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Dissertations / Theses on the topic 'Random walk'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Renlund, Henrik. "Reinforced Random Walk." Thesis, Uppsala University, Department of Mathematics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121389.

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2

Yip, Siu Kwan. "On the Pfaffian property of annihilating random walk and coalescing random walk." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/63894/.

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In this thesis we are to investigate two discrete interacting particle systems, namely annihilating random walk and coalescing random walk. By mapping the annihilating random walk to Glauber model and employing empty interval method respectively, we prove there is a similar structure behind them albeit their apparent differences, that is, they are both Pfaffian point process under a special initial condition. Then we extend the result to investigate whether the Pfaffian property preserves in the case of multi-time correlation function, which is called extended Pfaffian property. And we also in

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3

nl, jvdberg@cwi. "Randomly Coalescing Random Walk in Dimension $ge$ 3." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1051.ps.

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4

Lo, Chak Hei. "On some random walk problems." Thesis, Durham University, 2017. http://etheses.dur.ac.uk/12498/.

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We consider several random walk related problems in this thesis. In the first part, we study a Markov chain on R₊ x S, where R₊ is the non-negative real numbers and S is a finite set, in which when the R₊-coordinate is large, the S-coordinate of the process is approximately Markov with stationary distribution πi on S. Denoting by μi(x) the mean drift of the R₊-coordinate of the process at (x,i) Ε R₊ x S, we give an exhaustive recurrence classification in the case where Σiπiμi(x) → 0, which is the critical regime for the recurrence-transience phase transition. If μi(x) → 0 for all i, it is natu

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5

Zhao, Kai. "QUANTUM RANDOM WALK ON FRACTALS." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/490714.

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Mathematics<br>Ph.D.<br>Quantum walks are the quantum mechanical analogue of classical random walks. Discrete-time quantum walks have been introduced and studied mostly on the line Z or higher dimensional space Z d but rarely defined on graphs with fractal dimensions because the coin operator depends on the position and the Fourier transform on the fractals is not defined. Inspired by its nature of classical walks, different quantum walks will be defined by choosing different shift and coin operators. When the coin operator is uniform, the results of classical walks will be obtained upon measu

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6

Zhang, Zhihan. "Random walk on simplicial complexes." Electronic Thesis or Diss., université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM010.

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La notion de laplacien d’un graphe peut être généralisée aux complexes simpliciaux et aux hypergraphes. Cette notion contient des informations sur la topologie de ces structures. Dans la première partie de cette thèse,nous définissons une nouvelle chaîne de Markov sur les complexes simpliciaux. Pour un degré donné k de simplexes, l’espace d’états n’est pas les k-simplexes comme dans les articles précédents sur ce sujet mais plutôt l’ensemble des k-chaines ou k-co-chaines. Ce nouveau cadre est la généralisation naturelle sur les chaînes de Markov canoniques sur des graphes. Nous montrons que le

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7

Shiraishi, Daisuke. "Random walk on non-intersecting two-sided random walk trace is subdiffusive in low dimensions." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157839.

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8

Phetpradap, Parkpoom. "Intersections of random walks." Thesis, University of Bath, 2011. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.548100.

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We study the large deviation behaviour of simple random walks in dimension three or more in this thesis. The first part of the thesis concerns the number of lattice sites visited by the random walk. We call this the range of the random walk. We derive a large deviation principle for the probability that the range of simple random walk deviates from its mean. Our result describes the behaviour for deviation below the typical value. This is a result analogous to that obtained by van den Berg, Bolthausen, and den Hollander for the volume of the Wiener sausage. In the second part of the thesis, we

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9

Bui, Hoai Thang Computer Science &amp Engineering Faculty of Engineering UNSW. "Guided random-walk based model checking." Awarded by:University of New South Wales. Computer Science & Engineering, 2009. http://handle.unsw.edu.au/1959.4/44829.

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The ever increasing use of computer systems in society brings emergent challenges to companies and system designers. The reliability of software and hardware can be financially critical, and lives can depend on it. The growth in size and complexity of software, and increasing concurrency, compounds the problem. The potential for errors is greater than ever before, and the stakes are higher than ever before. Formal methods, particularly model checking, is an approach that attempts to prove mathematically that a model of the behaviour of a product is correct with respect to certain properties. C

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10

Thomson, D. J. "Random walk models of turbulent dispersion." Thesis, Brunel University, 1988. http://bura.brunel.ac.uk/handle/2438/5549.

