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1
Rosén, Emil. "Random covering times, a simulation study." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-269338.
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Obanubi, Olasunkanmi Olubunmi. "Particle filters with random resampling times." Thesis, Imperial College London, 2010. http://hdl.handle.net/10044/1/6339.
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The ability to analyse, interpret and make inferences about evolving dynamical systems is of great importance in different areas of the world we live in today. Examples of such areas include audio engineering, finance and econometrics. In general, the dynamical systems are not directly measureable and only incomplete observations, quite often deteriorated by the presence noise are available. This leads us to the main objective of stochastic filtering: the estimation of an evolving dynamical system whose trajectory is modelled by a stochastic process called the signal, given the information available through its partial observation. Particle filters, which use clouds of weighted particles that evolve according to the law of the signal process, can be used to approximate the solution of the filtering problem. In time, as some of the particles become redundant, a procedure which eliminates these particles and multiplies the ones that contribute most to the resulting approximation is introduced at points in time called resampling/correction times. Practitioners normally use certain overall characteristics of the approximating system of particles (such as the effective sample size of the system) to determine when to correct the system. There are currently no results to justify the convergence of particle filters with random correction times to the solution of the filtering problem in continuous time. In this thesis, we analyse particle filters in a continuous time framework where resampling takes place at times that form a sequence of (predictable) stopping times. The particular focus will be on the case where the signal is a diffusion process on a d-dimensional Euclidean space. We will also look at central limit theorem type results for the approximating particle system. The results will then be used to make inferences about the threshold used in the effective sample size approach of approximating the signal.
3
Wallén, Daniel. "Cover times of random walks on graphs." Thesis, Uppsala University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-125278.
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4
Sbihi, Amine M. (Amine Mohammed). "Covering times for random walks on graphs." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74538.
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This thesis is a contribution to the covering times problems for random walks on graphs. By considering uniform random walks on finite connected graphs, the covering time is defined as the time (number of steps) taken by the random walk to visit every vertex. The motivating problem of this thesis is to find bounds for the expected covering times. We provide explicit bounds that are uniformly valid over all starting points and over large classes of graphs. In some cases the asymptotic distribution of the suitably normalized covering time is given as well.
5
Abe, Yoshihiro. "Cover times and extrema of local times for random walks on graphs." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215283.
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Kang, Sungyeol. "Extreme values of random times in stochastic networks." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/24305.
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Carlsund, Anna. "Cover Times, Sign-dependent Random Walks, and Maxima." Doctoral thesis, KTH, Mathematics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3624.
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8
Kenyon, Astrid Sandrine. "Stochastic vehicle routing problems with random travel times /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.
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9
Mussini, Filipe. "Random cover times using the Poisson cylinder process." Licentiate thesis, Uppsala universitet, Analys och sannolikhetsteori, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-329351.
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10
Forghani, Behrang. "Transformed Random Walks." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32538.
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We consider transformations of a given random walk on a countable group determined by Markov stopping times. We prove that these transformations preserve the Poisson boundary. Moreover, under some mild conditions, the asymptotic entropy (resp., rate of escape) of the transformed random walks is equal to the asymptotic entropy (resp., rate of escape) of the original random walk multiplied by the expectation of the corresponding stopping time. This is an analogue of the well-known Abramov's formula from ergodic theory.
11
SOUZA, RODRIGO MARINHO DE. "MIXING TIMES FOR RANDOM WALKS ON THE SYMMETRIC GROUP." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=33139@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE EXCELENCIA ACADEMICA<br>O objetivo desta dissertação é apresentar algumas técnicas e ferramentas para a obtenção de cotas superiores e inferiores para tempos de mistura de cadeias de Markov. Para que isso se torne mais interessante, apresentaremos estes conceitos através de cadeias de Markov que atuam sobre o grupo
simétrico, que podem ser vistas como embaralhamentos de cartas. Ademais, usaremos um destes embaralhamentos como toy model para o processo de exclusão simples simétrico, o que nos ajudará a determinar os tempos de mistura do embaralhamento e do famoso sistema de partículas.<br>The aim of this dissertation is to introduce some techniques and tools to obtain upper and lower bounds for Markov chains mixing times. To make it more interesting, we introduce these concepts through Markov chains that act on the symmetric group, which can be seen as card shuffles. Furthermore, we use one of these shuffles as a toy model for the symmetric simple exclusion process, which helps us to determine mixing times for the shuffle and for the famous particle system.
12
Wolff, Tilman [Verfasser], and Wolfgang [Akademischer Betreuer] König. "Random Walk Local Times, Dirichlet Energy and Effective Conductivity in the Random Conductance Model / Tilman Wolff. Betreuer: Wolfgang König." Berlin : Technische Universität Berlin, 2013. http://d-nb.info/1064810357/34.
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13
Katzenbeisser, Walter, and Wolfgang Panny. "On the Number of Times where a simple Random Walk reaches its Maximum." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1990. http://epub.wu.ac.at/834/1/document.pdf.
