Em decorrência do grande avanço alcançado pela mecânica estatística devido a introdução das idéias de invariância conforme às teorias de escala para sistemas finitos, retomamos, neste trabalho, o estudo do modelo XY em campo transverso. A princípio, apresentamos uma análise detalhada do comportamento \"crossover\" característico do modelo, onde incluímos cálculos melhorados dos expoentes da susceptibilidade e do gap de energia anteriormente apresentados por dos Santos e Stinch-combe. Em seguida, uma análise numérica do espectro foi desenvolvida, considerando-se condições livres de contorno, e comparada com as previsões da invariância conforme. Finalmente, as correções à energia do estado fundamental de cadeias finitas foram utilizadas para obter o parâmetro que caracteriza as classes de universalidade (a carga central c). / In view of the great advance attached from statistical mechanics due to the conformal invariance ideas introduced to the scale theories, we take over at this work, the study of the XY model in a transverse field. At first, we present a detailed analysis on the sample\'s typical crossover behavior. An improved calculation of the susceptibility and gap exponents early presented by dos Santos and Stinchcombe is included. Nest, a numerical analysis of the spectrum, regarding free boundary condi¬tions was developed and compared with conformal invariance predictions. Finally, the fundamental state energy corrections of finite chains were used to obtain the parameter which ,distingoishes the universality classes (the central charge c).

Submitted by Jaqueline Silva (jtas29@gmail.com) on 2016-11-10T16:53:27Z No. of bitstreams: 2 Dissertação - Uyara Ferreira Silva - 2016.pdf: 3332903 bytes, checksum: 8fbe7281ebca1862814d7f28b271c9ca (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2016-11-10T16:53:40Z (GMT) No. of bitstreams: 2 Dissertação - Uyara Ferreira Silva - 2016.pdf: 3332903 bytes, checksum: 8fbe7281ebca1862814d7f28b271c9ca (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-11-10T16:53:40Z (GMT). No. of bitstreams: 2 Dissertação - Uyara Ferreira Silva - 2016.pdf: 3332903 bytes, checksum: 8fbe7281ebca1862814d7f28b271c9ca (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-10-26 / The purpose of this work is to calculate the Surge and Swab geopressures inside eccentrics wells. There is eccentricity between the drill string and the well. The traditional theory to calculate these geopressures considers that the drill string and the well remain concentric throughout the process, which does not occur in reality. The analysis of this phenomenon is carried out, in which the fluid is confined between the two cylinders, the drill string and the well. The conformal mapping are used to transform the eccentric domain in concentric domain and thus find the real values of geopressures. The results obtained using the proposed methodology are presented and discussed. / O intuito deste trabalho é calcular as geopressões Surge e Swab em poços onde há excentricidade entre a coluna de perfuração e o poço. A teoria tradicional para cálculo destas geopressões considera que a coluna de perfuração e o poço permanecem concêntricos durante todo o processo, o que não ocorre na realidade. Realiza-se análise deste fenômeno, no qual o fluido é confinado entre os dois cilindros, coluna de perfuração e o poço. As transformações conformes são utilizadas para transformar o domínio excêntrico no domínio concêntrico e assim, encontrar os valores reais das geopressões, , não considerar a excentricidade nos cálculos, pode induzir a erros graves nos valores das pressões. Os resultados obtidos, utilizando a metodologia proposta, são apresentados e discutidos.

In this work we apply the method of hydrodynamic reductions to study the integrability of the class of second order quasilinear equations.

