Дисертації з теми "Random walks on network"
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De, Bacco Caterina. "Decentralized network control, optimization and random walks on networks." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112164/document.
Повний текст джерелаIn the last years several problems been studied at the interface between statistical physics and computer science. The reason being that often these problems can be reinterpreted in the language of physics of disordered systems, where a big number of variables interacts through local fields dependent on the state of the surrounding neighborhood. Among the numerous applications of combinatorial optimisation the optimal routing on communication networks is the subject of the first part of the thesis. We will exploit the cavity method to formulate efficient algorithms of type message-passing and thus solve several variants of the problem through its numerical implementation. At a second stage, we will describe a model to approximate the dynamic version of the cavity method, which allows to decrease the complexity of the problem from exponential to polynomial in time. This will be obtained by using the Matrix Product State formalism of quantum mechanics. Another topic that has attracted much interest in statistical physics of dynamic processes is the random walk on networks. The theory has been developed since many years in the case the underneath topology is a d-dimensional lattice. On the contrary the case of random networks has been tackled only in the past decade, leaving many questions still open for answers. Unravelling several aspects of this topic will be the subject of the second part of the thesis. In particular we will study the average number of distinct sites visited during a random walk and characterize its behaviour as a function of the graph topology. Finally, we will address the rare events statistics associated to random walks on networks by using the large-deviations formalism. Two types of dynamic phase transitions will arise from numerical simulations, unveiling important aspects of these problems. We will conclude outlining the main results of an independent work developed in the context of out-of-equilibrium physics. A solvable system made of two Brownian particles surrounded by a thermal bath will be studied providing details about a bath-mediated interaction arising for the presence of the bath
Maddalena, Daniela. "Stationary states in random walks on networks." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10170/.
Повний текст джерелаZimmermann, Jochen [Verfasser], and Andreas [Akademischer Betreuer] Buchleitner. "Random walks with nonlinear interactions on heterogeneous networks = Random Walk mit nichtlinearen Wechselwirkungen auf heterogenen Netzwerken." Freiburg : Universität, 2015. http://d-nb.info/1123482381/34.
Повний текст джерелаKolgushev, Oleg. "Influence of Underlying Random Walk Types in Population Models on Resulting Social Network Types and Epidemiological Dynamics." Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc955128/.
Повний текст джерелаLinn, Hanna. "Detecting quantum speedup for random walks with artificial neural networks." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-289347.
Повний текст джерелаSlumpvandringar på grafer är essensiella i viktiga algoritmer för att lösa olika problem, till exempel SAT, booleska uppfyllningsproblem (the satisfiability problem). Genom att göra slumpvandringar snabbare går det att förbättra dessa algoritmer. Kvantversionen av slumpvandringar, kvantvandringar, har visats vara snabbare än klassiska slumpvandringar i specifika fall, till exempel på vissa linjära grafer. Det går att analysera, analytiskt eller genom att simulera vandringarna på grafer, när kvantvandringen är snabbare än slumpvandingen. Problem uppstår dock när graferna blir större, har fler noder samt fler kanter. Det finns inga kända generella regler för vad en godtycklig graf, som inte har några explicita symmetrier, borde uppfylla för att främja kvantvandringen. Simuleringar kommer bara besvara frågan för ett enda fall. De kommer inte att ge några generella regler för vilka egenskaper grafer borde ha. Artificiella neuronnät (ANN) har tidigare används som hjälpmedel för att upptäcka när kvantvandringen är snabbare än slumpvandingen på grafer. Då jämförs tiden det tar i genomsnitt att ta sig från startnoden till slutnoden. Dock är det inte säkert att få kvantacceleration för vandringen om initialtillståndet för kvantvandringen är helt i startnoden. I det här projektet undersöker vi om det går att få en större kvantacceleration hos kvantvandringen genom att starta den i superposition med en extra nod. Vi föreslår olika sätt att lägga till den extra noden till grafen och sen väljer vi en för att använda i resen av projektet. De superpositionstillstånd som undersöks är två av stabilisatortillstånden och två magiska tillstång. Valen av dessa tillstånd är inspirerat av Gottesmann- Knill satsen. Enligt satsen så kan en algoritm som startar i ett magiskt tillstånd ha en exponetiell uppsnabbning, men att starta i någon stabilisatortillstånden inte kan ha det. Detta givet att grindarna som används i algoritmen är från Cliffordgruppen samt att alla mätningar är i Paulibasen. I projektet visar vi att det är möjligt att träna en ANN så att den kan klassificera grafer utifrån vilken kvantvandring, med olika initialtillstånd, som var snabbast. Artificiella neuronnätet kan klassificera linjära grafer och slumpmässiga grafer bättre än slumpen. Vi visar också att faltningsnätverk med en djupare arkitektur än tidigare föreslaget för uppgiften är bättre på att klassificera grafer än innan. Våra resultat banar vägen för en automatiserad forskning i nya kvantvandringsbaserade algoritmer.
