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Quantifying the properties of interest is an important problem in many domains, e.g., assessing the condition of a patient, estimating the risk of an investment or relevance of the search result. However, the properties of interest are often latent and hard to assess directly, making it difficult to obtain classification or regression labels, which are needed to learn a predictive models from observable features. In such cases, it is typically much easier to obtain relative comparison of two instances, i.e. to assess which one is more intense (with respect to the property of interest). One framework able to learn from such kind of supervised information is ranking SVM, and it will make a basis of our approach. Applications in bio-medical datasets typically have specific additional challenges. First, and the major one, is the limited amount of data examples, due to an expensive measuring technology, and/or infrequency of conditions of interest. Such limited number of examples makes both identification of patterns/models and their validation less useful and reliable. Repeated samples from the same subject are collected on multiple occasions over time, which breaks IID sample assumption and introduces dependency structure that needs to be taken into account more appropriately. Also, feature vectors are highdimensional, and typically of much higher cardinality than the number of samples, making models less useful and their learning less efficient. Hypothesis of this dissertation is that use of the functional norm regularization can help alleviating mentioned challenges, by improving generalization abilities and/or learning efficiency of predictive models, in this case specifically of the approaches based on the ranking SVM framework. The temporal nature of data was addressed with loss that fosters temporal smoothness of functional mapping, thus accounting for assumption that temporally proximate samples are more correlated. Large number of feature variables was handled using the sparsity inducing L1 norm, such that most of the features have zero effect in learned functional mapping. Proposed sparse (temporal) ranking objective is convex but non-differentiable, therefore smooth dual form is derived, taking the form of quadratic function with box constraints, which allows efficient optimization. For the case where there are multiple similar tasks, joint learning approach based on matrix norm regularization, using trace norm L* and sparse row L21 norm was also proposed. Alternate minimization with proximal optimization algorithm was developed to solve the mentioned multi-task objective. Generalization potentials of the proposed high-dimensional and multi-task ranking formulations were assessed in series of evaluations on synthetically generated and real datasets. The high-dimensional approach was applied to disease severity score learning from gene expression data in human influenza cases, and compared against several alternative approaches. Application resulted in scoring function with improved predictive performance, as measured by fraction of correctly ordered testing pairs, and a set of selected features of high robustness, according to three similarity measures. The multi-task approach was applied to three human viral infection problems, and for learning the exam scores in Math and English. Proposed formulation with mixed matrix norm was overall more accurate than formulations with single norm regularization. / Computer and Information Science

<p dir="ltr"> The widespread adoption of Convolutional Neural Networks (CNNs) in real-world applications, particularly on resource-constrained devices, is hindered by their computational complexity and memory requirements. This research investigates the application of pruning and quantization techniques to optimize CNNs for arrhythmia classification using the MIT-BIH Arrhythmia Database. By combining magnitude-based pruning, regularization-based pruning, filter map-based pruning, and quantization at different bit-widths (4-bit, 8-bit, 2-bit, and 1-bit), the study aims to develop a more compact and efficient CNN model while maintaining high accuracy. The experimental results demonstrate that these techniques effectively reduce model size, improve inference speed, and maintain accuracy, adapting them for use on devices with limited resources. The findings highlight the potential of these optimization techniques for real-time applications in mobile health monitoring and edge computing, paving the way for broader adoption of deep learning in resource-limited environments.</p>

There are various ways to regularize ill-posed operator equations in Hilbert space. If the underlying operator is accretive then Lavrentiev regularization (singular perturbation) is an immediate choice. The corresponding convergence rates for the regularization error depend on the given smoothness assumptions, and for general accretive operators these may be both with respect to the operator or its adjoint. Previous analysis revealed different convergence rates, and their optimality was unclear, specifically for adjoint source conditions. Based on the fundamental study by T. Kato, Fractional powers of dissipative operators. J. Math. Soc. Japan, 13(3):247--274, 1961, we establish power type convergence rates for this case. By measuring the optimality of such rates in terms on limit orders we exhibit optimality properties of the convergence rates, for general accretive operators under direct and adjoint source conditions, but also for the subclass of nonnegative selfadjoint operators.

