Dissertations / Theses on the topic 'Branching processes'
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Harris, John William. "Branching diffusion processes." Thesis, University of Bath, 2006. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.428379.
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Fittipaldi, María Clara. "Representation results for continuos-state branching processes and logistic branching processes." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/116458.
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Doctora en Ciencias de la Ingeniería, Mención Modelación MatemáticaEl objetivo de este trabajo es explorar el comportamiento de los procesos de rami ficación evolucionando a tiempo y estados continuos, y encontrar representaciones para su trayectoria y su genealogía. En el primer capítulo se muestra que un proceso de ramifi cación condicionado a no extinguirse es la única solución fuerte de una ecuación diferencial estocástica conducida por un movimiento Browniano y una medida puntual de Poisson, más un subordinador que representa la inmigración, dónde estos procesos son mutuamente independientes. Para esto se usa el hecho de que es posible obtener la ley del proceso condicionado a partir del proceso original, a través de su h-transformada, y se da una manera trayectorial de construir la inmigración a partir de los saltos del proceso. En el segundo capítulo se encuentra una representación para los procesos de rami ficación con crecimiento logístico, usando ecuaciones estocásticas. En particular, usando la de finición general dada por A. Lambert, se prueba que un proceso logístico es la única solución fuerte de una ecuación estocástica conducida por un movimiento Browniano y una medida puntual de Poisson, pero con un drift negativo fruto de la competencia entre individuos. En este capítulo se encuentra además una ecuación diferencial estocástica asociada con un proceso logístico condicionado a no extinguirse, suponiendo que éste existe y que puede ser de finido a través de una h-transformada. Esta representación muestra que nuevamente el condicionamiento da origen a un término correspondiente a la inmigración, pero en este caso dependiente de la población. Por último, en el tercer capítulo se obtiene una representación de tipo Ray-Knight para los procesos de ramifi cación logísticos, lo que da una descripción de su genealogía continua. Para esto, se utiliza la construcción de árboles aleatorios continuos asociados con procesos de Lévy generales dada por J.-F. Le Gall e Y. Le Jan, y una generalización del procedimiento de poda desarrollado por R. Abraham, J.-F. Delmas. Este resultado extiende la representación de Ray-Knight para procesos de difusión logísticos dada por V. Le, E. Pardoux y A. Wakolbinger.
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Ku, Ho Ming. "Interacting Markov branching processes." Thesis, University of Liverpool, 2014. http://livrepository.liverpool.ac.uk/2002759/.
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In engineering, biology and physics, in many systems, the particles or members give birth and die through time. These systems can be modeled by continuoustime Markov Chains and Markov Processes. Applications of Markov Processes are investigated by many scientists, Jagers [1975] for example . In ordinary Markov branching processes, each particles or members are assumed to be identical and independent. However, in some cases, each two members of the species may interact/collide together to give new birth. In considering these cases, we need to have some more general processes. We may use collision branching processes to model such systems. Then, in order to consider an even more general model, i.e. each particles can have branching and collision effect. In this case the branching component and collision component will have an interaction effect. We consider this model as interacting branching collision processes. In this thesis, in Chapter 1, we firstly look at some background, basic concepts of continuous-time Markov Chains and ordinary Markov branching processes. After revising some basic concepts and models, we look into more complicated models, collision branching processes and interacting branching collision processes. In Chapter 2, for collision branching processes, we investigate the basic properties, criteria of uniqueness, and explicit expressions for the extinction probability and the expected/mean extinction time and expected/mean explosion time. In Chapter 3, for interacting branching collision processes, similar to the structure in last chapter, we investigate the basic properties, criteria of uniqueness. Because of the more complicated model settings, a lot more details are required in considering the extinction probability. We will divide this section into several parts and consider the extinction probability under different cases and assumptions. After considering the extinction probability for the interacting branching processes, we notice that the explicit form of the extinction probability may be too complicated. In the last part of Chapter 3, we discuss the asymptotic behavior for the extinction probability of the interacting branching collision processes. In Chapter 4, we look at a related but still important branching model, Markov branching processes with immigration, emigration and resurrection. We investigate the basic properties, criteria of uniqueness. The most interesting part is that we investigate the extinction probability with our technique/methods using in Chapter 4. This can also be served as a good example of the methods introducing in Chapter 3. In Chapter 5, we look at two interacting branching models, One is interacting collision process with immigration, emigration and resurrection. The other one is interacting branching collision processes with immigration, emigration and resurrection. we investigate the basic properties, criteria of uniqueness and extinction probability. My original material starts from Chapter 4. The model used in chapter 4 were introduced by Li and Liu [2011]. In Li and Liu [2011], some calculation in cases of extinction probability evaluation were not strictly defined. My contribution focuses on the extinction probability evaluation and discussing the asymptotic behavior for the extinction probability in Chapter 4. A paper for this model will be submitted in this year. While two interacting branching models are discussed in Chapter 5. Some important properties for the two models are studied in detail.
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Collins, Joseph P. "Branching processes with varying environments." Thesis, University of Bath, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607471.
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This thesis concentrates on Branching Processes. We look at applying spine techniques and martingale changes of measure in order to first provide alternative proofs of well known discrete-time results concerning Branching Processes in Random Environments. We then apply the same ideas in a different setting to study Branching Brownian Motion with a Random Environment, focussing on the long-term spatial behaviour of the process. The final area of interest is Branching Brownian Motion with absorption at the origin, where we consider t he asymptotic behaviour of the survival probabilities near criticality in variations on an original model.
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Cole, D. J. "Stochastic branching processes in biology." Thesis, University of Kent, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270684.
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Janarthanan, Sivarjalingam. "Spatial spread in general branching processes." Thesis, University of Sheffield, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265577.
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Marguet, Aline. "Branching processes for structured populations and estimators for cell division." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX073/document.
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Cette thèse porte sur l'étude probabiliste et statistique de populations sans interactions structurées par un trait. Elle est motivée par la compréhension des mécanismes de division et de vieillissement cellulaire. On modélise la dynamique de ces populations à l'aide d'un processus de Markov branchant à valeurs mesures. Chaque individu dans la population est caractérisé par un trait (l'âge, la taille, etc...) dont la dynamique au cours du temps suit un processus de Markov. Ce trait détermine le cycle de vie de chaque individu : sa durée de vie, son nombre de descendants et le trait à la naissance de ses descendants. Dans un premier temps, on s'intéresse à la question de l'échantillonnage uniforme dans la population. Nous décrivons le processus pénalisé, appelé processus auxiliaire, qui correspond au trait d'un individu "typique" dans la population en donnant son générateur infinitésimal. Dans un second temps, nous nous intéressons au comportement asymptotique de la mesure empirique associée au processus de branchement. Sous des hypothèses assurant l'ergodicité du processus auxiliaire, nous montrons que le processus auxiliaire correspond asymptotiquement au trait le long de sa lignée ancestrale d'un individu échantillonné uniformément dans la population. Enfin, à partir de données composées des traits à la naissance des individus dans l'arbre jusqu'à une génération donnée, nous proposons des estimateurs à noyau de la densité de transition de la chaine correspondant au trait le long d'une lignée ainsi que de sa mesure invariante. De plus, dans le cas d'une diffusion réfléchie sur un compact, nous estimons par maximum de vraisemblance le taux de division du processus. Nous montrons la consistance de cet estimateur ainsi que sa normalité asymptotique. L'implémentation numérique de l'estimateur est par ailleurs réaliséeWe study structured populations without interactions from a probabilistic and a statistical point of view. The underlying motivation of this work is the understanding of cell division mechanisms and of cell aging. We use the formalism of branching measure-valued Markov processes. In our model, each individual is characterized by a trait (age, size, etc...) which moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event occurs, the trait of the descendants at birth depends on the trait of the mother and on the number of descendants. First, we study the trait of a uniformly sampled individual in the population. We explicitly describe the penalized Markov process, named auxiliary process, corresponding to the dynamic of the trait of a "typical" individual by giving its associated infinitesimal generator. Then, we study the asymptotic behavior of the empirical measure associated with the branching process. Under assumptions assuring the ergodicity of the auxiliary process, we prove that the auxiliary process asymptotically corresponds to the trait along its ancestral lineage of a uniformly sampled individual in the population. Finally, we address the problem of parameter estimation in the case of a branching process structured by a diffusion. We consider data composed of the trait at birth of all individuals in the population until a given generation. We give kernel estimators for the transition density and the invariant measure of the chain corresponding to the trait of an individual along a lineage. Moreover, in the case of a reflected diffusion on a compact set, we use maximum likelihood estimation to reconstruct the division rate. We prove consistency and asymptotic normality for this estimator. We also carry out the numerical implementation of the estimator
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Bocharov, Sergey. "Branching Lévy Processes with Inhomogeneous Breeding Potentials." Thesis, University of Bath, 2012. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.571868.
