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.

Esta pesquisa investiga o desenvolvimento das formas silábicas CCV (Consoante1 + Consoante2 + Vogal) do Português Brasileiro na fala infantil. Presente em palavras como triste, blusa, madrinha, tigre, a sílaba CCV é a última a ser adquirida pela criança, após os 5;0 anos de idade (LAMPRECHT, 1993). No entanto, palavras contendo contextos CCV podem figurar na produção infantil mesmo antes dos 2;0 anos: ab(r)e aqui (Lz. 1;09 anos); (o)b(r)igado (Ar. 1;09 anos). O objetivo deste trabalho é observar como o ataque ramificado manifesta seu desenvolvimento na fonologia infantil, questionando se o molde CCV estaria presente na Fonologia da criança mesmo antes das primeiras realizações-alvo desta sílaba. Analisam-se dados experimentais de 49 crianças, que elicitaram estímulos familiares ou logatomas do tipo /CCV.CV/ e /CV.CV/, e produções longitudinais de três crianças. Os corpora foram categorizados em cinco grupos conforme o percentual de realizações-alvo CCV, de 0%-%5 (G1) a acima de 76% (G5). Para acessar o conhecimento fonológico infantil sobre a ramificação de ataque, três fontes de evidência foram tomadas: (i) observação de padrões fonotáticos e estratégias de reparo impostas à produção da sílaba CCV; (ii) interação entre o ataque ramificado e a regra de palatalização de oclusivas alveolares; e (iii) comparação da duração de sílabas CCV reduzidas a C1V e de sílabas CV. Os resultados em (i) apontam que antes de produtivamente realizar o ataque ramificado como na forma-alvo, parte dos informantes em G1 empregou estratégias de reparo visando modificar a qualidade do segmento em C2, como em entrar [etja] e Dlato [pwa.t]. Observou-se ausência de uma ordem específica de desenvolvimento dos filtros fonotáticos no molde CCV. Contudo, detectou-se tendência significativa por evitar sílabas oclusiva coronal + líquida e preferência por sílabas oclusiva labial + líquida, o que creditamos ao Princípio de Contorno Obrigatório (McCarthy, 1986) e ao desenvolvimento do controle articulatório infantil (Goldstein, 2003). Em (ii) verificou-se que a palatalização em contextos /ti, di, tli, dli/ reduzidos à C1V (como trilho [ti.], Dlibo [i.b] e triângulo [tiã.g.l]) foi bloqueada por uma parcela dos informantes em G1, e não foi bloqueada pelo desenvolvimento do molde CCV na fala de informantes específicos dos grupos G2-G4. Observou-se, em (iii), que a duração é uma propriedade de aquisição ainda em curso: mesmo quando a ramificação de ataque foi produzida, constatou-se duração variável (mais longa, similar ou mais curta) entre C(C)V e CV. Os resultados em (i) e (ii) apontam manifestações da ramificação de ataque na produção de uma parcela de nossos informantes mesmo antes de suas primeiras realizações-alvo do CCV. Já a ausência de tais manifestações nos dados de parte das crianças em G1 sugere que a ramificação de ataque ainda deve emergir na Fonologia infantil. Atribuímos esta emergência à marcação do Parâmetro de Ataque Máximo, propondo que a variabilidade e a gradualidade pós-marcação paramétrica observada no percurso de aquisição pode ser devida à aquisição segmental, ao domínio articulatório-motor das sequências consonantais e ao design do experimento, causas também reportadas na literatura. / This research investigates the development of the syllabic forms CCV (Consonant1 + Consonant2 + Vowel) within Brazilian Portugueses child speech. Being present in words such as triste, blusa, madrinha, tigre, the CCV syllable is the last one to be acquired by the child, after 5;0 years old (LAMPRECHT, 1993). However, words containing CCV contexts may figure in child production even before 2;0 years old: ab(r)e aqui (Lz.1;09y.o.); (o)b(r)igado (Ar.1;09y.o). The main goal of this work is to observe how the branched onset presents its development in child phonology, questioning whether the CCV pattern would be available to the childs Phonology prior to the first target realizations of that syllable. There were analyzed experimental data from 49 children, who elicited habitual stimuli or logathomes of the type /CCV.CV/ and /CV.CV/, as well as longitudinal productions from three children. The corpora were categorized into five groups based on the percentage of CCV target realizations, from 0%-%5 (G1) to above 76% (G5). In order to access the child phonological knowledge of onset branching, three evidence sources were selected: (i) observation of phonotactic patterns and repair strategies imposed to the production of the CCV syllable; (ii) interaction between the branched onset and the rule for palatalization of alveolar implosives; and (iii) comparing the duration of CCV syllables reduced to C1V and CV syllables. The results in (i) point out that, before effectively realizing the branched onset as in the target form, part of the informants in G1 employed repair strategies aiming to modify the segments quality in C2, as in entrar [etja] and Dlato [pwa.t]. An absence of a specific order of development of phonotactic filters for the CCV pattern could be observed. However, there was detected a significant tendency to avoid coronal implosive+liquid syllables and a preference for labial implosive+liquid, which we credit to the Obligatory Contour Principle (McCarthy, 1986) and the development of child articulatory control (Goldstein, 2003). In (ii) it was verified that the palatalization within contexts /ti, di, tli, dli/ reduced to C1V (as trilho [ti.], Dlibo [i.b] and triângulo [tiã.g.l]) was blocked by a parcel of the informants in G1, yet it was not blocked by the development of the pattern CCV at the speech of specific informants from the groups G2-G4. It was observed in (iii) that duration is a property of acquisition still under development: even when onset branching was produced, it was found variable duration (longer, similar or shorter) between C(C)V and CV. The results in (i) and (ii) point towards expression of onset branching on the production of a parcel of the informants even before their first target realizations of CCV. On the other hand, the absence of such manifestation in the data of part of the children from G1 suggests that onset branching is yet to emerge at those childrens Phonology. It is claimed that this emergency is attributed to the setting of the Maximum Onset Parameter, and the post-parameter setting variability and gradualness observed in the course of acquisition can be due to the segment acquisition, to the motor-articulatory of the consonant sequences and to experiments design, as already reported by the literature.

