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Eggemann, Nicole. "Some applications of graph theory." Thesis, Brunel University, 2009. http://bura.brunel.ac.uk/handle/2438/3953.
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Pappone, Francesco. "Graph neural networks: theory and applications." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23893/.
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Le reti neurali artificiali hanno visto, negli ultimi anni, una crescita vertiginosa nelle loro applicazioni e nelle architetture dei modelli impiegati. In questa tesi introduciamo le reti neurali su domini euclidei, in particolare mostrando l’importanza dell’equivarianza di traslazione nelle reti convoluzionali, e introduciamo, per analogia, un’estensione della convoluzione a dati strutturati come grafi. Inoltre presentiamo le architetture dei principali Graph Neural Network ed esponiamo, per ognuna delle tre architetture proposte (Spectral graph Convolutional Network, Graph Convolutional Network, Graph Attention neTwork) un’applicazione che ne mostri sia il funzionamento che l’importanza. Discutiamo, ulteriormente, l’implementazione di un algoritmo di classificazione basato su due varianti dell’architettura Graph Convolutional Network, addestrato e testato sul dataset PROTEINS, capace di classificare le proteine del dataset in due categorie: enzimi e non enzimi.
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Al-Shimary, Abbas. "Applications of graph theory to quantum computation." Thesis, University of Leeds, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608359.
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Systems with topologically ordered ground states are considered to be promising candidates for quantum memories. These systems are characterised by a degenerate ground eigenspace separated by an energy gap from the rest of the spectrum. Consequently, topologically ordered systems are resilient to local noise since local errors are suppressed by the gap. Often, knowledge of the gap is not available and a direct approach to the problem is impractical. The first half of this thesis considers the problem of estimating the energy gap of a general class of Hamiltonians in the thermodynamical limit. In particular, we consider a remarkable result from spectral graph theory known as Cheeger inequalities. Cheeger inequalities give an upper and lower bound on the spectral gap of discrete Laplaeians defined on a graph in terms of the geometric characteristics of the graph. We generalise this approach and we employ it to determine if a given discrete Hamiltonian is gapped or not in the thermodynamic limit. A large class of 2D topologically ordered systems, including the Kitaev toric code, were proven to be unstable against thermal fluctuations. There systems can store information for a finite time known as the memory lifetime. The second half of this thesis will be devoted to investigating possible theoretical ways to extend the lifetime of thc 2D toric code. Firstly, we investigate the effect lattice geometry has on the lifetime of the qubit toric code. Importantly, we demonstrate how lattice geometries can be employed to enhance topological systems with intrinsically biased couplings due to physical implementation. Secondly, we improve the error correction properties and lifetime of the generalised 2D toric code by using charge-modifying domain walls. Specifically, we show that we can inhibit the propagation of anyons by introducing domain walls, provided the masses of the anyon types of the model are imbalanced.
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Rittenhouse, Michelle L. "Properties and Recent Applications in Spectral Graph Theory." VCU Scholars Compass, 2008. http://scholarscompass.vcu.edu/etd/1126.
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There are numerous applications of mathematics, specifically spectral graph theory, within the sciences and many other fields. This paper is an exploration of recent applications of spectral graph theory, including the fields of chemistry, biology, and graph coloring. Topics such as the isomers of alkanes, the importance of eigenvalues in protein structures, and the aid that the spectra of a graph provides when coloring a graph are covered, as well as others.The key definitions and properties of graph theory are introduced. Important aspects of graphs, such as the walks and the adjacency matrix are explored. In addition, bipartite graphs are discussed along with properties that apply strictly to bipartite graphs. The main focus is on the characteristic polynomial and the eigenvalues that it produces, because most of the applications involve specific eigenvalues. For example, if isomers are organized according to their eigenvalues, a pattern comes to light. There is a parallel between the size of the eigenvalue (in comparison to the other eigenvalues) and the maximum degree of the graph. The maximum degree of the graph tells us the most carbon atoms attached to any given carbon atom within the structure. The Laplacian matrix and many of its properties are discussed at length, including the classical Matrix Tree Theorem and Cayley's Tree Theorem. Also, an alternative approach to defining the Laplacian is explored and compared to the traditional Laplacian.
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Simmons, Dayton C. (Dayton Cooper). "Applications of Rapidly Mixing Markov Chains to Problems in Graph Theory." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc277740/.
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In this dissertation the results of Jerrum and Sinclair on the conductance of Markov chains are used to prove that almost all generalized Steinhaus graphs are rapidly mixing and an algorithm for the uniform generation of 2 - (4k + 1,4,1) cyclic Mendelsohn designs is developed.
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Cohen, Nathann. "Three years of graphs and music : some results in graph theory and its applications." Phd thesis, Université Nice Sophia Antipolis, 2011. http://tel.archives-ouvertes.fr/tel-00645151.
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Cette thèse présente différents aperçus de problèmes de mathématiques discrètes en lien avec la théorie des graphes. Elle s'intéresse en particulier à la coloration de graphes, i.e. l'assignation de couleurs aux sommets (ou arêtes) d'un graphes sous certaines contraintes locales, notamment l'exclusion de motifs. Pour différents types de coloration (choisissabilité des sommets, des arêtes, coloration acyclique ou linéaire, ...), un état de l'art est présenté, accompagné de résultats d'existence sur les graphes planaires ou leurs sous-classes, ayant pour but de minimiser le nombre de couleurs nécessaires pour un degré maximum ou un degré moyen maximum (Mad) donnés. Cette thèse traite également de décompositions induites de graphes, et démontre qu'il existe pour tout graphe $H$ une suite infinie de graphes denses dont les arêtes peuvent être partitionnées en copies induites de $H$. Cette preuve requiert le formalisme des hypergraphes, pour lesquels un autre résultat de décomposition est démontré, i.e. une décomposition optimale de l'hypergraphe complet 3-régulier en hypergraphes $\alpha$-acycliques. La troisième parti porte sur des questions algorithmiques. Elles consistent en problèmes d'optimisation ou d'existence, motivés par le routage d'information dans les réseaux, analysés par le formalisme classique de complexité algorithmique, ou traitent de la recherche de sous-graphes dans le formalisme de la complexité paramétrée. Dans une quatrième partie sont considérés des problèmes de comptage issus de la chimie, suivis de la présentation de Programmes Linéaires Entiers utilisés dans le logiciel de mathématiques Sage.
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Shiping, Liu. "Synthetic notions of curvature and applications in graph theory." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-102197.
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The interaction between the study of geometric and analytic aspects of Riemannian manifolds and that of graphs is a very amazing subject. The study of synthetic curvature notions on graphs adds new contributions to this topic. In this thesis, we mainly study two kinds of synthetic curvature notions: the Ollivier-Ricci cuvature on locally finite graphs and the combinatorial curvature on infinite semiplanar graphs.
In the first part, we study the Ollivier-Ricci curvature. As known in Riemannian geometry, a lower Ricci curvature bound prevents geodesics from diverging too fast on average. We translate this Riemannian idea into a combinatorial setting using the Olliver-Ricci curvature notion. Note that on a graph, the analogue of geodesics starting in different directions, but eventually approaching each other again, would be a triangle. We derive lower and upper Ollivier-Ricci curvature bounds on graphs in terms of number of triangles, which is sharp for instance for complete graphs. We then describe the relation between Ollivier-Ricci curvature and the local clustering coefficient, which is an important concept in network analysis introduced by Watts-Strogatz.
Furthermore, positive lower boundedness of Ollivier-Ricci curvature for neighboring vertices imply the existence of at least one triangle. It turns out that the existence of triangles can also improve Lin-Yau\'s curvature dimension inequality on graphs and then produce an implication from Ollivier-Ricci curvature lower boundedness to the curvature dimension inequality.
The existence of triangles prevents a graph from being bipartite. A finite graph is bipartite if and only if its largest eigenvalue equals 2. Therefore it is natural that Ollivier-Ricci curvature is closely related to the largest eigenvalue estimates. We combine Ollivier-Ricci curvature notion with the neighborhood graph method developed by Bauer-Jost to study the spectrum estimates of a finite graph. We can always obtain nontrivial estimates on a non-bipartite graph even if its curvature is nonpositive. This answers one of Ollivier\'s open problem in the finite graph setting.
In the second part of this thesis, we study systematically infinite semiplanar graphs with nonnegative combinatorial curvature. Unlike the previous Gauss-Bonnet formula approach, we explore an Alexandrov approach based on the observation that the nonnegative combinatorial curvature on a semiplanar graph is equivalent to nonnegative Alexandrov curvature on the surface obtained by replacing each face by a regular polygon of side length one with the same facial degree and gluing the polygons along common edges.
Applying Cheeger-Gromoll splitting theorem on the surface, we give a metric classification of infinite semiplanar graphs with nonnegative curvature. We also construct the graphs embedded into the projective plane minus one point. Those constructions answer a question proposed by Chen.
We further prove the volume doubling property and Poincare inequality which make the running of Nash-Moser iteration possible. We in particular explore the volume growth behavior on Archimedean tilings on a plane and prove that they satisfy a weak version of relative volume comparison with constant 1.
With the above two basic inequalities in hand, we study the geometric function theory of infinite semiplanar graphs with nonnegative curvature. We obtain the Liouville type theorem for positive harmonic functions, the parabolicity. We also prove a dimension estimate for polynomial growth harmonic functions, which is an extension of the solution of Colding-Minicozzi of a conjecture of Yau in Riemannian geometry.
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Sutinuntopas, Somporn. "Applications of Graph Theory and Topology to Combinatorial Designs." Thesis, University of North Texas, 1988. https://digital.library.unt.edu/ark:/67531/metadc331968/.
