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Dissertations / Theses on the topic 'Spectral graph theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Peng, Richard. "Algorithm Design Using Spectral Graph Theory." Research Showcase @ CMU, 2013. http://repository.cmu.edu/dissertations/277.

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Spectral graph theory is the interplay between linear algebra and combinatorial graph theory. Laplace’s equation and its discrete form, the Laplacian matrix, appear ubiquitously in mathematical physics. Due to the recent discovery of very fast solvers for these equations, they are also becoming increasingly useful in combinatorial optimization, computer vision, computer graphics, and machine learning. In this thesis, we develop highly efficient and parallelizable algorithms for solving linear systems involving graph Laplacian matrices. These solvers can also be extended to symmetric diagonally

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2

Florkowski, Stanley F. "Spectral graph theory of the Hypercube." Thesis, Monterey, Calif. : Naval Postgraduate School, 2008. http://edocs.nps.edu/npspubs/scholarly/theses/2008/Dec/08Dec%5FFlorkowski.pdf.

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Thesis (M.S. in Applied Mathematics)--Naval Postgraduate School, December 2008.<br>Thesis Advisor(s): Rasmussen, Craig W. "December 2008." Description based on title screen as viewed on January 29, 2009. Includes bibliographical references (p. 51-52). Also available in print.

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3

Huang, Peng. "Spectral radius and signless Laplacian spectral radius of k-connected graphs /Huang Peng." HKBU Institutional Repository, 2016. https://repository.hkbu.edu.hk/etd_oa/373.

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The adjacency matrix of a graph is a (0, 1)-matrix indexed by the vertex set of the graph. And the signless Laplacian matrix of a graph is the sum of its adjacency matrix and its diagonal matrix of vertex degrees. The eigenvalues and the signless Laplacian eigenvalues of a graph are the eigenvalues of the adjacency matrix and the signless Laplacian matrix, respectively. These two matrices of a graph have been studied for several decades since they have been applied to many research field, such as computer science, communication network, information science and so on. In this thesis, we study k

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4

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 ma

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Morisi, Rita. "Graph–based techniques and spectral graph theory in control and machine learning." Thesis, IMT Alti Studi Lucca, 2016. http://e-theses.imtlucca.it/188/1/Morisi_phdthesis.pdf.

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Graphs are powerful data structure for representing objects and their relationships. They are extremely useful in the study of dynamical systems, evaluating how different agents interact among each other and behave. An example is represented by the consensus problem where a graph models a set of agents that locally interact and exchange their opinions with the aim of reaching a common opinion (consensus state). At the same time, many learning techniques rely on graphs exploiting their potentialities in modeling the relationships between data and determining additional features relate

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6

Johnson, Jamie L. "Software defined network monitoring scheme using spectral graph theory and phantom nodes." Thesis, Monterey, California: Naval Postgraduate School, 2014. http://hdl.handle.net/10945/43933.

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Approved for public release; distribution is unlimited<br>In this thesis, we propose a new software defined network monitoring scheme that provides the controller with a method to determine network states for the purpose of updating flow rules for network control and management. Network centrality and nodal influence metrics derived from the dual basis concept of the graph theory are used to monitor changes in a network. The proposed scheme uses a phantom node and the concept of a reference node to determine changes in these metrics in order to identify disconnected, congested, underutilized,

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7

Lucas, Claire. "Trois essais sur les relations entre les invariants structuraux des graphes et le spectre du Laplacien sans signe." Phd thesis, Ecole Polytechnique X, 2013. http://pastel.archives-ouvertes.fr/pastel-00956183.

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Le spectre du Laplacien sans signe a fait l'objet de beaucoup d'attention dans la communauté scientifique ces dernières années. La principale raison est l'intuition, basée sur une étude des petits graphes et sur des propriétés valides pour des graphes de toutes tailles, que plus de graphes sont déterminés par le spectre de cette matrice que par celui de la matrice d'adjacence et du Laplacien. Les travaux présentés dans cette thèse ont apporté des éléments nouveaux sur les informations contenues dans le spectre cette matrice. D'une part, on y présente des relations entre les invariants de struc

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8

Ghenciu, Eugen Andrei. "Dimension spectrum and graph directed Markov systems." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5226/.