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An understanding of the dispersion of contaminants in turbulent flows is important in many fields ranging from air pollution to chemical engineering, and random walk models provide one approach to understanding and calculating aspects of dispersion. Two types of random walk model are investigated in this thesis. The first type, so-called "one-particle models", are capable of predicting only mean concentrations while the second type, "two-particle models", are able to give some information on the fluctuations in concentration as well. Many different one-particle random walk models have been pro

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11

Zimmermann, 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.

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12

Stewart, Jeffrey A. D. "The random-walk model and the distribution of latencies, a test of the random-walk theory of decision." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0012/MQ31254.pdf.

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13

Antal, Peter. "Trapping problems for the simple random walk /." [S.l.] : [s.n.], 1994. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10759.

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14

Li, Dan. "Shortest paths through a reinforced random walk." Thesis, Uppsala universitet, Analys och tillämpad matematik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-153802.

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15

Helmuth, Tyler. "Heaps, graphical models, and random walk representations." Thesis, University of British Columbia, 2014. http://hdl.handle.net/2429/51774.

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Spin systems such as the Ising model are central topics in statistical mechanics and probability theory. In the late 1960s Symanzik made the important discovery that properties of spin systems could be expressed in terms of the behaviour of random walks. This thesis contributes to the understanding of these connections by developing and analyzing random walk representations of graphical models arising in statistical mechanics. Concretely, the results of this thesis can be divided into two parts. The first part is a lace expansion analysis of a model called loop-weighted walk. Loop-weighted wal

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16

Luhar, Ashok Kumar. "Random walk modelling of air pollution dispersion." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387006.

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17

Allen, Andrew. "A Random Walk Version of Robbins' Problem." Thesis, University of North Texas, 2018. https://digital.library.unt.edu/ark:/67531/metadc1404568/.

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Robbins' problem is an optimal stopping problem where one seeks to minimize the expected rank of their observations among all observations. We examine random walk analogs to Robbins' problem in both discrete and continuous time. In discrete time, we consider full information and relative ranks versions of this problem. For three step walks, we give the optimal stopping rule and the expected rank for both versions. We also give asymptotic upper bounds for the expected rank in discrete time. Finally, we give upper and lower bounds for the expected rank in continuous time, and we show that the ex

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18

Ampuero, Fernanda. "Networks: a random walk in degree space." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/100/100132/tde-25072018-200138/.

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The present work aims to contribute to the study of networks by mapping the temporal evolution of the degree to a random walk in degree space. We analyzed how and when the degree approximates a pre-established value through a parallel with the first-passage problem of random walks. The mean time for the first-passage was calculated for the dynamical versions the Watts-Strogatz and Erdos-Renyi models. We also analyzed the degree variance for the random recursive tree and Barabasi-Albert models<br>O presente trabalho visa contribuir com a pesquisa na área de redes através do mapeamento da evoluç

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19

Sinibaldi, Alessandro. "Quantum Random Walk e localizzazione di Anderson." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23647/.

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I due nuclei tematici principali del presente elaborato sono il modello del Quantum Random Walk (QRW) e il fenomeno della localizzazione di Anderson, i quali vengono prima trattati separatamente nei loro aspetti più rilevanti e in seguito ne viene esaminata la relazione reciproca. In particolare, dopo una breve introduzione sul Random Walk classico, si espone la formalizzazione teorica del QRW e si procede ad un'analisi dettagliata della distribuzione di probabilità del processo, con maggiore attenzione rivolta al QRW di Hadamard. La localizzazione di Anderson viene illustrata a partire dal mo

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20

Celikkanat, Abdulkadir. "Graph Representation Learning with Random Walk Diffusions." Electronic Thesis or Diss., université Paris-Saclay, 2021. http://www.theses.fr/2021UPASG030.