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The object of study in this thesis is a number of different models of branching Levy processes in inhomogeneous breeding potential. We employ some widely-used spine techniques to investigate various features of these models for their subsequent comparison. The thesis is divided into 5 chapters. In the first chapter we introduce the general framework for branching Markov processes within which we are going to present all our results. In the second chapter we consider a branching Brownian motion in the potential β|·|p, β> 0, p ≥0. We give a new proof of the result about the critical value of p for the explosion time of the population. The main advantage of the new proof is that it can be easily generalised to other models. The third chapter is devoted to continuous-time branching random walks in the potential β|·|p, β> 0, p ≥0. We give results about the explosion time and the right most particle behaviour comparing them with the known results for the branching Brownian motion. In the fourth chapter we look at general branching Levy processes in the potential β|·|p, β> 0, p ≥0. Subject to certain assumptions we prove some results about the explosion time and the rightmost particle. We exhibit how the corresponding results for the branching Brownian motion and and the branching random walk fit into the general structure. The last chapter considers a branching Brownian motion with branching taking place at the origin on the local time scale. We present some results about the population dynamics and the right most particle behaviour. We also prove the Strong Law of Large Numbers for this model.
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Hautphenne, Sophie. "An algorithmic look at phase-controlled branching processes." Doctoral thesis, Universite Libre de Bruxelles, 2009. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210255.
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Branching processes are stochastic processes describing the evolution of populations of individuals which reproduce and die independently of each other according to specific probability laws. We consider a particular class of branching processes, called Markovian binary trees, where the lifetime and birth epochs of individuals are controlled by a Markovian arrival process. Our objective is to develop numerical methods to answer several questions about Markovian binary trees. The issue of the extinction probability is the main question addressed in the thesis. We first assume independence between individuals. In this case, the extinction probability is the minimal nonnegative solution of a matrix fixed point equation which can generally not be solved analytically. In order to solve this equation, we develop a linear algorithm based on functional iterations, and a quadratic algorithm, based on Newton's method, and we give their probabilistic interpretation in terms of the tree.
Next, we look at some transient features for a Markovian binary tree: the distribution of the population size at any given time, of the time until extinction and of the total progeny. These distributions are obtained using the Kolmogorov and the renewal approaches.
We illustrate the results mentioned above through an example where the Markovian binary tree serves as a model for female families in different countries, for which we use real data provided by the World Health Organization website.
Finally, we analyze the case where Markovian binary trees evolve under the external influence of a random environment or a catastrophe process. In this case, individuals do not behave independently of each other anymore, and the extinction probability may no longer be expressed as the solution of a fixed point equation, which makes the analysis more complicated. We approach the extinction probability, through the study of the population size distribution, by purely numerical methods of resolution of partial differential equations, and also by probabilistic methods imposing constraints on the external process or on the maximal population size.
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Les processus de branchements sont des processus stochastiques décrivant l'évolution de populations d'individus qui se reproduisent et meurent indépendamment les uns des autres, suivant des lois de probabilités spécifiques.
Nous considérons une classe particulière de processus de branchement, appelés arbres binaires Markoviens, dans lesquels la vie d'un individu et ses instants de reproduction sont contrôlés par un MAP. Notre objectif est de développer des méthodes numériques pour répondre à plusieurs questions à propos des arbres binaires Markoviens.
La question de la probabilité d'extinction d'un arbre binaire Markovien est la principale abordée dans la thèse. Nous faisons tout d'abord l'hypothèse d'indépendance entre individus. Dans ce cas, la probabilité d'extinction s'exprime comme la solution minimale non négative d'une équation de point fixe matricielle, qui ne peut être résolue analytiquement. Afin de résoudre cette équation, nous développons un algorithme linéaire, basé sur l'itération fonctionnelle, ainsi que des algorithmes quadratiques, basés sur la méthode de Newton, et nous donnons leur interprétation probabiliste en termes de l'arbre que l'on étudie.
Nous nous intéressons ensuite à certaines caractéristiques transitoires d'un arbre binaire Markovien: la distribution de la taille de la population à un instant donné, celle du temps jusqu'à l'extinction du processus et celle de la descendance totale. Ces distributions sont obtenues en utilisant l'approche de Kolmogorov ainsi que l'approche de renouvellement.
Nous illustrons les résultats mentionnés plus haut au travers d'un exemple où l'arbre binaire Markovien sert de modèle pour des populations féminines dans différents pays, et pour lesquelles nous utilisons des données réelles fournies par la World Health Organization.
Enfin, nous analysons le cas où les arbres binaires Markoviens évoluent sous une influence extérieure aléatoire, comme un environnement Markovien aléatoire ou un processus de catastrophes. Dans ce cas, les individus ne se comportent plus indépendamment les uns des autres, et la probabilité d'extinction ne peut plus s'exprimer comme la solution d'une équation de point fixe, ce qui rend l'analyse plus compliquée. Nous approchons la probabilité d'extinction au travers de l'étude de la distribution de la taille de la population, à la fois par des méthodes purement numériques de résolution d'équations aux dérivées partielles, ainsi que par des méthodes probabilistes en imposant des contraintes sur le processus extérieur ou sur la taille maximale de la population.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Wang, Ying. "Branching Processes: Optimization, Variational Characterization, and Continuous Approximation." Doctoral thesis, Universitätsbibliothek Leipzig, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-62048.
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In this thesis, we use multitype Galton-Watson branching processes in random environments as individual-based models for the evolution of structured populations with both demographic stochasticity and environmental stochasticity, and investigate the phenotype allocation
problem. We explore a variational characterization for the stochastic evolution of a structured population modeled by a multitype Galton-Watson branching process. When the population under consideration is large and the time scale is fast, we deduce the continuous approximation for multitype Markov branching processes in random environments.
Many problems in evolutionary biology involve the allocation of some limited resource among several investments. It is often of interest to know whether, and how, allocation strategies can be optimized for the evolution of a structured population with randomness. In our
work, the investments represent different types of offspring, or alternative strategies for allocations to offspring. As payoffs we consider the long-term growth rate, the expected number
of descendants with some future discount factor, the extinction probability of the lineage, or the expected survival time. Two different kinds of population randomness are considered: demographic stochasticity and environmental stochasticity. In chapter 2, we solve the allocation problem w.r.t. the above payoff functions in three stochastic population models depending on different kinds of population randomness.
Evolution is often understood as an optimization problem, and there is a long tradition to look at evolutionary models from a variational perspective. In chapter 3, we deduce a variational characterization for the stochastic evolution of a structured population modeled by a
multitype Galton-Watson branching process. In particular, the so-called retrospective process plays an important role in the description of the equilibrium state used in the variational characterization. We define the retrospective process associated with a multitype Galton-Watson
branching process and identify it with the mutation process describing the type evolution along typical lineages of the multitype Galton-Watson branching process.
Continuous approximation of branching processes is of both practical and theoretical interest. However, to our knowledge, there is no literature on approximation of multitype branching processes in random environments. In chapter 4, we firstly construct a multitype Markov
branching process in a random environment. When conditioned on the random environment, we deduce the Kolmogorov equations and the mean matrix for the conditioned branching process. Then we introduce a parallel mutation-selection Markov branching process in a random
environment and analyze its instability property. Finally, we deduce a weak convergence result for a sequence of the parallel Markov branching processes in random environments and give
examples for applications.
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Ragab, Mahmoud [Verfasser]. "Partial Quicksort and weighted branching processes / Mahmoud Ragab." Kiel : Universitätsbibliothek Kiel, 2011. http://d-nb.info/1020244569/34.
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Jones, Owen Dafydd. "Random walks on pre-fractals and branching processes." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.388440.
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Penington, Sarah. "Branching processes with spatial structure in population models." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:361e5c58-e6dd-47a0-9a52-303e897547e8.
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We consider three different settings for branching processes with spatial structure which appear in population models. Firstly, we consider the effect of adding a competitive interaction between nearby individuals in a branching Brownian motion. Each individual has a mass which decays when other individuals are nearby. We study the front location: the location at which the local mass density drops to o(1). We show that there are arbitrarily large times t at which the front location is order of t^(1/3) behind the maximum displacement of a particle from the origin. Secondly, we study the strength of selection in favour of a particular allele in a spatially structured population required to cause a detectable trace in the patterns of genetic variation observed in the contemporary population. We suppose that the effective local population density is small. We show that whereas in dimensions at least three, selection is barely impeded by the spatial structure, in the most relevant dimension, d=2, selection must be stronger (by a factor of log(1/m) where m is the neutral mutation rate) if we are to have a chance of detecting it. Finally, we model the behaviour of what are known in population genetics as hybrid zones. These occur when two genetically distinct groups are able to reproduce, but the hybrid offspring have a lower fitness. We prove that on an appropriate time and space scale, the hybrid zone in our model evolves approximately according to mean curvature flow. We also give a probabilistic proof of a (well-known) analogous result for a special case of the Allen-Cahn equation. In the last two cases, we use the spatial Lambda-Fleming-Viot process to model the population (with different selection mechanisms), and our proofs rely on a duality with a system of branching and coalescing particles.
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Wu, Yadong Carleton University Dissertation Mathematics. "Dynamic particle systems and multilevel measure branching processes." Ottawa, 1991.
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Nicholson, Michael David. "Applications of branching processes to cancer evolution and initiation." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33034.
