This thesis concentrates on different approaches of solving decision making problems with an aspect of randomness. The basic methodologies of converting stochastic optimization problems to deterministic optimization problems are described. The proximity of solution of a problem and its empirical counterpart is shown. The empirical counterpart is used when we don't know the distribution of the random elements of the former problem. The distribution with heavy tails, stable distribution and their relationship is described. The stochastic dominance and the possibility of defining problems with stochastic dominance is introduced. The proximity of solution of problem with second order stochastic dominance and the solution of its empirical counterpart is proven. A portfolio management problem with second order stochastic dominance is solved by solving the equivalent empirical problem. Powered by TCPDF (www.tcpdf.org)

Cette thèse est divisée en trois parties. Dans la première partie, nous commençons par décrire des résultats très connus en théorie du contrôle géométrique tels que le théorème de Chow-Rashevsky, la condition de rang de Kalman, l'application Entrée-Sortie et le test linéaire. De plus, nous définissons et nous étudions brièvement la contrôlabilité locale au voisinage d'un contrôle de référence au premier et au second ordre. Dans la deuxième partie, nous donnons une preuve élémentaire du lemme de Franks linéaire pour les flots géodésiques qui utilise des techniques basiques de théorie du contrôle géométrique. Dans la dernière partie, étant donnée une variété Riemanienne compacte, nous prouvons un lemme de Franks uniforme au second ordre pour les flots géodésiques et on applique le résultat à la théorie de la persistance. Dans cette partie, nous introduisons avec plus de détails les notions de contrôlabilité locale au premier et au second ordre. En effet, nous donnons un résultat de contrôlabilité au second ordre dont la preuve est longue et technique. / This thesis is devided into three parts. In the first part we begin by describing some well known results in geometric control theory such as the Chow Rashevsky Theorem, the Kalman rank condition, the End-Point Mapping and the linear test. Moreover, we define and study briefly local controllability around a reference control at first and second order. In the second part we provide an elementary proof of the Franks lemma for geodesic flows using basic tools of geometric control theory. In the last part, given a compact Riemannian manifold, we prove a uniform Franks' lemma at second order for geodesic flows and apply the result in persistence theory. In this part we introduce with more details notions of local controllability at first and second order. In fact, we provide a second order controllability result whose proof is long and technical.

No description available.

No description available.

The purpose of this qualitative study is to investigate how social science teachers perceive and express the concept of society in social studies. The study consists of focus group interviews with nine social science teachers at two upper secondary schools and its results are analyzed against the theoretical backdrop of Odenstad's orientation topics, analytical subjects and discussion topics and Sandahl’s first-order and second-order concepts. In short, the two different conceptual devices can be described as the skills and abilities that are most important for the students to master in order to develop advanced thinking skills in social science. Particular emphasis is put on critical thinking, that is, the ability to seek, structure and evaluate information from different sources and to draw conclusions from this process. The emerging results show a certain consensus on the concept of society among social science teachers as the potential subject of study and analysis that would simplify and clarify the analyses of the different levels in society which, in turn, would contribute to adding significance and bringing cohesion to the subject as a whole. As for the skills and abilities that stem from Odenstad's orientation topics and Sandahl’s first-order concepts, the interviewed teachers all emphasize conceptual ability as well as good external knowledge to have knowledge of how society is made up. With reference to Odenstad's analytical subject and discussion topics and Sandahl's second-order concepts, it would seem that it is not only important but a prerequisite that students develop an analytical ability and critical thinking as well as the ability to sift through and process large amounts of information and assume different perspectives on the topic or issue at hand.