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Let Q, denote the number of times where a simple random walk reaches its maximum, where the random walk starts at the origin and returns to the origin after 2n steps. Such random walks play an important r6le in probability and statistics. In this paper the distribution and the moments of Q, are considered and their asymptotic behavior is studied. (author's abstract)<br>Series: Forschungsberichte / Institut für Statistik
14
Aksamit, Anna Natalia. "Temps aléatoires, grossissement de filtration et arbitrages." Thesis, Evry-Val d'Essonne, 2014. http://www.theses.fr/2014EVRY0007/document.
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Cette thèse traite des problèmes associés à la théorie de grossissement de filtration. Elle est divisée en deux parties.La première partie est consacrée aux temps aléatoires. On étudie les propriétés des différentes classes de temps aléatoires du point de vue du grossissement de la filtration.La deuxième partie concerne l'étude de la stabilité de condition d'arbitrage sur le grossissement de la filtration. On se concentre sur la condition no unbounded profit with bounded risk. Dans un premier temps, on étudie l'absence d'arbitrage dans le cas de grossissement progressif avec un temps aléatoire. Puis on regarde le grossissement initial avec une variable aléatoire qui vérifie l'hypothèse de Jacod<br>This thesis treats the problems settled in elargement of filtration theory. It consists of two parts.The first part is devoted to random times. We study the properties of different classes of random times from enlargement of filtration point of view.The second part concerns the study of the stability of the non-arbitrage condition under anlargement of filtration. We are mainly interested in no bounded profit with bounded risk condition. We study absence of arbitrage in the case progressive enlargement up to random time. Then we look at the case of initial enlargement with random variable satisfying Jacod's hypothesis
15
Katzenbeisser, Walter, and Wolfgang Panny. "On The Number of Times where a Simple Random Walk reaches a Nonnegative Height." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1998. http://epub.wu.ac.at/600/1/document.pdf.
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The purpose of this note is to generalize the distribution of the local time of a purely binomial random walk for simple random walks allowing for three directions with different probabilities. (author's abstract)<br>Series: Forschungsberichte / Institut für Statistik
16
Sonntag, Danja R. [Verfasser]. "Safety stock determination in production systems with random yield and positive lead times / Danja R. Sonntag." Magdeburg : Universitätsbibliothek, 2017. http://d-nb.info/1149124393/34.
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Sonntag, Danja [Verfasser]. "Safety stock determination in production systems with random yield and positive lead times / Danja R. Sonntag." Magdeburg : Universitätsbibliothek, 2017. http://d-nb.info/1149124393/34.
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Schulmann, Viktor [Verfasser], Michael [Akademischer Betreuer] Voit, and Jeannette [Gutachter] Woerner. "Estimation of stopping times for some stopped random processes / Viktor Schulmann ; Gutachter: Jeannette Woerner ; Betreuer: Michael Voit." Dortmund : Universitätsbibliothek Dortmund, 2019. http://d-nb.info/1186969113/34.
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Sankaran, Vinodh. "A particle swarm optimization using random keys for flexible flow shop scheduling problem with sequence dependent setup times." Connect to this title online, 2009. http://etd.lib.clemson.edu/documents/1263396761/.
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20
Salvi, Michele [Verfasser], and Wolfgang [Akademischer Betreuer] Koenig. "The Random Conductance Model: local times large deviations, law of large numbers and effective conductance / Michele Salvi. Betreuer: Wolfgang Koenig." Berlin : Universitätsbibliothek der Technischen Universität Berlin, 2013. http://d-nb.info/1034952757/34.
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21
Suryawan, Herry Pribawanto [Verfasser]. "A White Noise Approach to Self-intersection Local Times and Feynman Integrals for Quantum Particles in Random Media / Herry Pribawanto Suryawan." München : Verlag Dr. Hut, 2013. http://d-nb.info/1045987778/34.
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22
Amor, Tatiana María Alonso. "Characterizing and modeling visual persistence, search strategies and fixation times." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/22495.
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AMOR, T. M. A. Characterizing and modeling visual persistence, search strategies and fixation times. 2017. 114 f. Tese (Doutorado em Física) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.<br>Submitted by Pós-Graduação em Física (posgrad@fisica.ufc.br) on 2017-04-05T18:55:10Z
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Previous issue date: 2017<br>To gather information from the world around us, we move our eyes constantly. In different
occasions we find ourselves performing visual searches, such as trying to find someone in a
crowd or a book in a shelf. While searching, our eyes “jump” from one location to another
giving rise to a wide repertoire of patterns, exhibiting distinctive persistent behaviors.