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There is a growing appreciation for the insight mathematical models can yield on biological systems. In particular, due to the challenges inherent in experimental observation of disease progression, models describing the genesis, growth and evolution of cancer have been developed. Many of these models possess the common feature that one particular type of cellular population initiates a further, distinct population. This thesis explores two models containing this feature, which also employ branching processes to describe population growth. Firstly, we consider a deterministically growing wild type population which seeds stochastically developing mutant clones. This generalises the classic Luria- Delbruck model of bacterial evolution. We focus on how differing wild type growth manifests itself in the distribution of clone sizes. In our main result we prove that for a large class of wild type growth, the long-time limit of the clone size distribution has a general two-parameter form, whose tail decays as a power-law. In the second model, we consider a fully stochastic system of cells in a growing population that can undergo birth, death and transitions. New cellular types appear via transitions, examples of which are genetic mutations or migrations bringing cells into a new environment. We concentrate on the scenario where the original cell type has the largest net growth rate, which is relevant for modelling drug resistance, due to fitness costs of resistance, or cells migrating into contact with a toxin. Two questions are considered in our main results. First, how long do we wait until a cell with a specific target type, an arbitrary number of transitions from the original population, exists. Second, which particular sequence of transitions initiated the target population. In the limit of small final transition rates, simple, explicit formulas are given to answer these questions.
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Kielisch, Fridolin Wilhelm [Verfasser]. "Lookdown-Constructions of Symbiotic Branching Processes / Fridolin Wilhelm Kielisch." Mainz : Universitätsbibliothek Mainz, 2020. http://d-nb.info/1204596611/34.
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Cheng, Tak Sum. "Stochastic optimal control in randomly-branching environments." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/713.
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Jang, Sa-Han. "An analytical and numerical study of Galton-Watson branching processes relevant to population dynamics." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 425 p, 2007. http://proquest.umi.com/pqdweb?did=1362537711&sid=18&Fmt=2&clientId=8331&RQT=309&VName=PQD.
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Pénisson, Sophie. "Continuous-time multitype branching processes conditioned on very late extinction." Universität Potsdam, 2009. http://opus.kobv.de/ubp/volltexte/2011/4954/.
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Multitype branching processes and Feller diffusion processes are conditioned on very late extinction. The conditioned laws are expressed as Doob h-transforms of the unconditioned laws, and an interpretation of the conditioned paths for the branching process is given, via the immortal particle. We study different limits for the conditioned process (increasing delay of extinction, long-time behavior, scaling limit) and provide an exhaustive list of exchangeability results.
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Alstott, Jeffrey Daniel. "The behaviour and utility of branching processes on complex networks." Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708131.
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Nikopoulos, George N. "NRAGE in Branching Morphogenesis of the Developing Murine Kidney." Fogler Library, University of Maine, 2009. http://www.library.umaine.edu/theses/pdf/NikopoulosG2009.pdf.
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Hermann, Felix [Verfasser], and Peter [Akademischer Betreuer] Pfaffelhuber. "On dualities of random graphs and branching processes with disasters to Piecewise deterministic Markov processes." Freiburg : Universität, 2019. http://d-nb.info/1182225985/34.
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Hartung, Lisa Bärbel [Verfasser]. "Extremal Processes in Branching Brownian Motion and Friends / Lisa Bärbel Hartung." Bonn : Universitäts- und Landesbibliothek Bonn, 2016. http://d-nb.info/1113688432/34.
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Murphy, Philip. "Nonrelativistic quark model calculation of the K-P --> [Lambda gamma] and K-P --> [Sigma]0[gamma] branching ratios." Thesis, University of British Columbia, 1991. http://hdl.handle.net/2429/30167.
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The radiative annihilation of K⁻p atoms to Λγ and ∑°γ is investigated using a non-relativistic harmonic oscillator quark model. A nonrelativistic reduction of the first order Feynman diagrams is performed to yield a gauge invariant interaction, which is sandwiched between three quark wave functions. Pseudoscalar and pseudovector coupling schemes are used for the strong vertex and the effects of SU(3)flavour breaking is explored. We obtain results which are in agreement with experiment for the ∑°γ but are somewhat high for the Λγ calculation.Science, Faculty of
Physics and Astronomy, Department of
Graduate
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Pénisson, Sophie. "Conditional limit theorems for multitype branching processes and illustration in epidemiological risk analysis." Phd thesis, Université Paris Sud - Paris XI, 2010. http://tel.archives-ouvertes.fr/tel-00570458.
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Cette thèse s'articule autour de la problématique de l'extinction de populations comportant différents types d'individus, et plus particulièrement de leur comportement avant extinction et/ou en cas d'une extinction très tardive. Nous étudions cette question d'un point de vue strictement probabiliste, puis du point de vue de l'analyse des risques liés à l'extinction pour un modèle particulier de dynamique de population, et proposons plusieurs outils statistiques. La taille de la population est modélisée soit par un processus de branchement de type Bienaymé-Galton-Watson à temps continu multitype (BGWc), soit par son équivalent dans un espace de valeurs continu, le processus de diffusion de Feller multitype. Nous nous intéressons à différents types de conditionnement à la non-extinction, et aux états d'équilibre associés. Ces conditionnements ont déjà été largement étudiés dans le cas monotype. Cependant la littérature relative aux processus multitypes est beaucoup moins riche, et il n'existe pas de travail systématique établissant des connexions entre les résultats concernant les processus BGWc et ceux concernant les processus de diffusion de Feller. Nous nous y sommes attelés. Dans la première partie de cette thèse, nous nous intéressons au comportement de la population avant son extinction, en conditionnant le processus de branchement X_t à la non-extinction (X_t≠0), ou plus généralement à la non-extinction dans un futur proche 0≤θ<∞ (X_{t+θ}≠0), et en faisant tendre t vers l'infini. Nous prouvons le résultat, nouveau dans le cadre multitype et pour θ>0, que cette limite existe et est non-dégénérée, traduisant ainsi un comportement stationnaire pour la dynamique de la population conditionnée à la non-extinction, et offrant une généralisation de la limite dite de Yaglom (correspondant au cas θ=0). Nous étudions dans un second temps le comportement de la population en cas d'une extinction très tardive, obtenu comme limite lorsque θ tends vers l'infini du processus X_t conditionné par X_{t+θ}≠0. Le processus conditionné ainsi obtenu est un objet connu dans le cadre monotype (parfois dénommé Q-processus), et a également été étudié lorsque le processus X_t est un processus de diffusion de Feller multitype. Nous examinons le cas encore non considéré où X_t est un BGWc multitype, prouvons l'existence du Q-processus associé, examinons ses propriétés, notamment asymptotiques, et en proposons plusieurs interprétations. Enfin, nous nous intéressons aux échanges de limites en t et en θ, ainsi qu'à la commutativité encore non étudiée de ces limites vis-à-vis de la relation de type grande densité reliant processus BGWc et processus de Feller. Nous prouvons ainsi une liste exhaustive et originale de tous les échanges de limites possibles (limite en temps t, retard de l'extinction θ, limite de diffusion). La deuxième partie de ce travail est consacrée à l'analyse des risques liés à l'extinction d'une population et à son extinction tardive. Nous considérons un certain modèle de population branchante (apparaissant notamment dans un contexte épidémiologique) pour lequel un paramètre lié aux premiers moments de la loi de reproduction est inconnu, et construisons plusieurs estimateurs adaptés à différentes phases de l'évolution de la population (phase de croissance, phase de décroissance, phase de décroissance lorsque l'extinction est supposée tardive), prouvant de plus leurs propriétés asymptotiques (consistance, normalité). En particulier, nous construisons un estimateur des moindres carrés adapté au Q-processus, permettant ainsi une prédiction de l'évolution de la population dans le meilleur ou le pire des cas (selon que la population est menacée ou au contraire invasive), à savoir celui d'une extinction tardive. Ces outils nous permettent d'étudier la phase d'extinction de l'épidémie d'Encéphalopathie Spongiforme Bovine en Grande-Bretagne, pour laquelle nous estimons le paramètre d'infection correspondant à une possible source d'infection horizontale persistant après la suppression en 1988 de la voie principale d'infection (farines animales). Cela nous permet de prédire l'évolution de la propagation de la maladie, notamment l'année d'extinction, le nombre de cas à venir et le nombre d'animaux infectés, et en particulier de produire une analyse très fine de l'évolution de l'épidémie dans le cas peu probable d'une extinction très tardive.
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Nordvall, Lagerås Andreas. "Markov Chains, Renewal, Branching and Coalescent Processes : Four Topics in Probability Theory." Doctoral thesis, Stockholm University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-6637.
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This thesis consists of four papers.
In paper 1, we prove central limit theorems for Markov chains under (local) contraction conditions. As a corollary we obtain a central limit theorem for Markov chains associated with iterated function systems with contractive maps and place-dependent Dini-continuous probabilities.
In paper 2, properties of inverse subordinators are investigated, in particular similarities with renewal processes. The main tool is a theorem on processes that are both renewal and Cox processes.
In paper 3, distributional properties of supercritical and especially immortal branching processes are derived. The marginal distributions of immortal branching processes are found to be compound geometric.
