Bien que de nombreuses séquences génomiques soient maintenant connues, les mécanismes évolutifs qui déterminent la taille des génomes, et notamment leur part d’ADN non codant, sont encore débattus. Ainsi, alors que de nombreux mécanismes faisant grandir les génomes (prolifération d’éléments transposables, création de nouveaux gènes par duplication, ...) sont clairement identifiés, les mécanismes limitant la taille des génomes sont moins bien établis. La sélection darwinienne pourrait directement défavoriser les génomes les moins compacts, sous l’hypothèse qu’une grande quantité d’ADN à répliquer limite la vitesse de reproduction de l’organisme. Cette hypothèse étant cependant contredite par plusieurs jeux de données, d’autres mécanismes non sélectifs ont été proposés, comme la dérive génétique et/ou un biais mutationnel rendant les petites délétions d’ADN plus fréquentes que les petites insertions. Dans ce manuscrit, nous montrons à l’aide d’un modèle matriciel de population que la taille du génome peut aussi être limitée par la dynamique spontanée des duplications et des grandes délétions, qui tend à raccourcir les génomes même si les deux types de réarrangements se produisent à la même fréquence. En l’absence de sélection darwinienne, nous prouvons l’existence d’une distribution stationnaire pour la taille du génome même si les duplications sont deux fois plus fréquentes que les délétions. Pour tester si la sélection darwinienne peut contrecarrer cette dynamique spontanée, nous simulons numériquement le modèle en choisissant une fonction de fitness qui favorise directement les génomes contenant le plus de gènes, tout en conservant des duplications deux fois plus fréquentes que les délétions. Dans ce scénario où tout semblait pousser les génomes à grandir infiniment, la taille du génome reste pourtant bornée. Ainsi, notre étude révèle une nouvelle force susceptible de limiter la croissance des génomes. En mettant en évidence des comportements contre-intuitifs dans un modèle pourtant minimaliste, cette étude souligne aussi les limites de la simple « expérience de pensée » pour penser l’évolution. / Even though numerous genome sequences are now available, evolutionary mechanisms that determine genome size, notably their fraction of non-coding DNA, are still debated. In particular, although several mechanisms responsible for genome growth (proliferation of transposable elements, gene duplication and divergence, etc.) were clearly identified, mechanisms limiting the overall genome size remain unclear. Darwinian selection could directly disadvantage less compact genomes, under the hypothesis that a larger quantity of DNA could slow down the speed of reproduction of the organism. Because this hypothesis was proven wrong by several datasets, non selective mechanisms have been proposed, e.g. genetic drift and/or a mutational bias towards small DNA deletions compared to small DNA insertions. In this manuscript, we use a matrix model to show that genome size can also be limited by the spontaneous dynamics of duplications and large deletions, which tends to decrease genome size even if the two types of rearrangements occur at the same rate. In the absence of Darwinian selection, we prove the existence of a stationary distribution of genome size even if duplications are twice as frequent as large deletions. To test whether selection can overcome this spontaneous dynamics, we simulate our model numerically and choose a fitness function that directly favors genomes containing more genes, while keeping duplications twice as frequent as large deletions. In this scenario where, at first sight, everything seems to favor infinite genome growth, genome size remains nonetheless bounded. As a result, our study reveals a new pressure that could be responsible for limiting genome growth. By illustrating counter-intuitive behaviors in a minimal model, this study also underlines the limits of simple "thought experiments" to understand evolution.

