence of maps) and 5 (for the Stochastic Sandpile model)
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Budzinski, Thomas. "Cartes aléatoires hyperboliques." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS426/document.

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Cette thèse s'inscrit dans la théorie des cartes planaires aléatoires, active depuis une quizaine d'années, et plus précisément dans l'étude de modèles de nature hyperbolique.Dans un premier temps, nous nous intéressons à un modèle de triangulations aléatoires dynamiques basé sur les flips d'arêtes, et nous montrons une borne inférieure sur le temps de mélange de ce modèle.Dans la suite, l'objet d'étude principal est une famille de triangulations aléatoires hyperboliques, appelées PSHT. Il s'agit de variantes de la triangulation uniforme du plan (UIPT), qui ont été introduites en 2014 par Nicolas Curien. Nous commençons par établir un résultat de limite d'échelle quasi-critique : si on renormalise les distances tout en faisant tendre le paramètre d'hyperbolicité vers sa valeur critique, les triangulations étudiées convergent vers un espace métrique aléatoire appelé plan brownien hyperbolique. Nous étudions également des propriétés métriques fines des PSHT et du plan brownien hyperbolique, et notamment la structure de leurs géodésiques infinies. Nous présentons aussi de nouvelles propriétés de la frontière de Poisson des PSHT.Enfin, nous nous intéressons à un autre modèle naturel de cartes aléatoires hyperboliques : les cartes causales surcritiques, qui sont construites à partir d'arbres de Galton--Watson surcritiques, en ajoutant des arêtes entre sommets de même hauteur. Nous établissons des résultats d'hyperbolicité métrique, ainsi que des propriétés de la marche aléatoire sur ces cartes, dont un résultat de vitesse positive. Certaines des propriétés obtenues sont robustes, et peuvent se généraliser à n'importe quelle carte planaire contenant un arbre de Galton--Watson surcritique
This thesis falls into the theory of random planar maps, which has been active in the last fifteen years, and more precisely into the study of hyperbolic models.We are first interested in a model of dynamical random triangulations based on edge-flips, where we prove a lower bound on the mixing time.In the rest of this thesis, the main objects that we study are the random hyperbolic triangulations called PSHT. These are hyperbolic variants of the Uniform Infinite Planar Triangulation (UIPT), and were introduced by Nicolas Curien in 2014. We first establish a near-critical scaling limit result: if we let the hyperbolicity parameter go to its critical value at the same time as the distances are renormalized, the PSHT converge to a random metric space that we call the hyperbolic Brownian plane. We also study precise metric properties of the PSHT and of the hyperbolic Brownian plane, such as the structure of their infinite geodesics. We obtain as well new properties of the Poisson boundary of the PSHT.Finally, we are interested in another natural model of hyperbolic random maps: supercritical causal maps, which are obtained from supercritical Galton--Watson trees by adding edges between vertices at the same height. We establish metric hyperbolicity results about these maps, as well as properties of the simple random walk (including a positive speed result). Some of the properties we obtain are robust, and may be generalized to any planar map containing a supercritical Galton--Watson tree
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Ravelomanana, Vlady. "Graphes multicycliques étiquetés : aspects combinatoires et probabilistes." Amiens, 2000. http://www.theses.fr/2000AMIE0122.

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Broutin, Nicolas. "Random trees, graphs and recursive partitions." Habilitation à diriger des recherches, Université Pierre et Marie Curie - Paris VI, 2013. http://tel.archives-ouvertes.fr/tel-00842019.