In paper 4, a description of a dynamic population model is presented, such that samples from the population have genealogies as given by a Lambda-coalescent with mutations. Depending on whether the sample is grouped according to litters or families, the sampling distribution is either regenerative or non-regenerative.
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Nordvall, Lagerås Andreas. "Markov chains, renewal, branching and coalescent processes : four topics in probability theory /." Stockholm : Department of Mathematics, Stockholm university, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-6637.
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Plazzotta, Giacomo. "Linking tree shapes to the spread of infection using generalised branching processes." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/44829.
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In this work we look at the shapes of pathogen phylogenetic trees derived from the the spread of an infection. The mathematical framework is the general Crump-Mode-Jager branching process. In an exploratory, simulation study we look at how memory affects the general shape of the tree. By general shape we intend measures such as the imbalance of the tree, the average ladder length, and others. Memory is introduced by defining a non-constant infectivity function which, through a non-honogeneous Poisson process, defines the spread of the infection between hosts. We found that memory, in the way we introduced it, has less effect than expected on the overall shape, but has a marked effect on the size of the tree, even if the Malthusian parameter is kept constant. With a more theoretical approach, we investigate the frequency of subshapes in supercritical branching processes. Through characteristic functions we were able to count the number of subshapes within a growing tree. We prove that the ratio between the number of such shapes and the tips converges to a limit as the tree grows. In the case of homogeneous processes, the limit of the cherries to tips ratio depends only on a simple function of the basic reproduction number of the pathogen. We used this relation to develop a new method of inference of the basic reproduction number. This method increase precision for larger sets of taxa, which are becoming more and more available after the advent of next generation DNA sequences. However, the correctness of the tree reconstructed with the methods currently available still remains dubious, thus the number of cherries may be incorrect. To by-pass the reconstruction, we develop an algorithm able to provide an estimate of the number of the cherries directly from the sequences. Its precision is similar or higher than other methods that reconstruct the tree first to provide the cherries estimate. Its high level of parallelisability enables time complexity to be linear, but it is quadratic if not parallelised. This technique combined with the inference of the basic reproduction number constitutes the first phylodynamics method without a tree. On a side project we evaluate the prevalence of tuberculosis mixed infection, which is likely to be twice as high of the detected 15%.
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Blauth, Jérôme [Verfasser]. "Infinite rate mutually catalytic branching driven by alpha-stable Lévy processes / Jérôme Blauth." Mainz : Universitätsbibliothek Mainz, 2017. http://d-nb.info/1125910283/34.
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Glöde, Patric Karl [Verfasser], and Andreas [Akademischer Betreuer] Greven. "Dynamics of Genealogical Trees for Autocatalytic Branching Processes / Patric Karl Glöde. Betreuer: Andreas Greven." Erlangen : Universitätsbibliothek der Universität Erlangen-Nürnberg, 2013. http://d-nb.info/1033029912/34.
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Hammer, Matthias [Verfasser]. "Ergodicity and regularity of invariant measure for branching Markov processes with immigration / Matthias Hammer." Mainz : Universitätsbibliothek Mainz, 2012. http://d-nb.info/1029390975/34.
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Glöde, Patric [Verfasser], and Andreas [Akademischer Betreuer] Greven. "Dynamics of Genealogical Trees for Autocatalytic Branching Processes / Patric Karl Glöde. Betreuer: Andreas Greven." Erlangen : Universitätsbibliothek der Universität Erlangen-Nürnberg, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:29-opus-45453.
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Cyran, Krzysztof. "Artifical intelligence, branching processes and coalescent methods in evolution of humans and early life." Praca habilitacyjna, Wydawnictwo Politechniki Śląskiej, 2011. https://delibra.bg.polsl.pl/dlibra/docmetadata?showContent=true&id=13205.
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Bansaye, Vincent. "Applications des processus de Lévy et processus de branchement à des études motivées par l'informatique et la biologie." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2008. http://tel.archives-ouvertes.fr/tel-00339230.
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Dans une première partie, j'étudie un processus de stockage de données en temps continu où le disque dur est identifié à la droite réelle. Ce modèle est une version continu du problème original de Parking de Knuth. Ici l'arrivée des fichiers est Poissonienne et le fichier se stocke dans les premiers espaces libres à droite de son point d'arrivée, quitte à se fragmenter. Dans un premier temps, je construis le modèle et donne une caractérisation géométrique et analytique de la partie du disque recouverte au temps t. Ensuite j'étudie les régimes asymptotiques au moment de saturation du disque. Enfin, je décris l'évolution en temps d'un block de données typique. La deuxième partie est constituée de l'étude de processus de branchement, motivée par des questions d'infection cellulaire. Dans un premier temps, je considère un processus de branchement en environnement aléatoire sous-critique, et détermine les théorèmes limites en fonction de la population initiale, ainsi que des propriétes sur les environnements, les limites de Yaglom et le Q-processus. Ensuite, j'utilise ce processus pour établir des résultats sur un modèle décrivant la prolifération d'un parasite dans une cellule en division. Je détermine la probabilité de guérison, le nombre asymptotique de cellules inféctées ainsi que les proportions asymptotiques de cellules infectées par un nombre donné de parasites. Ces différents résulats dépendent du régime du processus de branchement en environnement aléatoire. Enfin, j'ajoute une contamination aléatoire par des parasites extérieures.
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Dávila-Felipe, Miraine. "Pathwise decompositions of Lévy processes : applications to epidemiological modeling." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066651.
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Cette thèse est consacrée à l'étude de décompositions trajectorielles de processus de Lévy spectralement positifs et des relations de dualité pour des processus de ramification, motivée par l'utilisation de ces derniers comme modèles probabilistes d'une dynamique épidémiologique. Nous modélisons l'arbre de transmission d'une maladie comme un arbre de ramification, où les individus évoluent indépendamment les uns des autres, ont des durées de vie i.i.d. (périodes d'infectiosité) et donnent naissance (infections secondaires) à un taux constant durant leur vie. Le processus d'incidence dans ce modèle est un processus de Crump-Mode-Jagers (CMJ) et le but principal des deux premiers chapitres est d'en caractériser la loi conjointement avec l'arbre de transmission partiellement observé, inferé à partir des données de séquences. Dans le Chapitre I, nous obtenons une description en termes de fonctions génératrices de la loi du nombre d'individus infectieux, conditionnellement à l'arbre de transmission reliant les individus actuellement infectés. Une version plus élégante de cette caractérisation est donnée dans le Chapitre II, en passant par un résultat général d'invariance par retournement du temps pour une classe de processus de ramification. Finallement, dans le Chapitre III nous nous intéressons à la loi d'un processus de ramification (sous)critique vu depuis son temps d'extinction. Nous obtenons un résultat de dualité qui implique en particulier l'invariance par retournement du temps depuis leur temps d'extinction des processus CMJ (sous)critiques et de l'excursion hors de 0 de la diffusion de Feller critique (le processus de largeur de l'arbre aléatoire de continuum)This dissertation is devoted to the study of some pathwise decompositions of spectrally positive Lévy processes, and duality relationships for certain (possibly non-Markovian) branching processes, driven by the use of the latter as probabilistic models of epidemiological dynamics. More precisely, we model the transmission tree of a disease as a splitting tree, i.e. individuals evolve independently from one another, have i.i.d. lifetimes (periods of infectiousness) that are not necessarily exponential, and give birth (secondary infections) at a constant rate during their lifetime. The incidence of the disease under this model is a Crump-Mode-Jagers process (CMJ); the overarching goal of the two first chapters is to characterize the law of this incidence process through time, jointly with the partially observed (inferred from sequence data) transmission tree. In Chapter I we obtain a description, in terms of probability generating functions, of the conditional likelihood of the number of infectious individuals at multiple times, given the transmission network linking individuals that are currently infected. In the second chapter, a more elegant version of this characterization is given, passing by a general result of invariance under time reversal for a class of branching processes. Finally, in Chapter III we are interested in the law of the (sub)critical branching process seen from its extinction time. We obtain a duality result that implies in particular the invariance under time reversal from their extinction time of the (sub)critical CMJ processes and the excursion away from 0 of the critical Feller diffusion (the width process of the continuum random tree)
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Hartfield, Matthew. "Evolution of sex and recombination in large, finite populations." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/6212.