A informação sobre a dinâmica espaço-temporal de doenças de plantas é de importância fundamental em estudos epidemiológicos, podendo ser utilizada para descrever e entender o desenvolvimento das doenças, desenvolver planos de amostragem, planejar experimentos controlados e caracterizar perdas na produção ocasionadas pela doença. O estudo de padrões espaciais de doenças de plantas, que são reflexos do processo de dispersão dos patógenos, é importante em estudos epidemiológicos, como o de doenças dos citros, para se definirem estratégias mais adequadas para o controle das doenças, diminuindo os prejuízos causados. A Citricultura é uma das principais atividades agrícolas do Brasil e representa a principal atividade econômica de mais de 400 municípios do Triângulo Mineiro e do Estado de São Paulo, onde se encontra a maior área de citros do país e a maior região produtora de laranjas do mundo. Na avaliação do padrão espacial, diferentes métodos têm sido utilizados, dentre os quais incluem-se o ajuste de distribuições, como, por exemplo, a distribuição beta-binomial, o estudo da relação variância-média, o cálculo de correlação ao intraclasse, a utilização de técnicas de autocorrelação espacial, métodos de classes de distâncias e o ajuste de modelos estocásticos espaço-temporais. Diante da importância de se estudarem padrões espaciais da incidência de doenças em plantas e da necessidade de se conhecer melhor a epidemiologia da morte súbita dos citros e do cancro cítrico, uma técnica baseada em verossimilhança para o ajuste de modelos estocásticos espaço-temporais foi utilizada na caracterização de padrões espaciais. Modificações na metodologia original, buscando uma diminuição do tempo gasto nas análises, foram propostas nesse estudo. Os resultados mostram que as modificações propostas resultaram em uma diminuição significativa no tempo de análise, sem perda de acurácia na estimação dos parâmetros dos modelos considerados. / The information about the spatial-temporal dynamics is of fundamental importance in epidemiological studies for describing and understanding the development of diseases, for developing efficient sampling plans, for planning controlled experiments, for evaluating the effect of different treatments, and for determining crop losses. The Citriculture is the major economic activity of more than 400 municipalities in Minas Gerais and São Paulo States. This is the largest citrus area in Brazil, and the largest sweet orange production area in the world. Therefore, it is very important to study and to characterize spatial patterns of plant diseases, such as citrus canker and citrus sudden death. In the spatial dynamics study, many different methods have been used to characterize the spatial aggregation. These include the fitting of distributions, such as the beta-binomial distribution, the study of variance-mean relationships, the calculation of intraclass correlation, the use of spatial autocorrelation techniques, distance class methods and, the fitting of continuous time spatiotemporal stochastic models. In this work, an improved technique for fitting models to the spatial incidence data by using MCMC methods is proposed. This improved technique, which is used to investigate the spatial patterns of plant disease incidence, is considerably faster than Gibson’s methodology, in terms of computational time, without any loss of accuracy.

<p>The Swedish National Debt Office (SNDO) is the Swedish Government’s financial administration. It has several tasks and the main one is to manage the central government’s debt in a way that minimizes the cost with due regard to risk. The debt management problem is to choose currency composition and maturity profile - a problem made difficult because of the many stochastic factors involved. </p><p>The SNDO has created a simulation model to quantitatively analyze different aspects of this problem by evaluating a set of static strategies in a great number of simulated futures. This approach has a number of drawbacks, which might be handled by using a financial optimization approach based on Stochastic Programming. </p><p>The objective of this master’s thesis is thus to apply financial optimization on the Swedish government’s strategic debt management problem, using the SNDO’s simulation model to generate scenarios, and to evaluate this approach against a set of static strategies in fictitious future macroeconomic developments. </p><p>In this report we describe how the SNDO’s simulation model is used along with a clustering algorithm to form future scenarios, which are then used by an optimization model to find an optimal decision regarding the debt management problem. </p><p>Results of the evaluations show that our optimization approach is expected to have a lower average annual real cost, but with somewhat higher risk, than a set of static comparison strategies in a simulated future. These evaluation results are based on a risk preference set by ourselves, since the government has not expressed its risk preference quantitatively. We also conclude that financial optimization is applicable on the government debt management problem, although some work remains before the method can be incorporated into the strategic work of the SNDO.</p>

The Swedish National Debt Office (SNDO) is the Swedish Government’s financial administration. It has several tasks and the main one is to manage the central government’s debt in a way that minimizes the cost with due regard to risk. The debt management problem is to choose currency composition and maturity profile - a problem made difficult because of the many stochastic factors involved. The SNDO has created a simulation model to quantitatively analyze different aspects of this problem by evaluating a set of static strategies in a great number of simulated futures. This approach has a number of drawbacks, which might be handled by using a financial optimization approach based on Stochastic Programming. The objective of this master’s thesis is thus to apply financial optimization on the Swedish government’s strategic debt management problem, using the SNDO’s simulation model to generate scenarios, and to evaluate this approach against a set of static strategies in fictitious future macroeconomic developments. In this report we describe how the SNDO’s simulation model is used along with a clustering algorithm to form future scenarios, which are then used by an optimization model to find an optimal decision regarding the debt management problem. Results of the evaluations show that our optimization approach is expected to have a lower average annual real cost, but with somewhat higher risk, than a set of static comparison strategies in a simulated future. These evaluation results are based on a risk preference set by ourselves, since the government has not expressed its risk preference quantitatively. We also conclude that financial optimization is applicable on the government debt management problem, although some work remains before the method can be incorporated into the strategic work of the SNDO.

