Esse trabalho visa a investigar a estrutura bi-Hamiltoniana de uma classe de sistemas dinâmicos. Depois de introduzir as ferramentas necessárias, a saber, as noções de variedade de Poisson, de grupo de PoissonLieedenetworknodiscoenoanêl,introduziremosossistemasdinâmicos relevantes nessa dissertação, chamados de reticulados de Coxeter-Toda. Esses sistemas dinâmicos, cujo espaço de fase pode ser identicado com umoportunoquocientedeumacéluladupladeCoxeter-Bruhatdogrupo linear geral, são obtidos por redução do sistema de Toda em GLn. Na parte nal do presente trabalho apresentaremos alguns resultados relacionado à um sistema dinâmico discreto chamado de aplicação do pentagrama, o qual pode ser obtido através uma oportuna discretização do sistema dinâmico de Boussinesq. / This work aims to study the bi-Hamiltonian structure of a class of dynamical systems. After introducing the relevant tools, namely the notions of Poisson manifold, Poisson-Lie group and of network dened in a disc and in an annulus, we will introduce the dynamical systems of interest for this dissertation, i.e., the Coxeter-Toda lattices. These dynamical systems, whose phase-space can be identied with a suitable quotient of a Coxeter double Bruhat cell of the general linear group, are obtained by reduction starting from the Toda ow on GLn. In the nal part of the present work will be presented some results concerning a discrete integrable system close to the so called Pentagram map, which is a discretization of the Boussinesq dynamical system..

O Problema dos K Menores Caminhos é uma generalização do Problema do Menor Caminho, em que desejamos encontrar os K caminhos de menor custo entre dois vértices de um grafo. Estudamos e implementamos algoritmos que resolvem esse problema em grafos dirigidos, com peso nos arcos e que permitem apenas caminhos sem repetição de vértices na resposta. Comparamos seus desempenhos utilizando grafos do 9th DIMACS Implementation Challenge. Identificamos os pontos fortes e fracos de cada algoritmo, e propusemos uma variante híbrida dos algoritmos de Feng e de Pascoal. Essa variante proposta obteve desempenho superior aos algoritmos base em alguns grafos, e resultado superior a pelo menos um deles na grande maioria dos testes. / The K-Shortest Path Problem is a generalization of the Shortest Path Problem, in which we must find the K paths between two vertices in a graph that have the lowest costs. We study some K-Shortest Path Problem algorithms applied to weighted directed graphs, allowing only paths with no repeated vertices. We compare empirically implementation of some algorithms, using instance graphs from the 9th DIMACS Implementation Challenge. We identify the strengths and weaknesses of each algorithm, and we propose a hybrid version of Feng\'s and Pascoal\'s algorithms. This proposed variant achieve better perfomance compared to both base algorithms in some graphs, and it is better than at least one of them in most cases.

OBJETIVO: O objetivo deste estudo é descrever as características do sinal nas lesões císticas da neurocisticercose nas imagens ponderadas em difusão e os metabólitos encontrados na espectroscopia de prótons. MATERIAL E MÉTODOS: Estudaram-se 38 pacientes (39 lesões) com neurocisticercose, usando-se difusão e espectroscopia de prótons. Os exames foram realizados em um magneto de 1,5 T (Signa Horizon LX: GE Medical Systems). A difusão foi realizada no plano axial, com múltiplos cortes com seqüência eco planar. A espectroscopia de prótons utilizou a seqüência PRESS (point-resolved spectroscopy) com TR of 1500 ms e TE de 30/135 ms. RESULTADOS: Os cistos apresentaram intensidade de sinal similar a do líquido cefalorraqueano (LCR) na difusão e valores de CDA sobreponíveis, variando de 1,36 a 3,18 x 10-3 mm2/s. Os picos detectáveis na espectroscopia foram lactato (96,3%), succinato (48%), alanina (40%), lipídeos (15%), aminoácidos citosólicos (7,5%) e acetato (3,7%). CONCLUSÃO: As lesões císticas da neurocisticercose apresentaram hipossinal na difusão e os picos encontrados na espectroscopia de prótons, em ordem decrescente de freqüência, foram lactato, succinato, alanina, lipídeos, aminoácidos citosólicos e acetato / PURPOSE: The objective of this study is to describe the signal behavior of cystic neurocysticercotic lesions on diffusion-weighted imaging (DWI) and single voxel proton spectroscopy findings. MATERIALS AND METHODS: We studied 38 patients (39 lesions) with neurocysticercosis, using diffusion-weighted images and proton MR spectroscopy. The examinations were performed on a 1.5 T scanner (Signa Horizon LX: GE Medical Systems). DWI was performed in the axial plane, using a multisection single shot echo planar pulse sequence. The single voxel proton spectroscopy technique used was the point-resolved spectroscopy (PRESS) sequence with a TR of 1500 ms, short and long TE of 30/135 ms. RESULTS: The cysts presented similar signal intensity to the CSF on DWI, with comparable ADC values, ranging from 1.36 to 3.18 x 10-3 mm2/s. The detectable peaks were lactate (96.3%), succinate (48%), alanine (40%), lipids (15%), cytosolic amino acids (7.5%) and acetate (3.7%). CONCLUSION: The cysts of neurocysticercosis presented hyposignal on DWI and peaks of lactate, succinate, alanine, lipids, cytosolic amino acids and acetate in proton spectroscopy, in decreasing order of frequency

