Gene transcription in individual living cells is inevitably a stochastic and dynamic process. Little is known about how cells and organisms learn to balance the fidelity of transcriptional control and the stochasticity of transcription dynamics. In an effort to elucidate the contribution of environmental signals to this intricate balance, a Three State Model was recently proposed, and the transcription system was assumed to transit among three different functional states randomly. In this work, we employ this model to demonstrate how the stochastic dynamics of gene transcription can be characterized by the three transition parameters. We compute the probability distribution of a zero transcript event and its conjugate, the distribution of the time durations in gene on or gene off periods, the transition frequency between system states, and the transcriptional bursting frequency. We also exemplify the mathematical results by the experimental data on prokaryotic and eukaryotic transcription. The analysis reveals that no promoters will be definitely turned on to transcribe within a finite time period, no matter how strong the induction signals are applied, and how abundant the activators are available. Although stronger extrinsic signals could enhance promoter activation rate, the promoter creates an intrinsic ceiling that no signals could cross over in a finite time. Consequently, among a large population of isogenic cells, only a portion of the cells, but not the whole population, could be induced by environmental signals to express a particular gene within a finite time period. We prove that the gene on duration follows an exponential distribution, and the gene off intervals show a local maximum that is best described by assuming two sequential exponential process. The transition frequencies are determined by a system of stochastic differential equations, or equivalently, an iterative scheme of integral operators. We prove that for each positive integer n , there associates a unique time, called the peak instant, at which the nth transcript synthesis cycle since time zero proceeds most likely. These moments constitute a time series preserving the nature order of n.

Made available in DSpace on 2014-06-12T17:35:03Z (GMT). No. of bitstreams: 2 arquivo3630_1.pdf: 2374215 bytes, checksum: 64f9cdc75ffa8167dff3140c0b1e48a2 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009 / Petróleo Brasileiro S/A / Processos semi-Markovianos (SMP) contínuos no tempo são importantes ferramentas estocásticas para modelagem de métricas de confiabilidade ao longo do tempo para sistemas para os quais o comportamento futuro depende dos estados presente e seguinte assim como do tempo de residência. O método clássico para resolver as probabilidades intervalares de transição de SMP consiste em aplicar diretamente um método geral de quadratura às equações integrais. Entretanto, esta técnica possui um esforço computacional considerável, isto é, N2 equações integrais conjugadas devem ser resolvidas, onde N é o número de estados. Portanto, esta tese propõe tratamentos matemáticos e numéricos mais eficientes para SMP. O primeiro método, o qual é denominado 2N-, é baseado em densidades de frequência de transição e métodos gerais de quadratura. Basicamente, o método 2N consiste em resolver N equações integrais conjugadas e N integrais diretas. Outro método proposto, chamado Lap-, é baseado na aplicação de transformadas de Laplace as quais são invertidas por um método de quadratura Gaussiana, chamado Gauss Legendre, para obter as probabilidades de estado no domínio do tempo. Formulação matemática destes métodos assim como descrições de seus tratamentos numéricos, incluindo questões de exatidão e tempo para convergência, são desenvolvidas e fornecidas com detalhes. A efetividade dos novos desenvolvimentos 2N- e Lap- serão comparados contra os resultados fornecidos pelo método clássico por meio de exemplos no contexto de engenharia de confiabilidade. A partir destes exemplos, é mostrado que os métodos 2N- e Lap- são significantemente menos custosos e têm acurácia comparável ao método clássico

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La modélisation du comportement vibroacoustique en flexion des structures sandwich est devenue aujourd’hui de plus en plus d’un grand intérêt dans les différents secteurs industriels. Cette tendance est principalement due aux propriétés mécaniques avantageuses des structures sandwich. L’un des principaux avantages de ce type de structures réside principalement dans le rapport rigidité-poids élevé. En revanche, acoustiquement la diminution de la masse du panneau avec une rigidité élevée conduit à un confort acoustique insatisfait. Pour cette raison, il y a une demande croissante pour des approches de modélisation du comportement vibroacoustique des structures sandwich avec une précision maximale. La présente thèse propose une approche méso-macro basée sur une méthode numérique pour la prédiction des caractéristiques dynamiques des structures sandwich. La méthode est principalement utilisée pour résoudre le problème de transparence acoustique considéré dans ce projet de thèse. Le travail présenté porte principalement sur la topologie du coeur du sandwich pour traiter le problème abordé. Le principal avantage du modèle proposé réside dans les effets du cœur prises en compte telle que l’effet du cisaillement et celle de l’orthotropie du panneau sandwich. L’approche de modélisation proposée est basée sur la méthode des éléments finis ondulatoire, qui combine la méthode des éléments finis classique et la théorie des structures périodiques. La structure sandwich a été modélisée comme un guide des ondes tridimensionnelles qui garde absolument les informations à l’échelle mésoscopique du panneau modélisé. La fréquence de transition définie la fréquence à laquelle le cisaillement du coeur devient important. Cette fréquence spéciale a été identifié via deux méthodes numériques. Une expression de transmission acoustique à travers un panneau sandwich a également été dérivée. Ensuite, une étude paramétrique a été menée dans le but de révéler l’effet des différents paramètres géométriques sur les indicateurs vibroacoustiques. / Prediction of the flexural vibroacoustic behavior of honeycomb sandwich structures in the low-mid frequency is nowadays becoming of high interest in different industrial sectors. This trend is mainly owing to the advantageous mechanical properties of the sandwich structures. One of the main advantages of this kind of structures lies principally in the high stiffness-to-weight ratio. Even though, acoustically the decrease of the panel mass with a high stiffness leads to an unsuitable acoustic comfort. For this reason, there is an increasing demand for approaches modeling the vibroacoustic behavior of the sandwich structures with a maximum accuracy. The present thesis deals with a meso-macro approach based on a numerical method for modeling the vibroacoustic behavior of sandwich structures. The modeling description is mainly used to address the acoustic insulation problem considered in the thesis. The presented work focuses on the topology of the sandwich core to treat the addressed problem. The main advantage of the proposed model is that it takes into account the core shear and panel orthotropic effects. The modeling approach suggested here is based on the wave finite element method (WFE method), which combines the standard finite element method and the periodic structure theory. The sandwich structure has been modeled as a tridimensional waveguide which holds absolutely the meso-scale information of the modeled panel. The transition frequency, which indicates the frequency at which the core shear becomes important, was identified via two different numerical methods. An expression of the acoustic transmission for an equivalent isotropic sandwich panel was also derived. A parametric study was then conducted with a goal of revealing the effect of the geometric parameters of the sandwich core on the vibroacoustic indicators.