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This thesis investigates how breaking apart selection interference (‘Hill-Robertson’ effects) that arises between linked loci can select for higher levels of recombination. Specifically, it mainly studies how the presence of both advantageous and deleterious mutation affects selection for recombination. These evolutionary advantages are subsequently investigated with regards to sex resisting asexual invasion in a subdivided population. i) KEIGHTLEY and OTTO (2006) showed a strong advantage to recombination in breaking apart selection interference, if it acts across multiple, linked loci subject to recurrent deleterious mutation. Their model is modified to consider selection acting on recombination if a small proportion of mutations are advantageous. This leads to a greater increase in selection acting on a recombination modifier, compared to cases where only deleterious mutations are present. ii) Branching-process methods are developed to quantify how likely it is that a deleterious mutant hitchhikes with a selective sweep, and how recombination between the two loci affects this process. This is compared to the neutral hitchhiking model, to determine how levels of linked neutral diversity would differ between the two scenarios. A simple application with regards to human genetic data is provided. iii) Population subdivision can maintain costly sex, as a consequence of restricted gene flow slowing the spread of invading asexuals, which leads to an excessive accumulation of deleterious alleles. However, previous work did not quantify whether costly sex can be maintained with realistic levels of population subdivision. Simulations in this thesis show that the level of population subdivision (as measured by Fst) needed to maintain costly sex decreases with larger population size; however critical Fst values found are generally high, compared to surveys of geographicallyclose populations. The lowest levels of population subdivision that maintained sex were found if mutation is both advantageous and deleterious, and demes were arranged in a one-dimensional stepping-stone formation. iv) An analytical method is developed to calculate how long it takes an advantageous mutation (such as an invading asexual) to spread through a subdivided population. The flexibility of the methods created means that they can be applied to different types of stepping-stone populations. It is shown how to formulate the fixation time for one-dimensional and two-dimensional structures, with analytical methods showing a good fit to simulation data.
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Samuelsson, Love. "Introducing DevOps methods and processes for an existing organization." Thesis, Linnéuniversitetet, Institutionen för datavetenskap och medieteknik (DM), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-107150.
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DevOps is a cultural idea rather than a firm way to do software development, with the aim of reducing software lead times by bringing operations and development closer via principles that mainly deal with automation. This paper provides a potential DevOps solution for Wexnet, an internet service provider company. A requirements list is created by interviewing which is then used to evaluate existing web-based git solutions. Two viable candidates were selected, GitHub and GitLab which were compared against each other. GitLab was chosen because of its comparably low resource usage and lower overall setup complexity.
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Champagnat, Nicolas, and Sylvie Roelly. "Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions." Universität Potsdam, 2008. http://opus.kobv.de/ubp/volltexte/2008/1861/.
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A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every finite time interval, its distribution is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. Several results on the long time behavior of the conditioned mass process - the conditioned multitype Feller branching diffusion - are then proved. The general case is first considered, where the mutation matrix which models the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are analyzed too .
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Adam, Etienne. "Persistance et vitesse d'extinction pour des modèles de populations stochastiques multitypes en temps discret." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX019/document.
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Cette thèse porte sur l'étude mathématique de modèles stochastiques de dynamique de populations structurées.Dans le premier chapitre, nous introduisons un modèle stochastique à temps discret prenant en compte les diverses interactions possibles entre les individus, que ce soit de la compétition, de la migration, des mutations, ou bien de la prédation. Nous montrons d'abord un résultat de type ``loi des grands nombres'', où on montre que si la population initiale tend vers l'infini, alors sur un intervalle de temps fini, le processus stochastique converge en probabilité vers un processus déterministe sous-jacent. Nous quantifions aussi les écarts entre ces deux processus par un résultat de type ``théorème central limite''. Enfin, nous donnons un critère de persistance/extinction afin de déterminer le comportement en temps long de notre processus stochastique. Ce critère met en exergue un cas critique qui sera étudié plus en détail dans les chapitres suivants.Dans le deuxième chapitre, nous donnons un critère de croissance illimitée pour des processus vérifiant le cas critique évoqué plus haut. Nous illustrons en particulier ce critère avec l'exemple d'une métapopulation constituée de parcelles de type puits (c'est à dire dont la population s'éteint sans tenir compte de la migration), où l'on montre que la survie de la population est possible.Dans le troisième chapitre, nous nous intéressons au comportement du processus critique lorsqu'il croît vers l'infini. Nous montrons en particulier une convergence en loi vers une loi gamma de notre processus renormalisé et dans un cadre plus général, en renormalisant aussi en temps, nous obtenons une convergence en loi d'une fonction de notre processus vers la solution d'une équation différentielle stochastique appelée un processus de Bessel carré.Dans le quatrième et dernier chapitre, nous nous plac{c}ons dans le cas où le processus critique ne tend pas vers l'infini et étudions le temps d'atteinte de certains ensembles compacts. Nous donnons un encadrement asymptotique de la queue de ce temps d'atteinte. Lorsque le processus s'éteint, ces résultats nous permettent en particulier d'encadrer la queue du temps d'extinction. Dans le cas où notre processus est une chaîne de Markov, nous en déduisons un critère de récurrence nulle ou récurrence positive et dans ce cas, nous obtenons un taux de convergence sous-géométrique du noyau de transition de notre chaîne vers sa mesure de probabilité invarianteThis thesis is devoted to the mathematical study of stochastic modelds of structured populations dynamics.In the first chapter, we introduce a discrete time stochastic process taking into account various ecological interactions between individuals, such as competition, migration, mutation, or predation. We first prove a ``law of large numbers'': where we show that if the initial population tends to infinity, then, on any finite interval of time, the stochastic process converges in probability to an underlying deterministic process. We also quantify the discrepancy between these two processes by a kind of ``central limit theorem''. Finally, we give a criterion of persistence/extinction in order to determine the long time behavior of the process. This criterion highlights a critical case which will be studied in more detail in the following chapters.In the second chapter, we give a criterion for the possible unlimited growth in the critical case mentioned above. We apply this criterion to the example of a source-sink metapopulation with two patches of type source, textit{i.e.} the population of each patch goes to extinction if we do not take into account the migration. We prove that there is a possible survival of the metapopulation.In the third chapter, we focus on the behavior of our critical process when it tends to infinity. We prove a convergence in distribution of the scaled process to a gamma distribution, and in a more general framework, by also rescaling time, we obtain a distribution limit of a function of our process to the solution of a stochastic differential equation called a squared Bessel process.In the fourth and last chapter, we study hitting times of some compact sets when our process does not tend to infinity. We give nearly optimal bounds for the tail of these hitting times. If the process goes to extinction almost surely, we deduce from these bounds precise estimates of the tail of the extinction time. Moreover, if the process is a Markov chain, we give a criterion of null recurrence or positive recurrence and in the latter case, we obtain a subgeometric convergence of its transition kernel to its invariant probability measure
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Sinkovic, John Henry. "The Relationship Between the Minimal Rank of a Tree and the Rank-Spreads of the Vertices and Edges." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1622.pdf.
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Henry, Benoit. "Processus de branchements non Markoviens en dynamique et génétique des populations." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0135/document.
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Dans cette thèse nous considérons une population branchante générale où les individus vivent et se reproduisent de manière i.i.d. La durée de vie de chaque individu est distribuée suivant une mesure de probabilité arbitraire et chacun d'eux donne naissance à taux exponentiel. L'arbre décrivant la dynamique de cette population est connu sous le nom de splitting tree. Le processus comptant le nombre d’individus vivant au temps t est connu sous le nom de processus de Crump-Mode-Jagers binaire homogène, et il est connu que ce processus, quand correctement renormalisé, converge presque sûrement en temps long vers une variable aléatoire. Grâce à l'étude du splitting tree sous-jacent à la population via les outils introduit par A. Lambert en 2010, nous montrons un théorème central limite pour cette convergence p.s. dans le cas surcritique. Nous supposons, de plus, que les individus subissent des mutations à taux exponentiel sous l'hypothèse d'infinité d'allèles. Nous nous intéressons alors au spectre de fréquence allélique de la population qui compte la fréquence des tailles de familles dans la population à un instant donnée. Grâce aux méthodes développées dans cette thèse, nous obtenons des résultats d’approximations du spectre de Fréquence. Enfin nous nous intéressons à des questions statistiques sur des arbres de Galton-Watson conditionnés par leurs tailles. Le but est d'estimer la variance de la loi de naissance rendue inaccessible par le conditionnement. On utilise le fait que le processus de contour d'un tel arbre converge vers une excursion Brownienne quand la taille de l'arbre grandit afin de construire des estimateurs de la variance à partir de forêtsIn this thesis we consider a general branching population. The lifetimes of the individuals are supposed to be i.i.d. random variables distributed according to an arbitrary distribution. Moreover, each individual gives birth to new individuals at Poisson rate independently from the other individuals. The tree underlying the dynamics of this population is called a splitting tree. The process which count the number of alive individuals at given times is known as binary homogeneous Crump-Mode-Jagers processes. Such processes are known, when properly renormalized, to converge almost surely to some random variable. Thanks to the study of the underlying splitting tree through the tools introduced by A. Lambert in 2010, we show a central limit theorem associated to this a.s. convergence. Moreover, we suppose that individuals undergo mutation at Poisson rate under the infinitely many alleles assumption. We are mainly interested in the so called allelic frequency spectrum which describes the frequency of sizes of families (i.e. sets of individuals carrying the same type) at fixed times. Thanks to the methods developedin this thesis, we are able to get approximation results for the frequency spectrum. In a last part, we study some statistical problems for size constrained Galton-Watson trees. Our goal is to estimate the variance of the birth distribution. Using that the contour process of such tree converges to a Brownian excursion as the size of the tree growth, we construct estimators of the variance of the birth distribution
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Smadi, Charline. "Modèles probabilistes de populations : branchement avec catastrophes et signature génétique de la sélection." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1035/document.
