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 / This work is concerned with the definition and study of the Q-process of some branching processes (inhomogeneous superprocesses) or recombination processes (Lambda-Fleming-Viot process). In the first case, the Q-process is defined as the process conditioned on non-extinction, whereas in the second case, it is defined as the process conditioned on non-absorbtion. A pathwise construction of the Q-process is given in both cases. A link between a class of homogeneous superprocesses and Lambda-Fleming-Viot processes is provided. Last, a study of the Q-process in the more general framework of regenerative processes is performed

Neste trabalho estudamos um passeio aleatório, unidimensional com ramificação em Z+ em um meio aleatório não identicamente distribuído. Definimos recorrência e transiência para este processo e apresentamos um critério de classificação. / We study a \"supercritical\" branching random walk on Z+ in a one-dimensional non i.i.d. random environment, which considers both the branching mechanism and the step transition. Criteria of (strong) recurrence and transience are presented for this model.

Cette thèse est consacrée à l'étude du comportement asymptotique de grands graphes et arbres aléatoires. Le premier modèle étudié est un modèle de graphe aléatoire inhomogène introduit par Bo Söderberg. Un chapitre de ce manuscrit est consacré à l'étude asymptotique de la taille des composantes connexes à proximité de la fenêtre critique, en le reliant à la longueur des excursions d'un mouvement brownien avec dérive parabolique, étendant les résultats obtenus par Aldous. Le chapitre suivant est consacré à un processus de graphes aléatoires proposé par Itai Benjamini, défini ainsi : les arêtes sont ajoutées indépendamment, à taux fixe. Lorsqu'un sommet atteint le degré k, toutes les arêtes adjacentes à ce sommet sont immédiatement supprimées. Ce processus n'est pas croissant, ce qui empêche d'utiliser directement certaines approches usuelles. L'utilisation de limites locales permet de montrer la présence (resp. l'absence) d'une composante géante à certaines étapes dans le cas k>=5 (resp. k<=3). Dans le cas k=4, ces résultats permettent de caractériser la présence d'une composante géante en fonction du caractère surcritique ou non d'un processus de branchement associé. Dans le dernier chapitre est étudiée la hauteur d'un arbre de Lyndon associé à un mot de Lyndon choisi uniformément parmi les mots de Lyndon de longueur n, prouvant que cette hauteur est approximativement c ln n, avec c=5,092... la solution d'un problème d'optimisation. Afin d'obtenir ce résultat, nous couplons d'abord l'arbre de Lyndon à un arbre de Yule, que nous étudions ensuite à l'aide de techniques provenant des théories des marches branchantes et des grandes déviations. / This thesis is dedicated to the study of the asymptotic behavior of some large random graphs and trees. First is studied a random graph model introduced by Bo Söderberg in 2002. One chapter of this manuscript is devoted to the study of the asymptotic behavior of the size of the connected components near the critical window, linking it to the lengths of excursion of a Brownian motion with parabolic drift. The next chapter talks about a random graph process suggested by Itai Benjamini, defined as follows: edges are independently added at a fixe rate. Whenever a vertex reaches degree k, all adjacent edges are removed. This process is non-increasing, preventing the use of some commonly used methods. By using local limits, in the spirit of the PWIT, we were able to prove the presence (resp. absence) of a giant component at some stages of the process when k>=5 (resp. k<=3). In the case k=4, these results allows to link the presence (resp. absence) of a giant component to the supercriticality (resp. criticality or subcriticality) of an associated branching process. In the last chapter, the height of random Lyndon tree is studied, and is proven to be approximately c ln n, in which c=5.092... the solution of an optimization problem. To obtain this result, we couple the Lyndon tree with a Yule tree, then studied with the help of branching walks and large deviations