Lau, Hon Wai. "Random walk in networks : first passage time and speed analysis /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202009%20LAU.
Повний текст джерелаMalmros, Jens. "Studies in respondent-driven sampling : Directed networks, epidemics, and random walks." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-129287.
Повний текст джерелаAt the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: In press. Paper 3: Accepted. Paper 4: Manuscript.
Russo, Elena Tea. "Fluctuation properties in random walks on networks and simple integrate and fire models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/9565/.
Повний текст джерелаXu, Keyulu. "Graph structures, random walks, and all that : learning graphs with jumping knowledge networks." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/121660.
Повний текст джерелаThesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2019
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 51-54).
Graph representation learning aims to extract high-level features from the graph structures and node features, in order to make predictions about the nodes and the graphs. Applications include predicting chemical properties of drugs, community detection in social networks, and modeling interactions in physical systems. Recent deep learning approaches for graph representation learning, namely Graph Neural Networks (GNNs), follow a neighborhood aggregation procedure, where the representation vector of a node is computed by recursively aggregating and transforming feature vectors of its neighboring nodes. We analyze some important properties of these models, and propose a strategy to overcome the limitations. In particular, the range of neighboring nodes that a node's representation draws from strongly depends on the graph structure, analogous to the spread of a random walk. To adapt to local neighborhood properties and tasks, we explore an architecture - jumping knowledge (JK) networks that flexibly leverages, for each node, different neighborhood ranges to enable better structure-aware representation. In a number of experiments on social, bioinformatics and citation networks, we demonstrate that our model achieves state-of-the-art performance. Furthermore, combining the JK framework with models like Graph Convolutional Networks, GraphSAGE and Graph Attention Networks consistently improves those models' performance.
by Keyulu Xu.
S.M.
S.M. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science
Uguccioni, Marco. "Introduzione alla meccanica statistica dei random walk su network." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21027/.
Повний текст джерелаRatner, Michael. "Quantum Walks and Structured Searches on Free Groups and Networks." Diss., Temple University Libraries, 2017. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/442825.
Повний текст джерелаPh.D.
Quantum walks have been utilized by many quantum algorithms which provide improved performance over their classical counterparts. Quantum search algorithms, the quantum analogues of spatial search algorithms, have been studied on a wide variety of structures. We study quantum walks and searches on the Cayley graphs of finitely-generated free groups. Return properties are analyzed via Green’s functions, and quantum searches are examined. Additionally, the stopping times and success rates of quantum searches on random networks are experimentally estimated.
Temple University--Theses
Yuan, Yuchen. "Advanced Visual Computing for Image Saliency Detection." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/17039.
Повний текст джерелаErten, Mehmet Sinan. "Network Based Prioritization of Disease Genes." Cleveland, Ohio : Case Western Reserve University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=case1258743578.
Повний текст джерелаTitle from PDF (viewed on 2010-01-28) Department of Electrical Engineering and Computer Science -- Computer and Information Sciences Includes abstract Includes bibliographical references and appendices Available online via the OhioLINK ETD Center
Battistoni, Luigi. "Sistemi dinamici stocastici su network." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8950/.