O presente trabalho trata da aplicação do Método de Resíduos Ponderados, mais especificamente do Método dos Mínimos Quadrados, na obtenção de soluções aproximadas de problemas de estruturas em casca, em especial os reservatórios cilíndricos submetidos a carregamento hidrostático em regime de comportamento linear. Os meios empregados para a obtenção das soluções aproximadas referem-se à adoção de bases aproximativas lineares, polinomiais, além da possibilidade de enriquecimento da aproximação mediante a adição de funções com características similares à própria solução exata. Uma outra alternativa utilizada refere-se à aplicação do Método dos Mínimos Quadrados com divisão do domínio de integração. Tais procedimentos podem ser úteis na análise de estruturas por evitar, de modo significativo, a elevação do esforço computacional, mediante a utilização de uma base aproximativa que corresponda às características requeridas pela solução analítica do problema. / The present dissertation deals with the application of the Weighed Residual Method to analysis of cilindrical shells, more specifically of the Least Squared Method, in the attainment of approach solutions of shells structural problems, in special the cylindrical reservoirs submitted the hydrostatic shipment in regimen of linear behavior. The half employees for obtention of the approach solutions refer to adotion of linear, polynomial approaches bases, beyond the possibility of enrichment of the approach by means of the addition of functions with similar characteristics to the proper accurate solution.One another used alternative mentions the application to Least Squared Method with division of the integration domain. Such procedures can be useful in the analysis of structures for preventing, in significant way, the rise of the computational effort, by means of the use of a aproximativa base that correspond to the characteristics required for the analytical solution of the problem.

Der Laplace-Operator auf kompakten Riemannschen Mannigfaltigkeiten besitzt eine natürliche Verallgemeinerung auf kompakte Riemannsche Orbifolds und das Spektrum des so gewonnenen Operators besteht ausschließlich aus Eigenwerten endlicher Vielfachheit. Die Feststellung, dass das Spektrum Informationen über die Geometrie einer Mannigfaltigkeit (oder, allgemeiner, einer Orbifold) enthält, begründete ein ganzes Teilgebiet der Mathematik. Es ist eine offene Frage der sogenannten Spektralgeometrie, ob eine Mannigfaltigkeit und eine singuläre Orbifold isospektral sein (d.h., dasselbe Spektrum mitsamt den Vielfachheiten der Eigenwerte besitzen) können. Angesichts diverser Obstruktionen zur Existenz eines solchen Beispiels für die bekannten Beispiele isospektraler guter Orbifolds, soll diese Arbeit die Spektralgeometrie schlechter Orbifolds erhellen. Zu diesem Zweck geben wir die ersten Beispiele für isospektrale Metriken auf schlechten Orbifolds an. Diese basieren auf bestimmten gewichteten projektiven Räumen, auf denen wir mittels einer Verallgemeinerung von Schüths Version der Torus-Methode nicht-trivial isospektrale Metriken konstruieren. / The Laplace Operator on compact Riemannian manifolds naturally generalizes to compact Riemannian orbifolds and the spectrum of the resulting operator consists only of eigenvalues with finite multiplicities. The observation that the spectrum contains information about the geometry of a manifold (and, more generally, an orbifold) gave rise to a whole field of mathematics. It is an open question of so-called spectral geometry, whether a manifold and a singular orbifold can be isospectral (i.e., have the same spectrum with the same multiplicities of the eigenvalues). Given the various obstructions to the existence of such an example for the known examples of isospectral good orbifolds, this work is an attempt to shed light on the spectral geometry of bad orbifolds by giving the first examples of isospectral Riemannian metrics on bad orbifolds. In our case these are particular fixed weighted projective spaces equipped with non-trivially isospectral metrics obtained by a generalization of Schüth''s version of the torus method.