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This dissertation is concerned with the existence and the isomorphism of designs. The first part studies the existence of designs. Chapter I shows how to obtain a design from a difference family. Chapters II to IV study the existence of an affine 3-(p^m,4,λ) design where the v-set is the Galois field GF(p^m). Associated to each prime p, this paper constructs a graph. If the graph has a 1-factor, then a difference family and hence an affine design exists. The question arises of how to determine when the graph has a 1-factor. It is not hard to see that the graph is connected and of even order. Tutte's theorem shows that if the graph is 2-connected and regular of degree three, then the graph has a 1-factor. By using the concept of quadratic reciprocity, this paper shows that if p Ξ 53 or 77 (mod 120), the graph is almost regular of degree three, i.e., every vertex has degree three, except two vertices each have degree tow. Adding an extra edge joining the two vertices with degree tow gives a regular graph of degree three. Also, Tutte proved that if A is an edge of the graph satisfying the above conditions, then it must have a 1-factor which contains A. The second part of the dissertation is concerned with determining if two designs are isomorphic. Here the v-set is any group G and translation by any element in G gives a design automorphism. Given a design B and its difference family D, two topological spaces, B and D, are constructed. We give topological conditions which imply that a design isomorphism is a group isomorphism.
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Marchand-Maillet, Stephane. "Graph theory and discrete geometry for digital image analysis : theory and applications." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267485.
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Chen, Zhiqian. "Graph Neural Networks: Techniques and Applications." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99848.
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Effective information analysis generally boils down to the geometry of the data represented by a graph. Typical applications include social networks, transportation networks, the spread of epidemic disease, brain's neuronal networks, gene data on biological regulatory networks, telecommunication networks, knowledge graph, which are lying on the non-Euclidean graph domain. To describe the geometric structures, graph matrices such as adjacency matrix or graph Laplacian can be employed to reveal latent patterns. This thesis focuses on the theoretical analysis of graph neural networks and the development of methods for specific applications using graph representation. Four methods are proposed, including rational neural networks for jump graph signal estimation, RemezNet for robust attribute prediction in the graph, ICNet for integrated circuit security, and CNF-Net for dynamic circuit deobfuscation.
For the first method, a recent important state-of-art method is the graph convolutional networks (GCN) nicely integrate local vertex features and graph topology in the spectral domain. However, current studies suffer from drawbacks: graph CNNs rely on Chebyshev polynomial approximation which results in oscillatory approximation at jump discontinuities since Chebyshev polynomials require degree $Omega$(poly(1/$epsilon$)) to approximate a jump signal such as $|x|$. To reduce complexity, RatioanlNet is proposed to integrate rational function and neural networks for graph node level embeddings. For the second method, we propose a method for function approximation which suffers from several drawbacks: non-robustness and infeasibility issue; neural networks are incapable of extracting analytical representation; there is no study reported to integrate the superiorities of neural network and Remez. This work proposes a novel neural network model to address the above issues. Specifically, our method utilizes the characterizations of Remez to design objective functions. To avoid the infeasibility issue and deal with the non-robustness, a set of constraints are imposed inspired by the equioscillation theorem of best rational approximation. The third method proposes an approach for circuit security. Circuit obfuscation is a recently proposed defense mechanism to protect digital integrated circuits (ICs) from reverse engineering. Estimating the deobfuscation runtime is a challenging task due to the complexity and heterogeneity of graph-structured circuit, and the unknown and sophisticated mechanisms of the attackers for deobfuscation. To address the above-mentioned challenges, this work proposes the first graph-based approach that predicts the deobfuscation runtime based on graph neural networks. The fourth method proposes a representation for dynamic size of circuit graph. By analyzing SAT attack method, a conjunctive normal form (CNF) bipartite graph is utilized to characterize the complexity of this SAT problem. To overcome the difficulty in capturing the dynamic size of the CNF graph, an energy-based kernel is proposed to aggregate dynamic features.Doctor of Philosophy
Graph data is pervasive throughout most fields, including pandemic spread network, social network, transportation roads, internet, and chemical structure. Therefore, the applications modeled by graph benefit people's everyday life, and graph mining derives insightful opinions from this complex topology. This paper investigates an emerging technique called graph neural newton (GNNs), which is designed for graph data mining. There are two primary goals of this thesis paper: (1) understanding the GNNs in theory, and (2) apply GNNs for unexplored and values real-world scenarios. For the first goal, we investigate spectral theory and approximation theory, and a unified framework is proposed to summarize most GNNs. This direction provides a possibility that existing or newly proposed works can be compared, and the actual process can be measured. Specifically, this result demonstrates that most GNNs are either an approximation for a function of graph adjacency matrix or a function of eigenvalues. Different types of approximations are analyzed in terms of physical meaning, and the advantages and disadvantages are offered. Beyond that, we proposed a new optimization for a highly accurate but low efficient approximation. Evaluation of synthetic data proves its theoretical power, and the tests on two transportation networks show its potentials in real-world graphs. For the second goal, the circuit is selected as a novel application since it is crucial, but there are few works. Specifically, we focus on a security problem, a high-value real-world problem in industry companies such as Nvidia, Apple, AMD, etc. This problem is defined as a circuit graph as apply GNN to learn the representation regarding the prediction target such as attach runtime. Experiment on several benchmark circuits shows its superiority on effectiveness and efficacy compared with competitive baselines. This paper provides exploration in theory and application with GNNs, which shows a promising direction for graph mining tasks. Its potentials also provide a wide range of innovations in graph-based problems.
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Ahadi, Moghaddam Masoumeh [Verfasser], and Dietmar [Akademischer Betreuer] Schweigert. "Graph Coloring Applications and Defining Sets in Graph Theory / Masoumeh Ahadi Moghaddam ; Betreuer: Dietmar Schweigert." Kaiserslautern : Technische Universität Kaiserslautern, 2017. http://d-nb.info/1127044435/34.
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Rautiainen, Mikko [Verfasser]. "Sequence to graph alignment : theory, practice and applications / Mikko Rautiainen." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2020. http://d-nb.info/1217656928/34.
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Andersen, Aaron. "GraphShop: An Interactive Software Environment for Graph Theory Research and Applications." DigitalCommons@USU, 2011. https://digitalcommons.usu.edu/etd/896.
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Graph Theory is the mathematical study of the structure of abstract relationships between objects. Although these constructions (graphs) are themselves purely theoretical, their ability to model pair-wise relationships in systems of arbitrary complexity yields abundant direct correspondence with numerous important physical and societal systems in the real world. Additionally, the simple discrete nature of fundamental graph structures allows for easy pseudo-geometric visualization of graphs in a wide variety of ways. Taken together, these two properties suggest that graph theory teaching, research, and applications would benefit greatly from the use of a unified software environment for graph construction, interaction, and visualization.
Based on this need, a comprehensive survey was undertaken of existing graph theory software packages, programs, and libraries to determine the suitability of each for use as a graph theory teaching and research tool. Some of the desired components (especially in the realm of graph visualization) were found to be implemented in several current tools and systems, but no single system was located with the ability to perform all such functions together in a coordinated way.
Graph Shop (the Graph Theory Workshop) is a new software package for graph theory research and applications. It was designed to be usable by students and graph theory beginners yet powerful enough to assist with advanced graph theory research. It runs on a variety of platforms and is available for free under the GNU GPL open source license.
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Freeman, Andre. "Dual-Eulerian graphs with applications to VLSI design." Link to electronic thesis, 2003. http://www.wpi.edu/Pubs/ETD/Available/etd-0430103-155731/.
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Donachy, Shaun. "Spiking Neural Networks: Neuron Models, Plasticity, and Graph Applications." VCU Scholars Compass, 2015. http://scholarscompass.vcu.edu/etd/3984.
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Networks of spiking neurons can be used not only for brain modeling but also to solve graph problems. With the use of a computationally efficient Izhikevich neuron model combined with plasticity rules, the networks possess self-organizing characteristics. Two different time-based synaptic plasticity rules are used to adjust weights among nodes in a graph resulting in solutions to graph prob- lems such as finding the shortest path and clustering.
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So, Anthony Man-Cho. "A semidefinite programming approach to the graph realization problem : theory, applications and extensions /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.
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Martinelli, Andres. "Advances in Functional Decomposition: Theory and Applications." Doctoral thesis, SICS, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-21180.
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Functional decomposition aims at finding efficient representations for Boolean functions. It is used in many applications, including multi-level logic synthesis, formal verification, and testing. This dissertation presents novel heuristic algorithms for functional decomposition. These algorithms take advantage of suitable representations of the Boolean functions in order to be efficient. The first two algorithms compute simple-disjoint and disjoint-support decompositions. They are based on representing the target function by a Reduced Ordered Binary Decision Diagram (BDD). Unlike other BDD-based algorithms, the presented ones can deal with larger target functions and produce more decompositions without requiring expensive manipulations of the representation, particularly BDD reordering. The third algorithm also finds disjoint-support decompositions, but it is based on a technique which integrates circuit graph analysis and BDD-based decomposition. The combination of the two approaches results in an algorithm which is more robust than a purely BDD-based one, and that improves both the quality of the results and the running time. The fourth algorithm uses circuit graph analysis to obtain non-disjoint decompositions. We show that the problem of computing non-disjoint decompositions can be reduced to the problem of computing multiple-vertex dominators. We also prove that multiple-vertex dominators can be found in polynomial time. This result is important because there is no known polynomial time algorithm for computing all non-disjoint decompositions of a Boolean function. The fifth algorithm provides an efficient means to decompose a function at the circuit graph level, by using information derived from a BDD representation. This is done without the expensive circuit re-synthesis normally associated with BDD-based decomposition approaches. Finally we present two publications that resulted from the many detours we have taken along the winding path of our research.
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Meeks, Kitty M. F. T. "Graph colourings and games." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:a805a379-f891-4250-9a7d-df109f9f52e2.