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Je présente dans ce mémoire mes travaux sur les limites d'échelle de grandes structures aléatoires. Il s'agit de décrire les structures combinatoires dans la limite des grandes tailles en prenant un point de vue objectif dans le sens où on cherche des limites des objets, et non pas seulement de paramètres caractéristiques (même si ce n'est pas toujours le cas dans les résultats que je présente). Le cadre général est celui des structures critiques pour lesquelles on a typiquement des distances caractéristiques polynomiales en la taille, et non concentrées. Sauf exception, ces structures ne sont en général pas adaptées aux applications informatiques. Elles sont cependant essentielles de part l'universalité de leurs propriétés asymptotiques, prouvées ou attendues. Je parle en particulier d'arbres uniformément choisis, de graphes aléatoires, d'arbres couvrant minimaux et de partitions récursives de domaines du plan:
Arbres aléatoires uniformes. Il s'agit ici de mieux comprendre un objet limite essentiel, l'arbre continu brownien (CRT). Je présente quelques résultats de convergence pour des modèles combinatoires ''non-branchants'' tels que des arbres sujets aux symétries et les arbres à distribution de degrés fixée. Je décris enfin une nouvelle décomposition du CRT basée sur une destruction partielle.
Graphes aléatoires. J'y décris la construction algorithmique de la limite d'échel-le des graphes aléatoires du modèle d'Erdös--Rényi dans la zone critique, et je fais le lien avec le CRT et donne des constructions de l'espace métrique limite. Arbres couvrant minimaux. J'y montre qu'une connection avec les graphes aléatoires permet de quantifier les distances dans un arbre convrant aléatoire. On obtient non seulement l'ordre de grandeur de l'espérance du diamètre, mais aussi la limite d'échelle en tant qu'espace métrique mesuré. Partitions récursives. Sur deux exemples, les arbres cadrant et les laminations du disque, je montre que des idées basées sur des théorèmes de point fixe conduisent à des convergences de processus, où les limites sont inhabituelles, et caractérisées par des décompositions récursives.
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El, Maftouhi Abdelhakim. "Méthodes probabilistes en combinatoire et théorie des graphes." Paris 11, 1994. http://www.theses.fr/1994PA112408.

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Cette thèse rassemble plusieurs travaux dont le point commun est l'utilisation de méthodes probabilistes. La première partie concerne l'étude des paramètres de domination et d'irredondance dans les graphes aléatoires de probabilité d'arête 1/2. Nos résultats apportent un point final à l'étude du trio: irredondance, domination et stabilité dans ces graphes. Dans la deuxième partie on délaisse momentanément les probabilités pour aborder les graphes signés. On s'intéresse plus particulièrement au problème de l'équilibre dans ces graphes. On introduit la notion de sous-graphes équilibrants dont on donne quelques caractérisations qui permettent d'obtenir de nouveaux résultats. Nous introduisons dans la troisième partie la notion de graphes signés aléatoires et nous étudions les principales propriétés statistiques de ces graphes. La quatrième partie est consacrée à l'énumération d'une classe d'ordres partiels. Nous donnons une procédure pour calculer le nombre d'ordres partiels gradués de largeur et de rang donnes. Pour une largeur fixée la procédure utilise un temps de calcul qui est une fonction linéaire du rang. Finalement, dans la dernière partie, on étudie le problème de la satisfiabilité d'un ensemble de 3-clauses aléatoires
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Murat, Cécile. "Les problèmes d'optimisation combinatoire probabilistes dans les graphes." Paris 9, 1997. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1997PA090054.

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L'objet de cette thèse est l'optimisation combinatoire probabiliste de problèmes définis en termes de graphes. Dans ce cadre, un système de probabilités est associé aux sommets du graphe afin de traduire le fait que nous ne connaissons pas le sous-graphe pour lequel le problème sera à résoudre. L'approche utilisée consiste alors à définir une solution dite a priori, qui sous-entend que tous les éléments du graphe d'origine soient présents. Pour une sous-instance donnée, pour laquelle certains éléments du graphe sont absents, il faudra adapter la solution a priori, à l'aide d'un algorithme appelé stratégie de modification, afin qu'elle devienne solution de l'instance considérée. Après avoir situé ces problèmes, par rapport à ceux étudiés dans le cadre de la théorie des graphes aléatoires, nous présentons la méthodologie employée et la formalisons. Nous proposons alors, un état de l'art des travaux réalisés avec cette approche pour les problèmes dont l'instance est un graphe. Puis, nous présentons les résultats que nous avons établis pour les problèmes du stable probabiliste, de la couverture de sommets probabiliste et de plus longs chemins probabilistes. Ceci nous amène a opérer une première classification et structuration de problèmes d'optimisation combinatoire probabilistes selon leur complexité et résolution. La dernière partie de cette thèse, constitue un développement du formalisme du cadre d'étude. Pour cela, nous présentons nos premières réflexions concernant l'utilisation de nouveaux critères. Enfin, nous finissons en introduisant les premières notions nécessaires à la mise en place d'un cadre structure pour l'étude de l'approximation des problèmes d'optimisation combinatoire probabilistes.
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Panafieu, Elie de. "Combinatoire analytique des graphes, hypergraphes et graphes inhomogènes." Paris 7, 2014. http://www.theses.fr/2014PA077167.