Повний текст джерелаNanongkai, Danupon. "Graph and geometric algorithms on distributed networks and databases." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41056.
Повний текст джерелаBagnato, Guilherme de Guzzi. "Análise estrutural de redes complexas modulares por meio de caminhadas auto-excludentes." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/76/76132/tde-21062018-152327/.
Повний текст джерелаThe progress in complex networks research has provided significant understanding of complex systems. A complex network is mathematically modeled by a graph, where each vertex represents a dynamic unit and its interactions are symbolized by groups of edges. To determine the system structural properties, random walks have shown to be a useful tool since they depend only on local information (neighboring vertices). Among them, the selfavoiding walk (SAW) stands out for not visiting vertices that have already been reached, meaning it can record the path that has been travelled. For this reason, SAW has shown better results when compared to non-restricted walkers network exploration methods. However, as SAW is not a Markovian process, it has a great analytical complexity and needs computational simulations to improve its dynamics in different topologies. Even with the analytical complexity, SAW has become a promising tool to identify the community structure. Despite its significance, detecting communities remains an unsolved problem due to its high computational complexity associated to optimization issues and the lack of a formal definition of communities. In this work, we propose a method to identify communities based on SAW to extract community structure of a network through optimization of the modularity score. Combining technical features of this dynamic with principal components analyses, we classify the vertices in groups by using hierarchical agglomerative clustering. To evaluate the performance of this new algorithm, we compare the results with four other popular techniques: Girvan-Newman, Fastgreedy, Walktrap and Infomap, applying the algorithm in two types of synthetic networks and nine different and well known real ones. For the benchmarks, this new technique shows satisfactory results for different combination of parameters as network size, degree distribution and number of communities. As for real networks, our data shows better modularity values when compared to traditional methods, indicating a group distribution most suitable to reality. Furthermore, the algorithm was adapted for general weighted networks and digraphs in addition to metadata incorporated to topological structure, in order to improve the results of groups classifications.
Yorgancioglu, Kaan. "Using Anchor Nodes for Link Prediction." Case Western Reserve University School of Graduate Studies / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=case1578499802599777.
Повний текст джерелаPettinari, Tommaso. "Analisi della dinamica su network." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/24679/.
Повний текст джерелаSinatra, Roberta. "High-order markov chains in complex networks: models and applications." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/935.
Повний текст джерелаDionigi, Pierfrancesco. "A random matrix theory approach to complex networks." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18513/.
Повний текст джерелаPoirel, Christopher L. "Bridging Methodological Gaps in Network-Based Systems Biology." Diss., Virginia Tech, 2013. http://hdl.handle.net/10919/23899.
Повний текст джерелаPh. D.
Daines, Kyle. "Fall Risk Classification for People with Lower Extremity Amputations Using Machine Learning and Smartphone Sensor Features from a 6-Minute Walk Test." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40948.
Повний текст джерелаPettarin, Alberto. "Graph Models of Information Spreading in Wireless Networks." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3422448.