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Cette thèse porte sur l'étude probabiliste des réponses démographique et génétique de populations à certains événements ponctuels. Dans une première partie, nous étudions l'impact de catastrophes tuant une fraction de la population et survenant de manière répétée, sur le comportement en temps long d'une population modélisée par un processus de branchement. Dans un premier temps nous construisons une nouvelle classe de processus, les processus de branchement à états continus avec catastrophes, en les réalisant comme l'unique solution forte d'une équation différentielle stochastique. Nous déterminons ensuite les conditions d'extinction de la population. Enfin, dans les cas d'absorption presque sûre nous calculons la vitesse d'absorption asymptotique du processus. Ce dernier résultat a une application directe à la détermination du nombre de cellules infectées dans un modèle d'infection de cellules par des parasites. En effet, la quantité de parasites dans une lignée cellulaire suit dans ce modèle un processus de branchement, et les "catastrophes" surviennent lorsque la quantité de parasites est partagée entre les deux cellules filles lors des divisions cellulaires. Dans une seconde partie, nous nous intéressons à la signature génétique laissée par un balayage sélectif. Le matériel génétique d'un individu détermine (pour une grande partie) son phénotype et en particulier certains traits quantitatifs comme les taux de naissance et de mort intrinsèque, ou sa capacité d'interaction avec les autres individus. Mais son génotype seul ne détermine pas son ``adaptation'' dans le milieu dans lequel il vit : l'espérance de vie d'un humain par exemple est très dépendante de l'environnement dans lequel il vit (accès à l'eau potable, à des infrastructures médicales,...). L'approche éco-évolutive cherche à prendre en compte l'environnement en modélisant les interactions entre les individus. Lorsqu'une mutation ou une modification de l'environnement survient, des allèles peuvent envahir la population au détriment des autres allèles : c'est le phénomène de balayage sélectif. Ces événements évolutifs laissent des traces dans la diversité neutre au voisinage du locus auquel l'allèle s'est fixé. En effet ce dernier ``emmène'' avec lui des allèles qui se trouvent sur les loci physiquement liés au locus sous sélection. La seule possibilité pour un locus de ne pas être ``emmené'' est l'occurence d'une recombination génétique, qui l'associe à un autre haplotype dans la population. Nous quantifions la signature laissée par un tel balayage sélectif sur la diversité neutre. Nous nous concentrons dans un premier temps sur la variation des proportions neutres dans les loci voisins du locus sous sélection sous différents scénarios de balayages. Nous montrons que ces différents scenari évolutifs laissent des traces bien distinctes sur la diversité neutre, qui peuvent permettre de les discriminer. Dans un deuxième temps, nous nous intéressons aux généalogies jointes de deux loci neutres au voisinage du locus sous sélection. Cela nous permet en particulier de quantifier des statistiques attendues sous certains scenari de sélection, qui sont utilisées à l'heure actuelle pour détecter des événements de sélection dans l'histoire évolutive de populations à partir de données génétiques actuelles. Dans ces travaux, la population évolue suivant un processus de naissance et mort multitype avec compétition. Si un tel modèle est plus réaliste que les processus de branchement, la non-linéarité introduite par les compétitions entre individus en rend l'étude plus complexeThis thesis is devoted to the probabilistic study of demographic and genetical responses of a population to some point wise events. In a first part, we are interested in the effect of random catastrophes, which kill a fraction of the population and occur repeatedly, in populations modeled by branching processes. First we construct a new class of processes, the continuous state branching processes with catastrophes, as the unique strong solution of a stochastic differential equation. Then we describe the conditions for the population extinction. Finally, in the case of almost sure absorption, we state the asymptotical rate of absorption. This last result has a direct application to the determination of the number of infected cells in a model of cell infection by parasites. Indeed, the parasite population size in a lineage follows in this model a branching process, and catastrophes correspond to the sharing of the parasites between the two daughter cells when a division occurs. In a second part, we focus on the genetic signature of selective sweeps. The genetic material of an individual (mostly) determines its phenotype and in particular some quantitative traits, as birth and intrinsic death rates, and interactions with others individuals. But genotype is not sufficient to determine "adaptation" in a given environment: for example the life expectancy of a human being is very dependent on his environment (access to drinking water, to medical infrastructures,...). The eco-evolutive approach aims at taking into account the environment by modeling interactions between individuals. When a mutation or an environmental modification occurs, some alleles can invade the population to the detriment of other alleles: this phenomenon is called a selective sweep and leaves signatures in the neutral diversity in the vicinity of the locus where the allele fixates. Indeed, this latter "hitchhiking” alleles situated on loci linked to the selected locus. The only possibility for an allele to escape this "hitchhiking" is the occurrence of a genetical recombination, which associates it to another haplotype in the population. We quantify the signature left by such a selective sweep on the neutral diversity. We first focus on neutral proportion variation in loci partially linked with the selected locus, under different scenari of selective sweeps. We prove that these different scenari leave distinct signatures on neutral diversity, which can allow to discriminate them. Then we focus on the linked genealogies of two neutral alleles situated in the vicinity of the selected locus. In particular, we quantify some statistics under different scenari of selective sweeps, which are currently used to detect recent selective events in current population genetic data. In these works the population evolves as a multitype birth and death process with competition. If such a model is more realistic than branching processes, the non-linearity caused by competitions makes its study more complex
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Hénard, Olivier. "Généalogie et Q-processus." Phd thesis, Université Paris-Est, 2012. http://tel.archives-ouvertes.fr/tel-00763378.
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Cette thèse étudie le Q-processus de certains processus de branchement (superprocessus inhomogènes) ou de recombinaison (processus de Lambda-Fleming-Viot) via une approche généalogique. Dans le premier cas, le Q-processus est défini comme le processus conditionné à la non-extinction, dans le second cas comme le processus conditionné à la non-absorption. Des constructions trajectorielles des Q-processus sont proposées dans les deux cas. Une nouvelle relation entre superprocessus homogènes et processus de Lambda-Fleming-Viot est établie. Enfin, une étude du Q-processus est menée dans le cadre général des processus régénératifs
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Jones, Cameron Lawrence, and cajones@swin edu au. "Image analysis of fungal biostructure by fractal and wavelet techniques." Swinburne University of Technology, 1997. http://adt.lib.swin.edu.au./public/adt-VSWT20051107.093036.
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Filamentous fungal colonies show a remarkable diversity of different mycelial branching patterns. To date, the characterization of this biostructural complexity has been based on subjective descriptions. Here, computerized image analysis in conjunction with video microscopy has been used to quantify several aspects of fungal growth and differentiation. This was accomplished by applying the new branch of mathematics called Fractal Geometry to this biological system, to provide an objective description of morphological and biochemical complexity. The fractal dimension is useful for describing irregularity and shape complexity in systems that appear to display scaling correlations (between structural units) over several orders of length or size. The branching dynamics of Pycnoporus cinnabarinus have been evaluated using fractals in order to determine whether there was a correlation between branching complexity and the amount of extracellular phenol-oxidase that accumulated during growth.
A non-linear branching response was observed when colonies were grown in the presence of the aminoanthraquinone dye, Remazol Brilliant Blue R. Branching complexity could be used to predict the generalized yield of phenol-oxidase that
accumulated in submerged culture, or identify paramorphogens that could be used to improve yield. A method to optimize growth of discrete fungal colonies for microscopy and image analysis on microporous membranes revealed secretion sites of the phenoloxidase, laccase as well as the intracellular enzyme, acid phosphatase. This method was further improved using microwave-accelerated heating to detect tip and sheath bound enzyme.
The spatial deposition of secreted laccase and acid phosphatase displayed antipersistent scaling in deposition and/or secretion pattern. To overcome inherent statistical limitations of existing methods, a new signal processing tool, called wavelets were applied to analyze both one and two-dimensional data to measure fractal scaling. Two-dimensional wavelet packet analysis (2-d WPA) measured the (i) mass fractal dimension of binary images, or the (ii) self-affine dimension of grey-scale images. Both 1- and 2-d WPA showed comparative accuracy with existing methods yet offered improvements in computational efficiency that were inherent with this multiresolution technique.
The fractal dimension was shown to be a sensitive indicator of shape complexity. The discovery of power law scaling was a hallmark of fractal geometry and in many cases returned values that were indicative of a self-organized critical state. This meant that the dynamics of fungal colony branching equilibrium. Hence there was potential for biostructural changes of all sizes, which would allow the system to efficiently adapt to environmental change at both the macro and micro levels.
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Mazoyer, Adrien. "Modèles de mutation : étude probabiliste et estimation paramétrique." Thesis, Université Grenoble Alpes (ComUE), 2017. http://www.theses.fr/2017GREAM032/document.