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Nous étudions deux modèles qui généralisent la notion de graphe : les hypergraphes non-uniformes et les graphes inhomogènes. Ces modèles sont proches de ceux définis par Darling et Norris (2004) et Sôderberg (2002). Nous étudions leur énumération et leur structure typique avant et autour de la naissance de la composante géante. Nous montrons que les graphes inhomogènes sont un cadre idéal pour la modélisation de nombreux problèmes de satisfaction de contraintes (CSP) de complexité polynomiale, tels que la 2-colorabilité, la satisfaisabilité de formules 2- Xor et de formules 2-Xor quantifiées. Nous relions la probabilité de satisfaisabilité de ces problèmes à l'énumération des graphes inhomogènes. En application, plusieurs résultats de transition de phase anciens et nouveaux reçoivent une preuve dans un cadre unifié. Enfin, nous proposons une nouvelle preuve simple du nombre de multigraphes connexes possédant un nombre d'arêtes proportionnel au nombre de sommets, Ce résultat a été obtenu dans le cadre des graphes simples par Bender, Canfield et McKay (1990). L'outil principale de cette thèse est la combinatoire analytique, telle que définie par Flajolet et Sedgewick dans leur livre (2009)
We investigate two graph-like models: the non-uniform hypergraphs and the inhomogeneous graphs. They are close to the models defined by Darling and Norris (2004) and Sôderberg (2002). We enumerate them and derive structure information before and near the birth of the giant component. The inhomogeneous graph model proves to be a convenient framework for the modeling of several tractable constraint satisfaction problems (CSP), such as the 2-colorability problem, the satisfiability of 2-Xor formulas and of quantified 2-Xor formulas. We link the probability of satisfiability of those problems to the enumeration of inhomogeneous graphs. As an application, proofs of old and new phase transition results are derived in a unified framework. Finally, we derive a new simple proof for the asymptotic number of connected multigraphs with a number of edges proportional to the number of vertices. This result was first derived for simple graphs by Bender, Canfield and McKay (1990). The main tool of this thesis is analytic combinatorics, as defined by Flajolet and Sedgewick in their book (2009)
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Hutchcroft, Thomas. "Discrete probability and the geometry of graphs." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/62595.

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We prove several theorems concerning random walks, harmonic functions, percolation, uniform spanning forests, and circle packing, often in combination with each other. We study these models primarily on planar graphs, on transitive graphs, and on unimodular random rooted graphs, although some of our results hold for more general classes of graphs. Broadly speaking, we are interested in the interplay between the geometry of a graph and the behaviour of probabilistic processes on that graph. Material taken from a total of nine papers is included. We have also included an extended introduction explaining the background and context to these papers.
Science, Faculty of
Mathematics, Department of
Graduate
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Mercier, Lucas. "Grands graphes et grands arbres aléatoires : analyse du comportement asymptotique." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0028/document.