Heutzutage besteht ein komplexes Software-System häufig aus lose gekoppelten, interagierenden Komponenten. Eine Komponente ist ein offenes System, das unabhängig von anderen offenen Systemen entwickelt und später mit diesen komponiert wird. Die Komposition L+R zweier offener Systeme L und R kann sich jedoch inkorrekt verhalten, beispielsweise verklemmen (die Komponenten warten gegenseitig aufeinander), in eine Endlosschleife geraten oder unbeschränkten Speicherplatz erfordern. Ist L+R dagegen ein korrektes System, bezeichnet man L und R als Partner voneinander. Formale Methoden der Modellierung, Analyse und Synthese ermöglichen die systematische Konstruktion eines korrekten Systems durch Komposition von Partnern. Die Kosten, die ein offenes System L verursacht, variieren in Abhängigkeit von der konkreten Wahl eines Partners. Es ist daher wünschenswert, L nur mit solchen Partnern zu komponieren, welche die Kosten von L beschränken oder sogar minimieren. Ein Partner, der die Kosten von L minimiert, ist ein optimaler Partner von L. Ziel dieser Arbeit ist die Erarbeitung von Techniken, die garantieren, dass L nur mit optimalen Partnern komponiert wird. Dazu entwickeln wir formale Methoden zur Modellierung, Analyse und Synthese kostenbehafteter offener Systeme und ihrer optimalen Partner. Wir präsentieren einen Formalismus zur Modellierung funktionaler (d.h. Zustandsübergänge) und nicht-funktionaler Verhaltenseigenschaften (d.h. Kosten). In diesem Formalismus definieren wir Kostenbeschränktheit und Optimalität von Partnern. Darauf aufbauend entwickeln wir formale Methoden zur Entscheidung der kostenbeschränkten Bedienbarkeit (d.h. der Existenz kostenbeschränkter Partner), der Synthese optimaler Partner und der endlichen Repräsentation aller optimalen Partner. / Nowadays, a complex software system usually consists of loosely-coupled, interacting components. Such a component is an independently developed open system that one composes with other open systems. The composition L+R of two open systems L and R can be faulty: For instance, the components deadlock (i.e. mutually wait for each other) or require an unbounded amount of memory. If L+R is correct, L and R are called partners of each other. Formal methods for modeling, analysis and synthesis yield a systematic approach to constructing a correct system by means of composing partners. The costs of executing a given open system L vary based on a chosen partner. Therefore, it is desirable to choose a partner that bounds or even minimizes the costs of executing L. If a partner R minimizes the costs of executing L, then R is an optimal partner of L. Our goal is to develop techniques that guarantee the composition of L with optimal partners. To this end, we develop formal methods of modeling, analysis and synthesis of open systems incorporating costs. We present a formalism to model functional aspects (i.e. states and transitions) and non-functional aspects (costs) of behavior. We define the properties of cost boundedness and cost optimality for partners in this formalism. Based thereon, we develop formal methods to decide cost bounded controllability (i.e. the existence of cost bounded partners), to synthesize optimal partners, and to finitely represent the set of all optimal partners.