Initially, by focusing on saccadic directions and intersaccadic angles, we disclose that the
probability distributions of these measures show a clear preference of participants towards a
reading-like mechanism (geometrical persistence), whose features and potential advantages
for searching/foraging are discussed.We then perform a Multifractal Detrended Fluctuation
Analysis (MF-DFA) over the time series of jump magnitudes in the eye trajectory and find
that it exhibits a typical multifractal behavior arising from the sequential combination
of saccades and fixations. By inspecting the time series composed of only fixational
movements, our results reveal instead a monofractal behavior with a Hurst exponent
H ∼ 0.7, which indicates the presence of long-range power-law positive correlations
(statistical persistence). Motivated by the experimental findings from the study of the
distribution of the intersaccadic angles, we developed a simple visual search model that
quantifies the wide variety of possible search strategies. From our experiments we know
that when searching a target within an image our brain can adopt different strategies. The
question then is which one does it choose? We present a simple two-parameter visual search
model (VSM) based on a persistent random walk and the experimental inter-saccadic
angle distribution. The model captures the basic observed visual search strategies that
range from systematic or reading-like to completely random. We compare the results
of the model to the experimental data by measuring the space-filling efficiency of the
searches. Within the parameter space of the model, we are able to quantify the strategies
used by different individuals for three searching tasks and show how the average search
strategy changes along these three groups. Even though participants tend to explore a vast
range of parameters, when all the items are placed on a regular lattice, participants are
more likely to perform a systematic search, whereas in a more complex field, the search
trajectories resemble a random walk. In this way we can discern with high sensitivity
the relation between the visual landscape and the average strategy, disclosing how small
variations in the image induce strategy changes. Finally, we move beyond visual search
and study the fixation time distributions across different visual tasks. Fixation times are
commonly associated to some cognitive process, as it is in this instances where most of the
visual information is gathered. However, the distribution for the fixation durations exhibits
certain similarities across a wide range of visual tasks and foveated species. We studied
how similar these distributions are, and found that, even though they share some common
properties, such as similar mean values, most of them are statistically different. Because
fixations durations can be controlled by two different mechanisms: cognitive or ocular, we
focus our research into finding a model for the fixation times distribution flexible enough
to capture the observed behaviors in experiments that tested these concepts. At the same
time, the candidate function to model the distribution needs to be the response of some
very robust inner mechanism found in all the aforementioned scenarios. Hence, we discuss
the idea of a model based on the microsacaddic inter event time statistics, resulting in the
sum of Gamma distributions, each of these related to the presence of a distinctive number
of microsaccades in a fixation.<br>To gather information from the world around us, we move our eyes constantly. In different
occasions we find ourselves performing visual searches, such as trying to find someone in a
crowd or a book in a shelf. While searching, our eyes “jump” from one location to another
giving rise to a wide repertoire of patterns, exhibiting distinctive persistent behaviors.
Initially, by focusing on saccadic directions and intersaccadic angles, we disclose that the
probability distributions of these measures show a clear preference of participants towards a
reading-like mechanism (geometrical persistence), whose features and potential advantages
for searching/foraging are discussed.We then perform a Multifractal Detrended Fluctuation
Analysis (MF-DFA) over the time series of jump magnitudes in the eye trajectory and find
that it exhibits a typical multifractal behavior arising from the sequential combination
of saccades and fixations. By inspecting the time series composed of only fixational
movements, our results reveal instead a monofractal behavior with a Hurst exponent
H ∼ 0.7, which indicates the presence of long-range power-law positive correlations
(statistical persistence). Motivated by the experimental findings from the study of the
distribution of the intersaccadic angles, we developed a simple visual search model that
quantifies the wide variety of possible search strategies. From our experiments we know
that when searching a target within an image our brain can adopt different strategies. The
question then is which one does it choose? We present a simple two-parameter visual search
model (VSM) based on a persistent random walk and the experimental inter-saccadic
angle distribution. The model captures the basic observed visual search strategies that
range from systematic or reading-like to completely random. We compare the results
of the model to the experimental data by measuring the space-filling efficiency of the
searches. Within the parameter space of the model, we are able to quantify the strategies
used by different individuals for three searching tasks and show how the average search
strategy changes along these three groups. Even though participants tend to explore a vast
range of parameters, when all the items are placed on a regular lattice, participants are
more likely to perform a systematic search, whereas in a more complex field, the search
trajectories resemble a random walk. In this way we can discern with high sensitivity
the relation between the visual landscape and the average strategy, disclosing how small
variations in the image induce strategy changes. Finally, we move beyond visual search
and study the fixation time distributions across different visual tasks. Fixation times are
commonly associated to some cognitive process, as it is in this instances where most of the
visual information is gathered. However, the distribution for the fixation durations exhibits
certain similarities across a wide range of visual tasks and foveated species. We studied
how similar these distributions are, and found that, even though they share some common
properties, such as similar mean values, most of them are statistically different. Because
fixations durations can be controlled by two different mechanisms: cognitive or ocular, we
focus our research into finding a model for the fixation times distribution flexible enough
to capture the observed behaviors in experiments that tested these concepts. At the same
time, the candidate function to model the distribution needs to be the response of some
very robust inner mechanism found in all the aforementioned scenarios. Hence, we discuss
the idea of a model based on the microsacaddic inter event time statistics, resulting in the
sum of Gamma distributions, each of these related to the presence of a distinctive number
of microsaccades in a fixation.
23
Shapira, Assaf. "Bootstrap percolation and kinetically constrained models in homogeneous and random environments." Thesis, Sorbonne Paris Cité, 2019. http://www.theses.fr/2019USPCC066.