No description available.

[pt] Devido à crescente utilização de fontes alternativas de energia, as do tipo renováveis têm se mostrado cada vez mais atraentes e viáveis. O etanol, oriundo da cana-de-açúcar, é considerado um combustível promissor e uma alternativa menos poluente que o petróleo nos dias de hoje. Além disso, o volume de produção de etanol no Brasil também tem crescido de forma consistente. Tendo em vista aos fatores supracitados, o estudo de quando a indústria maximiza lucros com a produção de etanol ou açúcar se faz importante.A escolha do modelo estocástico pode influenciar de forma determinante o valor da opção real avaliada. Sendo assim, na presente dissertação propõe-se modelar opções de conversão de acordo com o Movimento de Reversão à Média com saltos de Poisson. Será analisado o caso açúcar/etanol, ou melhor, quando será mais eficiente produzir açúcar (commodity alimentícia) ou etanol (commodity energética).Foi escolhido o Movimento de Reversão à Média com saltos de Poisson, pois apesar de os preços de commodities serem relativamente bem modelados pelo Movimento de Reversão à Média, o etanol e o açúcar sofrem variações bruscas em intervalos curtos de tempo. Essas variações se devem a agentes externos, tais como preço de petróleo e ações governamentais. Dependendo dos preços relativos de etanol e açúcar, há a possibilidade de alteração do mix de produção através da opção de conversão. Através da modelagem de opções citadas, e utilizando a simulação de Monte Carlo, esta dissertação determina o valor das opções disponíveis à indústria. / [en] Due to the increasing employment of alternative sources of energy, renewable type has been proved more and more attractive and viable. Ethanol, derived from sugar cane, in the present days is being considered a promising fuel and also a less polluting alternative to oil. In addition, the volume of ethanol production in Brazil has grown consistently. Given the above mentioned factors, the study of the moment when the industry maximizes profits from the production of ethanol or sugar becomes relevant. The choice of the stochastic model may have greater influence on the assessed value of real option. Thus, in this paper, we propose to model switch options in accordance with the Mean Reversion Process with Poisson jumps. Sugar/ethanol case will be analyzed, or rather, when it will be more efficient to produce sugar (food commodity) or ethanol (energy commodity). The Mean Reversion Process with Poisson jumps has been chosen, despite of commodity prices being relatively well modeled by the Mean Reversion Process, because ethanol and sugar suffer abrupt changes in short intervals. These variations are due to external agents, such as oil price and government actions. Depending on the relative prices of ethanol and sugar, there is a possibility of changing the mix of production through the switch option. Through modeling above mentioned options, and using the Monte Carlo simulation, this paper determines the value of the options available to the industry.