Fragestellung: Das von Dixon 1991 beschriebene tierexperimentelle Modell der 'controlled cortical impact injury'(CCII) wurde zur Untersuchung pathophysiologischer und pathomorphologischer Veränderungen nach traumatischer Hirnkontusion angewandt. Magnetresonanztomographische Techniken (MRT) einschließlich der diffusionswichtenden Bildgebung (DWI) wurden genutzt, um den Zeitverlauf der Hirnödementwicklung zu erfassen, eine Differenzierung unterschiedlicher Ödemformen zu ermöglichen und einen Blut-Hirn-Schrankenschaden zu detektieren. Desweiteren wurde die MRT genutzt, um den neuroprotektiven Effekt des NO-Synthase-Pathway-Modulators Lubeluzol, der bereits im Modell der zerebralen Ischämie nachgewiesen werden konnte, zu untersuchen. Material und Methoden: An 46 Sprague Dawley Ratten wurde eine links parieto-temporale Kontusion appliziert. Die Tiere wurden bis zu 7 Tage nach Trauma magnetresonanztomographisch untersucht. 36 Tiere erhielten Lubeluzol resp. Plazebo. Ergebnisse: Die T2-gewichtete Bildgebung zeigte eine maximale Ödemausbreitung 24 - 48 Stunden nach Trauma. Es ließ sich mithilfe der DWI ein Kontusionskern von einem Kontusionsrand differenzieren. Der Kontusionskern zeichnete sich bis 48 Stunden nach Trauma durch eine Abfall des apparenten Diffusionskoeffizienten (ADC) aus, einem zytotoxischem Ödem entsprechend, der Kontusionsrand wies während des gesamten Untersuchungszeitraums einen ADC-Anstieg auf, als Ausdruck eines vasogenen Ödems. Die T1-gewichtete Bildgebung konnte nach Kontrastmittel (KM)-Applikation durch die KM-Extravasation eine über 7 Tage anhaltende Störung der Blut-Hirnschranke detektieren. In der Lubeluzol-Studie ließ sich anhand der ADC-Veränderungen, des Ödemausmasses oder physiologischer Parameter wie Blutdruck, intrakranieller Druck oder Hirnschwellung kein signifikanter Unterschied zwischen den Tieren der Substanz- bzw. Plazebo-Gruppe aufzeigen. Schlußfolgerung: Die in dem Modell der CCII induzierte traumatische Hirnkontusion zeichnet sich bis 48 Stunden nach Trauma durch einen zytotoxischen Kontusionskern und einen diesen umgebenen vasogenen Kontusionrand aus. Desweiteren konnte ein anhaltender Blut-Hirnschrankendefekt nachgewiesen werden. Ein neuroprotektiver Effekt des Lubeluzols konnte in diesem Traumamodell in der hier applizierten Dosierung nicht nachgewiesen werden. / Objective: The controlled cortical impact injury (CCII) device, as described by Dixon 1991, was used to investigate the brain tissue damage in an animal model of severe traumatic brain injury. Magnetic resonance imaging (MRI) techniques including diffusion weighted imaging (DWI) have been applied to analyse the time course and the characteristics of edema formation and to detect blood-brain-barrier disruption. Furthermore MRI has been used to investigate a neuroprotective effect of the NO-synthase pathway modulator lubeluzole, which has proved markedly beneficial in a model of cerebral ischemia in rats. Material and Methods: a left parieto-temporal cortical contusion was inflicted upon 46 Sprague Dawley rats. Animals have been examined up to 7 days following trauma by MRI. 36 animals have been administered lubeluzole resp. placebo. Results: The most pronounced edema formation has been shown in T2-weighed imaging at 24 - 48 hours post trauma. DWI was able to distinguish between a contusion core and a contusion rim. The contusion core was marked by a decrease in the apparent diffusion coefficient (ADC) up to 48 hours post trauma, indicating cytotoxic edema, whereas the contusion rim has been characterised by vasogenic edema, as indicated by ADC-increase over the entire investigation period. In T1-weighted imaging contrast agent extravasation indicated a sustained blood brain barrier disruption up to 7 days after trauma. Compared to placebo administered rats in lubeluzole-treated animals no significant differences in ADC-changes, edema-extension or physiological parameters as blood pressure, intracranial pressure or brain swelling could be demonstrated. Conclusion: CCII induced traumatic brain injury is characterised by a cytotoxic edema up to 48 hours encircled by a vasogenic contusion rim accompanied by a sustained blood brain barrier disruption. In the model of CCII lubeluzole did not reveal a neuroprotective effect in the applied dosage.

