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<p dir="ltr">State estimation is a type of an <i>inverse problem</i> in which some amount of observed data needs to be processed using computer algorithms (which are designed using analytical techniques) to infer or reconstruct the underlying model that produced the data. Due to the ubiquity of data and interconnected control systems in the present day, many engineering domains have become replete with inverse problems that can be formulated as state estimation problems. The interconnectedness of these control systems imparts the associated state estimation problems with distinctive structural properties that must be taken into consideration. For instance, the observed data could be high-dimensional and have a dependency structure that is best described by a graph. Furthermore, the control systems of today interface with each other and with the internet, bringing in new possibilities for large-scale collaborative sensor fusion, while also (potentially) introducing new sources of disturbances, faults, and cyberattacks. </p><p dir="ltr">The main thesis of this document is to investigate the unique challenges related to the issues of robustness, resilience (to faults and cyberattacks), and scalability of state estimation algorithms. These correspond to research questions such as, <i>"Does the state estimation algorithm retain its performance when the measurements are perturbed by unknown disturbances or adversarial inputs?"</i> and <i>"Does the algorithm have any bottlenecks that restrict the size/dimension of the problems that it could be applied to?".</i> Most of these research questions are motivated by a singular domain of application: autonomous navigation of unmanned aerial vehicles (UAVs). Nevertheless, the mathematical methods and research philosophy employed herein are quite general, making the results of this document applicable to a variety of engineering tasks, including anomaly detection in time-series data, autonomous remote sensing, traffic monitoring, coordinated motion of dynamical systems, and fault-diagnosis of wireless sensor networks (WSNs), among others.</p>

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This thesis aims to contribute towards a better understanding of the optimal coordination of monetary and fiscal policy in complex economic environments. We analyze the characteristics of optimal dynamics in an economy in which neither prices nor wages adjust instantaneously and lump-sum taxes are unavailable as a source of government finance. We then propose that monetary and fiscal policy should be coordinated to satisfy a pair of simple `specific targeting rules', a rule for inflation and a rule for the growth of real wages. We show that such simple rule-based conduct of policy can do remarkably well in replicating the dynamics of the economy under optimal policy following a given shock. We study optimal policy coordination in the context of an economy where a constant proportion of agents lacks access to the asset market. We find that the optimal economy moves along an analogue of a conventional inflation-output variance frontier in response to a government spending shock, as the population share of non-Ricardian agents rises. The optimal output response rises, while inflation volatility subsides. There is little evidence that increased government spending would crowd in private consumption in the optimal economy. We investigate the optimal properties and wider implications of a macroeconomic policy framework aimed at meeting an unconditional debt target. We show that the best stationary policy in terms of an unconditional welfare measure is characterized by highly persistent debt dynamics, less history-dependence in the conduct of policy, less reliance on debt finance and more short-term volatility following a government spending shock compared with the non-stationary `timelessly optimal' plan.

Cette thèse est constituée de cinq parties distinctes. La première partie est consacrée au problème de rigidité quasi-symétrique associé à un nouveau modèle de tapis de Sierpinski, qui ne sont pas quasi-symétriquement équivalent aux tapis de Sierpinski usuels. La seconde partie est une discussion portant sur la géométrie quasi-symétrique des ensembles de tapis de Julia, incluant en outre le quasi-cercle uniforme, ainsi que certaines propriétés de séparation uniforme. Lors de la troisième partie, nous déterminerons une condition permettant de savoir quand deux rayons externes d'un polynôme tendent vers un même point. Comme application, nous montrerons également la monotonie de l'entropie associée à une famille de polynômes quadratiques. La quatrième partie est inspirée du travail récent de Cui Guizhen et Tan Lei. En utilisant des outils classiques (module d'anneau et chirurgie quasi-conforme), nous étudierons la convergence de certains rayons en campagne locus espace des paramètres. Enfin, la dernière partie pore sur la famille des transformations de renormalisations générées. Plus précisément, cette partie abordera la connexité de ces ensembles de Julia, et le lieu de confinement dans l'espace des paramètres, ainsi que la formule asymptotique de la dimension d'Hausdorff des ensembles de Julia. / The thesis consists of five parts. The first part is concerned with the quasisymmetric rigidity of a new Sierpinski carpet, which are not quasis-ymmetrically equivalent to the standard Sierpinski carpets. The second part discusses the quasisymmetrically geometry of the carpet Julia sets, including the uniformly quasicircle and uniformly separated properties. The third part is to determine when two external rays of a polynomial land at the same point. As an application, we also show the monotonicity of core-entropy on a family of quadratic polynomials. In the fourth part, following Cui and Tan's work, we use the classic tools modulus of annulus and quasi-conformal surgery to study the landing of some parameter rays in shift locus parameter space. The last part discusses a family of generated renormal-ization transformations. Specifically, it is on the connec-tivity of its Julia sets and the non-escaping locus in its parameter space, the asymptotic formula of the Hausdorff dimention of the Julia sets.