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Cette thèse est consacrée à l'étude du comportement asymptotique de grands graphes et arbres aléatoires. Le premier modèle étudié est un modèle de graphe aléatoire inhomogène introduit par Bo Söderberg. Un chapitre de ce manuscrit est consacré à l'étude asymptotique de la taille des composantes connexes à proximité de la fenêtre critique, en le reliant à la longueur des excursions d'un mouvement brownien avec dérive parabolique, étendant les résultats obtenus par Aldous. Le chapitre suivant est consacré à un processus de graphes aléatoires proposé par Itai Benjamini, défini ainsi : les arêtes sont ajoutées indépendamment, à taux fixe. Lorsqu'un sommet atteint le degré k, toutes les arêtes adjacentes à ce sommet sont immédiatement supprimées. Ce processus n'est pas croissant, ce qui empêche d'utiliser directement certaines approches usuelles. L'utilisation de limites locales permet de montrer la présence (resp. l'absence) d'une composante géante à certaines étapes dans le cas k>=5 (resp. k<=3). Dans le cas k=4, ces résultats permettent de caractériser la présence d'une composante géante en fonction du caractère surcritique ou non d'un processus de branchement associé. Dans le dernier chapitre est étudiée la hauteur d'un arbre de Lyndon associé à un mot de Lyndon choisi uniformément parmi les mots de Lyndon de longueur n, prouvant que cette hauteur est approximativement c ln n, avec c=5,092... la solution d'un problème d'optimisation. Afin d'obtenir ce résultat, nous couplons d'abord l'arbre de Lyndon à un arbre de Yule, que nous étudions ensuite à l'aide de techniques provenant des théories des marches branchantes et des grandes déviations
This thesis is dedicated to the study of the asymptotic behavior of some large random graphs and trees. First is studied a random graph model introduced by Bo Söderberg in 2002. One chapter of this manuscript is devoted to the study of the asymptotic behavior of the size of the connected components near the critical window, linking it to the lengths of excursion of a Brownian motion with parabolic drift. The next chapter talks about a random graph process suggested by Itai Benjamini, defined as follows: edges are independently added at a fixe rate. Whenever a vertex reaches degree k, all adjacent edges are removed. This process is non-increasing, preventing the use of some commonly used methods. By using local limits, in the spirit of the PWIT, we were able to prove the presence (resp. absence) of a giant component at some stages of the process when k>=5 (resp. k<=3). In the case k=4, these results allows to link the presence (resp. absence) of a giant component to the supercriticality (resp. criticality or subcriticality) of an associated branching process. In the last chapter, the height of random Lyndon tree is studied, and is proven to be approximately c ln n, in which c=5.092... the solution of an optimization problem. To obtain this result, we couple the Lyndon tree with a Yule tree, then studied with the help of branching walks and large deviations
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Books on the topic "Graphons de probabilités"

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Grimmett, Geoffrey. Probability on graphs: Random processes on graphs and lattices. Cambridge: Cambridge University Press, 2010.

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Wingard-Nelson, Rebecca. Graphing and probability word problems: No problem! Berkeley Heights, NJ: Enslow Publishers, 2011.

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Wingard-Nelson, Rebecca. Graphing and probability word problems: No problem! Berkeley Heights, NJ: Enslow Publishers, 2011.

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International Seminar on Random Graphs and Probabilistic Methods in Combinatorics. (2nd 1985 Uniwersytet im. Adama Mickiewicza w Poznaniu. Instytut Matematyki). Random graphs '85. New York: North-Holland, 1987.

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Yates, Daniel S. The practice of statistics: TI-83 graphing calculator enhanced. New York: W.H. Freeman, 1999.

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1947-, Weisberg Sanford, ed. Applied regression including computing and graphics. New York: Wiley, 1999.

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Palka, Zbigniew. Asymptotic properties of random graphs. Warszawa: Państwowe Wydawn. Nauk., 1988.

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Rossman, Allan J. Workshop statistics: Discovery with data and the graphing calculator. 2nd ed. Emeryville, CA: Key College Pub., 2001.

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L, Chance Beth, and Von Oehsen J. Barr, eds. Workshop statistics: Discovery with data and the graphing calculator. 3rd ed. Emeryville, CA: Key College Pub., 2008.

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Barr, Von Oehsen J., ed. Workshop statistics: Discovery with data and the graphing calculator. New York: Springer, 1997.

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Book chapters on the topic "Graphons de probabilités"

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Bonato, Anthony. "Graphs and probability." In Graduate Studies in Mathematics, 1–17. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/gsm/089/01.

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Godehardt, Erhard. "Probability Models of Classification." In Graphs as Structural Models, 97–114. Wiesbaden: Vieweg+Teubner Verlag, 1988. http://dx.doi.org/10.1007/978-3-322-96310-9_5.