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Graph colourings and combinatorial games are two very widely studied topics in discrete mathematics. This thesis addresses the computational complexity of a range of problems falling within one or both of these subjects. Much of the thesis is concerned with the computational complexity of problems related to the combinatorial game (Free-)Flood-It, in which players aim to make a coloured graph monochromatic ("flood" the graph) with the minimum possible number of flooding operations; such problems are known to be computationally hard in many cases. We begin by proving some general structural results about the behaviour of the game, including a powerful characterisation of the number of moves required to flood a graph in terms of the number of moves required to flood its spanning trees; these structural results are then applied to prove tractability results about a number of flood-filling problems. We also consider the computational complexity of flood-filling problems when the game is played on a rectangular grid of fixed height (focussing in particular on 3xn and 2xn grids), answering an open question of Clifford, Jalsenius, Montanaro and Sach. The final chapter concerns the parameterised complexity of list problems on graphs of bounded treewidth. We prove structural results determining the list edge chromatic number and list total chromatic number of graphs with bounded treewidth and large maximum degree, which are special cases of the List (Edge) Colouring Conjecture and Total Colouring Conjecture respectively. Using these results, we show that the problem of determining either of these quantities is fixed parameter tractable, parameterised by the treewidth of the input graph. Finally, we analyse a list version of the Hamilton Path problem, and prove it to be W[1]-hard when parameterised by the pathwidth of the input graph. These results answer two open questions of Fellows, Fomin, Lokshtanov, Rosamond, Saurabh, Szeider and Thomassen.
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Reutter, Juan L. "Graph patterns : structure, query answering and applications in schema mappings and formal language theory." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8931.
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Graph data appears in a variety of application domains, and many uses of it, such as querying, matching, and transforming data, naturally result in incompletely specified graph data, i.e., graph patterns. Queries need to be posed against such data, but techniques for querying patterns are generally lacking, and even simple properties of graph patterns, such as the languages needed to specify them, are not well understood. In this dissertation we present several contributions in the study of graph patterns. We analyze how to query them and how to use them as queries. We also analyze some of their applications in two different contexts: schema mapping specification and data exchange for graph databases, and formal language theory. We first identify key features of patterns, such as node and label variables and edges specified by regular expressions, and define a classification of patterns based on them. Next we study how to answer standard graph queries over graph patterns, and give precise characterizations of both data and combined complexity for each class of patterns. If complexity is high, we do further analysis of features that lead to intractability, as well as lower-complexity restrictions that guarantee tractability. We then turn to the the study of schema mappings for graph databases. As for relational and XML databases, our mapping languages are based on patterns. They subsume all previously considered mapping languages for graph databases, and are capable of expressing many data exchange scenarios in the graph database context. We study the problems of materializing solutions and query answering for data exchange under these mappings, analyze their complexity, and identify relevant classes of mappings and queries for which these problems can be solved efficiently. We also introduce a new model of automata that is based on graph patterns, and define two modes of acceptance for them. We show that this model has applications not only in graph databases but in several other contexts. We study the basic properties of such automata, and the key computational tasks associated with them.
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Martinelli, Andrés. "Advances in Functional Decomposition: Theory and Applications." Doctoral thesis, KTH, Mikroelektronik och Informationsteknik, IMIT, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4135.
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Functional decomposition aims at finding efficient representations for Boolean functions. It is used in many applications, including multi-level logic synthesis, formal verification, and testing. This dissertation presents novel heuristic algorithms for functional decomposition. These algorithms take advantage of suitable representations of the Boolean functions in order to be efficient. The first two algorithms compute simple-disjoint and disjoint-support decompositions. They are based on representing the target function by a Reduced Ordered Binary Decision Diagram (BDD). Unlike other BDD-based algorithms, the presented ones can deal with larger target functions and produce more decompositions without requiring expensive manipulations of the representation, particularly BDD reordering. The third algorithm also finds disjoint-support decompositions, but it is based on a technique which integrates circuit graph analysis and BDD-based decomposition. The combination of the two approaches results in an algorithm which is more robust than a purely BDD-based one, and that improves both the quality of the results and the running time. The fourth algorithm uses circuit graph analysis to obtain non-disjoint decompositions. We show that the problem of computing non-disjoint decompositions can be reduced to the problem of computing multiple-vertex dominators. We also prove that multiple-vertex dominators can be found in polynomial time. This result is important because there is no known polynomial time algorithm for computing all non-disjoint decompositions of a Boolean function. The fifth algorithm provides an efficient means to decompose a function at the circuit graph level, by using information derived from a BDD representation. This is done without the expensive circuit re-synthesis normally associated with BDD-based decomposition approaches. Finally we present two publications that resulted from the many detours we have taken along the winding path of our research.QC 20100909
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Kohl, Florian [Verfasser]. "Lattice Polytopes - Applications and Properties : Ehrhart Theory, Graph Colorings, and Level Algebras / Florian Kohl." Berlin : Freie Universität Berlin, 2018. http://d-nb.info/1176639625/34.
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Espinosa, Kristofer, and Tam Vu. "Graph theory applications in the energy sector : From the perspective of electric utility companies." Thesis, KTH, Skolan för industriell teknik och management (ITM), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-279516.
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Graph theory is a mathematical study of objects and their pairwise relations, also known as nodes and edges. The birth of graph theory is often considered to take place in 1736 when Leonhard Euler tried to solve a problem involving seven bridges of Königsberg in Prussia. In more recent times, graphs has caught the attention of companies from many industries due to its power of modelling and analysing large networks. This thesis investigates the usage of graph theory in the energy sector for a utility company, in particular Fortum whose activities consist of, but not limited to, production and distribution of electricity and heat. The output of the thesis is a wide overview of graph-theoretic concepts and their applications, as well as an evaluation of energy-related use-cases where some concepts are put into deeper analysis. The chosen use-case within the scope of this thesis is feature selection for electricity price forecasting. Feature selection is a process for reducing the number of features, also known as input variables, typically before a regression model is built to avoid overfitting and to increase model interpretability. Five graph-based feature selection methods with different points of view are studied. Experiments are conducted on realistic data sets with many features to verify the legitimacy of the methods. One of the data sets is owned by Fortum and used for forecasting the electricity price, among other important quantities. The obtained results look promising according to several evaluation metrics and can be used by Fortum as a support tool to develop prediction models. In general, a utility company can likely take advantage graph theory in many ways and add value to their business with enriched mathematical knowledge.Grafteori är ett matematiskt område där objekt och deras parvisa relationer, även kända som noder respektive kanter, studeras. Grafteorins födsel anses ofta ha ägt rum år 1736 när Leonhard Euler försökte lösa ett problem som involverade sju broar i Königsberg i Preussen. På senare tid har grafer fått uppmärksamhet från företag inom flera branscher på grund av dess kraft att modellera och analysera stora nätverk. Detta arbete undersöker användningen av grafteori inom energisektorn för ett allmännyttigt företag, närmare bestämt Fortum, vars verksamhet består av, men inte är begränsad till, produktion och distribution av el och värme. Arbetet resulterar i en bred genomgång av grafteoretiska begrepp och deras tillämpningar inom både allmänna tekniska sammanhang och i synnerhet energisektorn, samt ett fallstudium där några begrepp sätts in i en djupare analys. Den valda fallstudien inom ramen för arbetet är variabelselektering för elprisprognostisering. Variabelselektering är en process för att minska antalet ingångsvariabler, vilket vanligtvis genomförs innan en regressions- modell skapas för att undvika överanpassning och öka modellens tydbarhet. Fem grafbaserade metoder för variabelselektering med olika ståndpunkter studeras. Experiment genomförs på realistiska datamängder med många ingångsvariabler för att verifiera metodernas giltighet. En av datamängderna ägs av Fortum och används för att prognostisera elpriset, bland andra viktiga kvantiteter. De erhållna resultaten ser lovande ut enligt flera utvärderingsmått och kan användas av Fortum som ett stödverktyg för att utveckla prediktionsmodeller. I allmänhet kan ett energiföretag sannolikt dra fördel av grafteori på många sätt och skapa värde i sin affär med hjälp av berikad matematisk kunskap
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Inkmann, Torsten. "Tree-based decompositions of graphs on surfaces and applications to the traveling salesman problem." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/22583.
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Thesis (Ph. D.)--Mathematics, Georgia Institute of Technology, 2008.Committee Chair: Thomas, Robin; Committee Co-Chair: Cook, William J.; Committee Member: Dvorak, Zdenek; Committee Member: Parker, Robert G.; Committee Member: Yu, Xingxing.
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Kissinger, Aleks. "Pictures of processes : automated graph rewriting for monoidal categories and applications to quantum computing." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:61fb3161-a353-48fc-8da2-6ce220cce6a2.
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This work is about diagrammatic languages, how they can be represented, and what they in turn can be used to represent. More specifically, it focuses on representations and applications of string diagrams. String diagrams are used to represent a collection of processes, depicted as "boxes" with multiple (typed) inputs and outputs, depicted as "wires". If we allow plugging input and output wires together, we can intuitively represent complex compositions of processes, formalised as morphisms in a monoidal category. While string diagrams are very intuitive, existing methods for defining them rigorously rely on topological notions that do not extend naturally to automated computation. The first major contribution of this dissertation is the introduction of a discretised version of a string diagram called a string graph. String graphs form a partial adhesive category, so they can be manipulated using double-pushout graph rewriting. Furthermore, we show how string graphs modulo a rewrite system can be used to construct free symmetric traced and compact closed categories on a monoidal signature. The second contribution is in the application of graphical languages to quantum information theory. We use a mixture of diagrammatic and algebraic techniques to prove a new classification result for strongly complementary observables. Namely, maximal sets of strongly complementary observables of dimension D must be of size no larger than 2, and are in 1-to-1 correspondence with the Abelian groups of order D. We also introduce a graphical language for multipartite entanglement and illustrate a simple graphical axiom that distinguishes the two maximally-entangled tripartite qubit states: GHZ and W. Notably, we illustrate how the algebraic structures induced by these operations correspond to the (partial) arithmetic operations of addition and multiplication on the complex projective line. The third contribution is a description of two software tools developed in part by the author to implement much of the theoretical content described here. The first tool is Quantomatic, a desktop application for building string graphs and graphical theories, as well as performing automated graph rewriting visually. The second is QuantoCoSy, which performs fully automated, model-driven theory creation using a procedure called conjecture synthesis.