O Controle Contextual é descrito a partir de (a) uma contingência de cinco termos (Sx-Sc-Sd- R-Sr) em que o estímulo contextual (Sx) exerce controle condicional sobre as discriminações condicionais e (b) permite que um estímulo participe de mais de uma classe de equivalência sem que haja a fusão das classes. O matching-to-sample é o procedimento mais utilizado para investigar o controle contextual. O objetivo deste estudo foi avaliar se o procedimento go/nogo com estímulos compostos, no qual não é possível identificar as funções condicional e discriminativa, produziria classes de equivalência que compartilham estímulos. Se estas classes fossem produzidas, apenas uma parte da definição de controle contextual (b) seria atestada. Seis universitários realizaram uma tarefa nas fases de treino na qual respostas aos compostos A1C1, A2C2, B1D1, B2D2, X1Y1, X2Y2, X1A1B1, X1A2B2, X2A1B2, X2A2B1 eram seguidas, intermitentemente, por 10 pontos e respostas aos compostos A1C2, A2C1, B1D2, B2D1, X1Y2, X2Y1, X1A1B2, X1A2B1, X2A1B1, X2A2B2 não eram seguidas de consequências. Os estímulos eram formas abstratas. Para se atestar o estabelecimento do controle contextual, os participantes deveriam responder aos compostos Y1C1D1, Y1C2D2, Y2C1D2, Y2C2D1 e não deveriam responder aos compostos Y1C1D2, Y1C2D1, Y2C1D1, Y2C2D2. Este padrão de respostas indicaria a formação de quatro classes de equivalência que compartilham estímulos: X1A1B1Y1C1D1, X1A2B2Y1C2D2, X2A1B2Y2C1D2, X2A2B1Y2C2D1. Quatro dos seis participantes apresentaram desempenhos indicando que é possível estabelecer o controle contextual a partir do procedimento go/no-go com estímulos compostos, sem especificar diferentes funções (e.g., discriminativa, condicional e contextual) para os estímulos envolvidos nestas discriminações. Em função desses resultados, parte (a) da definição de controle contextual mais recorrentemente empregada pode ser questionada / Contextual control is described from (a) a five-term contingency in which the contextual stimulus (Sx) exerts conditional control over conditional discriminations (Sctx Sc Sd R Sr) and (b) allows one stimulus to participate in more than one equivalence class, without merging them into one. Matching-to-sample is the mostly employed procedure to investigate the contextual control. The presented study aimed to evaluate whether a go/no-go procedure that present stimuli in the same manner, without specifying any different stimuli functions, would produce equivalence classes that share stimuli. If equivalence classes could be established with this procedure, only one part of contextual control definition (b) would be met. Six undergraduate were submitted to a task in Training Phase in which responses to A1C1, A2C2, B1D1, B2D2, X1Y1, X2Y2, X1A1B1, X1A2B2, X2A1B2, X2A2B1 compound stimuli were intermittently followed by 10 points, and responses to A1C2, A2C1, B1D2, B2D1, X1Y2, X2Y1, X1A1B2, X1A2B1, X2A1B1, X2A2B2 were not. Two or three abstract forms composed compound stimuli. In Phase III, to certify the establishment of contextual control participants should respond to Y1C1D1, Y1C2D2, Y2C1D2, Y2C2D1 compounds and did not respond to Y1C1D2, Y1C2D1, Y2C1D1, Y2C2D2 compounds. This pattern of responses also indicates the formation of four equivalence classes: X1A1B1Y1C1D1, X1A2B2Y1C2D2, X2A1B2Y2C1D2, X2A2B1Y2C2D1. Four of six participants showed the establishment of contextual control using a go/no-go procedure that do not specify any specific functions for the stimuli. These results indicate that part (a) of the contextual control definition currently used can be questioned