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Les modèles de mutations décrivent le processus d’apparitions rares et aléatoires de mutations au cours de lacroissance d’une population de cellules. Les échantillons obtenus sont constitués de nombres finaux de cellules mutantes,qui peuvent être couplés avec des nombres totaux de cellules ou un nombre moyen de cellules en fin d’expérience.La loi du nombre final de mutantes est une loi à queue lourde : de grands décomptes, appelés “jackpots”,apparaissent fréquemment dans les données.Une construction générale des modèles se décompose en troisniveaux. Le premier niveau est l’apparition de mutations aléatoires au cours d’un processus de croissance de population.En pratique, les divisions cellulaires sont très nombreuses, et la probabilité qu’une de ces divisions conduise à une mutation est faible,ce qui justifie une approximation poissonnienne pour le nombre de mutations survenant pendant un temps d’observation donné.Le second niveau est celui des durées de développement des clones issus de cellules mutantes. Du fait de la croissance exponentielle,la majeure partie des mutations ont lieu à la fin du processus, et les durées de développement sont alors indépendanteset exponentiellement distribuées. Le troisième niveau concerne le nombre decellules qu’un clone issu d’une cellule mutante atteint pendant une durée de développement donnée.La loi de ce nombre dépend principalement de la loi des instants de division des mutantes.Le modèle classique, dit de Luria-Delbrück, suppose que les développements cellulaires des cellules normales aussi bien que mutantess’effectue selon un processus de Yule. On peut dans ce cas calculer expliciter la loi du nombre final de mutantes.Elle dépend de deux paramètres, qui sont le nombre moyen de mutations et le paramètre de fitness (ratio des taux de croissance des deux types de cellules).Le problème statistique consiste à estimer ces deux paramètres au vu d’un échantillon denombres finaux de mutantes. Il peut être résolu par maximisation de la vraisemblance,ou bien par une méthode basée sur la fonction génératrice. Diviser l'estimation du nombre moyen de mutations par le nombre total de cellulespermet alors d'estimer la probabilité d’apparition d’une mutation au cours d’une division cellulaire.L’estimation de cette probabilité est d’une importancecruciale dans plusieurs domaines de la médecine et debiologie: rechute de cancer, résistance aux antibiotiques de Mycobacterium Tuberculosis, etc.La difficulté provient de ce que les hypothèses de modélisation sous lesquelles la distribution du nombre final de mutants est explicitesont irréalistes.Or estimer les paramètres d’un modèle quand la réalité en suit un autre conduit nécessairement à un biais d’estimation.Il est donc nécessaire de disposer de méthodes d’estimation robustes pour lesquelles le biais, en particulier sur la probabilité de mutation,reste le moins sensible possible aux hypothèses de modélisation.Cette thèse contient une étude probabiliste et statistique de modèles de mutations prenant en compte les sources de biais suivantes : durées de vie non exponentielles, morts cellulaires,variabilité du nombre final de cellules, durées de vie non-exponentielles et non-identiquement distribuées, dilution de la population initiale.Des études par simulation des méthodes considérées sont effectuées afin de proposer, selon les caractéristiques du modèle,l’estimation la plus fiable possible. Ces méthodes ont également été appliquées à desjeux de données réelles, afin de comparer les résultats avec les estimations obtenues avec les modèles classiques.Un package R a été implémenté en collaboration avec Rémy Drouilhet et Stéphane Despréaux et est disponible sur le CRAN.Ce package est constitué des différents résultats obtenus au cours de ce travail. Il contient des fonctions dédiées aux modèles de mutations,ainsi qu'à l'estimation des paramètres. Les applications ont été développées pour le Labex TOUCAN (Toulouse Cancer)Mutation models are probabilistic descriptions of the growth of a population of cells, where mutationsoccur randomly during the process. Data are samples of integers, interpreted as final numbers ofmutant cells. These numbers may be coupled with final numbers of cells (mutant and non mutant) or a mean final number of cells.The frequent appearance in the data of very large mutant counts, usually called “jackpots”, evidencesheavy-tailed probability distributions.Any mutation model can be interpreted as the result of three ingredients. The first ingredient is about the number of mutations occuring with small probabilityamong a large number of cell divisions. Due to the law of small numbers, the number of mutations approximately follows aPoisson distribution. The second ingredient models the developing duration of the clone stemming from each mutation. Due to exponentialgrowth, most mutations occur close to the end of the experiment. Thus the developing time of arandom clone has exponential distribution. The last ingredients represents the number of mutant cells that any clone developing for a given time will produce. Thedistribution of this number depends mainly on the distribution of division times of mutants.One of the most used mutation model is the Luria-Delbrück model.In these model, division times of mutant cells were supposed to be exponentially distributed.Thus a clone develops according to a Yule process and its size at any given time follows a geometric distribution.This approach leads to a family of probability distributions which depend on the expected number of mutations and the relative fitness, which is the ratio between the growth rate of normal cells to that of mutants.The statistic purpose of these models is the estimation of these parameters. The probability for amutant cell to appear upon any given cell division is estimated dividing the mean number of mutations by the mean final number of cells.Given samples of final mutant counts, it is possible to build estimators maximizing the likelihood, or usingprobability generating function.Computing robust estimates is of crucial importance in medical applications, like cancer tumor relapse or multidrug resistance of Mycobacterium Tuberculosis for instance.The problem with classical mutation models, is that they are based on quite unrealistic assumptions: constant final number of cells,no cell deaths, exponential distribution of lifetimes, or time homogeneity. Using a model for estimation, when thedata have been generated by another one, necessarily induces a bias on estimates.Several sources of bias has been partially dealed until now: non-exponential lifetimes, cell deaths, fluctuations of the final count of cells,dependence of the lifetimes, plating efficiency. The time homogeneity remains untreated.This thesis contains probabilistic and statistic study of mutation models taking into account the following bias sources:non-exponential and non-identical lifetimes, cell deaths, fluctuations of the final count of cells, plating efficiency.Simulation studies has been performed in order to propose robust estimation methods, whatever the modeling assumptions.The methods have also been applied to real data sets, to compare the results with the estimates obtained under classical models.An R package based on the different results obtained in this work has been implemented (joint work with Rémy Drouilhetand Stéphane Despréaux) and is available on the CRAN. It includes functions dedicated to the mutation models and parameter estimation.The applications have been developed for the Labex TOUCAN (Toulouse Cancer)
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Castro, Diogo [UNIFESP]. "Simulação computacional e análise de um modelo fenotípico de evolução viral." Universidade Federal de São Paulo (UNIFESP), 2011. http://repositorio.unifesp.br/handle/11600/10085.
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Made available in DSpace on 2015-07-22T20:50:48Z (GMT). No. of bitstreams: 0
Previous issue date: 2011-01-26Uma grande quantidade dos vírus de importância médica, como o HIV, o vírus sincicial respiratório, o vírus da hepatite C, o vírus influenza A (H1N1), e o vírus da poliomielite, possui genoma RNA. Estes vírus apresentam taxas mutacionais extremamente altas, rápida cinética replicativa, população numerosa de partículas, e grande diversidade genética. Manifestas durante o processo infeccioso, tais características permitem a população viral adaptar-se rapidamente a ambientes dinâmicos, escapar ao sistema imunológico, desenvolver resistência às vacinas e drogas antivirais, e exibir dinâmica evolutiva complexa cuja compreensão representa um desafio para a genética de populações tradicional e para as estratégias de intervenção terapêutica efetiva. Para descrever biológica e matematicamente a evolução dos vírus RNA, modelos teóricos de evolução viral têm sido propostos, e muitas de suas predições foram confirmadas experimentalmente. O presente trabalho teve como objetivo simular computacionalmente e analisar um modelo de evolução viral que represente relações evolutivas existentes entre a população viral de genoma RNA e as diferentes pressões seletivas exercidas sobre ela na sua interação com o organismo hospedeiro. Também objetivou desenvolver um software de simulação computacional personalizado para o modelo de evolução viral, e demonstrar a possibilidade de descrever o modelo como um processo de ramificação de Galton-Watson. Entre os resultados e discussões delineados, encontram-se um critério analítico para estudo do tempo de recuperação e do regime crítico de um processo de ramificação de Galton-Watson aplicado à evolução viral; predições sobre a correlação entre fatores do organismo hospedeiro e a dinâmica evolutiva da população viral; predições sobre a contribuição da taxa mutacional, do tamanho e da capacidade replicativa máxima da população viral para o prognóstico e quatro fases da infecção: o tempo de recuperação, o equilíbrio mutação-seleção, o limiar da extinção, e a mutagênese letal.
A large amount of viruses of medical importance such as HIV, respiratory syncytial virus, the hepatitis C virus, influenza A (H1N1) and polio virus, has RNA genome. These viruses exhibit extremely high mutational rate, fast replicative kinetics, large population of particles and high genetic diversity. Manifested during the infectious process, these features allow the virus population to adapt quickly to dynamic environments, escape from the immune system, develop resistance to vaccines and antiviral drugs, and display complex evolutionary dynamics whose understanding represents a challenge to the traditional population genetics and for effective therapeutic intervention strategies. To describe mathematically and biological evolution of RNA viruses, theoretical models of virus evolution have been proposed, and many of their predictions were experimentally confirmed. This study aimed to simulate and analyze computationally a model of viral evolution that represents evolutionary relationships between the population of viral RNA genome and the different selective pressures on it in its interaction with the host organism. It also aimed to develop computational simulation software for the viral evolution model, and demonstrate the possibility of describing the model as a Galton-Watson branching process. Among the results and discussions outlined, there are an analytical criterion to study the recovery time and the critical regime of a Galton-Watson branching process applied to viral evolution; predictions about the correlation between factors of the host organism and the evolutionary dynamics of viral population; predictions about the contribution of mutational rate, the size and maximum replicative capacity of viral population for the prognosis and four stages of infection: recovery time, mutation-selection equilibrium, extinction threshold, and lethal mutagenesis.