Abnormal behaviour may indicate important objects and events in a wide variety of domains. One such domain is intelligence and surveillance, where there is a clear trend towards more and more advanced sensor systems producing huge amounts of trajectory data from moving objects, such as people, vehicles, vessels and aircraft. In the maritime domain, for example, abnormal vessel behaviour, such as unexpected stops, deviations from standard routes, speeding, traffic direction violations etc., may indicate threats and dangers related to smuggling, sea drunkenness, collisions, grounding, hijacking, piracy etc. Timely detection of these relatively infrequent events, which is critical for enabling proactive measures, requires constant analysis of all trajectories; this is typically a great challenge to human analysts due to information overload, fatigue and inattention. In the Baltic Sea, for example, there are typically 3000–4000 commercial vessels present that are monitored by only a few human analysts. Thus, there is a need for automated detection of abnormal trajectory patterns. In this thesis, we investigate algorithms appropriate for automated detection of anomalous trajectories in surveillance applications. We identify and discuss some key theoretical properties of such algorithms, which have not been fully addressed in previous work: sequential anomaly detection in incomplete trajectories, continuous learning based on new data requiring no or limited human feedback, a minimum of parameters and a low and well-calibrated false alarm rate. A number of algorithms based on statistical methods and nearest neighbour methods are proposed that address some or all of these key properties. In particular, a novel algorithm known as the Similarity-based Nearest Neighbour Conformal Anomaly Detector (SNN-CAD) is proposed. This algorithm is based on the theory of Conformal prediction and is unique in the sense that it addresses all of the key properties above. The proposed algorithms are evaluated on real world trajectory data sets, including vessel traffic data, which have been complemented with simulated anomalous data. The experiments demonstrate the type of anomalous behaviour that can be detected at a low overall alarm rate. Quantitative results for learning and classification performance of the algorithms are compared. In particular, results from reproduced experiments on public data sets show that SNN-CAD, combined with Hausdorff distance  for measuring dissimilarity between trajectories, achieves excellent classification performance without any parameter tuning. It is concluded that SNN-CAD, due to its general and parameter-light design, is applicable in virtually any anomaly detection application. Directions for future work include investigating sensitivity to noisy data, and investigating long-term learning strategies, which address issues related to changing behaviour patterns and increasing size and complexity of training data.

Cette thèse est consacrée à l'étude d'une famille des flots géométriques associés au problème de la courbure scalaire prescrite sur une variété riemannienne compacte. Plus précisément, si on désigne par (M,g0) une variété riemannienne compacte de dimension n≥3, et si F∈C∞ (M) est une fonction donnée, le problème de la courbure scalaire prescrite consiste à trouver une métrique g conforme à g0 telle que F soit sa courbure scalaire. Ce problème est équivalent à la résolution de l'EDP suivante :-4 (n-1)/(n-2) ∆u+R0 u=Fu((n+2)/(n-2 )) , u>0 , (E), Où R0 est la courbure scalaire de la métrique initiale g0 et ∆ est le laplacien associé à g0. Il s'agit d'une équation elliptique non-linéaire dont la difficulté principale provient du terme u((n+2)/(n-2 )). Hormis le cas de la sphère standard Sn , tous les travaux consacrés à l'étude de l'équation (E) sont basés sur la méthode variationnelle. Dans cette thèse, on développe une autre approche basée sur l'étude d'une famille de flots géométriques qui permet, entre autres, de résoudre l'équation (E). La question dépend bien entendu de la métrique initiale g0 et en particulier du signe de sa courbure scalaire R0. Les flots introduits sont des flots de gradient associés à deux fonctionnelles distinctes dépendant du signe de R0. La première partie de cette thèse est consacrée au cas R0<0 et dans la deuxième partie on traite le cas R0>0. Dans les deux cas, on démontre l'existence globale du flot et on étudie son comportement asymptotique à l'infini. / This thesis is devoted to the study of a family of geometric flows associated with the prescribed scalar curvature problem. More precisely, if we denote by (M,g0) a compact riemannian manifold with dimension n≥3, and if F∈C∞ (M) is a given function, the prescribed scalar curvature problem consists of finding a conformal metric g to g0 such that F is its scalar curvature. This problem is equivalent to the resolution of the following PDE : -4 (n-1)/(n-2) ∆u+R0 u=Fu((n+2)/(n-2 )) , u>0 , (E), Where R0 is the scalar curvature of the initial metric g0 and ∆ is the laplacian associated with g0.It is a nonlinear elliptic equation, whose the main difficulty comes from the term u((n+2)/(n-2 )). Apart from the case of the standard sphere Sn all the works that study the equation (E) are based on the variational method. In this thesis, we develop another approach based on the study of a family of geometric flows which allows to solve equation (E).The flows introduced are gradient flows associated with two distinct functional functions depending on the sign of R0.The first part of this thesis is devoted to the case R0<0 and in the second part we treat the case R0>0. In both cases, our aim is to proof the global existence of the flow and study its asymptotic behavior at infinity.