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Cette thèse est consacrée à l'étude des modèles aux contraintes cinétiques et de la percolation bootstrap, dans l'intersection entre les probabilités, la combinatoire et la physique statistique. Les modèles aux contraintes cinétiques ont été introduits dans les années 80 pour modéliser la transition liquide-verre, dont la compréhension reste toujours un des plus grands problèmes de la physique de la matière condensée. Ils ont été depuis profondément étudiés par des physiciens dans l'espoir d'éclaircir ce problème et la communauté mathématique s'en intéresse de plus en plus lors de la dernière décennie. Ces modèles sont des systèmes de particules en interaction dont la théorie générale est maintenant bien établie. Leur analyse rencontre tout de même des difficultés qui nécessitent le développement de nouveaux outils mathématiques.La percolation bootstrap est une classe d'automates cellulaires, i.e. déterministes en temps discret. Elle a été considérée pour la première fois en 1979 et son étude est depuis devenue un domaine actif en combinatoire et en probabilités.Les modéles aux contraintes cinétiques et la percolation bootstrap ont été introduits séparément mais sont fortement reliés – on verra que la percolation bootstrap est une version déterministe des modèles aux contraintes cinétiques et que ces derniers sont une version stochastique de la percolation bootstrap.On se concentrera sur les échelles de temps de ces deux modèles dans le but de comprendre le comportement des matériaux vitreux<br>This thesis concerns with Kinetically Constrained Models and Bootstrap Percolation, two topics in the intersection between probability, combinatorics and statistical mechanics. Kinetically constrained models were introduced by physicists in the 1980's to model the liquid-glass transition, whose understanding is still one of the big open questions in condensed matter physics. They have been studied extensively in the physics literature in the hope to shed some light on this problem, and in the last decade they have also received an increasing attention in the probability community. We will see that even though they belong to the well established field of interacting particle systems with stochastic dynamics, kinetically constrained models pose challenging and interesting problems requiring the development of new mathematical tools.Bootstrap percolation, on the other hand, is a class of monotone cellular automata, namely discrete in time and deterministic dynamics, the first example being the r-neighbor bootstrap percolation introduced in 1979. Since then, the study of bootstrap percolation has been an active domain in both the combinatorial and probabilistic communities, with several breakthroughs in the recent years.Though introduced in different contexts, kinetically constrained models and the bootstrap percolation, as we will see, are intimately related; and one may think of bootstrap percolation as a deterministic counterpart of kinetically constrained models, and of kinetically constrained models as the natural stochastic version of bootstrap percolation
24
Theopold, Adrian Pit [Verfasser], Mathias [Akademischer Betreuer] Vetter, and Viktor [Gutachter] Todorov. "Estimation of the Jump Activity Index in the Presence of Random Observation Times / Adrian Pit Theopold ; Gutachter: Viktor Todorov ; Betreuer: Mathias Vetter." Kiel : Universitätsbibliothek Kiel, 2019. http://d-nb.info/1225741386/34.
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Brennand, David Alexander Arthur. "Individual differences in recognition times to random dot stereograms, complex diamond stereograms and amplitude judgements in ridge stereograms : the role of tonic accommodation stereograms." Thesis, University of Sheffield, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.392544.
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MAURI, PIERCARLO. "MODULAZIONE DELL'AROUSAL MEDIANTE LA STIMOLAZIONE ELETTRICA TRANSCRANICA A FREQUENZE RANDOM." Doctoral thesis, Università Cattolica del Sacro Cuore, 2016. http://hdl.handle.net/10280/10724.
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Il lavoro di tesi si è focalizzato sullo studio dell’arousal come indice psicofisiologico di attivazione e sull’applicazione della metodica di stimolazione elettrica transcranica (tES) non invasiva con lo scopo di modulare tale indice. L’obiettivo è stato quello di indagare se, applicando la tES, fosse possibile migliorare la performance di soggetti giovani sani in compiti di tipo cognitivo. Il progetto di ricerca si è sviluppato in 2 studi principali per un totale di 4 esperimenti. Tali studi hanno previsto l’acquisizione e la successiva analisi sia di dati comportamentali (tempi di reazione, accuratezza), che di indici psicofisiologici (conduttanza cutanea, diametro pupillare). I risultati hanno evidenziato che è possibile modulare l’arousal con dei “bursts” di stimolazione elettrica transcranica, somministrati in concomitanza di stimoli salienti per il soggetto. Tale modulazione si è manifestata con una riduzione dei tempi di reazione ed un contemporaneo aumento della risposta di conduttanza cutanea. Questi dati supportano la possibilità di utilizzare questo protocollo in pazienti con difficoltà di attenzione o altri problemi cognitivi per aumentare l’efficacia di interventi di riabilitazione.<br>The thesis analyzed the role of the arousal as a psychophysiological index of activation, and the application of non-invasive transcranial electrical stimulation (tES) technique with the aim to modulate this index. In this work we investigated if the application of tES could increase the performance of healthy young subjects during cognitive tasks. The thesis is based on 2 main studies for a total of 4 experiments with the recording of behavioural (reaction times, accuracy) and psychophysiological (skin conductance, pupil diameter) indeces. The results showed that it is possible to modulate arousal with bursts of tES, administered during the presentation of salient stimuli for the subject. This modulation resulted in a reduction of reaction times and an increase of the skin conductance response. These data support the possibility to use this protocol of stimulation with patients with attentional and other cognitive deficits in a rehabilitative context.