Mapas pedológicos são importantes fontes de informação necessárias à agricultura, mas praticamente inexistentes em escalas adequadas para o Brasil, e seu levantamento pelo método convencional para a demanda brasileira é inviável. Como alternativa ao problema, mapeamento pedológico digital apresenta-se como uma área do conhecimento que envolve as relações das informações de campo, laboratório e pontuais de solos com métodos quantitativos via imagens de satélite e atributos do relevo para inferir atributos e classes. A literatura destaca, portanto, a importância do estudo da posição espacial de pontos amostrais na estimativa de atributos do solo a partir dos valores espectrais de imagens de satélite, aliado a isso, faz-se importante o cruzamento dos atributos do solo estimados e espacializados para chegar a classes de solo. Face ao exposto, o objetiva-se o desenvolvimento de uma técnica via imagem de satélite, dados espectrais e atributos do relevo, integrados por lógica booleana, para determinar mapas pedológicos. O trabalho foi realizado no município de Rio das Pedras, SP e entornos, numa área total de 47.882 ha. Onde, realizou-se processamento de imagens de satélites multitemporais, para obtenção da informação espectral da superfície de solo exposto. Esta informação foi correlacionada com espectro de laboratório de pontos amostrais em subsuperfície (profundidade 80-100 cm) e estimou-se os espectros simulando bandas de satélite para locais desconhecidos. Elaborou-se uma chave de classificação de solos por cruzamento de mapas de atributos via lógica booleana, onde definiu os seguintes atributos a serem mapeados: argila, V% e matéria orgânica (M.O) na profundidade 0-20 cm e argila, CTC, V%, m%, Al, ferro total, matiz, valor e croma na profundidade 80-100 cm. As estimativas de espectros em subsuperfície e dos atributos dos solos nas duas profundidades foram realizadas pela técnica multivariada regressão geograficamente ponderada (GWR), que teve seu desempenho preditivo avaliado pela comparação com desempenho preditivo da técnica de regressão linear múltipla (MRL). Os resultados mostraram correlação entre os espectros das duas profundidades, com R2 de validação acima 0.6. Argila (0-20 e 80-100 cm), matiz, valor e croma foram os atributos do solo que obtiveram as melhores estimativas com R2 acima 0.6. A técnica multivariada GWR obteve-se desempenho superior ao MRL. O mapa pedológico digital comparado aos mapas de solos detalhados de levantamentos convencionais obteve índice kappa de 34.65% e acurácia global de 54,46%. Tal resultado representa um nível regular de classificação. Por outro lado, deve se considerar que se trata de uma região de alta complexidade geológica e compreendendo heterogeneidade de solos. A técnica desenvolvida mostra-se com potencial de evolução no mapeamento digital de solos à medida que forem evoluindo as estimativas de atributos de solos e ajustes nos critérios da chave de classificação. / Soil maps are important sources of information necessary for agriculture, but practically absent in appropriate scales for Brazil, and its mapping by the conventional method for the brazilian demand is impracticable. How an alternative to the problem, digital pedological mapping appears as an area of knowledge that involves the relationship of field information, laboratory and point of soils with quantitative methods by satellite images and relief attributes to predict attributes and classes. The literature highlights therefore the importance of studying the spatial position of sampling points in the estimation of soil attributes from spectral values of satellite images, combined to this, is an important the crossing of the estimated and spatialized soil attributes to get the soil classes. In view of exposed, the objective is the development of a technique satellite image, spectral data and attributes of relief, integrated by boolean logic to determine soil maps. The work was carried out in Rio das Pedras county, SP, and surroundings, in a total area of 47,882 ha. Which was held processing multitemporal satellite images, to obtain spectral information of exposed soil surface. This information was correlated with laboratory spectra of sample points in the subsurface (depth 80-100 cm) and was estimated spectra simulating satellite bands to unknown locations. Produced is a soil classification key for cross attribute