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Brémaud, Pierre. "Random Graphs." In Discrete Probability Models and Methods, 255–86. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-43476-6_10.

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Dembo, Amir, Eyal Lubetzky, and Yumeng Zhang. "Empirical Spectral Distributions of Sparse Random Graphs." In Progress in Probability, 319–45. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60754-8_15.

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Brémaud, Pierre. "Random Walks on Graphs." In Discrete Probability Models and Methods, 185–214. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-43476-6_8.

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Brémaud, Pierre. "Markov Fields on Graphs." In Discrete Probability Models and Methods, 215–53. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-43476-6_9.

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du Toit, S. H. C., A. G. W. Steyn, and R. H. Stumpf. "Graphics for Selecting a Probability Model." In Springer Texts in Statistics, 36–53. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4612-4950-4_3.

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Stankiewicz, Olgierd, Krzysztof Wegner, and Marek Domanski. "Depth Estimation Based on Maximization of a Posteriori Probability." In Computer Vision and Graphics, 253–65. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-46418-3_23.

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Godehardt, Erhard. "Probability Theory of Completely Labelled Random Multigraphs." In Graphs as Structural Models, 115–56. Wiesbaden: Vieweg+Teubner Verlag, 1988. http://dx.doi.org/10.1007/978-3-322-96310-9_6.

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Boutillier, Cédric, and Béatrice de Tilière. "Statistical Mechanics on Isoradial Graphs." In Probability in Complex Physical Systems, 491–512. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23811-6_20.

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Conference papers on the topic "Graphons de probabilités"

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Igarashi, Daisuke, and Nobuaki Obata. "Asymptotic spectral analysis of growing graphs: odd graphs and spidernets." In Quantum Probability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2006. http://dx.doi.org/10.4064/bc73-0-18.

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Salcedo, Audy, Jesús González, Amalio Sarco LIra, and Johnnalid González. "Statistical Literacy of Citizens: The Interpretation of Statistical Graphs." In Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. International Association for Statistical Education, 2022. http://dx.doi.org/10.52041/iase.icots11.t7a1.

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This article analyzes how a group of Venezuelan citizens interprets two bar graphs. The reading, interpretation and evaluation of statistical graphs is part of the competences that an ordinary citizen must possess. It was therefore decided to ask ordinary citizens to interpret two statistical graphs. The questions are part of a broader questionnaire that was published on the survey administration platform and sent to potential participants, using non-probability sampling. The questions were answered by 407 citizens with different levels of academic training. The results show that most participants gave plausible arguments to support a specific position, but have difficulties in critically evaluating a graph. These results are a first approximation on how Venezuelan citizens interpret statistical graphics and can be a reference for statistical literacy processes.
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Liang, Song, Nobuaki Obata, and Shuji Takahashi. "Asymptotic spectral analysis of generalized Erdős–Rényi random graphs." In Noncommutative Harmonic Analysis with Applications to Probability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc78-0-16.

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Perju, Veaceslav, and Dorian Saranciuc. "Evaluation of the Multi-Algorithms Targets Recognition Systems." In 12th International Conference on Electronics, Communications and Computing. Technical University of Moldova, 2022. http://dx.doi.org/10.52326/ic-ecco.2022/cs.05.

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This paper presents the evaluation’s results of the new classes of the target recognition systems – multi- algorithms unimodal systems and multi-algorithms multimodal systems. The structures and the graphs of the systems are described. The mathematical descriptions and the formulas for evaluation of the system’s costs depending on the algorithm’s recognition probability and the relation between the costs of the algorithm’s software and the system’s hardware are presented. The approach to determine the cost of a system for an established threshold level of the system's recognition probability is proposed. The relation of the system's cost to the system's recognition probability for different values of the algorithm's recognition probability is evaluated as well as the rating of the target recognition systems based on their recognition probabilities and costs.
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Singh, Dhruv, Jayathi Y. Murthy, and Timothy S. Fisher. "Spectral Detail of Phonon Conduction and Scattering in Graphene." In ASME 2011 Pacific Rim Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Systems. ASMEDC, 2011. http://dx.doi.org/10.1115/ipack2011-52243.