27
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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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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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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Abdullah, Mohammed. "The cover time of random walks on graph." Thesis, King's College London (University of London), 2012. https://kclpure.kcl.ac.uk/portal/en/theses/the-cover-time-of-random-walks-on-graph(c23c303f-a6a2-4489-a059-4ade7c118106).html.
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A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex. Central to this thesis is the cover time of the walk, that is, the expectation of the number of steps required to visit every vertex, maximised over all starting vertices. In our rst contribution, we establish a relation between the cover times of a pair of graphs, and the cover time of their Cartesian product. This extends previous work on special cases of the Cartesian product, in particular, the square of a graph. We show that when one of the factors is in some sense larger than the other, its cover time dominates, and can become within a logarithmic factor of the cover time of the product as a whole. Our main theorem eectively gives conditions for when this holds. The techniques and lemmas we introduce may be of independent interest. In our second contribution, we determine the precise asymptotic value of the cover time of a random graph with given degree sequence. This is a graph picked uniformly at random from all simple graphs with that degree sequence. We also show that with high probability, a structural property of the graph called conductance, is bounded below by a constant. This is of independent interest. Finally, we explore random walks with weighted random edge choices. We present a weighting scheme that has a smaller worst case cover time than a simple random walk. We give an upper bound for a random graph of given degree sequence weighted according to our scheme. We demonstrate that the speed-up (that is, the ratio of cover times) over a simple random walk can be unbounded.
31
Oosthuizen, Joubert. "Random walks on graphs." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/86244.
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Thesis (MSc)--Stellenbosch University, 2014.<br>ENGLISH 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.<br>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.
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Tang, Ying. "Real-time automatic face tracking using adaptive random forests." Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=95172.
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Tracking is treated as a pixel-based binary classification problem in this thesis. An ensemble strong classifier obtained as a weighted combination of several random forests (weak classifiers), is trained on pixel feature vectors. The strong classifier is then used to classify the pixels belonging to the face or the background in the next frame. The classification margins are used to create a confidence map, whose peak indicates the new location of the face. The peak is located by Camshift which adjusts the size of the tracked face. The random forests in the ensemble are updated using AdaBoost by training new random forests to replace certain older ones to adapt to the changes between two frames. Tracking accuracy is monitored by a variable called the classification score. If the score detects a tracking anomaly, the system will stop tracking and restart by re-initializing using a Viola-Jones face detector. The tracker is tested on several sequences and proved to provide robust performance in different scenarios and illumination. The tracker can deal with complex changes of the face, a short period of occlusion, and the loss of tracking.<br>La localisation est traitée comme étant un problème de classification binaire à base de pixels dans cette thèse. Un ensemble de fort classificateur, obtenu à l'aide d'une combinaison pesée de plusieurs forêts (faibles classificateurs) aléatoires, est entraîné sur des vecteurs figurant des pixels. Le classificateur fort est ensuite utilisé pour classifier les pixels appartenant à la face ou au fond dans la prochaine image. Les marges de classifications sont utilisées pour créer une carte de confiance dont le sommet indique où est la nouvelle face. Le sommet est localisé par Camshift qui ajuste la grandeur de la face à localiser. Les forêts aléatoires dans l'ensemble sont mises à jours avec AdaBoost en entraînant des nouvelles forêts aléatoires pour remplacer certaines vieilles forêts pour s'adapter aux changements entre deux images. La précision de localisation est surveillée par une variable appelée note de classification. Si la note détecte une anomalie, le système arrêtera la localisation et redémarrera en réinitialisant en utilisant un détecteur de face Viola-Jones. Le localisateur est testé sur plusieurs séquences et s'est prouvé d'une performance robuste dans divers scénarios et illumination. Le localisateur peut agir bien à travers plusieurs changement complexes de la face, une courte période d'occlusion et la perte de la localisation.
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Wang, Yaqin. "Estimation of accelerated failure time models with random effects." [Ames, Iowa : Iowa State University], 2006.
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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 time results can be taken as a starting point to derive the corresponding results for randomized random walks by means of a limiting process. (author's abstract)<br>Series: Forschungsberichte / Institut für Statistik
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Kang, HiJee. "Memory for random time patterns in the sensory system." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLEE079.