Повний текст джерелаQuesta tesi studia le proprieta' strutturali di alcuni modelli a grafo di reti di agenti autonomi che comunicano via radio per completare un prefissato compito. Reti ad hoc, di sensori e veicolari sono forse gli esempi piu' immediati. Lo scopo di questa tesi e caratterizzare la diffusione dell’infor- mazione in questi modelli a grafo di reti wireless, considerata l’importanza di questo processo come primitiva fondamentale per realizzare protocolli piu' complessi. Gli approcci basati su tecniche combinatorie adottati per l’analisi di sistemi distribuiti “classici”, come le reti P2P o i cluster di calcolo, non possono essere estesi alle reti wireless, per varie ragioni: ad esempio a causa dei vincoli fisici che governano il funzionamento di questi sistemi (interferenza sul canale radio, scarse risorse energetiche/computazionali, ecc.) e per il fatto che la topologia della rete puo' essere ignota in fase di progettazione o puo' evolvere nel tempo. Questa tesi suggerisce come sia possibile affrontare tali problemi tramite l’opportuna definizione e l’analisi rigorosa di modelli a grafo (o processi su grafi) che catturino l’evoluzione e il funzionamento delle reti wireless. Mostriamo come sia possibile applicare quest’approccio a due scenari di riferimento. Innanzitutto studiamo una famiglia di grafi random nota come Bluetooth Topology, che ben rappresenta la connettivita' della rete creata dalla fase di device discovery in protocolli simili al Bluetooth, largamente utilizzati nelle reti wireless. Dal punto di vista formale, la Bluetooth Topology generalizza il ben noto modello Random Geometric Graph, introducendovi una selezione distribuita degli archi. Studiamo l’espansione e il diametro di questi grafi, poiche' quantificano la banda e la latenza della rete. Dimostriamo limiti stretti all’espansione e, sfruttando questa caratterizzazione, diamo dei limiti quasi stretti al diametro. I nostri risultati provano che la Bluetooth Topology presenta lo stesso livello globale di connettivita' del Random Geometric Graph, pur richiedendo molti meno link di comunicazione. Graph, pur richiedendo molti meno link di comunicazione. Motivati dal recente crescente interesse verso i sistemi mobili, nella seconda parte della tesi concentriamo la nostra attenzione sulle dinamiche di disseminazione dell’informazione tra agenti che effettuano random walk su una griglia planare e che comunicano su brevi distanze. Questo scenario puo' essere utilizzato per studiare fenomeni come la diffusione di malattie, dove le infezioni sono il risultato di interazioni locali tra gli agenti. Proviamo che, per un sistema sufficientemente sparso, il tempo di broadcast di un messaggio e indipendente dal raggio di trasmissione, dimostrando che esso e' dominato dal tempo necessario affinche' molti agenti si incontrino. I nostri risultati completano l’analisi, apparsa in lavori precedenti, di sistemi densi, dove viceversa vi e' dipendenza del tempo di broadcast dal raggio di trasmissione. Inoltre le nostre tecniche di analisi possono essere estese a modelli di mobilita'-comunicazione simili, suggerendo alcune interessanti linee di ulteriore ricerca.
Matteuzzi, Tommaso. "Network diffusion methods for omics big bio data analytics and interpretation with application to cancer datasets." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13660/.
Повний текст джерелаDejby, Jesper. "Capturing continuous human movement on a linear network with mobile phone towers." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-136388.
Повний текст джерелаCoskun, Mustafa Coskun. "ALGEBRAIC METHODS FOR LINK PREDICTIONIN VERY LARGE NETWORKS." Case Western Reserve University School of Graduate Studies / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=case1499436242956926.
Повний текст джерелаNykvist, Gustav. "Implementation of a Manycast Protocol in a Partitionable Mobile Ad hoc Network." Thesis, Linköping University, Department of Computer and Information Science, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-20846.
Повний текст джерелаWireless communication has grown very popular, and communication is the key
to success in many situations. However, most of the common technologies today
rely on infrastructure and in disaster situations infrastructure might be lost or
get severely overloaded. This master thesis concerns intermittently connected
mobile ad hoc networks. A network in which the devices may move freely in any
direction and still be able to communicate. To be able to demonstrate a network
protocol called random-walk gossip-based manycast (RWG) my assignment has been
to implement this protocol using off-the-shelf hardware and software.
RWG is a multi-hop and partition-tolerant mobile ad hoc manycast network
protocol. Multi-hop refers to information being able to hop between more than
two nodes in a network and partition-tolerant means that the protocol works even
though a network is partitioned. Manycast means that the information should
be successfully delivered to K of all the potential nodes in the area. The RWG
protocol makes use of four different packet types, request to forward (REQF), ac-
knowledgement (ACK), ok to forward (OKTF) and be silent (BS). The actual data
being sent is carried by REQFs, and is referred to as messages. When a message
is sent it takes what could be described as a random walk among the nodes in the
network, hence the name.