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L'objectif principal de l'Apprentissage de Représentations sur Graphes est de plonger les nœuds dans un espace vectoriel de petite dimension. Dans cette thèse, nous abordons plusieurs enjeux dans le domaine. Tout d'abord, nous étudions comment exploiter l'existence de communautés structurelles locales inhérentes aux graphes tout en apprenant les représentations. Nous apprenons des représentations améliorées de la communauté en combinant les informations latentes avec les représentations. De plus, nous nous concentrons sur l'expressivité des représentations. Nous mettons l'accent sur les distri

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21

Franke, Markus. "An update algorithm for restricted random walk clusters." Karlsruhe : Univ.-Verl. Karlsruhe, 2007. http://www.uvka.de/univerlag/volltexte/2007/273/.

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22

Gubiec, Tomasz, and Ryszard Kutner. "Two-step memory within Continuous Time Random Walk." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-183316.

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23

Sani, Aliakbar Rahimzadeh. "Martingale convergence in the multitype branching random walk." Thesis, University of Sheffield, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266032.

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24

Gonçalves, Antônio Renato Cruz. "Problema de perseguição-evasão baseado em random walk." Universidade Federal de Sergipe, 2016. https://ri.ufs.br/handle/riufs/5023.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>One of the greatest reasons to use robotics rather than human beings is to avoid hazardous situations such as activities related to search, surveillance and rescue. The pursuit-evasion problem is a fundamental theoretical base to apply robotics on these cases. This dissertation presents an approach to solve the pursuit-evasion problem with no previous knowledge of the map, which must be simply connected, using multi-robots systems with limited sensing. The approach is based on the random walk, since it is a mathematical for

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25

Wu, Tao. "Higher-order Random Walk Methods for Data Analysis." Thesis, Purdue University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10790747.

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<p> Markov random walk models are powerful analytical tools for multiple areas in machine learning, numerical optimizations and data mining tasks. The key assumption of a first-order Markov chain is memorylessness, which restricts the dependence of the transition distribution to the current state only. However in many applications, this assumption is not appropriate. We propose a set of higher-order random walk techniques and discuss their applications to tensor co-clustering, user trails modeling, and solving linear systems. First, we develop a new random walk model that we call the super-spa

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26

Gubiec, Tomasz, and Ryszard Kutner. "Two-step memory within Continuous Time Random Walk." Diffusion fundamentals 20 (2013) 64, S. 1, 2013. https://ul.qucosa.de/id/qucosa%3A13643.

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27

Boutaud, Pierre. "Branching random walk : limit cases and minimal hypothesis." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM025.

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La marche aléatoire branchante est un système de particules sur la droite réelle où partant au temps 0 d’une particule initiale en position 0, chaque particule vivante au temps n meurt au temps n + 1 en donnant indépendemment naissance à un nombre aléatoire de particules se dispersant aléatoirement autour de la position de la particule parente. Dans un premier chapitre introductif, nous définissons en détails le modèle de la marche aléatoire branchante ainsi que certains des enjeux de la recherche autour de ce modèle, notamment l’étude de la martingale additive. Cette martingale peut-être étud

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28

Chang, Qiang. "Continuous-time random-walk simulation of surface kinetics." The Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1166592142.

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29

Mulatier, Clélia de. "A random walk approach to stochastic neutron transport." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLS029/document.

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L’un des principaux objectifs de la physique des réacteurs nucléaires est de caractériser la répartition aléatoire de la population de neutrons au sein d’un réacteur. Les fluctuations de cette population sont liées à la nature stochastique des interactions des neutrons avec les noyaux fissiles du milieu : diffusion, capture stérile, ou encore émission de plusieurs neutrons lors de la fission d’un noyau. L’ensemble de ces mécanismes physiques confère une structure aléatoire branchante à la trajectoire des neutrons, alors modélisée par des marches aléatoires. Avec environs 10⁸ neutrons par centi

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30

Zou, Shanshan. "Empirical analysis on random walk behavior of foreign exchange rates." Thesis, Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/33836.

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This thesis conducts a comprehensive examination on the random walk behavior of 29 foreign exchange rates over the period of floating exchange regime, using variance-ratio tests. The cross-country and time-series test show that random walk model cannot be rejected on majority, and the random walk behavior is quite volatile across the whole floating exchange regime period. It then goes further to explore possible factors that can explain the probability of rejection/ non-rejections on random walk model using linear as well as nonlinear probability models, and find that the factors such as capit

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31

Gabucci, Ilenia. "Random walks classici e quantistici." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/17759/.

