2026-09-20T05:00:57Zhttps://dspace.mit.edu/server/oai/request

oai:dspace.mit.edu:1721.1/458732022-01-13T07:54:29Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022

George C. Verghese. Preciado, Víctor Manuel Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2009-06-30T16:29:49Z 2009-06-30T16:29:49Z 2008 2008 http://hdl.handle.net/1721.1/45873 320108817 Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008. Includes bibliographical references (p. 179-196). Research on large-scale complex networks has important applications in diverse systems of current interest, including the Internet, the World-Wide Web, social, biological, and chemical networks. The growing availability of massive databases, computing facilities, and reliable data analysis tools has provided a powerful framework to explore structural properties of such real-world networks. However, one cannot efficiently retrieve and store the exact or full topology for many large-scale networks. As an alternative, several stochastic network models have been proposed that attempt to capture essential characteristics of such complex topologies. Network researchers then use these stochastic models to generate topologies similar to the complex network of interest and use these topologies to test, for example, the behavior of dynamical processes in the network. In general, the topological properties of a network are not directly evident in the behavior of dynamical processes running on it. On the other hand, the eigenvalue spectra of certain matricial representations of the network topology do relate quite directly to the behavior of many dynamical processes of interest, such as random walks, Markov processes, virus/rumor spreading, or synchronization of oscillators in a network. This thesis studies spectral properties of popular stochastic network models proposed in recent years. In particular, we develop several methods to determine or estimate the spectral moments of these models. We also present a variety of techniques to extract relevant spectral information from a finite sequence of spectral moments. A range of numerical examples throughout the thesis confirms the efficacy of our approach. Our ultimate objective is to use such results to understand and predict the behavior of dynamical processes taking place in large-scale networks. by Víctor Manuel Preciado. Ph.D. 196 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. Spectral analysis for stochastic models of large-scale complex dynamical networks Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="bdb778ea-baf2-4daf-ba9a-3e1b43bc66f2"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Spectral analysis for stochastic models of large-scale complex dynamical networks</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2008</PublicationDate> <Authors> <Author> <DisplayName>Preciado, Víctor Manuel</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <Abstract>Research on large-scale complex networks has important applications in diverse systems of current interest, including the Internet, the World-Wide Web, social, biological, and chemical networks. The growing availability of massive databases, computing facilities, and reliable data analysis tools has provided a powerful framework to explore structural properties of such real-world networks. However, one cannot efficiently retrieve and store the exact or full topology for many large-scale networks. As an alternative, several stochastic network models have been proposed that attempt to capture essential characteristics of such complex topologies. Network researchers then use these stochastic models to generate topologies similar to the complex network of interest and use these topologies to test, for example, the behavior of dynamical processes in the network. In general, the topological properties of a network are not directly evident in the behavior of dynamical processes running on it. On the other hand, the eigenvalue spectra of certain matricial representations of the network topology do relate quite directly to the behavior of many dynamical processes of interest, such as random walks, Markov processes, virus/rumor spreading, or synchronization of oscillators in a network. This thesis studies spectral properties of popular stochastic network models proposed in recent years. In particular, we develop several methods to determine or estimate the spectral moments of these models. We also present a variety of techniques to extract relevant spectral information from a finite sequence of spectral moments. A range of numerical examples throughout the thesis confirms the efficacy of our approach. Our ultimate objective is to use such results to understand and predict the behavior of dynamical processes taking place in large-scale networks.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>