Este trabalho apresenta uma análise comparativa de diferentes sistemas estruturais para um edifício de 20 pavimentos. Cada um dos modelos foi dimensionado através dos princípios do método da análise direta, presente na ABNT NBR 8800:2008. O método da amplificação dos esforços solicitantes (MAES) foi usado para se obter de forma simplificada os esforços atuantes nos elementos do edifício considerando os efeitos locais e globais de segunda ordem. A incidência do vento foi simulada de duas formas diferentes. Na primeira, chamada de uniforme, o vento foi aplicado sem excentricidade, gerando apenas o efeito de tombamento nas estruturas. Na segunda hipótese, considerou-se uma excentricidade devida aos efeitos de vizinhança, prescrita pela ABNT NBR 6123:1988, responsável por ocasionar o tombamento e a torção dos edifícios. Todas as análises numéricas foram repetidas fazendo o uso de outro método simplificado de segunda ordem, conhecido como P-Delta. Por meio dos resultados obtidos, constatou-se que a possibilidade de se reduzir a sobrecarga para o dimensionamento de pilares proporciona uma economia de material, mas, por outro lado, tem como consequência o aumento do tempo de análise, pois exige a utilização de diferentes combinações de cálculo para o dimensionamento de vigas e pilares. A estratégia utilizada para simular os efeitos de vizinhança mostrou-se satisfatória, pois permitiu introduzir de maneira fácil e prática a torção ocasionada pela incidência excêntrica do vento. Observou-se também que esses efeitos ocasionaram o aumento dos momentos fletores e dos deslocamentos das estruturas analisadas. Em relação à avaliação dos efeitos de segunda ordem, comprovou-se que, para a classificação da deslocabilidade, a combinação de cálculo crítica é aquela que possui o maior carregamento gravitacional. Entretanto, para o dimensionamento dos elementos, foi constatado que outras hipóteses de cálculo, principalmente aquelas em que o vento é a ação variável principal, podem ser determinantes. Por fim, foi observado que os resultados obtidos pelo método P-Delta ficaram bastante semelhantes àqueles calculados pelo MAES, com desvios desprezíveis. O MAES, por sua vez, mostrou-se bastante trabalhoso, pois exige a modelagem de diferentes tipos de estruturas para a determinação dos esforços. / This work presents a comparative analysis of different structural systems for a 20-storey building. Each model has been designed using the principles of the direct analysis method (DAM), present in the ABNT NBR 8800:2008. The first-order amplification method (FOAM) was used to obtain, in a simplified manner, the forces acting on the building elements, including local and global second-order effects. The incidence of the wind was simulated in two different ways. In the first case, named uniform, the wind was applied without eccentricity, generating only structure overturning. In the second case, it was considered an eccentricity due to vicinity effects, prescribed by the ABNT NBR 6123:1988, responsible for causing twisting and building overturning. All numerical analysis were carried out a simplified second-order method known as P-Delta. From the results obtained it was found that the reduction of live loads in the design of columns provides material economy, but on the other hand, increases analysis time, since it requires different combinations for beams and columns. The strategy used to simulate the vicinity effects was satisfactory, because it allowed, in an easy and practical way, the consideration of the torsion produced by the wind eccentric impact. It was also observed that these effects increased the bending moments and the displacements of the structures. About the second-order effects, it was shown that, for sway or non-sway classification, the critical combination is one with greatest gravitational loading. However, for the design of the elements, it was observed that other loading conditions can be critical, especially those in which the wind is the main live load. Finally, the results obtained by the P-Delta method were very similar to those calculated by the first-order amplification method. The FOAM was, in turn, very laborious, because it requires the modeling of different types of structures for the determination of the forces.

Mortality information is very important for national planning and health of a country. Mortality rate forecasting is a basic contribution for the projection of financial improvement of pension plans, well-being and social strategy planning. In the first part of the thesis, we fit the selected mortality rate models, namely the Power-exponential function based model, the ModifiedPerks model and the Heligman and Pollard (HP4) model to the data obtained from the HumanMortality Database [22] for the male population ages 1–70 of the USA, Japan and Australia. We observe that the Heligman and Pollard (HP4) model performs well and better fit the data as compared to the Power-exponential function based model and the Modified Perks model. The second part is to systematically compare the quality of the mortality rate forecasting using the second order Lee–Carter method with the selected mortality rate models. The results indicate that Power-exponential function based model and the Heligman and Pollard (HP4) model gives a more reliable forecast depending on individual countries.