This thesis presents measurements of the branching fractions of the charmless baryonic decays B(s) → p anti-p h+ h'-, where h(') denotes a kaon or a pion. Three new modes (B → p anti-p pi+ pi-, Bs → p anti-p K+ K- and Bs → p anti-p K+(-) pi-(+)) are observed for the first time and evidence is found for a fourth (B → p anti-p K+ K-). The inclusive branching fraction of B → p anti-p K+(-) pi-(+) is measured for the first time and the upper limit is set on the branching fraction of the Bs → p anti-p pi+ pi- decay. This represents the first observation of four-body charmless baryonic decays of a Bs meson and one of the first observations of baryonic Bs decays. The implementation of the real-time alignment of LHCb's vertex detector is also described. The novel real-time alignment and calibration strategy adopted by LHCb is essential to allow more stable data taking conditions and an optimal 'offline-quality' reconstruction to be performed at the trigger level, ensuring more efficient trigger selections and the possibility to perform physics analyses directly on the trigger output.

Suffix tree is a data structure which enables the performing of fast search-like operations on the text. In order to be used efficiently, it must be created quickly. In this thesis, we focus on the new kind of suffix link simulation called "minimized branching", which aims to increase the speed of suffix tree construction by reducing the number of branching operations. Our main goal is to present a comparison of the currently used methods for the suffix tree construction and to point out some advantages and disadvantages of the individual approaches. We introduce, implement and practically evaluate multiple variations of the standard McCreight's and Ukkonen's algorithms, as well as Partition and Write Only Top Down (PWOTD) algorithm, originally developed for disk-based construction. Our main result is the integrated description and implementation of these algorithms, which are both well-suited to be further built upon. We also present a simple recommendations on when it is advisable to use a particular algorithm's variation and why.