No presente trabalho foram estudadas duas ligações viga-pilar de estruturas de concreto pré-moldado com ênfase na deformabilidade ao momento fletor. A primeira é muito utilizada em galpões com sistema estrutural de pórticos para telhado com duas águas. A segunda é utilizada em estruturas de edifícios com múltiplos pavimentos. Foram realizados ensaios físicos em dois modelos de cada tipo de ligação. Com base nos resultados experimentais, foram propostos modelos analíticos, baseados no Método dos Componentes, e realizadas simulações numéricas, baseadas no Método dos Elementos Finitos, através dos quais determinou-se a curva momento-rotação das ligações em estudo. As curvas momento rotação teóricas, para as duas ligações estudadas, ficaram bastante próximas das experimentais. De acordo com os resultados, pode-se dizer que a primeira ligação teve um comportamento próximo ao de uma ligação perfeitamente rígida. Isso porque, para uma estrutura típica, ela transmitiu mais de 90% do momento equivalente ao de uma estrutura monolítica. A segunda ligação também garantiu uma boa transferência de momento fletor. Observou-se que, ao considerar a semi-rigidez dessa ligação na análise estrutural, há uma redução significativa no momento na base dos pilares mais solicitados, o que permite uma redução na armadura dos pilares e nas dimensões da fundação / The present research deals with the study of two types of precast beam-to-column connections with emphasis on the deformability analysis. The first one is extensively used in precast concrete portal frames with sloping beams. The second one is used in multi-storey framed structures. Experimental tests on two models of each type of beam-to-column connections were done. Based on the experimental results, analytical models, based on the Component Method, were proposed and numerical simulations, based on the Finite Element Method, were developed, which provide the moment-rotation curves of the studied connections. The theoretical moment-rotation curves, for both studied connections, are in good agreement with the experimental ones. According to the results, the first connection had almost the same behaviour of a rigid one. It transmitted about 90% of the bending moment of an equivalent monolithic structure. The second connection also transmitted a good portion of bending moment. It was observed that when its semi-rigidity is considered on the structural analysis there was a significant reduction on the column base bending moment and on the foundation dimensions

Os sistemas pré-fabricados vêm conquistando espaço em todo o Brasil. Dentre eles, os pórticos planos de elementos pré-fabricados de concreto com sistema estrutural para telhado de duas águas, comumente denominados de galpões, tem sido amplamente aplicados. Os galpões, como a matona das estruturas pré-moldadas de concreto, apresentam suas ligações, em maior ou menor grau, deformáveis. Portanto, este trabalho refere-se ao estudo da deformabilidade de uma de suas ligações: a ligação viga-pilar executada através de consolo e chumbador, e da sua influência na distribuição dos esforços solicitantes destas estruturas. Neste sentido, foram realizadas simulações numéricas, com o emprego do Método dos Elementos Finitos e ensaios físicos. Através do ensaio físico realizado no modelo da ligação viga-pilar foi possível determinar sua deformabilidade à flexão e observar seu modo de ruptura. As simulações numéricas foram realizadas tanto para obter teoricamente o valor da deformabilidade à flexão da ligação em análise, como para avaliar sua influência no comportamento estrutural dos galpões pré-moldados. Com base nos resultados obtidos, foram elaboradas algumas recomendações de projeto para os galpões pré-moldados. / The use of precast concrete structures has increased in Brazil. Among them, the precast concrete portal frames with sloping beams have been extensively used in storehouses and commercial and industrial buildings. This type of portal frame, as the most precast concrete structures, has semirigid connections. So, this work deals with the study of the semi-rigid behavior of one beam-column connection type frequently used in these structures. In this kind of connection the beam rests on a corbel which has two projecting bolts connecting it. The aim of this thesis is also to determine the influence of the flexibility connection on the structure behavior. Numerical modeling applying the Finite Element Method and experimental tests were done to analyse these aspects. The test results of a beam-column model allowed the construction of the moment-rotation diagram and the failure mode observation. The numerical modeling was done to get the value of the connection flexibility and to study its influence on the precast concrete portal frame behavior. Based on the results some design recommendations were established.