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Le temps est une dimension universelle traitée par les systèmes sensoriels, qui est essentielle pour attribuer un sens à des stimuli comme la parole ou la musique pour l'audition. Cependant, les mécanismes requis pour le traitement temporel restent en grande part méconnus. Dans cette thèse, nous avons examiné un type de mécanisme faisant sans doute partie intégrante de tout traitement temporel : la formation de nouvelles traces mnésiques pour l’information temporelle. Nous avons étudié principalement la modalité auditive, mais aussi d'autres modalités sensorielles, comme le toucher, la vision, et la stimulation électrique directe du système auditif périphérique avec un implant cochléaire. Toutes les expériences ont utilisé un nouveau paradigme expérimental, adapté de précédentes études conçues pour étudier la mémoire auditive (Agus, Thorpe, & Pressnitzer, 2010). Au lieu d'utiliser du bruit comme stimulus, nous avons utilisé des séquences d’intervalles de temps irréguliers délimités par de brèves impulsions d'énergie, adaptées à la modalité étudiée. Dans une première série d'expériences, nous avons étudié la modalité auditive chez des auditeurs normo-entendants, en utilisant des trains de clics audio comme stimuli. Nous avons démontré, pour la première fois, un apprentissage rapide de sons contenant uniquement des informations temporelles. Dans une seconde série d'expériences, nous avons appliqué le même paradigme à trois modalités sensorielles (audition, toucher et vision), en utilisant des clics audio, des impulsions de mouvement au bout des doigts, et des flashs de lumière pour délimiter les intervalles de temps dans les différences modalités. Nous avons observé des formes qualitativement similaires d'apprentissage perceptif pour les trois modalités, avec un apprentissage rapide dans tous les cas, ainsi qu'un transfert d'apprentissage au toucher ou à la vision pour des séquences initialement apprises de façon auditive. Dans une troisième série d'expériences, nous avons testé des malentendants stimulés électriquement par leur implant cochléaire avec des séquences d'impulsions irrégulières. Nous avons trouvé des indications d’une plasticité préservée pour l'apprentissage rapide des informations temporelles chez ces auditeurs. Enfin, nous présentons des résultats préliminaires en utilisant une nouvelle technique susceptible de révéler certains des mécanismes neuronaux sous-jacents à l'apprentissage perceptuel rapide. Nous avons mesuré la dilatation pupillaire pendant que les auditeurs effectuaient la tâche de mémoire auditive et observé des changements systématiques de la taille de la pupille avec l'apprentissage. En conclusion, la thèse montre une capacité remarquable des systèmes perceptifs à apprendre des séquences temporelles complexes lorsqu'elles apparaissent plusieurs fois dans l'environnement, et suggère de nouvelles méthodes expérimentales pour étudier plus avant les mécanismes neuronaux sous-jacents<br>Time is a universal feature of all information processed by sensory systems, and temporal patterning is often essential for attributing meaning to external stimuli such as speech or music in audition. However, many of the mechanisms needed for temporal processing are still unclear. In this thesis, we investigated one type of mechanism arguably integral to any kind of temporal processing: the formation of novel memories for temporal patterns. We studied mainly the auditory modality, but also other sensory modalities such touch, vision, and electric hearing with a cochlear implant. All experiments used a novel experimental paradigm, adapted from a previous study designed to explore auditory memory of random noise (Agus, Thorpe, & Pressnitzer, 2010). Instead of using noise as the complex stimulus to learn, we used irregular time patterns made of random time intervals delineated by modality-adapted brief energy pulses. In a first series of experiments, we investigated the auditory modality in normal hearing listeners, using click trains as stimuli. We demonstrated for the first time a rapid learning of stimuli containing solely temporal cues. In a second series of experiments, we applied the same paradigm to multiple sensory modalities (audition, touch, and vision), using audio clicks, motion pulses to the fingertips, and light to delineate time intervals. We found a qualitatively similar forms of perceptual learning for all three modalities, with rapid learning in all cases, as well as a transfer of learning to touch or vision for patterns learnt initially learnt in audition. In a third series of experiments, we tested hearing impaired listeners stimulated through their cochlear implant with sequences of electrical pulses. We found evidence for preserved plasticity for the rapid learning of time patterns in those listeners. Finally, we present preliminary data using a novel technique for studying the underlying neural mechanisms of rapid perceptual learning. We measured pupil dilation while listeners performed the memory task and observed systematic changes in pupil size with perceptual learning. In conclusion, the thesis shows a remarkable ability of perceptual systems to learn complex time patterns as they re-occur in the environment, and suggests new experimental methods to further study the underlying neural mechanisms
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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 to a distinction between different types of \forward" and \backward" options, which are easily mapped onto each other in the standard Markovian framework, but exhibit significant dfferences in the non-Markovian case. The backward-type options require us in particular to include the multi-point statistics of the non-Markovian pricing model. Using a representation of the CTRW in terms of a subordination (time change) of a normal diffusive process with an inverse L evy-stable process, analytical results can be obtained. The extension of the formalism to arbitrary waiting time distributions and general payoff functions is discussed. The pricing of path-dependent Asian options leads to further distinctions between different variants of the subordination. We obtain analytical results that relate the option price to the solution of generalized Feynman-Kac equations containing non-local time derivatives such as the fractional substantial derivative. Results for L evy-stable and tempered L evy-stable subordinators, power options, arithmetic and geometric Asian options are presented.
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Bussian, Eric R. "Bounding the edge cover time of random walks on graphs." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/28953.
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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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Schenke, Andre [Verfasser]. "Regularisation and Long-Time Behaviour of Random Systems / Andre Schenke." Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1206592176/34.
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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.
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Das, Subhro. "Distributed Linear Filtering and Prediction of Time-varying Random Fields." Research Showcase @ CMU, 2016. http://repository.cmu.edu/dissertations/765.