maps by boolean logic, which defines the following attributes to be mapped: clay, cation saturation and organic matter (OM) in the 0-20 cm depth and clay, CEC, cation saturation, aluminiu saturation, Al, total iron, hue, value and chroma in depth 80-100 cm. The estimates spectra subsurface and soil attributes in two depths were performed by multivariate technique geographically weighted regression (GWR), which had its predictive performance is evaluated by comparison with predictive performance of multiple linear regression (MRL). The results showed a correlation between the spectra of the two depths, with validation R2 above 0.6. Clay (0-20 and 80-100 cm), hue, value and chroma were the soil attributes obtained the best estimates R2 above 0.6. The GWR multivariate technique yielded better performance than MRL. The digital soil map compared to the detailed soil maps of conventional surveys obtained kappa index of 34.65% and overall accuracy of 54.46%. This result is a regular level of classification. On the other hand, it must be considered that it is a highly complex geological region and comprising heterogeneity of soils. The technique developed shows with potential developments in digital soil mapping as they evolve estimates of soil attributes and adjustments to the classification key criteria.

Este trabalho trata do estudo para adaptação de um método de classificação de estradas não pavimentadas às condições encontradas em campo no município de São Carlos-SP. O trabalho foi desenvolvido a partir de avaliações subjetivas e objetivas levadas a efeito por um painel de avaliadores que executou levantamento de campo planejado, com base nas informações contidas nos relatórios técnicos sobre o desenvolvimento de dois métodos de classificação das condições de estradas - método do Pavement Condition Index e método do Unsurfaced Road Condition Index. O painel de avaliadores atribuiu notas a 140 unidades amostrais de 30 metros de comprimento, a cada defeito presente na unidade amostral e aos 14 trechos estudados. Paralelamente, cada unidade amostral e cada trecho receberam uma classificação de acordo com o método do Unsufaced Road Condition Index. Concluiu-se que, para o presente estudo, não há correlação entre os resultados da avaliação subjetiva executada apenas com o emprego de uma escala de notas e da objetiva, calculada segundo o método do Unsurfaced Road Condition Index. Conclui-se também que a avaliação subjetiva global do trecho tem uma boa correlação com a avaliação subjetiva do conjunto das unidades amostrais que compõem o referido trecho, indicando ser coerente a avaliação do painel de avaliadores. / This work deals with a study for adapting an unpaved road rating method to the field condition prevailing in São Carlos County. The research was carried out through subjective and objective evaluations performed by a panel of raters during field inspections. The experiment was planned accordingly to the technical reports information about the development of two roads condition rating methods - the Pavement Condition lndex and the Unsurfaced Road Condition lndex. The panel rated 140 sample unities of 30 m long attributing a value for the unity, for each defect they have and for 14 road sections studied. The ranks were also calculated accordingly to Unsurfaced Road Condition lndex method. It was concluded that, for the present research, there is no correlation between the subjective evaluation executed with a simple scale and the objective rating calculated following the Unsurfaced Road Condition lndex method. It was also concluded that the global subjective rank of the road section has a good correlation with the subjective rank of the set of sample unities that composes this section, indicating the coherence of the rating panel evaluation.

Este trabalho aborda os conceitos básicos da distribuição de temperaturas e cálculo das tensões térmicas nas estruturas de comportamento linear, utilizando o Método dos Resíduos Ponderados (variante de Galerkin). De modo a sedimentar os conceitos, foram desenvolvidos exemplos de aplicação. / This paper deals with the basic concepts of both temperature distribution and thermal stresses evaluation in structures of linear behavior, by means of the Method of Weighted Residuals (Galerkin\'s approach). Examples of application have been developed in order to sediment the concepts.