Two-dimensional (2-D) models of electrical resistivity are improved by jointly inverting radiomagnetotelluric (RMT) and direct-current resistivity (DCR) data or by allowing for displacement currents in the inversion of RMT data collected on highly resistive bedrock. Uniqueness and stability of the 2-D models are assessed with a model variance and resolution analysis that allows for the non-linearity of the inverse problem. Model variance and resolution are estimated with a truncated singular value decomposition (TSVD) of the sensitivity matrix. In the computation of model errors, inverse singular values are replaced by non-linear semi-axes and the number of included eigenvectors is increased until a given error threshold is reached. Non-linear error estimates are verified with most-squares inversions. For the obtained truncation levels, model resolution matrices are computed. For RMT data, non-linear error appraisals are smaller than linearized ones. Hence, the consideration of the non-linearity in RMT data leads to reduced model errors or enhanced model resolution. The dielectric effect on RMT data is investigated with a new 2-D forward and inverse code that allows for displacement currents. As compared to the quasi-static approximation, apparent resistivities and phases of the impedance tensor elements are found to be significantly smaller and the vertical magnetic transfer function exhibits more distinct sign reversals. More reliable models of electrical resistivity are obtained from areas with highly resistive bedrock, if displacement currents are allowed for. In contrast, inversions with a quasi-static scheme introduce artefactual structures with extremely low or high resistivities. A smoothness-constrained 2-D joint inversion of RMT and DCR data is presented. The non-linear model variance and resolution analysis is applied to single and joint inverse models. For DCR data, the errors estimated by most-squares inversions are consistently larger than those estimated by the non-linear semi-axes, indicating that DCR models are poorly resolved. Certain areas of the joint inverse models are better resolved than in the single inverse models.

Soit G un groupe de présentation finie. Un résultat de Gromov affirme l'existence de cycles géométriques réguliers qui représentent une classe d'homologie non nulle h dans le énième groupe d'homologie à coefficients entiers de G, cycles géométriques dont le volume systolique est aussi proche que souhaité du volume systolique de h. Ce théorème, dont aucune démonstration exhaustive n'avait été faite, a servi à obtenir plusieurs résultats importants en géométrie systolique. La première partie de cette thèse est consacrée à une démonstration complète de ce résultat. L'utilisation de ces cycles géométriques réguliers est connue sous le nom de technique de régularisation. Cette technique permet notamment de relier le volume systolique de certaines variétés fermées à d'autres invariants topologiques de ces variétés, tels que les nombres de Betti ou l'entropie minimale. La seconde partie de cette thèse propose d'examiner ces relations, et la mise en oeuvre de la technique de régularisation.La troisième partie est consacrée à trois problèmes liés à la géométrie systolique. Dans un premier temps on s'intéresse à une inégalité concernant les tores pleins plongés dans l'espace tridimensionnel. Puis, on s'intéresse ensuite aux triangulations minimales des surfaces compactes, afin d'obtenir des informations sur le volume systolique de ces surfaces. Enfin, on présente la notion de complexité simpliciale d'un groupe de présentation finie, et ses liens avec la géométrie systolique. / Let G be a finitely presented group. A theorem of Gromov asserts the existence of regular geometric cycles which represent a non null homology class h in the nth homology group with integral coefficients of G, geometric cycles which have a systolic volume as close as desired to the systolic volume of h. This theorem, of which no complete proof has been given, has lead to major results in systolic geometry. The first part of this thesis is devoted to a complete proof of this result.The regularizationtechnique consists in the use of these regular geometric cycles to obtain information about the class $h$. This technique allows to link the systolic volume of some closed manifolds to homotopical invariants of these manifolds, such as the minimal entropy and the Betti numbers. The second part of this thesis proposes to investigate these links.The third part of this thesis is devoted to three problems of systolic geometry. First we are investigating an inequality about embeded tori in $R^3$. Second, we are looking into minimal triangulations of compact surfaces and some information they can provide in systolic geometry. And finally, we are presenting the notion of simplicial complexity of a finitely-presented group and its links with the systolic geometry.