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Burkhart, Craig. "Approval Voting Theory with Multiple Levels of Approval." Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/26.
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Approval voting is an election method in which voters may cast votes for as many candidates as they desire. This can be modeled mathematically by associating to each voter an approval region: a set of potential candidates they approve. In this thesis we add another level of approval somewhere in between complete approval and complete disapproval. More than one level of approval may be a better model for a real-life voter's complex decision making. We provide a new definition for intersection that supports multiple levels of approval. The case of pairwise intersection is studied, and the level of agreement among voters is studied under restrictions on the relative size of each voter's preferences. We derive upper and lower bounds for the percentage of agreement based on the percentage of intersection.
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Vellambi, Badri Narayanan. "Applications of graph-based codes in networks: analysis of capacity and design of improved algorithms." Diss., Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/37091.
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The conception of turbo codes by Berrou et al. has created a renewed interest in modern graph-based codes. Several encouraging results that have come to light since then have fortified the role these codes shall play as potential solutions for present and future communication problems.
This work focuses on both practical and theoretical aspects of graph-based codes. The
thesis can be broadly categorized into three parts. The first part of the thesis focuses on
the design of practical graph-based codes of short lengths. While both low-density parity-check
codes and rateless codes have been shown to be asymptotically optimal under the message-passing (MP) decoder, the performance of short-length codes from these families under MP decoding is starkly sub-optimal. This work first addresses the
structural characterization of stopping sets to understand this sub-optimality. Using this
characterization, a novel improved decoder that offers several orders of magnitude improvement in bit-error rates is introduced. Next, a novel scheme for the design of a good rate-compatible family of punctured codes is proposed.
The second part of the thesis aims at establishing these codes as a good tool to develop
reliable, energy-efficient and low-latency data dissemination schemes in networks. The problems of broadcasting in wireless multihop networks and that of unicast in delay-tolerant networks are investigated. In both cases, rateless coding is seen to offer an elegant means of achieving the goals of the chosen communication protocols. It was noticed that the ratelessness and the randomness in encoding process make this scheme
specifically suited to such network applications.
The final part of the thesis investigates an application of a specific class of codes called
network codes to finite-buffer wired networks. This part of the work aims at establishing a framework for the theoretical study and understanding of finite-buffer networks. The
proposed Markov chain-based method extends existing results to develop an iterative
Markov chain-based technique for general acyclic wired networks. The framework not only estimates the capacity of such networks, but also provides a means to monitor network traffic and packet drop rates on various links of the network.
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Barr, Samuel Frederic. "Courcelle's Theorem: Overview and Applications." Oberlin College Honors Theses / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1589552348499388.
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Abuali, Faris Nabih. "Using determinant and cycle basis schemes in genetic algorithms for graph and network applications /." Access abstract and link to full text, 1995. http://0-wwwlib.umi.com.library.utulsa.edu/dissertations/fullcit/9529027.
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Vu, Duc Tam. "Applications of graph theory in the energy sector, demonstrated with feature selection in electricity price forecasting." Thesis, KTH, Optimeringslära och systemteori, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-276482.
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Graph theory is a mathematical study of objects and their pairwise relations, known as nodes and edges respectively. The birth of graph theory is often considered to take place in 1736 when the Swiss mathematician Leonhard Euler tried to solve a routing problem involving seven bridges of Königsberg in Prussia. In more recent times, graph theory has caught the attention of companies from all types of industries due to its power of modelling and analysing exceptionally large networks. This thesis investigates the usage of graph theory in the energy sector for a utility company, in particular Fortum whose activities consist of, but not limited to, production and distribution of electricity and heat. The output of the thesis is a wide overview of graph-theoretic concepts and their practical applications, as well as a study of a use-case where some concepts are put into deeper analysis. The chosen use-case within the scope of this thesis is feature selection - a process for reducing the number of features, also known as input variables, typically before a regression model is built to avoid overfitting and increase model interpretability. Five graph-based feature selection methods with different points of view are studied. Experiments are conducted on realistic data sets with many features to verify the legitimacy of the methods. One of the data sets is owned by Fortum and used for forecasting the electricity price, among other important quantities. The obtained results look promising according to several evaluation metrics and can be used by Fortum as a support tool to develop prediction models. In general, a utility company can likely take advantage graph theory in many ways and add value to their business with enriched mathematical knowledge.Grafteori är ett matematiskt område där objekt och deras parvisa relationer, även kallade noder respektive kanter, studeras. Grafteorins födsel anses ofta äga rum år 1736 när den schweiziske matematikern Leonhard Euler försökte lösa ett vägsökningsproblem som involverade sju broar av Königsberg i Preussen. På senare tid har grafteori fått uppmärksamhet från företag inom flera branscher på grund av dess kraft att modellera och analysera väsentligt stora nätverk. Detta arbete undersöker användningen av grafteori inom energisektorn för ett allmännyttigt företag, närmare bestämt Fortum vars verksamhet består av, dock ej begränsat till, produktion och distribution av elektricitet och värme. Arbetet resulterar i en bred översiktlig genomgång av grafteoretiska begrepp och deras praktiska tillämpningar, samt ett fallstudium där några begrepp sätts in i en djupare analys. Det valda fallstudiet inom ramen för arbetet är variabelselektering - en process för att minska antalet ingångsvariabler, vilket vanligtvis genomförs innan en regressionsmodell skapas för att undvika överanpassning och öka modellens tydbarhet. Fem grafbaserade metoder för variabelselektering med olika ståndpunkter studeras. Experiment genomförs på realistiska datamängder med många ingångsvariabler för att verifiera metodernas giltighet. En av datamängderna ägs av Fortum och används för att prognostisera elpriset, bland andra viktiga kvantiteter. De erhållna resultaten ser lovande ut enligt flera utvärderingsmått och kan användas av Fortum som ett stödverktyg för att utveckla prediktionsmodeller. I allmänhet kan ett energiföretag sannolikt dra fördel av grafteori på många sätt och skapa värde i sin affär med hjälp av berikad matematisk kunskap.
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Curado, Manuel. "Structural Similarity: Applications to Object Recognition and Clustering." Doctoral thesis, Universidad de Alicante, 2018. http://hdl.handle.net/10045/98110.
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In this thesis, we propose many developments in the context of Structural Similarity. We address both node (local) similarity and graph (global) similarity. Concerning node similarity, we focus on improving the diffusive process leading to compute this similarity (e.g. Commute Times) by means of modifying or rewiring the structure of the graph (Graph Densification), although some advances in Laplacian-based ranking are also included in this document. Graph Densification is a particular case of what we call graph rewiring, i.e. a novel field (similar to image processing) where input graphs are rewired to be better conditioned for the subsequent pattern recognition tasks (e.g. clustering). In the thesis, we contribute with an scalable an effective method driven by Dirichlet processes. We propose both a completely unsupervised and a semi-supervised approach for Dirichlet densification. We also contribute with new random walkers (Return Random Walks) that are useful structural filters as well as asymmetry detectors in directed brain networks used to make early predictions of Alzheimer's disease (AD). Graph similarity is addressed by means of designing structural information channels as a means of measuring the Mutual Information between graphs. To this end, we first embed the graphs by means of Commute Times. Commute times embeddings have good properties for Delaunay triangulations (the typical representation for Graph Matching in computer vision). This means that these embeddings can act as encoders in the channel as well as decoders (since they are invertible). Consequently, structural noise can be modelled by the deformation introduced in one of the manifolds to fit the other one. This methodology leads to a very high discriminative similarity measure, since the Mutual Information is measured on the manifolds (vectorial domain) through copulas and bypass entropy estimators. This is consistent with the methodology of decoupling the measurement of graph similarity in two steps: a) linearizing the Quadratic Assignment Problem (QAP) by means of the embedding trick, and b) measuring similarity in vector spaces. The QAP problem is also investigated in this thesis. More precisely, we analyze the behaviour of $m$-best Graph Matching methods. These methods usually start by a couple of best solutions and then expand locally the search space by excluding previous clamped variables. The next variable to clamp is usually selected randomly, but we show that this reduces the performance when structural noise arises (outliers). Alternatively, we propose several heuristics for spanning the search space and evaluate all of them, showing that they are usually better than random selection. These heuristics are particularly interesting because they exploit the structure of the affinity matrix. Efficiency is improved as well. Concerning the application domains explored in this thesis we focus on object recognition (graph similarity), clustering (rewiring), compression/decompression of graphs (links with Extremal Graph Theory), 3D shape simplification (sparsification) and early prediction of AD.Ministerio de Economía, Industria y Competitividad (Referencia TIN2012-32839 BES-2013-064482)
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Saha, Sudip. "Containing Cascading Failures in Networks: Applications to Epidemics and Cybersecurity." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/82711.
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Many real word networks exhibit cascading phenomena, e.g., disease outbreaks in social contact networks, malware propagation in computer networks, failures in cyber-physical systems such as power grids. As they grow in size and complexity, their security becomes increasingly important. In this thesis, we address the problems of controlling cascading failures in various network settings. We address the cascading phenomena which are either natural (e.g., disease outbreaks) or malicious (e.g., cyber attacks). We consider the nodes of a network as being individually or collectively controlled by self-interested autonomous agents and study their strategic decisions in the presence of these failure cascades. There are many models of cascading failures which specify how a node would fail when some neighbors have failed, such as: (i) epidemic spread models in which the cascading can be viewed as a natural and stochastic process and (ii) cyber attack models where the cascade is driven by malicious intents. We present our analyses and algorithms for these models in two parts.