TEDE
BV UNIFESP: Teses e dissertações
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García, García Beatriz. "Estudio de procesos de Migración y Plasticidad en el Sistema Nervioso Central: Papel de Semaforina 4F y kinasa de adhesión focal (FAK)." Doctoral thesis, Universitat de Barcelona, 2013. http://hdl.handle.net/10803/116772.
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La presente tesis doctoral presenta varios resultados fundamentales para la ampliación del conocimiento actual de procesos importantes en la generación de los circuitos neuronales, como son la migración y la ramificación de células neurales.
En primer lugar, se ha determinado la expresión de la semaforina transmembranal 4F en cerebro de ratón en desarrollo y adulto. Así, se ha visto que se expresa en diversas áreas del cerebro, y se ha encontrado expresión de esta proteína en precursores neuronales y en neuronas maduras, principalmente en dendritas, y en células del linaje oligodendroglial. Para profundizar más en este aspecto se llevaron a cabo varios marcajes dobles de Sema4F con proteínas marcadoras de oligodendrocitos, observándose marca en el nervio óptico y otras regiones cerebrales, incluídas la materia blanca y vías de migración de oligodendrocitos. La localización de esta semaforina en el nervio óptico a edades embrionarias y su expresión en células precursoras de oligodendrocitos (OPCs), comprobada in vitro, nos llevó a sugerir que Sema4F funciona controlando la migración de OPCs. Una serie de experimentos con explantes de nervio óptico tratados con medio control o medio condicionado 4F nos permitió determinar que Sema4F actúa inhibiendo la migración de OPCs, sin afectar a su proliferación. Además, Sema4F induce la diferenciación de OPCs a oligodendrocitos maduros. Todos estos datos sugieren un posible papel de Sema4F en procesos de remielinización.
Los efectos negativos de Sema4F sobre la migración de OPCs deben cursar con cambios en el citoesqueleto celular. La kinasa de adhesión focal (FAK) es un importante mediador de señales extracelulares (como factores tróficos, interacción de integrinas con proteínas de matriz extracelular, etc…) y el interior de las células. Actúa sobre el citoesqueleto de actina y de tubulina, influyendo en la generación de filopodios, lamelipodios y fibras de estrés. Tiene un papel crucial en migración, de modo que dedicimos estudiar si Sema4F ejerce sus efectos en OPCs a través FAK. Hemos visto que Sema4F es capaz de inducir la fosforilación en varios residuos tirosina de FAK en pocos minutos, y que ambas proteínas por separado ejercen efectos opuestos en la migración de oligodendrocitos. La vía de señalización de 4F, de la que se desconoce incluso el receptor, podría cursar mediante la modulación del estado de activación de FAK, aunque faltan experimentos definitivos.
FAK presenta varias isoformas específicas del sistema nervioso central, originadas mediante procesos de splicing alternativo. En la presente tesis hemos determinado con gran especificidad la forma mayoritaria expresada en varias áreas cerebrales y en el desarrollo embrionario o el adulto, tanto en neuronas como en células de la glía.
FAK responde a neurotrofinas y participa en procesos de ramificación neuronal, si bien su efecto final es controvertido. Otra proteína que responde a neurotrofinas, y actúa promoviendo la ramificación axonal, es la kinasa dependiente de cdc-42 activada 1 (Ack1). En esta tesis hemos determinado que ambas proteínas interaccionan en cerebro específicamente, de manera independiente de la isoforma de FAK presente. Mediante el uso de inhibidores hemos visto que la activación de FAK es necesaria para la fosforilación de Ack1 y viceversa. FAK es la responsable de la atracción ejercida por netrina-1, y hemos determinado que la ausencia de Ack1 elimina el efecto de esta molécula de señalización. Con técnicas de Espetrometría de Masas hemos identificado algunos posibles interactores de ambas proteínas. Además, hemos observado cambios en el estado de fosforilación de varios residuos de FAK y Ack1 en función del estado de desarrollo (ratones P5 Vs. Adultos) y del estado general de activación del cerebro (ratones inyectados con la droga epileptogénica PTZ Vs. Control).This thesis presents several results related to important processes regarding neural circuit formation, i.e. migration and ramification of Central Nervous System (CNS) cells. First, we have determined the expression of transmembrane semaphorin 4F (Sema4F) in developing and adult mice brain. Expression of this protein is high in neuronal and oligodendrocyte precursor cells (OPCs), and in different areas including optic nerve (ON) and different migratory pathways. In vitro experiments confirmed Sema4F expression in OPCs. We investigated the role of this protein in functions important for OPC physiology, and found that Sema4F inhibits OPC migration from ON explants and induces their differentiation into mature progenitors. Negative effects of Sema4F in migration must involve cytoskeleton changes. Focal adhesion kinase (FAK) is an important integrator of different extracellular signals and modulates cytoskeleton dynamics to control generation of lamellipodia, fillopodia and stress fibers. In the present project we found that Sema4F is able to phosphorylate FAK, and that FAK enhances OPC migration. The exact implications of Sema4F-FAK relationship remain to be elucidated. FAK exists in different spliced isoforms, expressed preferentially in brain. In this project, we characterised the exact isoform expressed in different areas of the brain and by different cell types. Finally, FAK response to neurotrophins is well characterised. FAK also participates in ramification processes, with controversial final effects in neurons. Ack1 is a crucial transducer of neurotrophin-induced ramification. In this thesis we show that both proteins interact specifically in neurons. We have also found that the activation of FAK is necessary for Ack1 phosphorylation upon stimulation, and viceversa. FAK mediates netrin-1 attraction, and here we have determined that knocking-down Ack1 avoids netrin-1 effects in hippocampal explants. By Mass Spectrometry (MS) techniques, we have observed changes in the phosphorylation state of both proteins depending on the developmental stage of the brain (P5 mice) or its activation state (epileptic mice).
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Hoffmann, Daniel [Verfasser], Frank [Akademischer Betreuer] Seifried, Frank [Gutachter] Seifried, Volker [Gutachter] Schulz, and Sören [Gutachter] Christensen. "Stochastic Particle Systems and Optimization - Branching Processes, Mean Field Games and Impulse Control / Daniel Hoffmann ; Gutachter: Frank Seifried, Volker Schulz, Sören Christensen ; Betreuer: Frank Seifried." Trier : Universität Trier, 2020. http://d-nb.info/1221825690/34.
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Cao, Xiaoou. "Growth of Galton-Watson trees with lifetimes, immigrations and mutations." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:beaa9fe1-d60c-4487-9520-e8f004b53e6f.
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In this work, we are interested in Growth of Galton-Watson trees under two different models: (1) Galton-Watson (GW) forests with lifetimes and/or immigrants, and (2) Galton-Watson forests with mutation, which we call Galton-Watson-Clone-Mutant forests, or GWCMforests. Under each model, we study certain consistent families (Fλ)λ≥0 of GW/GWCM forests and associated decompositions that include backbone decomposition as studied by many authors. Specifically, consistency here refers to the property that for each μ ≤ λ, the forest Fμ has the same distribution as the subforest of Fλ spanned by the blue leaves in a Bernoulli leaf colouring, where each leaf of Fλ is coloured in blue independently with probability μ/λ. In the first model, the case of exponentially distributed lifetimes and no immigration was studied by Duquesne and Winkel and related to the genealogy of Markovian continuous-state branching processes (CSBP). We characterise here such families in the framework of arbitrary lifetime distributions and immigration according to a renewal process, and show convergence to Sagitov’s (non-Markovian) generalisation of continuous-state branching renewal processes, and related processes with immigration. In the second model, we characterise such families in terms of certain bivariate CSBP with branching mechanisms studied previously by Watanabe and show associated convergence results. This is related to, but more general than Bertoin’s study of GWCM trees, and also ties in with work by Abraham and Delmas, who study directly some of the limiting processes.
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Driver, David Philip. "An optimisation-based approach to FKPP-type equations." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/277769.
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In this thesis, we study a class of reaction-diffusion equations of the form $\frac{\partial u}{\partial t} = \mathcal{L}u + \phi u - \tfrac{1}{k} u^{k+1}$ where $\mathcal{L}$ is the stochastic generator of a Markov process, $\phi$ is a function of the space variables and $k\in \mathbb{R}\backslash\{0\}$. An important example, in the case when $k > 0$, is equations of the FKPP-type. We also give an example from the theory of utility maximisation problems when such equations arise and in this case $k < 0$. We introduce a new representation, for the solution of the equation, as the optimal value of an optimal control problem. We also give a second representation which can be seen as a dual problem to the first optimisation problem. We note that this is a new type of dual problem and we compare it to the standard Lagrangian dual formulation. By choosing controls in the optimisation problems we obtain upper and lower bounds on the solution to the PDE. We use these bounds to study the speed of the wave front of the PDE in the case when $\mathcal{L}$ is the generator of a suitable Lévy process.