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Questa tesi si propone di fornire uno studio sul random walk. Partendo da un approfondimento sulla teoria della probabilita` alla base di tale processo ed in particolare le distribuzioni Binomiale e Gaussiana, si `e potuto studiare il caso del random walk classico, sia nel caso del reticolo monodimensionale che per reticoli a piu` dimensioni. Sempre nell’ambito classico si sono analizzati anche i processi stocastici dipendenti dal tempo, detti Processi di Markov, e il moto browniano, per cui si sono ricavate le equazioni del moto della particella browniana, ovvero le equazioni di Langevin. Si

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32

Chilukuri, Raghu N. "Spin Diffusion Associated with a Quantum Random Walk on a One-Dimensional Lattice." University of Cincinnati / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1406820159.

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33

fr, kaimanov@univ-rennes1. "Boundaries and Harmonic Functions for Random Walks with Random Transition Probabilities." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1085.ps.

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34

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/.

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Lo scopo della tesi è quello di studiare la dinamica stocastica di particelle che realizzano un random walk su network, focalizzandosi in particolare sulle proprietà dello stato stazionario del processo. Dopo aver introdotto i concetti fondamentali di network e random walk per singola particella, si generalizza la trattazione a N particelle non interagenti su network a capacità di trasporto e storage infinita (ISTC) e si ricava il relativo stato stazionario con una trattazione meccano-statistica, applicando il principio di massima entropia. Successivamente, per avvicinarsi a modelli di trasp

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35

Kipp, Andreas Michael. "Finanzprognosen versus Random-Walk-Theorie : Perspektiven eines nichtlinearen Kapitalmarktmodells /." Aachen : Shaker, 2002. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=010169925&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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36

Böhm, Walter. "The Correlated Random Walk with Boundaries. A Combinatorial Solution." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/1058/1/document.pdf.

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The transition fundions for the correlated random walk with two absorbing boundaries are derived by means of a combinatorial construction which is based on Krattenthaler's Theorem for counting lattice paths with turns. Results for walks with one boundary and for unrestricted walks are presented as special cases. Finally we give an asymptotic formula, which proves to be useful for computational purposes. (author's abstract)<br>Series: Forschungsberichte / Institut für Statistik

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37

Yu, Wei, and 余韡. "Reverse Top-k search using random walk with restart." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/197515.

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With the increasing popularity of social networking applications, large volumes of graph data are becoming available. Large graphs are also derived by structure extraction from relational, text, or scientific data (e.g., relational tuple networks, citation graphs, ontology networks, protein-protein interaction graphs). Nodeto-node proximity is the key building block for many graph based applications that search or analyze the data. Among various proximity measures, random walk with restart (RWR) is widely adapted because of its ability to consider the global structure of the whole network. A

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38

Katzenbeisser, Walter, and Wolfgang Panny. "Simple Random Walk Statistics. Part I: Discrete Time Results." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1990. http://epub.wu.ac.at/1078/1/document.pdf.

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In a famous paper Dwass [I9671 proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows to extend Dwass's results in several ways, viz. arbitrary endpoints, horizontal steps, and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete ti

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39

Li, Chao. "Option pricing with generalized continuous time random walk models." Thesis, Queen Mary, University of London, 2016. http://qmro.qmul.ac.uk/xmlui/handle/123456789/23202.

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The pricing of options is one of the key problems in mathematical finance. In recent years, pricing models that are based on the continuous time random walk (CTRW), an anomalous diffusive random walk model widely used in physics, have been introduced. In this thesis, we investigate the pricing of European call options with CTRW and generalized CTRW models within the Black-Scholes framework. Here, the non-Markovian character of the underlying pricing model is manifest in Black-Scholes PDEs with fractional time derivatives containing memory terms. The inclusion of non-zero interest rates leads t

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Hashimoto, Tatsunori B. (Tatsunori Benjamin). "Continuous representations and models from random walk diffusion limits." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/105670.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 193-202).<br>Structured data such as sequences and networks pose substantial difficulty for traditional statistical theory which has focused on data drawn independently from a vector space. A popular and empirically effective technique for dealing with such data is to map elements of the data to a vector space and to operate over the embedding as a summary statistic. Such a vector represent

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41

Sidenko, Sergiy. "Kac's random walk and coupon collector's process on posets." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43781.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.<br>Includes bibliographical references (p. 100-104).<br>In the first part of this work, we study a long standing open problem on the mixing time of Kac's random walk on SO(n, R) by random rotations. We obtain an upper bound mix = O (n2.5 log n) for the weak convergence which is close to the trivial lower bound [Omega] (n2). This improves the upper bound O (n4 log n) by Diaconis and SaloffCoste 1131. The proof is a variation on the coupling technique we develop to bound the mixing time for compact Markov chains,

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Alves, Gonçalo Filipe Rodrigues. "Testing the random walk hypothesis with technical trading rules." Master's thesis, Instituto Superior de Economia e Gestão, 2015. http://hdl.handle.net/10400.5/10939.