Part I focuses on problems of controlling epidemic spread. Epidemic outbreaks are generally modeled as stochastic diffusion processes. In particular, we consider the SIS model on networks. There exist heuristic centralized approaches in the literature for containing epidemic spread in SIS/SIR models; however no rigorous performance bounds are known for these approaches. We develop algorithms with provable approximation guarantees that involve either protective intervention (e.g., vaccination) or link removal (e.g., unfriending). Our approach relies on the characterization of the SIS model in terms of the spectral radius of the network. The centralized approaches, however, are sometimes not feasible in practice. For example, targeted vaccination is often not feasible because of limited compliance to directives. This issue has been addressed in the literature by formulating game theoretic models for the containment of epidemic spread. However they generally assume simplistic propagation models or homogeneous network structures. We develop novel game formulations which rely on the spectral characterization of the SIS model. In these formulations, the failures start from a random set of nodes and propagate through the network links. Each node acts as a self-interested agent and makes strategic intervention decisions (e.g., taking vaccination). Each agent decides its strategy to optimize its payoff (modeled by some payoff function). We analyze the complexity of finding Nash equilibria (NE) and study the structure of NE for different networks in these game settings.
Part II focuses on malware spread in networks. In cybersecurity literature malware spreads are often studied in the framework of ``attack graph" models. In these models, a node represents either a physical computing unit or a network configuration and an edge represents a physical or logical vulnerability dependency. A node gets compromised if a certain set of its neighbors are compromised. Attack graphs describe explicit scenarios in which a single vulnerability exploitation cascades further into the network exploiting inherent dependencies among the network components. Attack graphs are used for studying cascading effects in many cybersecurity applications, e.g., component failure in enterprise networks, botnet spreads, advanced persistent attacks. One distinct feature of cyber attack cascades is the stealthy nature of the attack moves. Also, cyber attacks are generally repeated. How to control stealthy and repeated attack cascades is an interesting problem. Dijk et. al.~cite{van2013flipit} first proposed a game framework called ``FlipIt" for reasoning about the stealthy interaction between a defender and an attacker over the control of a system resource. However, in cybersecurity applications, systems generally consists of multiple resources connected by a network. Therefore it is imperative to study the stealthy attack and defense in networked systems. We develop a generalized framework called ``FlipNet" which extends the work of Dijk et. al.~cite{van2013flipit} for network. We present analyses and algorithms for different problems in this framework. On the other hand, if the security of a system is limited to the vulnerabilities and exploitations that are known to the security community, often the objective of the system owner is to take cost-effective steps to minimize potential damage in the network. This problem has been formulated in the cybersecurity literature as hardening attack graphs. Several heuristic approaches have been shown in the litrature so far but no algorithmic analysis have been shown. We analyze the inherent vulnerability of the network and present approximation hardening algorithms.Ph. D.
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Molari, Marco. "Statistical mechanics of polymer models: rigorous results and applications." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10429/.
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Monomer-dimer models are amongst the models in statistical mechanics which found application in many areas of science, ranging from biology to social sciences. This model describes a many-body system in which monoatomic and diatomic particles subject to hard-core interactions get deposited on a graph.
In our work we provide an extension of this model to higher-order particles. The aim of our work is threefold: first we study the thermodynamic properties of the newly introduced model. We solve analytically some regular cases and find that, differently from the original, our extension admits phase transitions. Then we tackle the inverse problem, both from an analytical and numerical perspective. Finally we propose an application to aggregation phenomena in virtual messaging services.
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Passuello, Alberto. "Semidefinite programming in combinatorial optimization with applications to coding theory and geometry." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00948055.
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We apply the semidefinite programming method to obtain a new upper bound on the cardinality of codes made of subspaces of a linear vector space over a finite field. Such codes are of interest in network coding.Next, with the same method, we prove an upper bound on the cardinality of sets avoiding one distance in the Johnson space, which is essentially Schrijver semidefinite program. This bound is used to improve existing results on the measurable chromatic number of the Euclidean space.We build a new hierarchy of semidefinite programs whose optimal values give upper bounds on the independence number of a graph. This hierarchy is based on matrices arising from simplicial complexes. We show some properties that our hierarchy shares with other classical ones. As an example, we show its application to the problem of determining the independence number of Paley graphs.
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Wang, Jiayuan. "Algorithms for Guaranteed Denoising of Data and Their Applications." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1577966043088083.
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Shiping, Liu [Verfasser], Jürgen [Akademischer Betreuer] Jost, Jürgen [Gutachter] Jost, and Karl-Theodor [Gutachter] Sturm. "Synthetic notions of curvature and applications in graph theory / Liu Shiping ; Gutachter: Jürgen Jost, Karl-Theodor Sturm ; Betreuer: Jürgen Jost." Leipzig : Universitätsbibliothek Leipzig, 2013. http://d-nb.info/1238242057/34.
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Genevois, Anthony. "Cubical-like geometry of quasi-median graphs and applications to geometric group theory." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0569/document.
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La classe des graphes quasi-médians est une généralisation des graphes médians, ou de manière équivalente, des complexes cubiques CAT(0). L'objectif de cette thèse est d'introduire ces graphes dans le monde de la théorie géométrique des groupes. Dans un premier temps, nous étendons la notion d'hyperplan définie dans les complexes cubiques CAT(0), et nous montrons que la géométrie d'un graphe quasi-médian se réduit essentiellement à la combinatoire de ses hyperplans. Dans la deuxième partie de notre texte, qui est le cœur de la thèse, nous exploitons la structure particulière des hyperplans pour démontrer des résultats de combinaison. L'idée principale est que si un groupe agit d'une bonne manière sur un graphe quasi-médian de sorte que les stabilisateurs de cliques satisfont une certaine propriété P de courbure négative ou nulle, alors le groupe tout entier doit satisfaire P également. Les propriétés que nous considérons incluent : l'hyperbolicité (éventuellement relative), les compressions lp (équivariantes), la géométrie CAT(0) et la géométrie cubique. Finalement, la troisième et dernière partie de la thèse est consacrée à l'application des critères généraux démontrés précédemment à certaines classes de groupes particulières, incluant les produits graphés, les groupes de diagrammes introduits par Guba et Sapir, certains produits en couronne, et certains graphes de groupes. Les produits graphés constituent notre application la plus naturelle, où le lien entre le groupe et son graphe quasi-médian associé est particulièrement fort et explicite; en particulier, nous sommes capables de déterminer précisément quand un produit graphé est relativement hyperboliqueThe class of quasi-median graphs is a generalisation of median graphs, or equivalently of CAT(0) cube complexes. The purpose of this thesis is to introduce these graphs in geometric group theory. In the first part of our work, we extend the definition of hyperplanes from CAT(0) cube complexes, and we show that the geometry of a quasi-median graph essentially reduces to the combinatorics of its hyperplanes. In the second part, we exploit the specific structure of the hyperplanes to state combination results. The main idea is that if a group acts in a suitable way on a quasi-median graph so that clique-stabilisers satisfy some non-positively curved property P, then the whole group must satisfy P as well. The properties we are interested in are mainly (relative) hyperbolicity, (equivariant) lp-compressions, CAT(0)-ness and cubicality. In the third part, we apply our general criteria to several classes of groups, including graph products, Guba and Sapir's diagram products, some wreath products, and some graphs of groups. Graph products are our most natural examples, where the link between the group and its quasi-median graph is particularly strong and explicit; in particular, we are able to determine precisely when a graph product is relatively hyperbolic
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Gutekunst, Samuel C. "Characterizing Forced Communication in Networks." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/56.
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This thesis studies a problem that has been proposed as a novel way to disrupt communication networks: the load maximization problem. The load on a member of a network represents the amount of communication that the member is forced to be involved in. By maximizing the load on an important member of the network, we hope to increase that member's visibility and susceptibility to capture. In this thesis we characterize load as a combinatorial property of graphs and expose possible connections between load and spectral graph theory. We specifically describe the load and how it changes in several canonical classes of graphs and determine the range of values that the load can take on. We also consider a connection between load and liquid paint flow and use this connection to build a heuristic solver for the load maximization problem. We conclude with a detailed discussion of open questions for future work.
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Mantrach, Amin. "Novel measures on directed graphs and applications to large-scale within-network classification." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210033.
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Ces dernières années, les réseaux sont devenus une source importante d’informations dans différents domaines aussi variés que les sciences sociales, la physique ou les mathématiques. De plus, la taille de ces réseaux n’a cessé de grandir de manière conséquente. Ce constat a vu émerger de nouveaux défis, comme le besoin de mesures précises et intuitives pour caractériser et analyser ces réseaux de grandes tailles en un temps raisonnable.La première partie de cette thèse introduit une nouvelle mesure de similarité entre deux noeuds d’un réseau dirigé et pondéré :la covariance “sum-over-paths”. Celle-ci a une interprétation claire et précise :en dénombrant tous les chemins possibles deux noeuds sont considérés comme fortement corrélés s’ils apparaissent souvent sur un même chemin – de préférence court. Cette mesure dépend d’une distribution de probabilités, définie sur l’ensemble infini dénombrable des chemins dans le graphe, obtenue en minimisant l'espérance du coût total entre toutes les paires de noeuds du graphe sachant que l'entropie relative totale injectée dans le réseau est fixée à priori. Le paramètre d’entropie permet de biaiser la distribution de probabilité sur un large spectre :allant de marches aléatoires naturelles où tous les chemins sont équiprobables à des marches biaisées en faveur des plus courts chemins. Cette mesure est alors appliquée à des problèmes de classification semi-supervisée sur des réseaux de taille moyennes et comparée à l’état de l’art.