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In this dissertation we study graph directed Markov systems (GDMS) and limit sets associated with these systems. Given a GDMS S, by the Hausdorff dimension spectrum of S we mean the set of all positive real numbers which are the Hausdorff dimension of the limit set generated by a subsystem of S. We say that S has full Hausdorff dimension spectrum (full HD spectrum), if the dimension spectrum is the interval [0, h], where h is the Hausdorff dimension of the limit set of S. We give necessary conditions for a finitely primitive conformal GDMS to have full HD spectrum. A GDMS is said to be regular

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9

Behjat, Hamid. "Statistical Parametric Mapping of fMRI data using Spectral Graph Wavelets." Thesis, Linköpings universitet, Medicinsk informatik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-81143.

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In typical statistical parametric mapping (SPM) of fMRI data, the functional data are pre-smoothed using a Gaussian kernel to reduce noise at the cost of losing spatial specificity. Wavelet approaches have been incorporated in such analysis by enabling an efficient representation of the underlying brain activity through spatial transformation of the original, un-smoothed data; a successful framework is the wavelet-based statistical parametric mapping (WSPM) which enables integrated wavelet processing and spatial statistical testing. However, in using the conventional wavelets, the functional d

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10

Witt, Walter G. "Quantifying the Structure of Misfolded Proteins Using Graph Theory." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3244.

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The structure of a protein molecule is highly correlated to its function. Some diseases such as cystic fibrosis are the result of a change in the structure of a protein so that this change interferes or inhibits its function. Often these changes in structure are caused by a misfolding of the protein molecule. To assist computational biologists, there is a database of proteins together with their misfolded versions, called decoys, that can be used to test the accuracy of protein structure prediction algorithms. In our work we use a nested graph model to quantify a selected set of proteins that

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11

Pieper, Hannah E. "Comparing Two Thickened Cycles: A Generalization of Spectral Inequalities." Oberlin College Honors Theses / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528367417905844.

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12

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 deve

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Gkantsidis, Christos. "Algorithmic performance of large-scale distributed networks a spectral method approach /." Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-12062005-141254/.

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Thesis (Ph. D.)--Computing, Georgia Institute of Technology, 2006.<br>Mihail, Milena, Committee Chair ; Ammar, Mostafa, Committee Member ; Dovrolis, Constantinos, Committee Member ; Faloutsos, Michalis, Committee Member ; Zegura, Ellen, Committee Member.

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Casaca, Wallace Correa de Oliveira. "Graph Laplacian for spectral clustering and seeded image segmentation." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-24062015-112215/.

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Image segmentation is an essential tool to enhance the ability of computer systems to efficiently perform elementary cognitive tasks such as detection, recognition and tracking. In this thesis we concentrate on the investigation of two fundamental topics in the context of image segmentation: spectral clustering and seeded image segmentation. We introduce two new algorithms for those topics that, in summary, rely on Laplacian-based operators, spectral graph theory, and minimization of energy functionals. The effectiveness of both segmentation algorithms is verified by visually evaluating the re

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Kang, U. "Mining Tera-Scale Graphs: Theory, Engineering and Discoveries." Research Showcase @ CMU, 2012. http://repository.cmu.edu/dissertations/160.

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How do we find patterns and anomalies, on graphs with billions of nodes and edges, which do not fit in memory? How to use parallelism for such Tera- or Peta-scale graphs? In this thesis, we propose PEGASUS, a large scale graph mining system implemented on the top of the HADOOP platform, the open source version of MAPREDUCE. PEGASUS includes algorithms which help us spot patterns and anomalous behaviors in large graphs. PEGASUS enables the structure analysis on large graphs. We unify many different structure analysis algorithms, including the analysis on connected components, PageRank, and radi

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Masum, Mohammad. "Vertex Weighted Spectral Clustering." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3266.

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Spectral clustering is often used to partition a data set into a specified number of clusters. Both the unweighted and the vertex-weighted approaches use eigenvectors of the Laplacian matrix of a graph. Our focus is on using vertex-weighted methods to refine clustering of observations. An eigenvector corresponding with the second smallest eigenvalue of the Laplacian matrix of a graph is called a Fiedler vector. Coefficients of a Fiedler vector are used to partition vertices of a given graph into two clusters. A vertex of a graph is classified as unassociated if the Fiedler coefficient of the v

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Chakeri, Alireza. "Scalable Unsupervised Learning with Game Theory." Scholar Commons, 2017. http://scholarcommons.usf.edu/etd/6616.