Synchonisation ist ein universelles Phänomen welches in den Natur- und Ingenieurwissenschaften, aber auch in Sozialsystemen vorkommt. Verschiedene Modellsysteme wurden zur Beschreibung von Synchronisation vorgeschlagen, wobei das Kuramoto-Modell das am weitesten verbreitete ist. Das Kuramoto-Modell zweiter Ordnung beschreibt eigenständige Phasenoszillatoren mit heterogenen Eigenfrequenzen, die durch den Sinus ihrer Phasendifferenzen gekoppelt sind, und wird benutzt um nichtlineare Dynamiken in Stromnetzen, Josephson-Kontakten und vielen anderen Systemen zu analysieren. Im Laufe der letzten Jahre wurden insbesondere Netzwerke von Kuramoto-Oszillatoren studiert, da sie einfach genug für eine analytische Beschreibung und denoch reich an vielfältigen Phänomenen sind. Eines dieser Phänomene, explosive synchronization, entsteht in skalenfreien Netzwerken wenn eine Korrelation zwischen den Eigenfrequenzen der Oszillatoren und der Netzwerktopolgie besteht. Im ersten Teil dieser Dissertation wird ein Kuramoto-Netzwerk zweiter Ordnung mit einer Korrelation zwischen den Eigenfrequenzen der Oszillatoren und dem Netzwerkgrad untersucht. Die Theorie im Kontinuumslimit und für unkorrelierte Netzwerke wird für das Modell mit asymmetrischer Eigenfrequenzverteilung entwickelt. Dabei zeigt sich, dass Cluster von Knoten mit demselben Grad nacheinander synchronisieren, beginnend mit dem kleinsten Grad. Dieses neue Phänomen wird als cluster explosive synchronization bezeichnet. Numerische Untersuchungen zeigen, dass dieses Phänomen auch durch die Zusammensetzung der Netzwerkgrade beeinflusst wird. Zum Beispiel entstehen unstetige Übergänge nicht nur in disassortativen, sondern auch in stark assortativen Netzwerken, im Gegensatz zum Kuramoto-Modell erster Ordnung.Unstetige Phasenübergänge lassen sich anhand eines Ordnungsparameters und der Hysterese auf unterschiedliche Anfangsbedingungen zurückführen. Unter starken Störungen kann das System von wünschenswerten in nicht gewünschte Zustände übergehen. Diese Art der Stabilität unter starken Störungen kann mit dem Konzept der basin stability quantifiziert werden. Im zweiten Teil dieser Dissertation wird die basin stability der Synchronisation im Kuramoto-Modell zweiter Ordnung untersucht, wobei die Knoten separat gestört werden. Dabei wurde ein neues Phänomen mit zwei nacheinander auftretenden Übergängen erster Art entdeckt: Eine \emph{onset transition} von einer globalen Stabilität zu einer lokalen Instabilität, und eine suffusing transition von lokaler zu globaler Stabilität. Diese Abfolge wird als onset and suffusing transition bezeichnet.Die Stabilität von Netzwerknoten kann durch die lokale Netzwerktopologie beeinflusst werden, zum Beispiel haben Knoten neben Netzwerk-Endpunkten eine geringe basin stability. Daraus folgend wird ein neues Konzept der partiellen basin stability vorgeschlagen, insbesondere für cluster synchronization, um die wechselseitigen Stabilitätseinflüsse von Clustern zu quantifizieren.Dieses Konzept wird auf zwei wichtige reale Beispiele angewandt: Neuronale Netzwerke und das nordeuropäische Stromnetzwerk. Die neue Methode erlaubt es instabile und stabile Cluster in neuronalen Netzwerken zu identifizieren und erklärt wie Netzwerk-Endpunkte die Stabilität gefährden. / Synchronization phenomena are ubiquitous in the natural sciences and engineering, but also in social systems. Among the many models that have been proposed for a description of synchronization, the Kuramoto model is most popular. It describes self-sustained phase oscillators rotating at heterogeneous intrinsic frequencies that are coupled through the sine of their phase differences. The second-order Kuramoto model has been used to investigate power grids, Josephson junctions, and other systems.The study of Kuramoto models on networks has recently been boosted because it is simple enough to allow for a mathematical treatment and yet complex enough to exhibit rich phenomena. In particular, explosive synchronization emerges in scale-free networks in the presence of a correlation between the natural frequencies and the network topology. The first main part of this thesis is devoted to study the networked second-order Kuramoto model in the presence of a correlation between the oscillators'' natural frequencies and the network''s degree. The theoretical framework in the continuum limit and for uncorrelated networks is provided for the model with an asymmetrical natural frequency distribution. It is observed that clusters of nodes with the same degree join the synchronous component successively, starting with small degrees. This novel phenomenon is named cluster explosive synchronization. Moreover, this phenomenon is also influenced by the degree mixing in the network connection as shown numerically. In particular, discontinuous transitions emerge not just in disassortative but also in strong assortative networks, in contrast to the first-order model. Discontinuous phase transitions indicated by the order parameter and hysteresis emerge due to different initial conditions. For very large perturbations, the system could move from a desirable state to an undesirable state. Basin stability was proposed to quantify the stability of a system to stay in the desirable state after being subjected to strong perturbations. In the second main part of this thesis, the basin stability of the synchronization of the second-order Kuramoto model is investigated via perturbing nodes separately. As a novel phenomenon uncovered by basin stability it is demonstrated that two first-order transitions occur successively in complex networks: an onset transition from a global instability to a local stability and a suffusing transition from a local to a global stability. This sequence is called onset and suffusing transition.Different nodes could have a different stability influence from or to other nodes. For example, nodes adjacent to dead ends have a low basin stability. To quantify the stability influence between clusters, in particular for cluster synchronization, a new concept of partial basin stability is proposed. The concept is implemented on two important real examples: neural networks and the northern European power grid. The new concept allows to identify unstable and stable clusters in neural networks and also explains how dead ends undermine the network stability of power grids.