La seconde partie de la thèse introduit trois nouveaux algorithmes de classification de noeuds en sein d’un large réseau dont les noeuds sont partiellement étiquetés. Ces algorithmes ont un temps de calcul linéaire en le nombre de noeuds, de classes et d’itérations, et peuvent dés lors être appliqués sur de larges réseaux. Ceux-ci ont obtenus des résultats compétitifs en comparaison à l’état de l’art sur le large réseaux de citations de brevets américains et sur huit autres jeux de données. De plus, durant la thèse, nous avons collecté un nouveau jeu de données, déjà mentionné :le réseau de citations de brevets américains. Ce jeu de données est maintenant disponible pour la communauté pour la réalisation de tests comparatifs.
La partie finale de cette thèse concerne la combinaison d’un graphe de citations avec les informations présentes sur ses noeuds. De manière empirique, nous avons montré que des données basées sur des citations fournissent de meilleurs résultats de classification que des données basées sur des contenus textuels. Toujours de manière empirique, nous avons également montré que combiner les différentes sources d’informations (contenu et citations) doit être considéré lors d’une tâche de classification de textes. Par exemple, lorsqu’il s’agit de catégoriser des articles de revues, s’aider d’un graphe de citations extrait au préalable peut améliorer considérablement les performances. Par contre, dans un autre contexte, quand il s’agit de directement classer les noeuds du réseau de citations, s’aider des informations présentes sur les noeuds n’améliora pas nécessairement les performances.
La théorie, les algorithmes et les applications présentés dans cette thèse fournissent des perspectives intéressantes dans différents domaines.
In recent years, networks have become a major data source in various fields ranging from social sciences to mathematical and physical sciences. Moreover, the size of available networks has grow substantially as well. This has brought with it a number of new challenges, like the need for precise and intuitive measures to characterize and analyze large scale networks in a reasonable time.
The first part of this thesis introduces a novel measure between two nodes of a weighted directed graph: The sum-over-paths covariance. It has a clear and intuitive interpretation: two nodes are considered as highly correlated if they often co-occur on the same -- preferably short -- paths. This measure depends on a probability distribution over the (usually infinite) countable set of paths through the graph which is obtained by minimizing the total expected cost between all pairs of nodes while fixing the total relative entropy spread in the graph. The entropy parameter allows to bias the probability distribution over a wide spectrum: going from natural random walks (where all paths are equiprobable) to walks biased towards shortest-paths. This measure is then applied to semi-supervised classification problems on medium-size networks and compared to state-of-the-art techniques.
The second part introduces three novel algorithms for within-network classification in large-scale networks, i.e. classification of nodes in partially labeled graphs. The algorithms have a linear computing time in the number of edges, classes and steps and hence can be applied to large scale networks. They obtained competitive results in comparison to state-of-the-art technics on the large scale U.S.~patents citation network and on eight other data sets. Furthermore, during the thesis, we collected a novel benchmark data set: the U.S.~patents citation network. This data set is now available to the community for benchmarks purposes.
The final part of the thesis concerns the combination of a citation graph with information on its nodes. We show that citation-based data provide better results for classification than content-based data. We also show empirically that combining both sources of information (content-based and citation-based) should be considered when facing a text categorization problem. For instance, while classifying journal papers, considering to extract an external citation graph may considerably boost the performance. However, in another context, when we have to directly classify the network citation nodes, then the help of features on nodes will not improve the results.
The theory, algorithms and applications presented in this thesis provide interesting perspectives in various fields.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Strang, Alexander. "Applications of the Helmholtz-Hodge Decomposition to Networks and Random Processes." Case Western Reserve University School of Graduate Studies / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=case1595596768356487.
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Tran, The Truyen. "On conditional random fields: applications, feature selection, parameter estimation and hierarchical modelling." Curtin University of Technology, Dept. of Computing, 2008. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=18614.
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There has been a growing interest in stochastic modelling and learning with complex data, whose elements are structured and interdependent. One of the most successful methods to model data dependencies is graphical models, which is a combination of graph theory and probability theory. This thesis focuses on a special type of graphical models known as Conditional Random Fields (CRFs) (Lafferty et al., 2001), in which the output state spaces, when conditioned on some observational input data, are represented by undirected graphical models. The contributions of thesis involve both (a) broadening the current applicability of CRFs in the real world and (b) deepening the understanding of theoretical aspects of CRFs. On the application side, we empirically investigate the applications of CRFs in two real world settings. The first application is on a novel domain of Vietnamese accent restoration, in which we need to restore accents of an accent-less Vietnamese sentence. Experiments on half a million sentences of news articles show that the CRF-based approach is highly accurate. In the second application, we develop a new CRF-based movie recommendation system called Preference Network (PN). The PN jointly integrates various sources of domain knowledge into a large and densely connected Markov network. We obtained competitive results against well-established methods in the recommendation field.On the theory side, the thesis addresses three important theoretical issues of CRFs: feature selection, parameter estimation and modelling recursive sequential data. These issues are all addressed under a general setting of partial supervision in that training labels are not fully available. For feature selection, we introduce a novel learning algorithm called AdaBoost.CRF that incrementally selects features out of a large feature pool as learning proceeds. AdaBoost.CRF is an extension of the standard boosting methodology to structured and partially observed data. We demonstrate that the AdaBoost.CRF is able to eliminate irrelevant features and as a result, returns a very compact feature set without significant loss of accuracy. Parameter estimation of CRFs is generally intractable in arbitrary network structures. This thesis contributes to this area by proposing a learning method called AdaBoost.MRF (which stands for AdaBoosted Markov Random Forests). As learning proceeds AdaBoost.MRF incrementally builds a tree ensemble (a forest) that cover the original network by selecting the best spanning tree at a time. As a result, we can approximately learn many rich classes of CRFs in linear time. The third theoretical work is on modelling recursive, sequential data in that each level of resolution is a Markov sequence, where each state in the sequence is also a Markov sequence at the finer grain. One of the key contributions of this thesis is Hierarchical Conditional Random Fields (HCRF), which is an extension to the currently popular sequential CRF and the recent semi-Markov CRF (Sarawagi and Cohen, 2004). Unlike previous CRF work, the HCRF does not assume any fixed graphical structures.
Rather, it treats structure as an uncertain aspect and it can estimate the structure automatically from the data. The HCRF is motivated by Hierarchical Hidden Markov Model (HHMM) (Fine et al., 1998). Importantly, the thesis shows that the HHMM is a special case of HCRF with slight modification, and the semi-Markov CRF is essentially a flat version of the HCRF. Central to our contribution in HCRF is a polynomial-time algorithm based on the Asymmetric Inside Outside (AIO) family developed in (Bui et al., 2004) for learning and inference. Another important contribution is to extend the AIO family to address learning with missing data and inference under partially observed labels. We also derive methods to deal with practical concerns associated with the AIO family, including numerical overflow and cubic-time complexity. Finally, we demonstrate good performance of HCRF against rivals on two applications: indoor video surveillance and noun-phrase chunking.
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Meek, Darrin Leigh. "On graph approximation heuristics : an application to vertex cover on planar graphs." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/24088.
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Baumann, Annika. "Network Science – Applications in Technology, Business and Social Media." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19216.
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Netzwerke stellen einen integralen Bestandteil unseres Lebens dar. Eines der wichtigsten Kommunikations-Netzwerke ist das Internet, welches zu starken Veränderungen im Alltag geführt hat. Diese werden in Teilaspekten in der vorliegenden Dissertation untersucht. Insgesamt ist die Dissertation in drei Bereiche unterteilt, welche auf der traditionellen Perspektive der drei Dimensionen von Informationssystemen basieren. Diese Dimensionen umfassen die Technologie, das Management und die Organisation.
Im Zentrum der Dissertation steht hierbei die Technologie-Dimension in dessen Rahmen die Struktur und Robustheit des Internets sowie anderer Netzwerke unter Nutzung des mathematisch-methodischen Aspekts der Graphentheorie analysiert werden.
Der zweite Teilbereich der vorliegenden Arbeit wechselt die Perspektive hin zum Management. Unter Nutzung von Methoden der prädikativen Modellierung stehen das bessere Verständnis und die Möglichkeit der Vorhersage von Nutzerverhalten im E-Commerce-Kontext im Fokus.
Der dritte Bereich umfasst die Organisations-Perspektive aus Sicht der Nutzer. Hierbei werden zwei spezielle Unterbereiche betrachtet. Der erste Unterbereich umfasst Webseiten Sozialer Medien und analysiert wie verschiedene Nutzergruppen diese verwenden. Der zweite Unterbereich befasst sich mit dem Einfluss der weitläufigen Verbreitung von mobilen Endgeräten auf Aspekte des persönlichen und beruflichen Lebens von Individuen.
Aufbauend auf diesen drei Dimensionen wurden im Rahmen dieser Dissertation insgesamt 18 Studien durchgeführt, die sich unterschiedlicher methodischer Anwendungen bedienen um wissenschaftliche Erkenntnisse zu den vorgestellten Teilbereichen zu erlangen.Networks constitute an integral part of our lives. One of the most important communication networks is the Internet which led to large changes in everyday life, which are examined in part in this dissertation. Overall, the present dissertation is subdivided into three areas, which are based on the traditional three dimensions of information systems, comprising perspectives technology, management and organization. At the core of this dissertation is the technological perspective, centered on an analysis of the structure and robustness of the Internet network using the mathematical-methodical aspect of graph theory. The second part of the thesis deals with the management perspective. The focus lies on the understanding and prediction of user behavior in the e-commerce context utilizing methods of predictive modeling. The third area includes the organizational perspective from the point of view of users. Here, two specific sub-areas are selected. The first sub-area revolves around social media websites, with the goal of understanding how sub-groups of users utilize them in different ways. The second area is centered around the aspect of how the propagation of mobile devices influences individuals in their personal and professional environments. Based on these three perspectives, a total of 18 studies were conducted within the scope of this dissertation, using different methodological applications to gain scientific insights with respect to the areas examined.