Atualmente a cultura da cana de açúcar tem ganhado destaque no cenário mundial devido a seu potencial uso na produção de bioenergia o qual poderia ser beneficiado desenvolvendo-se cultivares com aumento da produtividade de biomassa por unidade de área, o que é por sua vez, determinada pela arquitetura da planta. A brotação lateral é um dos principais fatores que regulam a arquitetura dos vegetais. Recentemente, esta fase do desenvolvimento tem sido estudada intensivamente em plantas consideradas modelo, elucidando em parte as vias genéticas, ambientais e hormonais que regulam este processo. Dentro desta vias, microRNAs, uma classe de pequenos RNAs não codantes que modula pós-transcricionalmente a expressão de genes endógenos, parecem ser importantes reguladores. Em cana de açúcar, a brotação lateral é importante para a arquitetura dos ramos laterais, germinação de gemas e perfilhamento. Entretanto, devido a sua complexidade genética e ausência de mutantes defectivos na brotação lateral, estudos nesta área ao nível molecular são limitados. Neste contexto, este trabalho teve por objetivos estudar em cana de açúcar a via microRNA156/fatores de transcrição do tipo SQUAMOSA promoter-binding-protein (SPL), a qual é associada à regulação do perfilhamento, bem como caracterizar molecularmente o processo de emergência de gemas axilares. Ferramentas computacionais usando o banco publico de ESTs TIGR gene índex permitiram identificar e classificar no genoma de cana de açúcar, diferentes genes associados ao processo de brotação lateral e resposta hormonal. Entres estes, seis genes SPL regulados pelo miR156 foram identificados, sendo um deles (SsSPL1) homólogo a SPLs envolvidas diretamente na regulação do perfilhamento. A expressão da SsSPL1 foi monitorada em diferentes tecidos e órgãos, juntamente com o miR156. Os dados sugerem que a SsPL1, é regulada negativamente pelo miR156, sendo esta via também conservada em cana de açúcar. Foram geradas plantas transgênicas da cultivar RB85486 com o gene endógeno SsmiR156a/b o qual codifica um precursor conservado do miR156 e parece estar associado com a evolução da arquitetura em monocotiledôneas. O acúmulo do miR156 foi avaliado em plantas transformadas via RT-qPCR encontrando variabilidade na sua expressão. Bibliotecas de pequenos RNAs foram geradas em gemas dormentes e em desenvolvimento, permitindo identificar membros de 26 famílias de miRNAs. A expressão de quatro deles, de seus genes-alvo e de outros genes selecionados foi monitorada em gemas dormentes e com 2 e 5 dias após o plantio. Interessantemente, o miR159 foi o mais expresso em gemas axilares de cana e parece ser um fator chave na emergência da gema, já que, segundo os resultados obtidos, esse miRNA parece modular a expressão do seu gene alvo SsGAMyB, o qual é um fator de transcrição implicado na ativação de genes de resposta a giberelina. Durante esta fase inicial do desenvolvimento também foi observado alterações na expressão de genes associados com processos de transdução de sinal associados aos fitohormônios auxina e etileno. Os resultados obtidos indicam que a emergência de gemas laterais é um processo dinâmico em que fitohormônios, fatores de transcrição e microRNAs participam conjuntamente para promover o crescimento e 12 desenvolvimento da nova plântula de cana de açúcar. / Sugarcane is an economically important biofuel crop that recently has become a target for improvement of sustainable biomaterial production due to its high biomass productivity and built-in containment features. Therefore, studies aiming to improve the production of biomass per area are among the most important issues in sugarcane production. Plant biomass is defined, at least in part, by its shoot architecture. Although shoot architecture (branching/tillering) is to some extend influenced by environmental factors, it is determined mainly by the plants genetic program. This includes developmental programs that are regulated by a complex network of genetic pathways that integrate endogenous and environmental cues. Several transcription factors as well as microRNAs are likely part of this network. In this study, we started to investigate the roles of the genetic pathway regulated by the microRNA156 and its targets, the transcription factors SQUAMOSA promoter-binding-protein (SPLs) in sugarcane branching/tillering. We identified six members of the SPL family that were further classified into four subfamilies. In both dicots and monocots, these SPLs are key regulators of the plant shoot architecture. We monitored the expression patterns of SsmiR156 e SsSPL1 in distinct sugarcane tissues/organs. Our observations suggest that miR156 regulates posttranscriptionally SsSPL1 mainly in leaf tissues. We generated transgenic sugarcane plants overexpressing the monocot-specific sugarcane miR156 precursor SsMIR156b/c via biolistic method. This precursor is thought to be important for the evolution of grass shoot architecture. Although we observed higher accumulation of mature SsmiR156b/c in leaf tissues of some transgenic plants as compared with tissues from non-transgenic plants, we could not detect any significant changes in their vegetative architecture. Using deep sequencing approaches, we have generated two small RNA libraries from