Esta tese tem como objetivo analisar os processos decisórios, as condições causais e os principais atores, seus interesses e suas influências que culminaram na criação da Política de Regularização Fundiária da Amazônia (PRFA), conhecida como Programa Terra Legal (Lei Federal nº 11.952/2009), durante o governo do presidente Luiz Inácio Lula da Silva (2003-2011). O propósito dessa política pública é regularizar ocupações consolidadas em terras públicas da União, situadas na Amazônia Legal, transferindo-as para domínio particular. Ao mesmo tempo que ela tem sido criticada por eventuais legalizações de grilagens e consumação de danos ambientais, tem recebido aplausos por fazer justiça social. A questão central que orienta esta pesquisa é a seguinte: por que o Estado brasileiro, no ano de 2009, adotou a PRFA? As hipóteses para a pergunta formulada consideram que, no interior do heterogêneo governo Lula, a política pública foi resultado da prevalência dos interesses de atores que utilizam a terra como um instrumento de poder e exploração predatória de elementos naturais (setores do agronegócio, políticos ruralistas, latifundiários e grileiros), ou então a política pública resultou da preocupação do Estado em regularizar pequenas e médias ocupações, sendo que eventuais legitimações de grilagens e danos ambientais seriam o resultado de imperfeições da lei. Para tanto, dentro da perspectiva interdisciplinar da Ciência Ambiental e utilizando-se de elementos teóricos do modelo dos Múltiplos Fluxos, de John W. Kingdon (1995), esta tese procura integrar conhecimentos da geografia, da ciência jurídica e, notadamente, da ciência política, de onde se extrai a base teórica e metodológica de análise. Assim, tendo como pano de fundo o neoinstitucionalismo, estudado por Hall e Taylor (2003), Immergut (2006) e outros, complementado pelo incrementalismo de Charles Lindblom (1959/2009; 1979/2009), este trabalho analisa a formação da agenda alusiva ao caos fundiário e ambiental da Amazônia, no começo do governo Lula (2003), a elaboração de alternativas de regularização fundiária e a tomada de decisão que resultou na PRFA (2009), identificando os atores chaves dentro e fora do governo, seus interesses e os espaços institucionais que ocuparam, as sequências históricas e os mecanismos causais que resultaram na política pública. O trabalho colheu evidências que corroboram a hipótese levantada a respeito da participação de membros da bancada ruralista, mas descortinou outros fatores que tiveram um peso muito maior dentro de um intricado xadrez político, como a pressão de vários atores que redundou em um humor amazônico para a regularização fundiária, a heterogeneidade da coalizão partidária do governo Lula, a saída da ministra Marina Silva do Ministério do Meio Ambiente (2008), o trabalho empreendedor o ministro Mangabeira Unger e de atores do Ministério do Desenvolvimento Agrário e do INCRA e disputas por jurisdição. / This thesis aims to analyze the decision-making processes, the causal conditions and the main actors, their interests and their influences that culminated in the creation of the The Amazonian Public Policy for Land Regularization (PRFA), known as Legal Land Program (Federal Law 11.952/2009), during the government of President Luiz Inácio Lula da Silva (2003-2011). The purpose of this public policy is to regularize consolidated occupations on public lands of the Union, located in the Legal Amazon, transferring them to private domain. But, at the same time that it has been criticized for possible legalization of land-grabbing and consummation of environmental damage, it has been receiving applauses for doing social justice. The central question that guides this research is the following: why did the Brazilian State, in 2009, adopt the PRFA? The hypotheses for the asked question consider that within the heterogeneous Lula government, the public policy was the result of the preponderance of actors who use the land as an instrument of power and perpetuation of the predatory exploitation pattern of natural resources (agribusiness sector, rural parliaments, landowners and land-grabber), or by the public policy derived from the State\'s concern to regulate small and medium occupations, and any legitimations of land grabbing and environmental damage would be the result of natural imperfections of the law. To do so, within the interdisciplinary perspective of Environmental Science, this thesis seeks to integrate knowledge of geography, legal science and, especially, political science, from where it has extracted the theoretical and methodological basis of analysis. Thus, in the context of the neoinstitutionalism, studied by Hall and Taylor (2003), Immergut (2006) and others, complemented by the incrementalism of Charles Lindblom (1959/2009, 1979/2009), this thesis analyzes the elaboration of the allusive agenda to the land and environmental chaos in Amazon in the beginning of Lula government (2003), the elaboration of land regularization alternatives and the decision-making process that resulted in the PRFA (2009), using theoretical elements of the Multiple Stream Model of John W. Kingdon (1995). In this sense, the thesis identifies and analyzes the key actors inside and outside the government, as well as the historical sequences and mechanisms, as well as the causal processes that have resulted in public policy. The thesis has gathered evidences that support the raised hypothesis regarding the participation of members of the ruralist parliments, but it revealed other factors that had a much greater weight within an intricate political chessboard, as the pressure of several actors that resulted in an amazonian mood for the land regularization, the heterogeneity of the party coalition of the Lula government, the departure of Minister Marina Silva from the Ministry of Environment (2008), the entrepreneurial work of Minister Mangabeira Unger, of actors from the Ministry of Agrarian Development and INCRA and jurisdiction disputes.

Modelos baseados em fatoração de matrizes estão entre as implementações mais bem sucedidas de Sistemas de Recomendação. Neste projeto, estudamos as possibilidades de incorporação de informações provindas de redes sociais, para melhorar a qualidade das predições do modelo tanto em modelos tradicionais de Filtragem Colaborativa, quanto em Filtragem Colaborativa Neural. / Models based on matrix factorization are among the most successful implementations of Recommender Systems. In this project, we study the possibilities of incorporating the information from social networks to improve the quality of predictions of the model both in traditional Collaborative Filtering and in Neural Collaborative Filtering.