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Dohmen, Klaus. "Improved Inclusion-Exclusion Identities and Bonferroni Inequalities with Applications to Reliability Analysis of Coherent Systems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2001. http://dx.doi.org/10.18452/13732.
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Viele Probleme der Kombinatorik, Zahlentheorie, Wahrscheinlichkeitstheorie, Zuverlässigkeitstheorie und Statistik lassen sich durch Anwendung einer einheitlichen Methode lösen, die als Prinzip der Inklusion-Exklusion bekannt ist. Das Prinzip der Inklusion-Exklusion drückt die Indikatorfunktion einer Vereinigung endlich vieler Ereignisse als alternierende Summe der Indikatorfunktionen ihrer Durchschnitte aus. Die vorliegende Schrift befasst sich mit verbesserten Inklusions-Exklusions-Identitäten und verbesserten Bonferroni-Ungleichungen, die voraussetzen, dass die Ereignisfamilie gewissen strukturellen Anforderungen genügt. Solche wohl-strukturierten Ereignisfamilien finden sich u.a. in der schließenden Statistik, der kombinatorischen Zuverlässigkeitstheorie und der chromatischen Graphentheorie.Many problems in combinatorics, number theory, probability theory , reliability theory and statistics can be solved by applying a unifying method, which is known as the principle of inclusion-exclusion. The principle of inclusion-exclusion expresses the indicator function of a union of finitely many events as an alternating sum of indicator functions of their intersections. This thesis deals with improved inclusion-exclusion identities and improved Bonferroni inequalities that require the family of events to satisfy some structural restrictions. Examples of such well-structured families arise in problems of statistical inference, combinatorial reliability theory and chromatic graph theory.
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Thwaites, Peter. "Chain event graphs : theory and application." Thesis, University of Warwick, 2008. http://wrap.warwick.ac.uk/49194/.
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This thesis is concerned with the Graphical model known as the Chain Event Graph (CEG) [1][60][61], and develops the theory that appears in the currently published papers on this work. Results derived are analogous to those produced for Bayesian Networks (BNs), and I show that for asymmetric problems the CEG is generally superior to the BN both as a representation of the problem and as an analytical tool. The CEG is designed to embody the conditional independence structure of problems whose state spaces are asymmetric and do not admit a natural Product Space structure. In this they differ from BNs and other structures with variable-based topologies. Chapter 1 details researchers' attempts to adapt BNs to model such problems, and outlines the advantages CEGs have over these adaptations. Chapter 2 describes the construction of CEGs. In chapter 3I create a semantic structure for the reading of CEGs, and derive results expressible in the form of context-specific conditional independence statements, that allow us to delve much more deeply into the independence structure of a problem than we can do with BNs. In chapter 4I develop algorithms for the updating of a CEG following observation of an event, analogous to the Local Message Passing algorithms used with BNs. These are more efficient than the BN-based algorithms when used with asymmetric problems. Chapter 5 develops the theory of Causal manipulation of CEGs, and introduces the singular manipulation, a class of interventions containing the set of interventions possible with BNs. I produce Back Door and Front Door Theorems analogous to those of Pearl [42], but more flexible as they allow asymmetric manipulations of asymmetric problems. The ideas and results of chapters 2 to 5 are summarised in chapter 6.
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Ferrer, Sumsi Miquel. "Theory and Algorithms on the Median Graph. Application to Graph-based Classification and Clustering." Doctoral thesis, Universitat Autònoma de Barcelona, 2008. http://hdl.handle.net/10803/5788.
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Donat un conjunt d'objectes, el concepte genèric de mediana està definit com l'objecte amb la suma de distàncies a tot el conjunt, més petita. Sovint, aquest concepte és usat per a obtenir el representant del conjunt. En el reconeixement estructural de patrons, els grafs han estat usats normalment per a representar objectes complexos. En el domini dels grafs, el concepte de mediana és conegut com median graph. Potencialment, té les mateixes aplicacions que el concepte de mediana per poder ser usat com a representant d'un conjunt de grafs.
Tot i la seva simple definició i les potencials aplicacions, s'ha demostrat que el seu càlcul és una tasca extremadament complexa. Tots els algorismes existents només han estat capaços de treballar amb conjunts petits de grafs, i per tant, la seva aplicació ha estat limitada en molts casos a usar dades sintètiques sense significat real. Així, tot i el seu potencial, ha restat com un concepte eminentment teòric.
L'objectiu principal d'aquesta tesi doctoral és el d'investigar a fons la teoria i l'algorísmica relacionada amb el concepte de medinan graph, amb l'objectiu final d'extendre la seva aplicabilitat i lliurar tot el seu potencial al món de les aplicacions reals. Per això, presentem nous resultats teòrics i també nous algorismes per al seu càlcul. Des d'un punt de vista teòric aquesta tesi fa dues aportacions fonamentals. Per una banda, s'introdueix el nou concepte d'spectral median graph. Per altra banda es mostra que certes de les propietats teòriques del median graph poden ser millorades sota determinades condicions. Més enllà de les aportacioncs teòriques, proposem cinc noves alternatives per al seu càlcul. La primera d'elles és una conseqüència directa del concepte d'spectral median graph. Després, basats en les millores de les propietats teòriques, presentem dues alternatives més per a la seva obtenció. Finalment, s'introdueix una nova tècnica per al càlcul del median basat en el mapeig de grafs en espais de vectors, i es proposen dos nous algorismes més.
L'avaluació experimental dels mètodes proposats utilitzant una base de dades semi-artificial (símbols gràfics) i dues amb dades reals (mollècules i pàgines web), mostra que aquests mètodes són molt més eficients que els existents. A més, per primera vegada, hem demostrat que el median graph pot ser un bon representant d'un conjunt d'objectes utilitzant grans quantitats de dades. Hem dut a terme experiments de classificació i clustering que validen aquesta hipòtesi i permeten preveure una pròspera aplicació del median graph a un bon nombre d'algorismes d'aprenentatge.
Given a set of objects, the generic concept of median is defined as the object with the smallest sum of distances to all the objects in the set. It has been often used as a good alternative to obtain a representative of the set.
In structural pattern recognition, graphs are normally used to represent structured objects. In the graph domain, the concept analogous to the median is known as the median graph. By extension, it has the same potential applications as the generic median in order to be used as the representative of a set of graphs.
Despite its simple definition and potential applications, its computation has been shown as an extremely complex task. All the existing algorithms can only deal with small sets of graphs, and its application has been constrained in most cases to the use of synthetic data with no real meaning. Thus, it has mainly remained in the box of the theoretical concepts.
The main objective of this work is to further investigate both the theory and the algorithmic underlying the concept of the median graph with the final objective to extend its applicability and bring all its potential to the world of real applications. To this end, new theory and new algorithms for its computation are reported. From a theoretical point of view, this thesis makes two main contributions. On one hand, the new concept of spectral median graph. On the other hand, we show that some of the existing theoretical properties of the median graph can be improved under some specific conditions. In addition to these theoretical contributions, we propose five new ways to compute the median graph. One of them is a direct consequence of the spectral median graph concept. In addition, we provide two new algorithms based on the new theoretical properties. Finally, we present a novel technique for the median graph computation based on graph embedding into vector spaces. With this technique two more new algorithms are presented.
The experimental evaluation of the proposed methods on one semi-artificial and two real-world datasets, representing graphical symbols, molecules and webpages, shows that these methods are much more ecient than the existing ones. In addition, we have been able to proof for the first time that the median graph can be a good representative of a class in large datasets. We have performed some classification and clustering experiments that validate this hypothesis and permit to foresee a successful application of the median graph to a variety of machine learning algorithms.
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Hanaf, Anas. "Algorithmes distribués de consensus de moyenne et leurs applications dans la détection des trous de couverture dans un réseau de capteurs." Thesis, Reims, 2016. http://www.theses.fr/2016REIMS018/document.
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Les algorithmes distribués de consensus sont des algorithmes itératifs de faible complexité où les nœuds de capteurs voisins interagissent les uns avec les autres pour parvenir à un accord commun sans unité coordinatrice. Comme les nœuds dans un réseau de capteurs sans fil ont une puissance de calcul et une batterie limitées, ces algorithmes distribués doivent parvenir à un consensus en peu de temps et avec peu d’échange de messages. La première partie de cette thèse s’est basée sur l’étude et la comparaison des différents algorithmes de consensus en mode synchrone et asynchrone en termes de vitesse de convergence et taux de communications. La seconde partie de nos travaux concerne l’application de ces algorithmes de consensus au problème de la détection de trous de couverture dans les réseaux de capteurs sans fil.Ce problème de couverture fournit aussi le contexte de la suite de nos travaux. Il se décrit comme étant la façon dont une région d’intérêt est surveillée par des capteurs. Différentes approches géométriques ont été proposées mais elles sont limitées par la nécessité de connaitre exactement la position des capteurs ; or cette information peut ne pas être disponible si les dispositifs de localisation comme par exemple le GPS ne sont pas sur les capteurs. À partir de l’outil mathématique appelé topologie algébrique, nous avons développé un algorithme distribué de détection de trous de couverture qui recherche une fonction harmonique d’un réseau, c’est-à-dire annulant l’opérateur du Laplacien de dimension 1. Cette fonction harmonique est reliée au groupe d’homologie H1 qui recense les trous de couverture. Une fois une fonction harmonique obtenue, la détection des trous se réalise par une simple marche aléatoire dans le réseauDistributed consensus algorithms are iterative algorithms of low complexity where neighboring sensors interact with each other to reach an agreement without coordinating unit. As the nodes in a wireless sensor network have limited computing power and limited battery, these distributed algorithms must reach a consensus in a short time and with little message exchange. The first part of this thesis is based on the study and comparison of different consensus algorithms synchronously and asynchronously in terms of convergence speed and communication rates. The second part of our work concerns the application of these consensus algorithms to the problem of detecting coverage holes in wireless sensor networks.This coverage problem also provides the context for the continuation of our work. This problem is described as how a region of interest is monitored by sensors. Different geometrical approaches have been proposed but are limited by the need to know exactly the position of the sensors; but this information may not be available if the locating devices such as GPS are not on the sensors. From the mathematical tool called algebraic topology, we have developed a distributed algorithm of coverage hole detection searching a harmonic function of a network, that is to say canceling the operator of the 1-dimensional Laplacian. This harmonic function is connected to the homology group H1 which identifies the coverage holes. Once a harmonic function obtained, detection of the holes is realized by a simple random walk in the network
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Tetley, Romain. "Analyse mixte de protéines basée sur la séquence et la structure - applications à l'annotation fonctionnelle." Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4111/document.