A stochastic operator is a positive linear contraction, P : L1 --+ L1, such that llPfII2 = llfll1 for f > 0. It is called asymptotically stable if the iterates pn f of each density converge in the norm to a fixed density. Pf(x) = f K(x,y)f(y)dy, where K( ·, y) is a density, defines a stochastic kernel operator. A general probabilistic/ deterministic model for biological systems is considered. This leads to the LMT operator P f(x) = Jo - Bx H(Q(>.(x)) - Q(y)) dy, where -H'(x) = h(x) is a density. Several particular examples of cell cycle models are examined. An operator overlaps supports iffor all densities f,g, pn f APng of 0 for some n. If the operator is partially kernel, has a positive invariant density and overlaps supports, it is asymptotically stable. It is found that if h( x) > 0 for x ~ xo ~ 0 and ["'" x"h(x) dx < liminf(Q(A(x))" - Q(x)") for a E (0, 1] lo x-oo then P is asymptotically stable, and an opposite condition implies P is sweeping. Many known results for cell cycle models follow from this. / Mathematical Science / M. Sc. (Mathematics)

De nombreux travaux récents ont démontré l’importance de la stochasticité dans l’expression des gènes à différentes échelles. On passera tout d’abord en revue les principaux résultats expérimentaux pour motiver l’étude de modèles mathèmatiques prenant en comptedes effets aléatoires. On étudiera ensuite deux modèles particuliers où les effets aléatoires induisent des comportements intéressants, en lien avec des résultats expérimentaux : une dynamique intermittente dans un modèle d’auto-régulation de l’expression d’un gène ; et l’émergence d’hétérogénéité à partir d’une population homogène de protéines par modification post-traductionnelle. Dans le Chapitre I, nous avons étudié le modèle standard d’expression des gènes à trois variables : ADN, ARN messager et protéine. L’ADN peut être dans deux états, respectivement “ON“ et “OFF“. La transcription (production d’ARN messagers) peut avoir lieu uniquement dans l’état “ON“. La traduction (production de protéines) est proportionnelleà la quantité d’ARN messager. Enfin la quantité de protéines peut réguler de manière non-linéaire les taux de production précédent. Nous avons utilisé des théorèmesde convergence de processus stochastique pour mettre en évidence différents régimes de ce modèle. Nous avons ainsi prouvé rigoureusement le phénomène de production intermittente d’ARN messagers et/ou de protéines. Les modèles limites obtenues sont alors des modèles hybrides, déterministes par morceaux avec sauts Markoviens. Nous avons étudié le comportement en temps long de ces modèles et prouvé la convergence vers des solutions stationnaires. Enfin, nous avons étudié en détail un modèle réduit, calculé explicitement la solution stationnaire, et étudié le diagramme de bifurcation des densités stationnaires. Ceci a permis 1) de mettre en évidence l’influence de la stochasticité en comparant aux modèles déterministes ; 2) de donner en retour un moyen théorique d’estimer la fonctionde régulation par un problème inverse. Dans le Chapitre II, nous avons étudié une version probabiliste du modèle d’agrégation fragmentation. Cette version permet une définition de la nucléation en accord avec les modèles biologistes pour les maladies à Prion. Pour étudier la nucléation, nous avons utilisé une version stochastique du modèle de Becker-Dôring. Dans ce modèle, l’agrégation est réversible et se fait uniquement par attachement/détachement d’un monomère. Le temps de nucléation est définit comme le premier temps où un noyau (c’est-à-dire un agrégat de taille fixé, cette taille est un paramètre du mod`ele) est formé. Nous avons alors caractérisé la loi du temps de nucléation dans ce modèle. La distribution de probabilitédu temps de nucléation peut prendre différente forme selon les valeurs de paramètres : exponentielle, bimodale, ou de type Weibull. Concernant le temps moyen de nucléation, nous avons mis en évidence deux phénomènes importants. D’une part, le temps moyen denucl´eation est une fonction non-monotone du paramètre cinétique d’agrégation. D’autre part, selon la valeur des autres paramètres, le temps moyen de nucléation peut dépendre fortement ou très faiblement de la quantité initiale de monomère . Ces caractérisations sont importantes pour 1) expliquer des dépendances très faible en les conditions initiales,observées expérimentalement ; 2) déduire la valeur de certains paramètres d’observations expérimentales. Cette étude peut donc être appliqué à des données biologiques. Enfin, concernant un modèle de polymérisation-fragmentation, nous avons montré un théorème limite d’un modèle purement discret vers un modèle hybride, qui peut-être plus utile pourdes simulations numériques, ainsi que pour une étude théorique. / The importance of stochasticity in gene expression has been widely shown recently. Wewill first review the most important related work to motivate mathematical models thattakes into account stochastic effects. Then, we will study two particular models where stochasticityinduce interesting behavior, in accordance with experimental results : a bursting dynamic in a self-regulating gene expression model ; and the emergence of heterogeneityfrom a homogeneous pool of protein by post-translational modification.In Chapter I, we studied a standard gene expression model, at three variables : DNA, messenger RNA and protein. DNA can be in two distinct states, ”ON“ and ”OFF“. Transcription(production of mRNA) can occur uniquely in the ”ON“ state. Translation (productionof protein) is proportional to the quantity of mRNA. Then, the quantity of proteincan regulate in a non-linear fashion