dormant and outgrown sugarcane lateral buds. Preliminary analyses indicate that a select group of small RNAs are expressed in lateral buds, including over 200 repeat-associated small interfering RNAs (rasiRNAs) and 25 conserved microRNAs (miRNAs). Amongst the miRNAs, miR159 was the most sequenced in the two libraries. We evaluated miR159 accumulation pattern in addition to other selected miRNAs via qRT-PCR in dormant and developing buds. The majority of the evaluated miRNAs accumulate differentially during bud development, though with distinct expression patterns. Interestingly, miR159 accumulates at high levels in dormant buds, but scarcely in developing buds. Conversely, the experimentally confirmed miR159 target, a sugarcane GAMyB-like gene (SsGAMyB), is lowly expressed in dormant buds while its transcripts accumulate at higher levels in developing buds. GAMyB-like genes encode R2R3 MYB domain transcription factors that have been implicated in gibberellin (GA) and abscisic acid (ABA) signaling in germinating seeds. Our data suggest miR159 regulates GAMyB-like genes during sugarcane bud outgrowth. Similarly, SsSPL1 is regulated posttranscriptionally by the miR529, though this gene has sites for both miR529 and miR156. Auxin and ethylene-associated regulatory pathways are affected during sugarcane bud development. Taken together,our data indicate that sugarcane bud outgrowth from rhizomes is a complex developmental process involving hormones, transcription factors as well as microRNAs and other regulatory RNAs.

<p>The discovery and utilization of novel starches with unique superb properties are highly demanded for modern industrial uses. Small-granule starch (SGS) is a category of unconventional starches with the granular size smaller than 10 μm. The potential use of SGS includes many conventional and novel high-value applications, such as texturizing, fat replacement, encapsulation, controlled delivery and nano-engineering. In the present work, we focused on three SGS isolated from amaranth (<i>Amaranth cruentus</i>), cow cockle (<i>Saponaria vaccaria</i>) and sweet corn (<i>sugary-1</i> maize mutant). The basic structural and unique physical properties of SGS were characterized and compared to common large-granule food starches. It was found that (1) the highly branched amylopectin contributed to low crystallinity and pasting viscosities of sweet corn starch, (2) cow cockle starch exhibited high shear-resistance and low retrogradation in prolonged storage, and (3) the amylopectin for amaranth starch was less branched with small clusters, which was associated with the high crystallinity, medium shear-resistance and low pasting viscosity of amaranth starch. Despite the small size of starch granules, SGS in both native and swelling states showed the capacity of retaining small molecules. Compared to large-granule starch, native SGS are more difficult for small molecules to reach an equilibrium permeation. This work provides insights to the fine structure and physicochemical behaviors of selected high-potent SGS, which is believed to support the industrial production and application of SGS in the future.</p> <p>The characteristics of local polymeric structure dominate many critical properties of glucan particles, such as starch retrogradation and the loading and stabilizing of active substance. Molecular rotor (MR), a fluorescent probe, was proposed to fulfill the simple, high-sensitive, and quantitative-based characterization of local glucan architecture (LGA). In the present work, two innovative studies relevant to this novel method were conducted: (1) MR was able to characterize glucans based on its unique fluorescent response to characteristic LGA, (2) MR was able to sensitively probe and visually demonstrate the transition of LGA induced by starch retrogradation. This novel MR-based approach is expected to advance carbohydrate-related researches in the future.</p>

Neste trabalho estudamos um passeio aleatório, unidimensional com ramificação em Z+ em um meio aleatório não identicamente distribuído. Definimos recorrência e transiência para este processo e apresentamos um critério de classificação. / We study a \"supercritical\" branching random walk on Z+ in a one-dimensional non i.i.d. random environment, which considers both the branching mechanism and the step transition. Criteria of (strong) recurrence and transience are presented for this model.