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Dans cette thèse, l'emphase est mise sur la réconciliation de l'analyse de structure et de séquence pour les protéines. L'analyse de séquence brille lorsqu'il s'agit de comparer des protéines présentant une forte identité de séquence (≤ 30\%) mais laisse à désirer pour identifier des homologues lointains. L'analyse de structure est une alternative intéressante. Cependant, les méthodes de résolution de structures sont coûteuses et complexes - lorsque toutefois elles produisent des résultats. Ces observations rendent évident la nécessité de développer des méthodes hybrides, exploitant l'information extraite des structures disponibles pour l'injecter dans des modèles de séquence. Cette thèse produit quatre contributions principales dans ce domaine. Premièrement, nous présentons une nouvelle distance structurale, le RMSDcomb, basée sur des patterns de conservation structurale locale, les motifs structuraux. Deuxièmement, nous avons développé une méthode pour identifier des motifs structuraux entre deux structures exploitant un bootstrap dépendant de filtrations. Notre approche n'est pas un compétiteur direct des aligneurs flexibles mais permet plutôt de produire des analyses multi-échelles de similarités structurales. Troisièmement, nous exploitons les méthodes suscitées pour construire des modèles de Markov cachés hybrides biaisés vers des régions mieux conservées structurellement. Nous utilisons un tel modèle pour caractériser les protéines de fusion virales de classe II, une tâche particulièrement ardue du fait de leur faible identité de séquence et leur conservation structurale moyenne. Ce faisant, nous parvenons à trouver un certain nombre d'homologues distants connues des protéines virales, notamment chez la Drosophile. Enfin, en formalisant un sous-problème rencontré lors de la comparaison de filtrations, nous présentons un nouveau problème théorique - le D-family matching - sur lequel nous démontrons des résultats algorithmiques variés. Nous montrons - d'une façon analogue à la comparaison de régions de deux conformations d'une protéine - comment exploiter ce modèle théorique pour comparer deux clusterings d'un même jeu de donnéesIn this thesis, the focus is set on reconciling the realms of structure and sequence for protein analysis. Sequence analysis tools shine when faced with proteins presenting high sequence identity (≤ 30\%), but are lack - luster when it comes to remote homolog detection. Structural analysis tools present an interesting alternative, but solving structures - when at all possible- is a tedious and expensive process. These observations make the need for hybrid methods - which inject information obtained from available structures in a sequence model - quite clear. This thesis makes four main contributions toward this goal. First we present a novel structural measure, the RMSDcomb, based on local structural conservation patterns - the so called structural motifs. Second, we developed a method to identify structural motifs between two structures using a bootstrap method which relies on filtrations. Our approach is not a direct competitor to flexible aligners but can provide useful to perform a multiscale analysis of structural similarities. Third, we build upon the previous methods to design hybrid Hidden Markov Models which are biased towards regions of increased structural conservation between sets of proteins. We test this tool on the class II fusion viral proteins - particularly challenging because of their low sequence identity and mild structural homology. We find that we are able to recover known remote homologs of the viral proteins in the Drosophila and other organisms. Finally, formalizing a sub - problem encountered when comparing filtrations, we present a new theoretical problem - the D-family matching - on which we present various algorithmic results. We show - in a manner that is analogous to comparing parts of two protein conformations - how it is possible to compare two clusterings of the same data set using such a theoretical model
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Yamak, Zaher Rabah. "Multiple identities detection in online social media." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMIR01/document.
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Depuis 2004, les médias sociaux en ligne ont connu une croissance considérable. Ce développement rapide a eu des effets intéressants pour augmenter la connexionet l'échange d'informations entre les utilisateurs, mais certains effets négatifs sont également apparus, dont le nombre de faux comptes grandissant jour après jour.Les sockpuppets sont les multiples faux comptes créés par un même utilisateur. Ils sont à l'origine de plusieurs types de manipulations comme la création de faux comptes pour louer, défendre ou soutenir une personne ou une organisation, ou pour manipuler l'opinion publique. Dans cette thèse, nous présentons SocksCatch, un processus complet de détection et de groupage des sockpuppets composé de trois phases principales : la première phase a pour objectif la préparation du processus et le pré-traitement des données; la seconde phase a pour objectif la détection des comptes sockpuppets à l'aide d'algorithmes d'apprentissage automatique; la troisième phase a pour objectif le regroupement des comptes sockpuppets créés par un même utilisateur à l'aide d'algorithmes de détection de communautés. Ces phases sont déclinées en trois étapes : une étape "modèle" pour représenter les médias sociaux en ligne, où nous proposons un modèle général de médias sociaux dédié à la détection et au regroupement des sockpuppets ; une étape d'adaptation pour ajuster le processus à un média social spécifique, où nous instancions et évaluons le modèle SocksCatch sur un média social sélectionné ; et une étape en temps réel pour détecter et grouper les sockpuppets en ligne, où SocksCatch est déployé en ligne sur un média social sélectionné. Des expérimentations ont été réalisées sur l'étape d'adaptation en utilisant des données réelles extraites de Wikipédia anglais. Afin de trouver le meilleur algorithme d'apprentissage automatique pour la phase de détection de sockpuppet, les résultats de six algorithmes d'apprentissage automatique sont comparés. En outre, ils sont comparés à la littérature où les résultats de la comparaison montrent que notre proposition améliore la précision de la détection des sockpuppets. De plus, les résultats de cinq algorithmes de détection de communauté sont comparés pour la phase de regroupement de Sockpuppet, afin de trouver le meilleur algorithme de détection de communauté qui sera utilisé en temps réelSince 2004, online social medias have grown hugely. This fast development had interesting effects to increase the connection and information exchange between users, but some negative effects also appeared, including fake accounts number growing day after day. Sockpuppets are multiple fake accounts created by a same user. They are the source of several types of manipulation such as those created to praise, defend or support a person or an organization, or to manipulate public opinion. In this thesis, we present SocksCatch, a complete process to detect and group sockpuppets, which is composed of three main phases: the first phase objective is the process preparation and data pre-processing; the second phase objective is the detection of the sockpuppet accounts using machine learning algorithms; the third phase objective is the grouping of sockpuppet accounts created by a same user using community detection algorithms. These phases are declined in three stages: a model stage to represent online social medias, where we propose a general model of social media dedicated to the detection and grouping of sockpuppets; an adaptation stage to adjust the process to a particular social media, where we instantiate and evaluate the SocksCatch model on a selected social media; and a real-time stage to detect and group the sockpuppets online, where SocksCatch is deployed online on a selected social media. Experiments have been performed on the adaptation stage using real data crawled from English Wikipedia. In order to find the best machine learning algorithm for sockpuppet's detection phase, the results of six machine learning algorithms are compared. In addition, they are compared with the literature, and the results show that our proposition improves the accuracy of the detection of sockpuppets. Furthermore, the results of five community detection algorithms are compared for sockpuppet's grouping phase, in order to find the best community detecton algorithm that will be used in real-time stage
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Wengle, Emil. "Modelling Hierarchical Structures in Networks Using Graph Theory : With Application to Knowledge Networks in Graph Curricula." Thesis, Uppsala universitet, Signaler och system, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-415044.
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Community detection is a topic in network theory that involves assigning labels to nodes based on some distance measure or centrality index. Detecting communities within a network can be useful to perform information condensation. In this thesis we explore how to use the approach for pedagogical purposes, and more precisely to condense and visualise the networks of facts, concepts and procedures (also called Knowledge Components (KCs)) that are offered in higher education programmes. In details, we consider one of the most common quantities used to evaluate the goodness of a community classification, which is the concept of modularity. Detecting communities by computing the maximum possible modularity indexes is indeed usually desired, but this approach is generally unavailable because the associated optimisation problem is NP-complete. This is why practitioners use other algorithms, that instead of computing the optimum they rely on various heuristics to find communities: some use modularity directly, some start from the entire graph and divide it repeatedly, and some contain random elements. This thesis investigates the trade-offs of using different community detection algorithms and variations of the concept of modularity first in general terms, and then for the purpose of identifying communities in knowledge graphs associated to higher education programmes, which can be modelled as directed graphs of KCs. We discover, tweaking and applying these algorithms both on synthetic but also field data that the Louvain algorithm is among the better algorithms of those that we considered, which is mostly thanks to its efficiency. It does not produce a full hierarchy, however, so we recommend Fast Newman if hierarchy is important.
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Kim, Pilho. "E-model event-based graph data model theory and implementation /." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29608.
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Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2010.Committee Chair: Madisetti, Vijay; Committee Member: Jayant, Nikil; Committee Member: Lee, Chin-Hui; Committee Member: Ramachandran, Umakishore; Committee Member: Yalamanchili, Sudhakar. Part of the SMARTech Electronic Thesis and Dissertation Collection.