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We study distributed estimation of dynamic random fields observed by a sparsely connected network of agents/sensors. The sensors are inexpensive, low power, and they communicate locally and perform computation tasks. In the era of large-scale systems and big data, distributed estimators, yielding robust and reliable field estimates, are capable of significantly reducing the large computation and communication load required by centralized estimators, by running local parallel inference algorithms. The distributed estimators have applications in estimation, for example, of temperature, rainfall or wind-speed over a large geographical area; dynamic states of a power grid; location of a group of cooperating vehicles; or beliefs in social networks. The thesis develops distributed estimators where each sensor reconstructs the estimate of the entire field. Since the local estimators have direct access to only local innovations, local observations or a local state, the agents need a consensus-type step to construct locally an estimate of their global versions. This is akin to what we refer to as distributed dynamic averaging. Dynamic averaged quantities, which we call pseudo-quantities, are then used by the distributed local estimators to yield at each sensor an estimate of the whole field. Using terminology from the literature, we refer to the distributed estimators presented in this thesis as Consensus+Innovations-type Kalman filters. We propose three distinct types of distributed estimators according to the quantity that is dynamically averaged: (1) Pseudo-Innovations Kalman Filter (PIKF), (2) Distributed Information Kalman Filter (DIKF), and (3) Consensus+Innovations Kalman Filter (CIKF). The thesis proves that under minimal assumptions the distributed estimators, PIKF, DIKF and CIKF converge to unbiased and bounded mean-squared error (MSE) distributed estimates of the field. These distributed algorithms exhibit a Network Tracking Capacity (NTC) behavior – the MSE is bounded if the degree of instability of the field dynamics is below a threshold. We derive the threshold for each of the filters. The thesis establishes trade-offs between these three distributed estimators. The NTC of the PIKF depends on the network connectivity only, while the NTC of the DIKF and of the CIKF depend also on the observation models. On the other hand, when all the three estimators converge, numerical simulations show that the DIKF improves 2dB over the PIKF. Since the DIKF uses scalar gains, it is simpler to implement than the CIKF. Of the three estimators, the CIKF provides the best MSE performance using optimized gain matrices, yielding an improvement of 3dB over the DIKF. Keywords: Kalman filter, distributed state estimation, multi-agent networks, sensor networks, distributed algorithms, consensus, innovation, asymptotic convergence, mean-squared error, dynamic averaging, Riccati equation, Lyapunov iterations, distributed signal processing, random dynamical systems.
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Veretennikova, Maria. "Controlled continuous time random walks and their position dependent extensions." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/66990/.
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Continuous Time Random Walks (CTRWs) are used widely for modelling anomalous diffusion. This thesis is the first research which focuses on optimal control of CTRWs, their modifications and their position dependent extensions. We derive the equation which may be called a fractional Hamilton Jacobi Bellman equation (FHJB), as it is similar to the HJB equation for controlled Markov processes. We present our original analysis of the FHJB equation, firstly working with its simpler linear version and obtaining useful regularity properties, and secondly, deriving the mild form of the FHJB, exploring its regularity properties and well-posedness. We present our novel theorems proving rigorous convergence for optimal payoffs of the scaled stochastic processes of our interest and give an interpretation of the solution of the FHJB equation as a solution to an optimization problem.
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Karlsson, Isak. "Order in the random forest." Doctoral thesis, Stockholms universitet, Institutionen för data- och systemvetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-142052.
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In many domains, repeated measurements are systematically collected to obtain the characteristics of objects or situations that evolve over time or other logical orderings. Although the classification of such data series shares many similarities with traditional multidimensional classification, inducing accurate machine learning models using traditional algorithms are typically infeasible since the order of the values must be considered. In this thesis, the challenges related to inducing predictive models from data series using a class of algorithms known as random forests are studied for the purpose of efficiently and effectively classifying (i) univariate, (ii) multivariate and (iii) heterogeneous data series either directly in their sequential form or indirectly as transformed to sparse and high-dimensional representations. In the thesis, methods are developed to address the challenges of (a) handling sparse and high-dimensional data, (b) data series classification and (c) early time series classification using random forests. The proposed algorithms are empirically evaluated in large-scale experiments and practically evaluated in the context of detecting adverse drug events. In the first part of the thesis, it is demonstrated that minor modifications to the random forest algorithm and the use of a random projection technique can improve the effectiveness of random forests when faced with discrete data series projected to sparse and high-dimensional representations. In the second part of the thesis, an algorithm for inducing random forests directly from univariate, multivariate and heterogeneous data series using phase-independent patterns is introduced and shown to be highly effective in terms of both computational and predictive performance. Then, leveraging the notion of phase-independent patterns, the random forest is extended to allow for early classification of time series and is shown to perform favorably when compared to alternatives. The conclusions of the thesis not only reaffirm the empirical effectiveness of random forests for traditional multidimensional data but also indicate that the random forest framework can, with success, be extended to sequential data representations.
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Curado, Manuel. "Structural Similarity: Applications to Object Recognition and Clustering." Doctoral thesis, Universidad de Alicante, 2018. http://hdl.handle.net/10045/98110.