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Recently dominant sets, a generalization of the notion of the maximal clique to edge-weighted graphs, have proven to be an effective tool for unsupervised learning and have found applications in different domains. Although, they were initially established using optimization and graph theory concepts, recent work has shown fascinating connections with evolutionary game theory, that leads to the clustering game framework. However, considering size of today's data sets, existing methods need to be modified in order to handle massive data. Hence, in this research work, first we address the limitat

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Pham, Hong Nhung. "Graph-based registration for biomedical images." Thesis, Poitiers, 2019. http://www.theses.fr/2019POIT2258/document.

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Le contexte de cette thèse est le recalage d'images endomicroscopiques. Le microendoscope multiphotonique fournit différentes trajectoires de balayage que nous considérons dans ce travail. Nous proposons d'abord une méthode de recalage non rigide dont l'estimation du mouvement est transformée en un problème d'appariement d'attributs dans le cadre des Log-Demons et d'ondelettes sur graphes. Nous étudions les ondelettes de graphe spectral (SGW) pour capturer les formes des images, en effet, la représentation des données sur les graphes est plus adaptée aux données avec des structures complexes.

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Hamidouche, Mounia. "Analyse spectrale de graphes géométriques aléatoires." Thesis, Université Côte d'Azur, 2020. http://www.theses.fr/2020COAZ4019.

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Nous étudions le graphe géométrique aléatoire (GGA) afin d'aborder des problèmes clés dans les réseaux complexes. Un GAA est construit en distribuant uniformément n nœuds sur un tore de dimension d et en connectant deux nœuds si leur distance ne dépasse pas un seuil. Trois régimes pour GGA présentent un intérêt particulier. Le régime de connectivité dans lequel le degré moyen d'un nœud a_n croît de manière logarithmique avec n ou plus vite. Le régime dense dans lequel a_n est linéaire avec n. Le régime thermodynamique dans lequel a_n est une constante. On étudie le spectre du Laplacien normali

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20

Gkantsidis, Christos. "Algorithmic performance of large-scale distributed networks: A spectral method approach." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/10420.

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Complex networks like the Internet, peer-to-peer systems, and emerging sensor and ad-hoc networks are large distributed decentralized communication systems arising repeatedly in today's technology. In such networks it is critical to characterize network performance as the size of the network scales. The focus of my work is to relate basic network performance metrics to structural characteristics of underlying network topologies, and to develop protocols that reinforce and exploit desired structural characteristics. For the case of the Internet at the Autonomous System level, we relate the grap

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21

Parra, Vogel Daniel Alejandro. "Théorie spectrale et de la diffusion pour les réseaux cristallins." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1001/document.

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Dans cette thèse les théories spectrale et de la diffusion sur des graphes périodiques sont investigué. Le chapitre 1 présente des résultats de préservation de la nature fine du spectre pour des opérateurs de Schrödinger perturbés dans le cadre de cristaux topologiques perturbés. Le chapitre 2 étend ses résultats à des opérateurs du première ordre connu sous le nom de opérateurs de Gauss-Bonnet discrets. Finalement, le chapitre 3 présente des résultats de continuité de composantes spectrales pour des familles de opérateurs de Schrödinger magnétiques sur Z^d<br>In this thesis we investigate the

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22

Farina, Sofia. "A physical interpretation of network laplacian: role of perturbations and masses." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16345/.

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Il presente elaborato si propone di studiare il laplaciano associato ad un network, oggetto di interesse sia perchè dalla sua analisi spettrale è possibile ricavare delle tecniche di ricostruzione e rappresentazione della rete efficienti e al contempo semplici da implementare, ma anche per la sua possibile intepretazione fisica. Il lavoro si struttura in due sezioni: la prima, riguardante l'analisi numerica dello spettro del laplaciano di un network con particolari proprietà di simmetria e regolarità anche in seguito alla sua perturbazione in termini di rimozone casuale di nodi e di link; la

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23

Kruzick, Stephen M. "Optimal Graph Filter Design for Large-Scale Random Networks." Research Showcase @ CMU, 2018. http://repository.cmu.edu/dissertations/1165.