these production rates. We used convergence theoremof stochastic processes to highlight different behavior of this model. Hence, we rigorously proved the bursting phenomena of mRNA and/or protein. Limiting models are then hybridmodel, piecewise deterministic with Markovian jumps. We studied the long time behaviorof these models and proved convergence toward a stationary state. Finally, we studied indetail a reduced model, explicitly calculated the stationary distribution and studied itsbifurcation diagram. Our two main results are 1) to highlight stochastic effects by comparisonwith deterministic model ; 2) To give back a theoretical tool to estimate non-linear regulation function through an inverse problem. In Chapter II, we studied a probabilistic version of an aggregation-fragmentation model. This version allows a definition of nucleation in agreement with biological model for Prion disease. To study the nucleation, we used a stochastic version of the Becker-Döring model. In this model, aggregation is reversible and through attachment/detachment of amonomer. The nucleation time is defined as a waiting time for a nuclei (aggregate of afixed size, this size being a parameter of the model) to be formed. In this work, we characterized the law of the nucleation time. The probability distribution of the nucleation timecan take various forms according parameter values : exponential, bimodal or Weibull. Wealso highlight two important phenomena for the mean nucleation time. Firstly, the mean nucleation time is a non-monotone function of the aggregation kinetic parameter. Secondly, depending of parameter values, the mean nucleation time can be strongly or very weakly correlated with the initial quantity of monomer. These characterizations are important for 1) explaining weak dependence in initial condition observed experimentally ; 2) deducingsome parameter values from experimental observations. Hence, this study can be directly applied to biological data. Finally, concerning a polymerization-fragmentation model, weproved a convergence theorem of a purely discrete model to hybrid model, which may beuseful for numerical simulations as well as a theoretical study.

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2015-10-16T18:00:48Z No. of bitstreams: 2 Dissertação - Wilder Francisco Soares Costa - 2014.pdf: 2068928 bytes, checksum: 053e3f6ebe769a97bc3032d2a3af31b9 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Rejected by Luciana Ferreira (lucgeral@gmail.com), reason: Na citação 0 nome do mestrado é Mestrado Profissional em Matemática em Rede Nacional. No final da citação coloque ponto final. on 2015-10-19T13:51:53Z (GMT) / Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2015-10-20T14:51:37Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Wilder Francisco Soares Costa - 2014.pdf: 2068928 bytes, checksum: 053e3f6ebe769a97bc3032d2a3af31b9 (MD5) / Approved for entry into archive by Cláudia Bueno (claudiamoura18@gmail.com) on 2015-10-20T15:15:33Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Wilder Francisco Soares Costa - 2014.pdf: 2068928 bytes, checksum: 053e3f6ebe769a97bc3032d2a3af31b9 (MD5) / Made available in DSpace on 2015-10-20T15:15:33Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Wilder Francisco Soares Costa - 2014.pdf: 2068928 bytes, checksum: 053e3f6ebe769a97bc3032d2a3af31b9 (MD5) Previous issue date: 2014-10-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Inventory control plays an important role in business because they help the financial structure and understanding of it. Due to this fact is of great value that high school students seize their definitions and applications as they are or will be included in the labor market. The purpose of this work was to unite the inventory control with stochastic process, which in this case was the Markov process, through mathematical modeling. To this end, a brief explanation of inventory control and stock was addressed, as stochastic processes and examples, arriving on the Markov Chain that was addressed in a very simple way geared more for matrix multiplication and how to get these matrices. Then took these theories and applied, through modeling, at a small supermarket in inventory control of tomato sauce using Markov chains, allowing a prediction of future orders with the supplier. The work is the result of the Professional Masters and was written with the intention that teachers and high school students can understand the resolutions of the examples presented. / O controle de estoque exerce um papel importante nas empresas, pois auxiliam na estrutura financeira e compreensão da mesma. Devido esse fato é de grande valor que estudantes do ensino médio apreendam suas definições e aplicações pois estão ou serão inseridos no mercado de trabalho. O proposito deste trabalho foi unir o controle de estoque com o processo estocástico, que nesse caso foi o processo Markoviano, através da modelagem matemática. Para tanto, uma breve explanação de controle de estoque e estoque foi abordada, bem como processos estocásticos e exemplificações, chegando nas Cadeias de Markov que foi abordada de uma forma bem simples voltada mais para multiplicação de matrizes e como chegar nessas matrizes. Depois pegou essas teorias e foi aplicada, através da modelagem, em um supermercado de pequeno porte no controle de estoque de molho de tomate usando as cadeias de Markov, possibilitando a previsão de pedidos futuros junto ao fornecedor. O trabalho é fruto do Mestrado Profissional e foi escrito com intenção de que docentes e estudantes do ensino médio possam compreender as resoluções dos exemplos apresentados.