Made available in DSpace on 2015-03-04T18:50:53Z (GMT). No. of bitstreams: 1 Tese Jairo.pdf: 2924101 bytes, checksum: 8a9716b369188f13960e4f2bc2fbbacb (MD5) Previous issue date: 2008-10-16 / Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior / The topological derivative provides the sensitivity of a given shape functional with respect to an infinitesimal non-smooth domain pertubation (insertion of hole or inclusion, for instance). Classically, this derivative comes from the second term of the topological asymptotic expansion, dealing only with inifinitesimal pertubations. However, for pratical applications, we need to insert pertubations of finite sizes.Therefore, we consider other terms in the expansion, leading to the concept of higher-order topological derivatives. In a particular, we observe that the topological-shape sensitivity method can be naturally extended to calculate these new terms, resulting in a systematic methodology to obtain higher-order topological derivatives. In order to present these ideas, initially we apply this technique in some problems with exact solution, where the topological asymptotic expansion is obtained until third order. Later, we calculate first as well as second order topological derivative for the total potential energy associated to the Laplace equation in two-dimensional domain pertubed with the insertion of a hole, considering homogeneous Neumann or Dirichlet boundary conditions, or an inclusion with thermal conductivity coefficient value different from the bulk material. With these results, we present some numerical experiments showing the influence of the second order topological derivative in the topological asymptotic expansion, which has two main features:it allows us to deal with pertubations of finite sizes and provides a better descent direction in optimization and reconstruction algorithms. / A derivada topológica fornece a sensibilidade de uma dada função custo quando uma pertubação não suave e infinitesimal (furo ou inclusão, por exemplo) é introduzida. Classicamente, esta derivada vem do segundo termo da expansão assintótica topológica considerando-se apenas pertubações infinitesimais. No entanto, em aplicações práticas, é necessário considerar pertubação de tamanho finito. Motivado por este fato, o presente trabalho tem como objetivo fundamental introduzir o conceito de derivadas topológicas de ordem superiores, o que permite considerar mais termos na expansão assintótica topológica. Em particular, observa-se que o topological-shape sensitivity method pode ser naturalmente estendido para o cálculo destes novos termos, resultando em uma metodologia sistemática de análise de sensibilidade topológica de ordem superior. Para se apresentar essas idéias, inicialmente essa técnica é verificada através de alguns problemas que admitem solução exata, onde se calcula explicitamente a expansão assintótica topológica até terceira ordem. Posteriormente, considera-se a equação de Laplace bidimensional, cujo domínio é topologicamente pertubado pela introdução de um furo com condição de contorno de Neumann ou de Dirichlet homogêneas, ou ainda de uma inclusão com propriedade física distinta do meio. Nesse caso, são calculadas explicitamente as derivadas topológicas de primeira e segunda ordens. Com os resultados obtidos em todos os casos, estuda-se a influência dos termos de ordem superiores na expansão assintótica topológica, através de experimentos numéricos. Em particular, observa-se que esses novos termos, além de permitir considerar pertubações de tamanho finito, desempenham ainda um importante papel tanto como fator de correção da expansão assintótica topológica, quanto como direção de descida em processos de otimização. Finalmente, cabe mencionar que a metodologia desenvolvida neste trabalho apresenta um grande potencial para aplicação na otimização e em algoritimos de reconstrução.