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Graph signal processing analyzes signals supported on the nodes of a network with respect to a shift operator matrix that conforms to the graph structure. For shift-invariant graph filters, which are polynomial functions of the shift matrix, the filter response is defined by the value of the filter polynomial at the shift matrix eigenvalues. Thus, information regarding the spectral decomposition of the shift matrix plays an important role in filter design. However, under stochastic conditions leading to uncertain network structure, the eigenvalues of the shift matrix become random, complicatin

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Wappler, Markus. "On Graph Embeddings and a new Minor Monotone Graph Parameter associated with the Algebraic Connectivity of a Graph." Doctoral thesis, Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-115518.

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We consider the problem of maximizing the second smallest eigenvalue of the weighted Laplacian of a (simple) graph over all nonnegative edge weightings with bounded total weight. We generalize this problem by introducing node significances and edge lengths. We give a formulation of this generalized problem as a semidefinite program. The dual program can be equivalently written as embedding problem. This is fifinding an embedding of the n nodes of the graph in n-space so that their barycenter is at the origin, the distance between adjacent nodes is bounded by the respective edge length, and the

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Erdem, Ozge. "Computation And Analysis Of Spectra Of Large Undirected Networks." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612233/index.pdf.

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Many interacting complex systems in biology, in physics, in technology and social systems, can be represented in a form of large networks. These large networks are mathematically represented by graphs. A graph is represented usually by the adjacency or the Laplacian matrix. Important features of the underlying structure and dynamics of them can be extracted from the analysis of the spectrum of the graphs. Spectral analysis of the so called normalized Laplacian of large networks became popular in the recent years. The Laplacian matrices of the empirical networks are in form of unstructured larg

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Reiß, Susanna. "Optimizing Extremal Eigenvalues of Weighted Graph Laplacians and Associated Graph Realizations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-93599.

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This thesis deals with optimizing extremal eigenvalues of weighted graph Laplacian matrices. In general, the Laplacian matrix of a (weighted) graph is of particular importance in spectral graph theory and combinatorial optimization (e.g., graph partition like max-cut and graph bipartition). Especially the pioneering work of M. Fiedler investigates extremal eigenvalues of weighted graph Laplacians and provides close connections to the node- and edge-connectivity of a graph. Motivated by Fiedler, Göring et al. were interested in further connections between structural properties of the graph and

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Sariaydin, Ayse. "Computation And Analysis Of Spectra Of Large Networks With Directed Graphs." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612249/index.pdf.

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Analysis of large networks in biology, science, technology and social systems have become very popular recently. These networks are mathematically represented as graphs. The task is then to extract relevant qualitative information about the empirical networks from the analysis of these graphs. It was found that a graph can be conveniently represented by the spectrum of a suitable difference operator, the normalized graph Laplacian, which underlies diffusions and random walks on graphs. When applied to large networks, this requires computation of the spectrum of large matrices. The normalized

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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 tra

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Goddet, Étienne. "Analyse spectrale et surveillance des réseaux maillés de retour de courant pour l'aéronautique." Thesis, Université Grenoble Alpes (ComUE), 2017. http://www.theses.fr/2017GREAT099/document.

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Depuis plusieurs années, l’aéronautique est confrontée à une mutation majeure due à l’émergence des matériaux composites. Ce changement, justifié par les excellentes propriétés mécaniques des matériaux composites et un gain de masse important, implique une révision complète des réseaux de retour de courant. Pour faciliter cette révision, la thèse propose de lier au travers de l’analyse spectrale des graphes les performances des réseaux électriques avec leur topologie. Deux objectifs couplés sont étudiés : un dimensionnement topologique visant un bon compromis masse/robustesse et une stratégie

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Behmo, Régis. "Visual feature graphs and image recognition." Phd thesis, Ecole Centrale Paris, 2010. http://tel.archives-ouvertes.fr/tel-00545419.