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Le premier problème qui se pose naturellement lors de l'étude des algèbres de Lie nilpotentes est la classification de celles-ci en petite dimension. La classification des algèbres de Lie nilpotentes complexes a été complétée jusqu'en dimension 7. Pour les dimensions inférieures ou égales à 6, il n'existe, sauf isomorphismes, qu'un nombre fini d'algèbres de Lie nilpotentes complexes. Ancochea a classé les algèbres de Lie nilpotentes complexes en dimension 7 selon leur suite caractéristique. On obtient ainsi, une liste plus étendue qui contient des familles d'algèbres de Lie non isomorphes entre elles.On envisage alors d'étudier les algèbres de Lie nilpotentes selon leur nilindice, en commençant par celles qui ont un nilindice maximal, c'est-à-dire , les algèbres de Lie filiformes. Dès 1970. Vergne a initié l'étude des algèbres de Lie filiformes. Elle a montré que sur un corps ayant une infinité d'éléments, il n'existe, sauf isomorphismes, que deux algèbres de Lie filiformes naturellement graduées de dimension paire 2n, nommées L2n et Q2n, et une seule en dimension impaire 2n + 1, appelée L2n+ avec n E N.Plus récemment, Snobl et Winternitz ont déterminé les algèbres de Lie ayant comme nilradical l'algèbre Ln, sur le corps des complexes et des réels. Afin de compléter cette classification à toutes les algèbres de Lie filiformes naturellement graduées, nous avons procéder de même avec les algèbres Q2n,. Nous démontrons ensuite que si une algèbre de Lie indécomposable de dimension finie possède un nilradical filiforme alors elle est forcément résoluble. Les algèbres de Lie filiformes ne présentent donc aucun intérêt dans l'étude des algèbres de Lie non résolubles.Ce résultat n'est plus vrai pour les algèbres de Lie quasi-filiformes dont leur nilradical est abaissé d'une unité par rapport aux filiformes. En effet, en cherchant toutes les algèbres de Lie dont le nilradical est quasi-filiforme naturellement gradué, on a trouvé des algèbres de Lie non résolubles ayant un nilradical quasi-filiforme.Ce même contre-exemple, révèle aussi des différences entre la notion de rigidité dans R et dans C. La classification des algèbres de Lie rigides complexes ayant été déjà faite jusqu'à dimension 8, on est alors amené à trouver cette classification dans le cas réel.Par ailleurs, on a déterminé les algèbres de Lie quasi-filiformes ayant un tore non nul, on obtient une liste beaucoup plus riche que pour le cas filiforme. Cette liste nous permet de prouver la complétude des algèbres de Lie quasi-filiformes. Rappelons que toutes les algèbres de Lie filiformes sont aussi complètes.Finalement, on s'intéresse à l'existence de structures complexes associées aux algèbres de Lie filiformes et quasi-filiformes. Goze et Remm ont démontré que les algèbres filiformes n'admettaient pas ce type de structure. Depuis une approche différente, nous allons redémontrer ce résultat et nous allons voir qu'il existe par contre des algèbres de Lie quasi-filiformes munies d'une structure complexe, mais seulement en dimension 4 et 6. / The first problem which arises naturally in the study of the nilpotenttie algebras is their classification in small dimension. The classification of nilpotent complex Lie algebras was completed until dimension 7. For dimensions lower or equal to 6, there is, except isomotphisms, a finite number of nilpotent complex Lie algebras. In dimension 7, Ancochea classified the nilpotent complex Lie algebras according to their characteristic sequence and he obtains a more extensive list which contains families of non isomorphic Lie algebras.We intend then to study the nilpotent Lie algebras according to their nilindex by beginning with those which have a maximal nilindex. also called filiform Lie algebras. From 1970. Vergne started the study of the filiform Lie algebras. She showed that on a field having an infinity of elements. there are, except isomorphisme, only two naturally graded Lie algebras of even dimension 2n, named L2n, and Q2n,. and there is only one in odd dimension 2n+1, called L2n+1.More recently, Snobl and Winternitz determined the complex and real Lie algebras having the algebra L„ as nilradieal. To generalize this classification to all filiform naturally graded Lie algebra_ we have proceed in a similar wav with the algebra Q2n,. Moreover, we prove that indecomposable Lie algebras with filiform nilradieal are necessarily solvable. Thus, the filiform Lie algebra are irrelevant in the study of the non solvable Lie algebras.This result is not truc for the quasi-filiform Lie algebras. Let us recall that the nilindex of quasi-filiform Lie algebras is, by definition, lowered by a unit with regard to the filiform. Indeed, by looking for all the Lie algebras having a quasifiliform naturally graded nilradieal, we found non solvable Lie algebras having a quasi-filiform nilradical.The same counterexample also reveals differences between the notion of rigidity in R and in C. The classification of complex rigid Lie algebras having been already made until dimension 8, we are then brought to find this classification in the real case.Besides, we determined the quasi-filiform Lie algebras admitting a tonus of derivations, we obtain a list much richer than for the filiform case. This list allows us to prove that all quasi-fi liform Lie algebras are complete. Let us remind that all the filiform Lie algebras are also complete.Finally, we are interested in the existence of complex structures associated to the filiform and quasi-filiform Lie algebras Goze and Remm proved that the filiform algebras did not admit this type of structure. Since a different approach, we are going to re-demonstrate this result and we see that there are, on the other hand, quasi-filiform Lie algebras provided with a complex structure, but only in dimension 4 and 6.