The implementation of the RWG protocol resides in user-space and depends on
the IEEE 802.11b standard and the raw socket that is specified in the BSD socket
API. It is written in C and was developed on a machine running Ubuntu. It runs
on systems that use Linux 2.6 kernels and it supports cross-compiling for ARM
based devices such as the Nokia N810 internet tablet and the Android dev phone
1. To be able to demonstrate the protocol I developed my own client application.
Moreover, an already existing application for Android, Portable Open Search and
Identification Tool (POSIT), was successfully extended to run on top of the RWG
implementation. The extension was developed by people in the POSIT project
and tested in a physical experiment covering five devices.
The report covers the RWG protocol, the system choice, the implementation
and the testing of the implementation.
Forghani, Behrang. "Transformed Random Walks." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32538.
Повний текст джерелаGnacik, Michal. "Quantum random walks." Thesis, Lancaster University, 2014. http://eprints.lancs.ac.uk/69946/.
Повний текст джерелаRamiro-Cid, Victor. "Caractérisation et applications de marches aléatoires temporelles dans les réseaux opportunistes." Thesis, Toulouse, ISAE, 2015. http://www.theses.fr/2015ESAE0023/document.
Повний текст джерелаThe Internet has entirely reshaped the way we communicate and interact with one another. The rapid development of the wireless infrastructure by network providers has being accompanied by an exponential growth in the number of mobile users. However, global Internet access and connectivity still face several challenges: scarce or poor quality connectivity in developing countries or places with limited accessibility, physical obstacles limiting the deployment of wireless networks and natural or man-made disasters. Delay tolerant networks (DTNs) were introduced to deal with environments where interruptions or disruptions of service were expected. Such networks usually lack of end-to-end paths or any infrastructure to help communications. In these networks, mobile nodes may interact using their contacts as a communication opportunity. The store-carry-forward paradigm allows nodes to exploit spatio-temporal paths created by contact opportunities in order to deliver messages over time. Instead we raise the question: can we design a mobile and opportunistic infrastructure that could help deliver messages? In the quest to provide such infrastructure, we study the application of temporal random walks (TRW) over the opportunistic networks. We explore the application and impact of TRW as a minimal and non invasive infrastructure from two points of view: data forwarding and data recollection/transmission
Windisch, David. "Random walks, disconnection and random interlacements /." [S.l.] : [s.n.], 2009. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=18343.
Повний текст джерелаPhetpradap, Parkpoom. "Intersections of random walks." Thesis, University of Bath, 2011. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.548100.
Повний текст джерелаOosthuizen, Joubert. "Random walks on graphs." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/86244.
Повний текст джерелаENGLISH ABSTRACT: We study random walks on nite graphs. The reader is introduced to general Markov chains before we move on more specifically to random walks on graphs. A random walk on a graph is just a Markov chain that is time-reversible. The main parameters we study are the hitting time, commute time and cover time. We nd novel formulas for the cover time of the subdivided star graph and broom graph before looking at the trees with extremal cover times. Lastly we look at a connection between random walks on graphs and electrical networks, where the hitting time between two vertices of a graph is expressed in terms of a weighted sum of e ective resistances. This expression in turn proves useful when we study the cover cost, a parameter related to the cover time.
AFRIKAANSE OPSOMMING: Ons bestudeer toevallige wandelings op eindige gra eke in hierdie tesis. Eers word algemene Markov kettings beskou voordat ons meer spesi ek aanbeweeg na toevallige wandelings op gra eke. 'n Toevallige wandeling is net 'n Markov ketting wat tyd herleibaar is. Die hoof paramaters wat ons bestudeer is die treftyd, pendeltyd en dektyd. Ons vind oorspronklike formules vir die dektyd van die verdeelde stergra ek sowel as die besemgra ek en kyk daarna na die twee bome met uiterste dektye. Laastens kyk ons na 'n verband tussen toevallige wandelings op gra eke en elektriese netwerke, waar die treftyd tussen twee punte op 'n gra ek uitgedruk word in terme van 'n geweegde som van e ektiewe weerstande. Hierdie uitdrukking is op sy beurt weer nuttig wanneer ons die dekkoste bestudeer, waar die dekkoste 'n paramater is wat verwant is aan die dektyd.