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Mestrado em Finanças<br>Neste trabalho são testadas as hipóteses de passeio aleatório ao mercado acionista português, examinando as dezoito ações e o índice PSI-20. Considerando cotações diárias e mensais durante o período de 1999-2015. Foram utilizados os testes Augmented Dickey-Fuller (ADF), os testes de rácio de variância automático assim como os rácios de variâncias individuais e múltiplos propostos por Lo e Mackinlay, e Chow e Denning, respetivamente. Os vários testes utilizados para confirmar a hipótese de passeio aleatório das dezoito ações assim como do índice PSI-20, obtiveram resulta

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43

Lains, João Luís da Silva. "Testing the random walk hypothesis with variance ratio statistics." Master's thesis, Instituto Superior de Economia e Gestão, 2015. http://hdl.handle.net/10400.5/11801.

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Mestrado em Finanças<br>Esta dissertação tem como objetivo testar a hipótese de passeio aleatório na curva das yields relativa ás obrigações do tesouro dos Estados Unidos da América para o period entre 1980 e 2014. Para alcançar este objetivo e após revisão da literatura foram efectuados testes de variância e de raiz unitária considerados os mais indicados e poderosos. Os dados necessários para a realização deste estudo foram recolhidos tendo por base um estudo da Reserva Federal dos Estados Unidos da América, que efectua cálculo das yields desde 1961 até ao presente. O método escolhido para o

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44

Chwu, Thomas Kai Yuan. "Random walk modelling of turbulent dispersion within the atmosphere." Thesis, University of Cambridge, 1997. https://www.repository.cam.ac.uk/handle/1810/272825.

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45

Rüdrich, Stefan [Verfasser]. "Random Walk Approaches to Clustering Directed Networks / Stefan Rüdrich." Berlin : Freie Universität Berlin, 2020. http://d-nb.info/1215572298/34.

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46

Falconer, Steven. "Subdiffusive transport in non-homogeneous media and nonlinear fractional equations." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/subdiffusive-transport-in-nonhomogeneous-media-and-nonlinear-fractional-equations(a695fe6e-02d2-4fa1-b90b-6a57505973fc).html.

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47

Jamshidpey, Arash. "Population Dynamics in Random Environment, Random Walks on Symmetric Group, and Phylogeny Reconstruction." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34623.

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This thesis concerns applications of some probabilistic tools to phylogeny reconstruction and population genetics. Modelling the evolution of species by continuous-time random walks on the signed permutation groups, we study the asymptotic medians of a set of random permutations sampled from simple random walks at time 0.25cn, for c> 0. Running k independent random walks all starting at identity, we prove that the medians approximate the ancestor (identity permutation) up to time 0.25n, while there exists a constant c>1 after which the medians loose credibility as an estimator. We study the me

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48

edu, rdlyons@indiana. "Markov Chain Intersections and the Loop--Erased Walk." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1058.ps.

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49

Niemann, Markus. "From Anomalous Deterministic Diffusion to the Continuous-Time Random Walk." Wuppertal Universitätsbibliothek Wuppertal, 2010. http://d-nb.info/1000127621/34.

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Sundequist, Blomdahl Kristofer. "An evaluation of random-walk based clustering of multiplex networks." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-333027.

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Abstract:

A network, or a graph, is a mathematical construct used for modeling relationships between different entities. An extension of an ordinary network is a multiplex network. A multiplex network enables one to model different kinds of relationships between the same entities, or even to model how relationships between entities change over time. A common network analysis task is to find groups of nodes that are unusually tightly connected. This is called community detection, and is a form of clustering. The multiplex extension complicates both the notion of what a community is, and the process of fi

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