本研究研究目的希望瞭解家庭因素與自殺危險性之間的關係是否為透過負向特質為中介變項的間接影響路徑，抑或是直接影響與間接影響路徑俱備。依據過去的研究，取自尊與問題解決能力為個體負向特質向度，以及與自尊、問題解決能力有關的家庭因素：家庭僵化、父母管教態度（嚴格，高期望、過度保護）與溝通為家庭因素的向度，以自殺危險性為探討的依變項，進行線性結構關係模式分析（LISREL）。 本研究以台北市信義區某國中一、二年級共411位男女學生為研究對象，有效樣本中一年級學生有190位，二年級學生221位，男生212人，女生199人，依研究變項選取已編製好且符合的量表為測量工具：包括父母管教態度量表、親子關係量表、親子溝通量表組合成「家庭分量表（一）（二）」，家庭適應與凝聚力量表為「家庭特性分量表」，自尊量表為「自我特質分量表（一）」，問題解決量表為「自我特質分量表（二）」，自殺危險程度量表為「生命興趣探索量表」。資料收集後以LISREL7為統計工具進行分析。 本研究的結果顯示家庭因素對自殺危險性而言，包括了直接影響與透過負向特質的間接影響，且家庭因素對自殺危險性的解釋力與預測力比負向特質大，顯示直接影響的效果比間接影響的效果要來得大。 此外，研究結果亦顯示將家庭因素不同向度獨立出來成為獨立的變項，來探討其與負向特質、自殺危險性之間的關係，可以得到對自殺危險性而言較好的解釋模式。顯示不同家庭因素的向度對自殺危險性有不同的影響方式，其中家庭僵化透過負向特質對自殺危險性有間接影響的效果，而父母管教態度的嚴格與高期待，對自殺危險性有直接的影響力。進一步探討父親與母親不同的管教態度與溝通對於青少年自殺危險性之間的關係為何，結果顯示父親過度保護透過負向特質，間接影響個體自殺危險性，而母親嚴格與期待的管教態度對個體而言，可以直接影響自殺危險性，也可透過負向特質間接影響自殺危險性。 / The purpose of this study was to detect the relationships of family factors, negative traits and suicidal risk and if the negative traits were the mediators between family factors and suicidal risk. This study predicted family factors indirectly affect suicidal risk. If not, the family factors would have both direct and indirect influences on suicidal risk. According to the previous researches, researcher took the family rigidity and child-rearing attitudes as the family factors, and the self-esteem and problem solving skills as the negative traits. The dependent variable was suicidal risk. The study applied the Linear Structure Relation（LISREL）to test its fitness. The 411 subjects were the junior high school students in Hsin-I area in Taipei City, including 212 boys and 199 girls. The measuring instruments were the Child-Rearing Attitudes Scale, the Family Adaptability and Cohesion Evaluation Scale II, the Rosenberg Self-Esteem Scale, the Personal Problem-Solving Scale, and the Suicidal Risk Scale. The data was analyzed by LISREL 7. The results revealed that the family factors affected suicidal risk both directly and indirectly. In terms of suicidal risk, the family factors were more predictive than negative traits. Besides, the present study also found that it would be a better model if taking the different dimensions of family factors as individual variables. And the different variables affected suicidal risk in different ways. The family rigidity indirectly affected suicidal risk through negative trait, and the sternness and high expectation attitudes of parents directly affected suicidal risk. Moreover there were differences between paternal and maternal child-rearing attitudes that affected suicidal risk. Paternal overprotection indirectly affected suicidal risk through negative trait. The sternness and high expectation of maternal attitudes affected suicidal risk both directly and indirectly.