Estudamos um sistema de partículas a tempo discreto cuja dinâmica é a seguinte. Considere que no instante inicial sobre cada inteiro não negativo há uma partícula, inicialmente inativa. A partícula da origem é ativada e instantaneamente ativa um conjunto aleatório contíguo de partículas que estão a sua direita. Como regra, no instante seguinte ao que foi ativada, cada partícula ativa realiza esta mesma dinâmica de modo independente de todo o resto. Dizemos que o processo sobrevive se em qualquer momento sempre há ao menos uma partícula ativa. Chamamos este processo de Firework, associando a dinâmica de ativação de uma partícula inativa a uma infecção ou explosão. Nosso interesse é estabelecer se o processo tem probabilidade positiva de sobrevivência e apresentar limites para esta probabilidade. Isto deve ser feito em função da distribuição da variável aleatória que define o raio de ação de uma partícula. Associando o processo de ativação a uma infecção, podemos pensar este modelo como um modelo epidêmico. Consideramos também algumas variações dessa dinâmica. Dentre elas, variantes com partículas distribuídas sobre a semirreta dos reais positivos (nesta vertente, existem condições para as distâncias entre partículas consecutivas) e também com as partículas distribuídas sobre vértices de árvores. Estudamos também para esses casos a transição de fase e probabilidade de sobrevivência. Nesta variante os resultados obtidos são funções da sequência de distribuições dos alcances das explosões e da estrutura dos lugares onde se localizam as partículas. Consideramos também variações do modelo onde cada partícula ao ser ativada, permanece ativa durante um tempo aleatório e nesse período emite explosões que ocorrem em instantes aleatórios. / We studied a discrete time particle system whose dynamic is as follows. Consider that at time zero, on each non-negative integer, there is a particle, initially inactive. A particle which is placed at origin is activated and instantly activates a contiguous random set of particles that is on its right. As a rule, the next moment to what it has been activated, each active particle carries the same behavior independently of the rest. We say that the process survives if the amount of particles activated along the process is infinite. We call this the Firework process, associating the activation dynamic of a particle to an infection or explosion process. Our interest is to establish whether the process has positive probability of survival and to present limits to this probability. This is done according to the distribution random variable that defines the radius of infection of each active particle, Associating the activation process to an infection, we think this model as a model epidemic. We also consider some variations of this dynamic. Among them, variants with particles distributed over the half line (there are conditions for the distances between consecutive particles) and also with particles distributed over the vertices of a tree. We studied phase transitions and the correspondent survival probability. In this variant the results depend on the sequence of probability distributions for the range of the explosions and on the particles displacement. We also consider a variation where each particle after activated, remains active during a random time period emitting explosions that occur in random moments.

Nessa tese procuramos o decaimento radioativo raro - -. É um dos resultados da experiência E761 realizada no Proton Center do Fermilab, usando o feixe de híperons carregados com momento de 377 GeV/c. Medimos a fração deste feixe que é constituída de -, sendo esta (3,9 ±0,3)X10-5. Não encontramos sinal do decaimento radiativo - - e determinamos um novo limite superior de 7,5X 10-4 (90% CL). / In this thesis we have searched for the rare hyperon radiative decay - -. It is one of the results of E761 experiment which was realized at Fermilab Proton Center using a 377 GevIc charged hyperon beam. We measure the - beam fraction, which is (3.9 ± 0.3)x10-5 at the start of the decay region. No signal for the radiative decay was found and we determine a new upper limit of 7.5 x 10-4 at 90% CL for the - - branching ratio.