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This paper examines the thermodynamic and thermal transport properties of the 2D graphene lattice. The interatomic interactions are modeled using the Tersoff interatomic potential and are used to evaluate phonon dispersion curves, density of states and thermodynamic properties of graphene as functions of temperature. Perturbation theory is applied to calculate the transition probabilities for three-phonon scattering. The matrix elements of the perturbing Hamiltonian are calculated using the anharmonic interatomic force constants obtained from the interatomic potential as well. An algorithm to accurately quantify the contours of energy balance for three-phonon scattering events is presented and applied to calculate the net transition probability from a given phonon mode. Under the linear approximation, the Boltzmann transport equation (BTE) is applied to compute the thermal conductivity of graphene, giving spectral and polarization-resolved information. Predictions of thermal conductivity for a wide range of parameters elucidate the behavior of diffusive phonon transport. The complete spectral detail of selection rules, important phonon scattering pathways, and phonon relaxation times in graphene are provided, contrasting graphene with other materials, along with implications for graphene electronics. We also highlight the specific scattering processes that are important in Raman spectroscopy based measurements of graphene thermal conductivity, and provide a plausible explanation for the observed dependence on laser spot size.
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Sarmin, Nor Haniza, Mustafa Anis El-sanfaz, and Sanaa Mohamed Saleh Omer. "Groups and graphs in probability theory." In ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23). Author(s), 2016. http://dx.doi.org/10.1063/1.4954600.

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Liu, Ruiyi, Xiaohu Wu, and Zheng Cui. "Photon Tunneling via Coupling Graphene Plasmons With Phonon Polaritons of Hexagonal Boron Nitride in Reststrahlen Bands." In ASME 2021 Heat Transfer Summer Conference collocated with the ASME 2021 15th International Conference on Energy Sustainability. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/ht2021-62180.

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Abstract The photon tunneling probability is the most important thing in near-field radiative heat transfer (NFRHT). This work study the photon tunneling via coupling graphene plasmons with phonon polaritons in hexagonal boron nitride (hBN). We consider two cases of the optical axis of hBN along z-axis and x-axis, respectively. We investigate the NFRHT between graphene-covered bulk hBN, and compare it with that of bare bulk hBN. Our results show that in Reststrahlen bands, the coupling of graphene plasmons and phonon polaritons in hBN can either suppress or enhance the photon tunneling probability, depending on the chemical potential of graphene and frequency. This conclusion holds when the optiacal axis of hBN is either along z-axis or x-axis. The findings in this work not only deepen our understanding of coupling mechanism between graphene plasmons with phonon polaritons, but also provide a theoretical basis for controlling photon tunneling in graphene covered hyperbolic materials.
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Nolau, Izabel, and Gustavo Ferreira. "An alternative class of models to position social network groups in latent spaces." In Congresso Brasileiro de Inteligência Computacional. SBIC, 2023. http://dx.doi.org/10.21528/cbic2023-036.

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Identifying key nodes, estimating the probability of connection between them, and distinguishing latent groups are some of the main objectives of social network analysis. In this paper, we propose a class of blockmodels to model stochastic equivalence and visualize groups in an unobservable space. In this setting, the proposed method is based on two approaches: latent distances and latent dissimilarities at the group level. The projection proposed in the paper is performed without needing to project individuals, unlike the main approaches in the literature. Our approach can be used in undirected or directed graphs and is flexible enough to cluster and quantify between and withingroup tie probabilities in social networks. The effectiveness of the methodology in representing groups in latent spaces was analyzed under artificial datasets and in a case study.
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Palmieri, Francesco, Krishna Pattipati, Giovanni Di Gennaro, Amedeo Buonanno, and Martina Merola. "Multiple Agents Interacting via Probability Flows on Factor Graphs." In 14th International Conference on Applied Human Factors and Ergonomics (AHFE 2023). AHFE International, 2023. http://dx.doi.org/10.54941/ahfe1003761.