Montgomery, Aaron. "Topics in Random Walks." Thesis, University of Oregon, 2013. http://hdl.handle.net/1794/13335.
Повний текст джерелаTouray, Barra. "Energy-efficient routing algorithms for wireless sensor networks." Thesis, Liverpool John Moores University, 2013. http://researchonline.ljmu.ac.uk/4352/.
Повний текст джерелаPowell, Sean K. "A quantitative study of diffusion in quasi-periodic fibre networks and complex porous media." Thesis, Queensland University of Technology, 2016. https://eprints.qut.edu.au/92506/12/92506%28thesis%29.pdf.
Повний текст джерелаBuckley, Stephen Philip. "Problems in random walks in random environments." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:06a12be2-b831-4c2a-87b1-f0abccfb9b8b.
Повний текст джерелаBowditch, Adam. "Biased randomly trapped random walks and applications to random walks on Galton-Watson trees." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/97359/.
Повний текст джерелаNgoc, Anh Do Hoang. "Anomalous diffusion and random walks on random fractals." Doctoral thesis, Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000205.
Повний текст джерелаGabucci, Ilenia. "Random walks classici e quantistici." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/17759/.
Повний текст джерелаCodling, Edward Alexander. "Biased random walks in biology." Thesis, University of Leeds, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275673.
Повний текст джерелаJanse, van Rensburg Esaias Johannes. "Field theory and random walks." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328723.
Повний текст джерелаKazhuthuveettil, Sreedharan Jithin. "Échantillonnage et inférence dans réseaux complexes." Thesis, Université Côte d'Azur (ComUE), 2016. http://www.theses.fr/2016AZUR4121/document.
Повний текст джерелаThe recent emergence of large networks, mainly due to the rise of online social networks, brought out the difficulty to gather a complete picture of a network and it prompted the development of new distributed techniques. In this thesis, we design and analyze algorithms based on random walks and diffusion for sampling, estimation and inference of the network functions, and for approximating the spectrum of graph matrices. The thesis starts with the classical problem of finding the dominant eigenvalues and the eigenvectors of symmetric graph matrices like Laplacian of undirected graphs. Using the fact that the eigenspectrum is associated with a Schrödinger-type differential equation, we develop scalable techniques with diffusion over the graph and with gossiping algorithms. They are also adaptable to a simple algorithm based on quantum computing. Next, we consider sampling and estimation of network functions (sum and average) using random walks on graph. In order to avoid the burn-in time of random walks, with the idea of regeneration at its revisits to a fixed node, we develop an estimator for the aggregate function which is non-asymptotically unbiased and derive an approximation to its Bayesian posterior. An estimator based on reinforcement learning is also developed making use of regeneration. The final part of the thesis deals with the use of extreme value theory to make inference from the stationary samples of the random walks. Extremal events such as first hitting time of a large degree node, order statistics and mean cluster size are well captured in the parameter “extremal index”. We theoretically study and estimate extremal index of different random walk sampling techniques
Dou, Carl C. Z. (Carl Changzhu). "Studies of random walks on groups and random graphs." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/13243.
Повний текст джерелаMa, Qi. "Reinforcement in Biology : Stochastic models of group formation and network construction." Doctoral thesis, Uppsala universitet, Analys och tillämpad matematik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-186989.
Повний текст джерелаBertacchi, D., and Andreas Cap@esi ac at. "Random Walks on Diestel--Leader Graphs." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1004.ps.
Повний текст джерелаDykiel, Patrik. "Asymptotic properties of coalescing random walks." Thesis, Uppsala University, Department of Mathematics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121369.
Повний текст джерелаHe, Mu. "The Torsion Angle of Random Walks." TopSCHOLAR®, 2013. http://digitalcommons.wku.edu/theses/1242.
Повний текст джерелаDeligiannidis, Georgios. "Some results associated with random walks." Thesis, University of Nottingham, 2010. http://eprints.nottingham.ac.uk/13104/.
Повний текст джерелаXu, Chang. "Convex hulls of planar random walks." Thesis, University of Strathclyde, 2017. http://digitool.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=28164.
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