L'évaluation précise de la surface équivalente radar (SER) large bande de cibles complexes et de grande dimension est réalisée par des méthodes numériques rigoureuses. Parmi celles-ci, la méthode des différences finies dans le domaine temporel (FDTD) est bien adaptée pour effectuer ce calcul de SER sur une large bande de fréquence et obtenir une signature temporelle de la cible. Le schéma de Yee, schéma FDTD historique pour la simulation de propagation d'ondes électromagnétiques en régime transitoire, souffre de deux points faibles cruciaux: la dispersion numérique imposant une finesse de maillage; et l'approximation de la géométrie curviligne par un maillage cartésien avec des marches d'escalier détériorant la qualité des résultats. Les schémas FDTD d'ordre supérieur en espace ont été investigués pour la réduction de l'effet de la dispersion numérique. Dans cette thèse, le schéma Conservative Modified FDTD(2,4) a été développé dont les performances, en précision et en ressources, sont très intéressantes pour le calcul de SER. Liés au problème de l'approximation de la géométrie curviligne, le traitement des bords de plaques métalliques reste une difficulté non résolue pour les schémas FDTD(2,4) à stencil élargi. Les techniques conformes sont des approches développées pour le schéma de Yee, lesquelles ont été étudiées pour les schémas FDTD(2,4) afin de prendre en compte correctement la géométrie curviligne. Nous proposons une nouvelle approche reposant sur le modèle des fils obliques pour la modélisation des éléments surfaciques métalliques. Des applications SER de cibles montrent que celle-ci est prometteuse. / Rigorous numerical methods are used to compute an accurate wideband radar cross section (RCS) evaluation of large complex targets. Among these, finite differences in time domain method is appropriated for the wideband characteristic and also to obtain a transient responses of the target. The Yee scheme, known historically as an FDTD scheme for Maxwell equations, is hindered by two crucial weak points: numerical dispersion which imposes a high mesh resolution; and staircase approximation of curve geometry which deteriorates results quality. High-order space differential operator for FDTD schemes have been investigated to limit numerical dispersion errors. In this thesis, the Conservative Modified FDTD(2,4) scheme has been developed and its performance has shown very accurate results with reasonable workload for RCS computation. Relating to curve geometry modeling problem, metallic edges modeling is still an unsolved problem for FDTD(2,4) schemes with enlarged stencil. Conformal techniques have been developed for the Yee scheme and has been studied for FDTD(2,4) to accurately model curve geometry. We propose a new approach based on oblique thin wire model to model metallic surfaces. RCS computations of several targets have shown that this method is promising.

Structure-based drug design and virtual screening are areas of computational medicinal chemistry that use 3D models of target proteins. It is important to develop better methods in this field with the aim of increasing the speed and quality of early stage drug discovery. The first part of this thesis focuses on the application of structure-based drug design in the search for inhibitors for the protein 1-deoxy-D-xylulose-5-phosphate reductoisomerase (DXR), one of the enzymes in the DOXP/MEP synthetic pathway. This pathway is found in many bacteria (such as Mycobacterium tuberculosis) and in the parasite Plasmodium falciparum. In order to evaluate and improve current virtual screening methods, a benchmarking data set was constructed using publically available high-throughput screening data. The exercise highlighted a number of problems with current data sets as well as with the use of publically available high-throughput screening data. We hope this work will help guide further development of well designed benchmarking data sets for virtual screening methods. Conformal prediction is a new method in the computer-aided drug design toolbox that gives the prediction range at a specified level of confidence for each compound. To demonstrate the versatility and applicability of this method we derived models of skin permeability using two different machine learning methods; random forest and support vector machines.