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La problèmatique dont nous nous occupons dans cette thèse est la classification automatique d'images bidimensionnelles, ainsi que la détection d'objets génériques dans des images. Les avancées de ce champ de recherche contribuent à l'élaboration de systèmes intelligents, tels que des robots autonomes et la création d'un web sémantique. Dans ce contexte, la conception de représentations d'images et de classificateurs appropriés constituent des problèmes ambitieux. Notre travail de recherche fournit des solutions à ces deux problèmes, que sont la représentation et la classification d'images. Afi

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Braida, Arthur. "Analog Quantum Computing for NP-Hard Combinatorial Graph Problems." Electronic Thesis or Diss., Orléans, 2024. http://www.theses.fr/2024ORLE1017.

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L'objectif principal de cette thèse est de fournir un éclairage théorique de la complexité du calcul quantique en temps continu (QA et AQC), de la compréhension du phénomène physique (AC) qui conduit à l'échec de l'AQC jusqu'à des preuves de performance de QA en temps court et constant. Pour atteindre cet objectif, nous utilisons différents outils analytiques empruntés à la physique théorique, comme l'analyse perturbative des systèmes quantiques et la borne de Lieb-Robinson sur la vitesse de corrélation dans les systèmes quantiques. La manipulation des graphes et la théorie spectrale des graph

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Samavat, Reza. "Mean Eigenvalue Counting Function Bound for Laplacians on Random Networks." Doctoral thesis, Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-159578.

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Spectral graph theory widely increases the interests in not only discovering new properties of well known graphs but also proving the well known properties for the new type of graphs. In fact all spectral properties of proverbial graphs are not acknowledged to us and in other hand due to the structure of nature, new classes of graphs are required to explain the phenomena around us and the spectral properties of these graphs can tell us more about the structure of them. These both themes are the body of our work here. We introduce here three models of random graphs and show that the eigenvalue

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Raak, Fredrik. "Investigation of Power Grid Islanding Based on Nonlinear Koopman Modes." Thesis, KTH, Elektriska energisystem, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-136834.

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To view the electricity supply in our society as just sockets mountedin our walls with a constant voltage output is far from the truth. Inreality, the power system supplying the electricity or the grid, is themost complex man-made dynamical system there is. It demands severecontrol and safety measures to ensure a reliable supply of electric power.Throughout the world, incidents of widespread power grid failures havebeen continuously reported. The state where electricity delivery to customersis terminated by a disturbance is called a blackout. From a stateof seemingly stable operating condition

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Balestrini, Robinson Santiago. "A modeling process to understand complex system architectures." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29621.

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Thesis (Ph.D)--Aerospace Engineering, Georgia Institute of Technology, 2010.<br>Committee Chair: Mavris, Dimitri; Committee Member: Bishop, Carlee; Committee Member: German, Brian; Committee Member: Nixon, Janel; Committee Member: Schrage, Daniel. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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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

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Amaro, Bruno Dias 1984. "A soma dos maiores autovalores da matriz laplaciana sem sinal em famílias de grafos." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306808.

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Orientadores: Carlile Campos Lavor, Leonardo Silva de Lima<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T08:31:47Z (GMT). No. of bitstreams: 1 Amaro_BrunoDias_D.pdf: 1369520 bytes, checksum: a36663d5fd23193d66bb22c83cb932aa (MD5) Previous issue date: 2014<br>Resumo: A Teoria Espectral de Grafos é um ramo da Matemática Discreta que se preocupa com a relação entre as propriedades algébricas do espectro de certas matrizes associadas a grafos, como a matriz de adjacência, laplaciana

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Oliveira, Alessandro Bof de. "Descritor de forma 2D baseado em redes complexas e teoria espectral de grafos." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/134397.

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A identificação de formas apresenta inúmeras aplicações na área de visão computacional, pois representa uma poderosa ferramenta para analisar as características de um objeto. Dentre as aplicações, podemos citar como exemplos a interação entre humanos e robôs, com a identificação de ações e comandos, e a análise de comportamento para vigilância com a biometria não invasiva. Em nosso trabalho nós desenvolvemos um novo descritor de formas 2D baseado na utilização de redes complexas e teoria espectral de grafos. O contorno da forma de um objeto é representado por uma rede complexa, onde cada ponto

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Kadavankandy, Arun. "L’analyse spectrale des graphes aléatoires et son application au groupement et l’échantillonnage." Thesis, Université Côte d'Azur (ComUE), 2017. http://www.theses.fr/2017AZUR4059/document.