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In this thesis, we propose many developments in the context of Structural Similarity. We address both node (local) similarity and graph (global) similarity. Concerning node similarity, we focus on improving the diffusive process leading to compute this similarity (e.g. Commute Times) by means of modifying or rewiring the structure of the graph (Graph Densification), although some advances in Laplacian-based ranking are also included in this document. Graph Densification is a particular case of what we call graph rewiring, i.e. a novel field (similar to image processing) where input graphs are rewired to be better conditioned for the subsequent pattern recognition tasks (e.g. clustering). In the thesis, we contribute with an scalable an effective method driven by Dirichlet processes. We propose both a completely unsupervised and a semi-supervised approach for Dirichlet densification. We also contribute with new random walkers (Return Random Walks) that are useful structural filters as well as asymmetry detectors in directed brain networks used to make early predictions of Alzheimer's disease (AD). Graph similarity is addressed by means of designing structural information channels as a means of measuring the Mutual Information between graphs. To this end, we first embed the graphs by means of Commute Times. Commute times embeddings have good properties for Delaunay triangulations (the typical representation for Graph Matching in computer vision). This means that these embeddings can act as encoders in the channel as well as decoders (since they are invertible). Consequently, structural noise can be modelled by the deformation introduced in one of the manifolds to fit the other one. This methodology leads to a very high discriminative similarity measure, since the Mutual Information is measured on the manifolds (vectorial domain) through copulas and bypass entropy estimators. This is consistent with the methodology of decoupling the measurement of graph similarity in two steps: a) linearizing the Quadratic Assignment Problem (QAP) by means of the embedding trick, and b) measuring similarity in vector spaces. The QAP problem is also investigated in this thesis. More precisely, we analyze the behaviour of $m$-best Graph Matching methods. These methods usually start by a couple of best solutions and then expand locally the search space by excluding previous clamped variables. The next variable to clamp is usually selected randomly, but we show that this reduces the performance when structural noise arises (outliers). Alternatively, we propose several heuristics for spanning the search space and evaluate all of them, showing that they are usually better than random selection. These heuristics are particularly interesting because they exploit the structure of the affinity matrix. Efficiency is improved as well. Concerning the application domains explored in this thesis we focus on object recognition (graph similarity), clustering (rewiring), compression/decompression of graphs (links with Extremal Graph Theory), 3D shape simplification (sparsification) and early prediction of AD.<br>Ministerio de Economía, Industria y Competitividad (Referencia TIN2012-32839 BES-2013-064482)
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Telcs, Andras, and h197tel@ella hu. "Volume and Time Doubling of Graphs and Random Walks, the Strongly." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1016.ps.
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Nava-Sedeño, Josue Manik, Haralampos Hatzikirou, Rainer Klages, and Andreas Deutsch. "Cellular automaton models for time-correlated random walks: derivation and analysis." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-231568.
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Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is “data-driven”. Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.
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Smith, Peter Jeffry. "Estimation techniques for ARMA time series models and random geometric series." Thesis, Royal Holloway, University of London, 1988. http://repository.royalholloway.ac.uk/items/974d14d1-8a3b-4872-8eab-cd0599c8d6a8/1/.
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The thesis falls naturally into two sections. Firstly is a study of estimation techniques for ARMA models. Secondly is the work on random geometric series stemming from industrial collaboration with G.E.C. Telecommunications Laboratories. The unifying theory between these topics is discussed in the introduction. In the first section of the thesis the problem of estimation for ARMA models is considered. This is of long standing interest and the problem of maximum likelihood estimation is substantially solved. However the relationship between approximate and exact maximum likelihood estimation is less well known. The approximate procedures of A.M. Walker and E.J. Godolphin are considered in detail. Some results are produced which compare the two methods to each other and to various exact procedures. These comparisons are used to evaluate the success of some well known approximations. Finally a new approach to exact maximum likelihood estimation is developed which is simple to formulate and implement. This is used to study some numerical problems in estimation which occur near the boundary of the unit circle. The random geometric series considered in the second section have applications in both statistics and telecommunications. Specific examples of these series have been used to study infinite Bernoulli convolutions, intersymbol interference, error detection and many other subjects. In most applications it is the distribution of the series that is of interest. Initially the problem of calculating the distribution is considered in detail for a specific example concerning error detection. Several approaches are developed and compared to existing methods. It is shown that the most effective procedure is dependent on numerical properties of the series. Finally the new methods are extended to give two techniques, which can be used in all situations. These procedures are based on the semi-contraction mapping principles and the use of the Poisson summation formula to invert Fourier transforms.
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Nava-Sedeño, Josue Manik, Haralampos Hatzikirou, Rainer Klages, and Andreas Deutsch. "Cellular automaton models for time-correlated random walks: derivation and analysis." Nature Publishing Group, 2017. https://tud.qucosa.de/id/qucosa%3A30690.
Full textAbstract:
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is “data-driven”. Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.
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Lopez-Castellanos, Victor. "Ultrawideband Time Domain Radar for Time Reversal Applications." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1301040987.
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Niemann, Markus [Verfasser]. "From Anomalous Deterministic Diffusion to the Continuous-Time Random Walk / Markus Niemann." Wuppertal : Universitätsbibliothek Wuppertal, 2010. http://d-nb.info/1000127621/34.
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