Ces deux dernières décennies, les techniques de somme connexe essentiellement basées sur des outils d'analyse ont permis de faire des progrès importants dans la compréhension de nombreux problèmes non linéaires issus de la géométrie (étude des métriques à courbure scalaire constante en géométrie Riemannienne, métriques auto-duales, métrique ayant des groupes d'holonomie spéciaux, métriques extrémales en géométrie Kaehlerienne, équations de Yang-Mills, étude des surfaces minimales et des surfaces à courbure moyenne constante, métriques d'Einstein, etc.). Ces techniques se sont avérées être un outil puissant pour démontrer l'existence de solutions à des problèmes hautement non linéaires. Si les techniques permettant d'effectuer des sommes connexes en des points isolés sont bien comprises et fréquemment utilisées, les techniques permettant d'effectuer des sommes connexes le long de sous-variétés ne sont pas encore bien maîtrisées. Le principal objectif de cette thèse est de combler (partiellement) cette lacune en développant de telles techniques applicables dans le cadre de l'étude des métriques à courbure scalaire constante et aussi dans le cadre de l'étude des équations de comptabilité d'Einstein en relativité générale / These last two decades the connected sum techniques, essentially based on analytical tools, are revealed to be a powerful instrument to understand solutions of several nonlinear problem issued from the geometry (constant scalar curvature metrics in Riemannian geometry, self-dual metrics, metrics with special holonomy group, extremal Kaehler metrics, Yang-Mills equations, minimal and constant mean curvature surfaces, Einstein metrics, etc.). Even tough the techniques which allows one to consider the connected sum at points for solutions of nonlinear PDE's are frequently used and deeply understood, the analogous techniques for connected sums along sub-manifolds have not been mastered yet. The main purpose of this thesis is to (partially) plug this gap by developing such techniques in the context of the constant scalar curvature metrics and the Einstein constraint equations in general relativity

Please read the abstract in the section 00front of this document / Thesis (PhD (Electronic Engineering))--University of Pretoria, 2007. / Electrical, Electronic and Computer Engineering / PhD / unrestricted

Human operators of modern surveillance systems are confronted with an increasing amount of trajectory data from moving objects, such as people, vehicles, vessels, and aircraft. A large majority of these trajectories reflect routine traffic and are uninteresting. Nevertheless, some objects are engaged in dangerous, illegal or otherwise interesting activities, which may manifest themselves as unusual and abnormal trajectories. These anomalous trajectories can be difficult to detect by human operators due to cognitive limitations. In this thesis, we study algorithms for the automated detection of anomalous trajectories in surveillance applications. The main results and contributions of the thesis are two-fold. Firstly, we propose and discuss a novel approach for anomaly detection, called conformal anomaly detection, which is based on conformal prediction (Vovk et al.). In particular, we propose two general algorithms for anomaly detection: the conformal anomaly detector (CAD) and the computationally more efficient inductive conformal anomaly detector (ICAD). A key property of conformal anomaly detection, in contrast to previous methods, is that it provides a well-founded approach for the tuning of the anomaly threshold that can be directly related to the expected or desired alarm rate. Secondly, we propose and analyse two parameter-light algorithms for unsupervised online learning and sequential detection of anomalous trajectories based on CAD and ICAD: the sequential Hausdorff nearest neighbours conformal anomaly detector (SHNN-CAD) and the sequential sub-trajectory local outlier inductive conformal anomaly detector (SSTLO-ICAD), which is more sensitive to local anomalous sub-trajectories. We implement the proposed algorithms and investigate their classification performance on a number of real and synthetic datasets from the video and maritime surveillance domains. The results show that SHNN-CAD achieves competitive classification performance with minimum parameter tuning on video trajectories. Moreover, we demonstrate that SSTLO-ICAD is able to accurately discriminate realistic anomalous vessel trajectories from normal background traffic.