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Dans cette thèse, nous étudions les graphes aléatoires en utilisant des outils de la théorie des matrices aléatoires et l’analyse probabilistique afin de résoudre des problèmes clefs dans le domaine des réseaux complexes et Big Data. Le premier problème qu’on considère est de détecter un sous graphe Erdős–Rényi G(m,p) plante dans un graphe Erdős–Rényi G(n,q). Nous dérivons les distributions d’une statistique basée sur les propriétés spectrales d’une matrice définie du graphe. Ensuite, nous considérons le problème de la récupération des sommets du sous graphe en présence de l’information supplé

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Akkouche, Sofiane. "Sur la theorie spectrale des opérateurs de Schrödinger discrets." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14098/document.

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Cette thèse traite de la théorie spectrale des opérateurs de Schrödinger discrets H(λ) := - Δ + b sur Zd et plus généralement sur des graphes pondérés infinis. Plus précisément, nous étudions le comportement des fonctions spectrales qui représentent les bornes du spectre de ces opérateurs. Un des principaux résultats est l'obtention d'une condition nécessaire et suffisante sur le potentiel b pour que le bas du spectre soit strictement positif. L'étude du haut du spectre est également considérée.Nous étudions tout d'abord ces questions pour les opérateurs de Schrödinger discrets sur Zd. La régu

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Passey, Jr David Joseph. "Growing Complex Networks for Better Learning of Chaotic Dynamical Systems." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8146.

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This thesis advances the theory of network specialization by characterizing the effect of network specialization on the eigenvectors of a network. We prove and provide explicit formulas for the eigenvectors of specialized graphs based on the eigenvectors of their parent graphs. The second portion of this thesis applies network specialization to learning problems. Our work focuses on training reservoir computers to mimic the Lorentz equations. We experiment with random graph, preferential attachment and small world topologies and demonstrate that the random removal of directed edges increases p

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Ferreira, Anselmo Castelo Branco. "Um estudo comparativo de segmentação de imagens por aplicações do corte normalizado em grafos." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/267798.

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Orientador: Marco Antonio Garcia de Carvalho<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Tecnologia<br>Made available in DSpace on 2018-08-17T11:47:27Z (GMT). No. of bitstreams: 1 Ferreira_AnselmoCasteloBranco_M.pdf: 7338510 bytes, checksum: 593cb683d0380e0c894f0147a4129c77 (MD5) Previous issue date: 2011<br>Resumo: O particionamento de grafos tem sido amplamente utilizado como meio de segmentação de imagens. Uma das formas de particionar grafos é por meio de uma técnica conhecida como Corte Normalizado, que analisa os autovetores da matriz laplaciana de um gr

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Liu, Chenang. "Smart Additive Manufacturing Using Advanced Data Analytics and Closed Loop Control." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/91900.

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Additive manufacturing (AM) is a powerful emerging technology for fabrication of components with complex geometries using a variety of materials. However, despite promising potential, due to the complexity of the process dynamics, how to ensure product quality and consistency of AM parts efficiently during the process still remains challenging. Therefore, the objective of this dissertation is to develop effective methodologies for online automatic quality monitoring and improvement, i.e., to build a basis for smart additive manufacturing. The fast-growing sensor technology can easily generat

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Gustavsson, Hanna. "Clustering Based Outlier Detection for Improved Situation Awareness within Air Traffic Control." Thesis, KTH, Optimeringslära och systemteori, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-264215.

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The aim of this thesis is to examine clustering based outlier detection algorithms on their ability to detect abnormal events in flight traffic. A nominal model is trained on a data-set containing only flights which are labeled as normal. A detection scoring function based on the nominal model is used to decide if a new and in forehand unseen data-point behaves like the nominal model or not. Due to the unknown structure of the data-set three different clustering algorithms are examined for training the nominal model, K-means, Gaussian Mixture Model and Spectral Clustering. Depending on the nom

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Male, Camille. "Forte et fausse libertés asymptotiques de grandes matrices aléatoires." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00673551.