Esta pesquisa investiga o desenvolvimento das formas silábicas CCV (Consoante1 + Consoante2 + Vogal) do Português Brasileiro na fala infantil. Presente em palavras como triste, blusa, madrinha, tigre, a sílaba CCV é a última a ser adquirida pela criança, após os 5;0 anos de idade (LAMPRECHT, 1993). No entanto, palavras contendo contextos CCV podem figurar na produção infantil mesmo antes dos 2;0 anos: ab(r)e aqui (Lz. 1;09 anos); (o)b(r)igado (Ar. 1;09 anos). O objetivo deste trabalho é observar como o ataque ramificado manifesta seu desenvolvimento na fonologia infantil, questionando se o molde CCV estaria presente na Fonologia da criança mesmo antes das primeiras realizações-alvo desta sílaba. Analisam-se dados experimentais de 49 crianças, que elicitaram estímulos familiares ou logatomas do tipo /CCV.CV/ e /CV.CV/, e produções longitudinais de três crianças. Os corpora foram categorizados em cinco grupos conforme o percentual de realizações-alvo CCV, de 0%-%5 (G1) a acima de 76% (G5). Para acessar o conhecimento fonológico infantil sobre a ramificação de ataque, três fontes de evidência foram tomadas: (i) observação de padrões fonotáticos e estratégias de reparo impostas à produção da sílaba CCV; (ii) interação entre o ataque ramificado e a regra de palatalização de oclusivas alveolares; e (iii) comparação da duração de sílabas CCV reduzidas a C1V e de sílabas CV. Os resultados em (i) apontam que antes de produtivamente realizar o ataque ramificado como na forma-alvo, parte dos informantes em G1 empregou estratégias de reparo visando modificar a qualidade do segmento em C2, como em entrar [etja] e Dlato [pwa.t]. Observou-se ausência de uma ordem específica de desenvolvimento dos filtros fonotáticos no molde CCV. Contudo, detectou-se tendência significativa por evitar sílabas oclusiva coronal + líquida e preferência por sílabas oclusiva labial + líquida, o que creditamos ao Princípio de Contorno Obrigatório (McCarthy, 1986) e ao desenvolvimento do controle articulatório infantil (Goldstein, 2003). Em (ii) verificou-se que a palatalização em contextos /ti, di, tli, dli/ reduzidos à C1V (como trilho [ti.], Dlibo [i.b] e triângulo [tiã.g.l]) foi bloqueada por uma parcela dos informantes em G1, e não foi bloqueada pelo desenvolvimento do molde CCV na fala de informantes específicos dos grupos G2-G4. Observou-se, em (iii), que a duração é uma propriedade de aquisição ainda em curso: mesmo quando a ramificação de ataque foi produzida, constatou-se duração variável (mais longa, similar ou mais curta) entre C(C)V e CV. Os resultados em (i) e (ii) apontam manifestações da ramificação de ataque na produção de uma parcela de nossos informantes mesmo antes de suas primeiras realizações-alvo do CCV. Já a ausência de tais manifestações nos dados de parte das crianças em G1 sugere que a ramificação de ataque ainda deve emergir na Fonologia infantil. Atribuímos esta emergência à marcação do Parâmetro de Ataque Máximo, propondo que a variabilidade e a gradualidade pós-marcação paramétrica observada no percurso de aquisição pode ser devida à aquisição segmental, ao domínio articulatório-motor das sequências consonantais e ao design do experimento, causas também reportadas na literatura. / This research investigates the development of the syllabic forms CCV (Consonant1 + Consonant2 + Vowel) within Brazilian Portugueses child speech. Being present in words such as triste, blusa, madrinha, tigre, the CCV syllable is the last one to be acquired by the child, after 5;0 years old (LAMPRECHT, 1993). However, words containing CCV contexts may figure in child production even before 2;0 years old: ab(r)e aqui (Lz.1;09y.o.); (o)b(r)igado (Ar.1;09y.o). The main goal of this work is to observe how the branched onset presents its development in child phonology, questioning whether the CCV pattern would be available to the childs Phonology prior to the first target realizations of that syllable. There were analyzed experimental data from 49 children, who elicited habitual stimuli or logathomes of the type /CCV.CV/ and /CV.CV/, as well as longitudinal productions from three children. The corpora were categorized into five groups based on the percentage of CCV target realizations, from 0%-%5 (G1) to above 76% (G5). In order to access the child phonological knowledge of onset branching, three evidence sources were selected: (i) observation of phonotactic patterns and repair strategies imposed to the production of the CCV syllable; (ii) interaction between the branched onset and the rule for palatalization of alveolar implosives; and (iii) comparing the duration of CCV syllables reduced to C1V and CV syllables. The results in (i) point out that, before effectively realizing the branched onset as in the target form, part of the informants in G1 employed repair strategies aiming to modify the segments quality in C2, as in entrar [etja] and Dlato [pwa.t]. An absence of a specific order of development of phonotactic filters for the CCV pattern could be observed. However, there was detected a significant tendency to avoid coronal implosive+liquid syllables and a preference for labial implosive+liquid, which we credit to the Obligatory Contour Principle (McCarthy, 1986) and the development of child articulatory control (Goldstein, 2003). In (ii) it was verified that the palatalization within contexts /ti, di, tli, dli/ reduced to C1V (as trilho [ti.], Dlibo [i.b] and triângulo [tiã.g.l]) was blocked by a parcel of the informants in G1, yet it was not blocked by the development of the pattern CCV at the speech of specific informants from the groups G2-G4. It was observed in (iii) that duration is a property of acquisition still under development: even when onset branching was produced, it was found variable duration (longer, similar or shorter) between C(C)V and CV. The results in (i) and (ii) point towards expression of onset branching on the production of a parcel of the informants even before their first target realizations of CCV. On the other hand, the absence of such manifestation in the data of part of the children from G1 suggests that onset branching is yet to emerge at those childrens Phonology. It is claimed that this emergency is attributed to the setting of the Maximum Onset Parameter, and the post-parameter setting variability and gradualness observed in the course of acquisition can be due to the segment acquisition, to the motor-articulatory of the consonant sequences and to experiments design, as already reported by the literature.