A informação sobre a dinâmica espaço-temporal de doenças de plantas é de importância fundamental em estudos epidemiológicos, podendo ser utilizada para descrever e entender o desenvolvimento das doenças, desenvolver planos de amostragem, planejar experimentos controlados e caracterizar perdas na produção ocasionadas pela doença. O estudo de padrões espaciais de doenças de plantas, que são reflexos do processo de dispersão dos patógenos, é importante em estudos epidemiológicos, como o de doenças dos citros, para se definirem estratégias mais adequadas para o controle das doenças, diminuindo os prejuízos causados. A Citricultura é uma das principais atividades agrícolas do Brasil e representa a principal atividade econômica de mais de 400 municípios do Triângulo Mineiro e do Estado de São Paulo, onde se encontra a maior área de citros do país e a maior região produtora de laranjas do mundo. Na avaliação do padrão espacial, diferentes métodos têm sido utilizados, dentre os quais incluem-se o ajuste de distribuições, como, por exemplo, a distribuição beta-binomial, o estudo da relação variância-média, o cálculo de correlação ao intraclasse, a utilização de técnicas de autocorrelação espacial, métodos de classes de distâncias e o ajuste de modelos estocásticos espaço-temporais. Diante da importância de se estudarem padrões espaciais da incidência de doenças em plantas e da necessidade de se conhecer melhor a epidemiologia da morte súbita dos citros e do cancro cítrico, uma técnica baseada em verossimilhança para o ajuste de modelos estocásticos espaço-temporais foi utilizada na caracterização de padrões espaciais. Modificações na metodologia original, buscando uma diminuição do tempo gasto nas análises, foram propostas nesse estudo. Os resultados mostram que as modificações propostas resultaram em uma diminuição significativa no tempo de análise, sem perda de acurácia na estimação dos parâmetros dos modelos considerados. / The information about the spatial-temporal dynamics is of fundamental importance in epidemiological studies for describing and understanding the development of diseases, for developing efficient sampling plans, for planning controlled experiments, for evaluating the effect of different treatments, and for determining crop losses. The Citriculture is the major economic activity of more than 400 municipalities in Minas Gerais and São Paulo States. This is the largest citrus area in Brazil, and the largest sweet orange production area in the world. Therefore, it is very important to study and to characterize spatial patterns of plant diseases, such as citrus canker and citrus sudden death. In the spatial dynamics study, many different methods have been used to characterize the spatial aggregation. These include the fitting of distributions, such as the beta-binomial distribution, the study of variance-mean relationships, the calculation of intraclass correlation, the use of spatial autocorrelation techniques, distance class methods and, the fitting of continuous time spatiotemporal stochastic models. In this work, an improved technique for fitting models to the spatial incidence data by using MCMC methods is proposed. This improved technique, which is used to investigate the spatial patterns of plant disease incidence, is considerably faster than Gibson’s methodology, in terms of computational time, without any loss of accuracy.