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Cette thèse s'inscrit dans la théorie des matrices aléatoires, à l'intersection avec la théorie des probabilités libres et des algèbres d'opérateurs. Elle s'insère dans une démarche générale qui a fait ses preuves ces dernières décennies : importer les techniques et les concepts de la théorie des probabilités non commutatives pour l'étude du spectre de grandes matrices aléatoires. On s'intéresse ici à des généralisations du théorème de liberté asymptotique de Voiculescu. Dans les Chapitres 1 et 2, nous montrons des résultats de liberté asymptotique forte pour des matrices gaussiennes, unitaire

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Humari, Juan Herbert Chuctaya. "Estudo do espectro Laplaciano na categorização de imagens." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/59/59135/tde-04072016-091446/.

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Uma imagem engloba informação que precisa ser organizada para interpretar e compreender seu conteúdo. Existem diversas técnicas computacionais para extrair a principal informação de uma imagem e podem ser divididas em três áreas: análise de cor, textura e forma. Uma das principais delas é a análise de forma, por descrever características de objetos baseadas em seus pontos fronteira. Propomos um método de caracterização de imagens, por meio da análise de forma, baseada nas propriedades espectrais do laplaciano em grafos. O procedimento construiu grafos G baseados nos pontos fronteira do objeto,

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Al-Doujan, Fawwaz Awwad. "Spectra of graphs." Thesis, University of East Anglia, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306195.

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Parmentier, Frédéric. "Modélisation et prédiction de la dynamique moléculaire de la maladie de Huntington par la théorie des graphes au travers des modèles et des espèces, et priorisation de cibles thérapeutiques." Thesis, Sorbonne Paris Cité, 2015. http://www.theses.fr/2015PA05T030.

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La maladie de Huntington est une maladie neurodégénérative héréditaire qui est devenue un modèle d'étude pour comprendre la physiopathologie des maladies du cerveau associées à la production de protéines mal conformées et à la neurodégénérescence. Bien que plusieurs mécanismes aient été mis en avant pour cette maladie, dont plusieurs seraient aussi impliqués dans des pathologies plus fréquentes comme la maladie d’Alzheimer ou la maladie de Parkinson, nous ne savons toujours pas quels sont les mécanismes ou les profils moléculaires qui déterminent fondamentalement la dynamique des processus de

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Li, Yuemeng. "Spectral Analysis of Directed Graphs using Matrix Perturbation Theory." Thesis, The University of North Carolina at Charlotte, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10618933.

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<p> The spectral space of the adjacency matrix contains important structural information of a given network (graph), where such information can be leveraged in developing a variety of algorithms in applications such as graph partition, structural hierarchy discovery, and anomaly detection. Although many prominent works have laid the foundation for studying the graph spectra, it is still challenging to analyze the spectral space properties for directed graphs due to possible complex valued decompositions. Matrix factorization techniques such as Laplacian and normalized Laplacian have been widel

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Saade, Alaa. "Spectral inference methods on sparse graphs : theory and applications." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEE024/document.

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Face au déluge actuel de données principalement non structurées, les graphes ont démontré, dans une variété de domaines scientifiques, leur importance croissante comme language abstrait pour décrire des interactions complexes entre des objets complexes. L’un des principaux défis posés par l’étude de ces réseaux est l’inférence de propriétés macroscopiques à grande échelle, affectant un grand nombre d’objets ou d’agents, sur la seule base des interactions microscopiquesqu’entretiennent leurs constituants élémentaires. La physique statistique, créée précisément dans le but d’obtenir les lois mac

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Ong, Beng Seong. "Spectral problems of optical waveguides and quantum graphs." Texas A&M University, 2006. http://hdl.handle.net/1969.1/4352.

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In this dissertation, we consider some spectral problems of optical waveguide and quantum graph theories. We study spectral problems that arise when considerating optical waveguides in photonic band-gap (PBG) materials. Specifically, we address the issue of the existence of modes guided by linear defects in photonic crystals. Such modes can be created for frequencies in the spectral gaps of the bulk material and thus are evanescent in the bulk (i.e., confined to the guide). In the quantum graph part we prove the validity of the limiting absorption principle for finite graphs with infinite lead

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