>Magister Scientiae - MSc / An increasing number of measurements reveal the presence of a low-energy enhancement in the gamma-ray strength function (GSF). The GSF, which is the ability of nuclei to absorb or emit rays, provides insight into the statistical properties of atomic nuclei. For this project the GSF was studied for 74Ge which was populated in the reaction 74Ge(p,p')74Ge* at a beam energy of 18 MeV. The data were collected with the STARS-LIBERACE array at Lawrence Berkeley National Laboratory. Silicon detector telescopes were used for particle identi cation and rays in coincidence were detected with 5 clover-type high-purity germanium detectors. Through the analysis particle- - coincidence events were constructed. These events, together with well-known energy levels, were used to identify primary rays from the quasicontinuum. Primary rays from a broad excitation energy region, which decay to six 2+ states could be identi ed. These states and the associated primary rays are used to measure the GSF for 74Ge with the Ratio Method [1], which entails taking ratios of e ciency-corrected primary -ray intensities from the quasicontinuum. Results from the analysis of the data and focus on the existence of the low-energy enhancement in 74Ge will be discussed. The results are further discussed in the context of other work done on 74Ge using the ( , ') [2], (3He,3He') [3] and ( , ') [4] reactions.

Nessa tese procuramos o decaimento radioativo raro - -. É um dos resultados da experiência E761 realizada no Proton Center do Fermilab, usando o feixe de híperons carregados com momento de 377 GeV/c. Medimos a fração deste feixe que é constituída de -, sendo esta (3,9 ±0,3)X10-5. Não encontramos sinal do decaimento radiativo - - e determinamos um novo limite superior de 7,5X 10-4 (90% CL). / In this thesis we have searched for the rare hyperon radiative decay - -. It is one of the results of E761 experiment which was realized at Fermilab Proton Center using a 377 GevIc charged hyperon beam. We measure the - beam fraction, which is (3.9 ± 0.3)x10-5 at the start of the decay region. No signal for the radiative decay was found and we determine a new upper limit of 7.5 x 10-4 at 90% CL for the - - branching ratio.

Ce travail concerne la reconstruction 3D de vaisseaux sanguins à partir de coupes transversales en nombre éventuellement réduit. Si des données sont manquantes, une reconstruction cohérente avec un réseau de vaisseaux est obtenue. Cette approche permet en outre de limiter les interventions humaines lors du traitement des images des coupes transversales 2D. Sachant que les images utilisées sont obtenues par scanner,la difficulté est de connecter les vaisseaux sanguins entre deux coupes espacées pour obtenir un graphe qui correspond au cœur des vaisseaux. En associant les vaisseaux sanguins sur les coupes à des masses à transporter, on construit un graphe solution d’un problème de transport ramifié. La reconstruction 3D de la géométrie résulte des données 2D d’imagerie issues des différentes coupes transversales et du graphe. La géométrie 3D des vaisseaux sanguins est représentée par la donnée d’une fonction Level Set définie en tout point de l’espace dont l’iso-valeur zéro correspond aux parois des vaisseaux. On s’intéresse ensuite à résoudre numériquement le modèle de Navier-Stokes en écoulement incompressible sur un maillage cartésien inclus dans la géométrie reconstruite. Ce choix est motivé par la rapidité d’assemblage du maillage et des opérateurs discrets de dérivation, en vue d’éventuelles déformation des vaisseaux. L’inadaptation du maillage avec l’interface de la géométrie amène à considérer une condition limite modifiée permettant un calcul consistant des contraintes aux parois. / This work concerns the 3D reconstruction of blood vessels from a limited number of 2D transversal cuts obtained from scanners. If data are missing, a coherentreconstruction with a vessel network is obtained. This approach allows to limit human interventions in processing images of 2D transversal cuts. Knowing that the images used are obtained by scanner, the difficulty is to connect the blood vessels between some widely spaced cuts in order to produce the graph corresponding to the network of vessels. We identify the vessels on each trnasversal cut as a mass to be transported, we construct a graph solution of a branched transport problem. At this stage, we are able to reconstruct the 3D geometry by using the 2D Level Set Functions given by the transversal cuts and the graph information. The 3D geometry of blood vessels is represented by the data of the Level Set function defined at any point of the space whose 0-level corresponds to the vessel walls. The resulting geometry is usually integrated in a fluid mechanic code solving the incompressible Navier-Stokes equations on a Cartesian grid strictly included in a reconstructed geometry. The inadequacy of the mesh with the interface of the geometry is overcomed thanks to a modified boundary condition leading to an accurate computation of the constraints to the walls.