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2018-03-05T11:48:46Z No. of bitstreams: 2 Dissertação - Joan Jesus Amaya Triana - 2018.pdf: 11320340 bytes, checksum: daee9afd4ae2db3c36dee6d85ae3be27 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-03-05T11:50:52Z (GMT) No. of bitstreams: 2 Dissertação - Joan Jesus Amaya Triana - 2018.pdf: 11320340 bytes, checksum: daee9afd4ae2db3c36dee6d85ae3be27 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-03-05T11:50:52Z (GMT). No. of bitstreams: 2 Dissertação - Joan Jesus Amaya Triana - 2018.pdf: 11320340 bytes, checksum: daee9afd4ae2db3c36dee6d85ae3be27 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-02-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this work, we study the information transmission models in infinite graphs introduced in \cite{Thecone} and \cite{article}, that is, models of transmission of information on infinite graphs subject to the following rules: (1) at time zero, only the root of the graph has the information, (2) in a time greater than or equal to one, a new vertex is informed and transmits the information to neighbors that are within a finite random neighborhood, and (3) informed vertices remain forever informed. They are considered variants of this process in the spherically symmetrical tree that includes as particular cases the periodic tree and the homogeneous tree. In addition, the model is considered in random trees. In this model, we study phase transition, probability of survival, among other important numerical characteristics for this process. It is also considered the particular case in which the influence radius has a Bernoulli distribution. The proofs are based on comparisons with branching processes. / Neste trabalho, são estudados modelos de transmissão de informação em grafos infinitos introduzidos em \cite{Thecone} e \cite{article}, isto é, modelos de transmissão de infomação sobre grafos infinitos sujeitos as seguintes regras: (1) no tempo zero, somente a raiz do grafo possui a informação, (2) em um tempo maior ou igual a um, um novo vértice é informado e transmite a informação para vizinhos que estejam dentro de uma vizinhança aleatória finita, e (3) vértices informados permanecem informados para sempre. Serão consideradas variantes deste processo na árvore esfericamente simétrica que inclui como casos particulares a árvore periódica e a árvore homogênea. Além disso, é considerado o modelo em árvores aleatórias. Para este modelo são estudados transição de fase, probabilidade de sobrevivência, dentre outros característicos numéricos importantes para este processo. Também é considerado o caso particular em que o raio de influência tem uma distribuição de Bernoulli. As provas são baseadas fazendo comparações com processos de ramificação.

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Disturbances in the supply of electric power can have serious implications for everyday life as well as for national (homeland) security. A power outage can be initiated by natural disasters, adverse weather, technical failures, human errors, sabotage, terrorism, and acts of war. The vulnerability of a system is described as a sensitivity to threats and hazards, and is measured by P (Q(t) &gt; q), i.e. the probability of at least one disturbance with negative societal consequences Q larger than some critical value q, during a given period of time (0,t]. The aim of the thesis is to present methods for quantitative vulnerability analysis of electric power delivery networks to enable effective strategies for prevention, mitigation, response, and recovery to be developed. Paper I provides a framework for vulnerability assessment of infrastructure systems. The paper discusses concepts and perspectives for developing a methodology for vulnerability analysis, and gives examples related to power systems. Paper II analyzes the vulnerability of power delivery systems by means of statistical analysis of Swedish disturbance data. It is demonstrated that the size of large disturbances follows a power law, and that the occurrence of disturbances can be modeled as a Poisson process. Paper III models electric power delivery systems as graphs. Statistical measures for characterizing the structure of two empirical transmission systems are calculated, and a structural vulnerability analysis is performed, i.e. a study of the connectivity of the graph when vertices and edges are disabled. Paper IV discusses the origin of power laws in complex systems in terms of their structure and the dynamics of disturbance propagation. A branching process is used to model the structure of a power distribution system, and it is shown that the disturbance size in this analytical network model follows a power law. Paper V shows how the interaction between an antagonist and the defender of a power system can be modeled as a game. A numerical example is presented, and it is studied if there exists a dominant defense strategy, and if there is an optimal allocation of resources between protection of components, and recovery. / QC 20100831