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Expert team decision-making demonstrates that effective teams have shared goals, shared mental models to coordinate with minimal communication, establish trust through cross-training, and match task structures through planning. The key questions: Do best practices of human teams translate to hybrid human-AI agent teams, or autonomous agents alone? Is there a mathematical framework for studying shared goals and mental models? We propose factor graphs for studying multi-agent interaction and agile cooperative planning. One promising avenue for modeling interacting agents in real environments is with stochastic approaches, where probability distributions describe uncertainties and imperfect observations. Stochastic dynamic programming provides a framework for modeling multiple agents as scheduled and interacting Markov Decision Processes (MDPs), wherein each agent has partial information about other agents in the team. Each agent acts by accounting for both its objectives and anticipated behaviors of others, even implicitly. We have shown that Dynamic Programming, Maximum likelihood, Maximum entropy and Free-energy-based methods for stochastic control are special cases of probabilistic message propagation rules on modeled factor graphs. Now we show how multiple agents, modeled as multiple interacting factor graphs, exchange probability distributions carrying partial mutual knowledge. We demonstrate the ideas in contexts of moving agents on a discrete grid with obstacles and pre-defined semantic areas (grassy areas, pathways), where each subject has a different destination (goal). The scheduling of agents is fixed a priori or changes over time, and the forward-backward flow for each agent’s MDP is computed every time step, with additional branches that inject probability distributions into and from other agent MDPs. These interactions avoid collisions among agents and enable dynamic planning by agents, accounting for estimates of posterior probabilities of other agents states at future times, the precision and timing being adjustable. Simulations included limited interacting agents (three) on small rectangular discrete grid with starting points and destination goals, obstacles in various positions, narrow passages, small mazes, destinations that require coordination, etc. Solely due to probability distributions flowing in the interacting agent system, the solutions provided by the probabilistic model are interesting because agents that encounter potential conflicts in some regions autonomously adapt strategies, like waiting to let others pass, or taking different paths. The information available to each agent is a combination of rewards received from the environment and inferences about other agents. Previously, we described a scheme for a hierarchy (prioritized order) of agents and unique value function for each agent. Now, we propose a different, tunable interaction, wherein each agent dynamically transmits the posterior probability of its position at future time steps to other agents. The new framework allows flexibility in tuning the information that each agent has on others, ranging from complete knowledge of goals and positions about others out to a limited probabilistic awareness, both in precision and in time, for where others may be located at future time steps. This framework systematically addresses questions, such as the minimal amount of information needed for effective team coordination in the face of changes in goals, communication bandwidth, grid parameters and agent status.
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Avrachenkov, Konstantin, and Alexandra Borodina. "On the Escape Probability Estimation in Large Graphs." In 2019 24th Conference of Open Innovations Association (FRUCT). IEEE, 2019. http://dx.doi.org/10.23919/fruct.2019.8711919.

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Reports on the topic "Graphons de probabilités"

1

Alameda, Joseph. Probability recurrences on simple graphs in a forest building process. Ames (Iowa): Iowa State University, January 2019. http://dx.doi.org/10.31274/cc-20240624-1155.

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Kriegel, Francesco. Learning description logic axioms from discrete probability distributions over description graphs (Extended Version). Technische Universität Dresden, 2018. http://dx.doi.org/10.25368/2022.247.

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Description logics in their standard setting only allow for representing and reasoning with crisp knowledge without any degree of uncertainty. Of course, this is a serious shortcoming for use cases where it is impossible to perfectly determine the truth of a statement. For resolving this expressivity restriction, probabilistic variants of description logics have been introduced. Their model-theoretic semantics is built upon so-called probabilistic interpretations, that is, families of directed graphs the vertices and edges of which are labeled and for which there exists a probability measure on this graph family. Results of scientific experiments, e.g., in medicine, psychology, or biology, that are repeated several times can induce probabilistic interpretations in a natural way. In this document, we shall develop a suitable axiomatization technique for deducing terminological knowledge from the assertional data given in such probabilistic interpretations. More specifically, we consider a probabilistic variant of the description logic EL⊥, and provide a method for constructing a set of rules, so-called concept inclusions, from probabilistic interpretations in a sound and complete manner.
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