Ces travaux contribuent à la théorie des tests non paramétriques minimax dans le modèle de grandes matrices de covariance. Plus précisément, nous observons $n$ vecteurs indépendants, de dimension $p$, $X_1,ldots, X_n$, ayant la même loi gaussienne $mathcal {N}_p(0, Sigma)$, où $Sigma$ est la matrice de covariance inconnue. Nous testons l'hypothèse nulle $H_0:Sigma = I$, où $I$ est la matrice identité. L'hypothèse alternative est constituée d'un ellipsoïde avec une boule de rayon $varphi$ autour de $I$ enlevée. Asymptotiquement, $n$ et $p$ tendent vers l'infini. La théorie minimax des tests, les autres approches considérées pour le modèle de matrice de covariance, ainsi que le résumé de nos résultats font l'objet de l'introduction.Le deuxième chapitre est consacré aux matrices de covariance $Sigma$ de Toeplitz. Le lien avec le modèle de densité spectrale est discuté. Nous considérons deux types d'ellipsoïdes, décrits par des pondérations polynomiales (dits de type Sobolev) et exponentielles, respectivement.Dans les deux cas, nous trouvons les vitesses de séparation minimax. Nous établissons également des équivalents asymptotiques exacts de l'erreur minimax de deuxième espèce et de l'erreur minimax totale. La procédure de test asymptotiquement minimax exacte est basée sur une U-statistique d'ordre 2 pondérée de façon optimale.Le troisième chapitre considère une hypothèse alternative de matrices de covariance pas nécessairement de Toeplitz, appartenant à un ellipsoïde de type Sobolev de paramètre $alpha$. Nous donnons des équivalents asymptotiques exacts des erreurs minimax de 2ème espèce et totale. Nous proposons une procédure de test adaptative, c-à-d libre de $alpha$, quand $alpha$ appartient à un compact de $(1/2, + infty)$.L'implémentation numérique des procédures introduites dans les deux premiers chapitres montrent qu'elles se comportent très bien pour de grandes valeurs de $p$, en particulier elles gagnent beaucoup sur les méthodes existantes quand $p$ est grand et $n$ petit.Le quatrième chapitre se consacre aux tests adaptatifs dans un modèle de covariance où les observations sont incomplètes. En effet, chaque coordonnée du vecteur est manquante de manière indépendante avec probabilité $1-a$, $ ain (0,1)$, où $a$ peut tendre vers 0. Nous traitons ce problème comme un problème inverse. Nous établissons ici les vitesses minimax de séparation et introduisons de nouvelles procédures adaptatives de test. Les statistiques de test définies ici ont des poids constants. Nous considérons les deux cas: matrices de Toeplitz ou pas, appartenant aux ellipsoïdes de type Sobolev / Our work contributes to the theory of non-parametric minimax tests for high dimensional covariance matrices. More precisely, we observe $n$ independent, identically distributed vectors of dimension $p$, $X_1,ldots, X_n$ having Gaussian distribution $mathcal{N}_p(0,Sigma)$, where $Sigma$ is the unknown covariance matrix. We test the null hypothesis $H_0 : Sigma =I$, where $I$ is the identity matrix. The alternative hypothesis is given by an ellipsoid from which a ball of radius $varphi$ centered in $I$ is removed. Asymptotically, $n$ and $p$ tend to infinity. The minimax test theory, other approaches considered for testing covariance matrices and a summary of our results are given in the introduction.The second chapter is devoted to the case of Toeplitz covariance matrices $Sigma$. The connection with the spectral density model is discussed. We consider two types of ellipsoids, describe by polynomial weights and exponential weights, respectively. We find the minimax separation rate in both cases. We establish the sharp asymptotic equivalents of the minimax type II error probability and the minimax total error probability. The asymptotically minimax test procedure is a U-statistic of order 2 weighted by an optimal way.The third chapter considers alternative hypothesis containing covariance matrices not necessarily Toeplitz, that belong to an ellipsoid of parameter $alpha$. We obtain the minimax separation rate and give sharp asymptotic equivalents of the minimax type II error probability and the minimax total error probability. We propose an adaptive test procedure free of $alpha$, for $alpha$ belonging to a compact of $(1/2, + infty)$.We implement the tests procedures given in the previous two chapters. The results show their good behavior for large values of $p$ and that, in particular, they gain significantly over existing methods for large $p$ and small $n$.The fourth chapter is dedicated to adaptive tests in the model of covariance matrices where the observations are incomplete. That is, each value of the observed vector is missing with probability $1-a$, $a in (0,1)$ and $a$ may tend to 0. We treat this problem as an inverse problem. We establish the minimax separation rates and introduce new adaptive test procedures. Here, the tests statistics are weighted by constant weights. We consider ellipsoids of Sobolev type, for both cases : Toeplitz and non Toeplitz matrices

Cette thèse concerne l’étude de grandes déviations précises pour deux statistiques de test:le coefficient de corrélation empirique de Pearson et la statistique de Moran.Les deux premiers chapitres sont consacrés à des rappels sur les grandes déviations précises et sur la méthode de Laplace qui seront utilisés par la suite. Par la suite, nous étudions les grandes déviations précises pour des coefficients de Pearson empiriques qui sont définis par:$r_n=\sum_{i=1}^n(X_i-\bar X_n)(Y_i-\bar Y_n)/\sqrt{\sum_{i=1}(X_i-\bar X_n)^2 \sum_{i=1}(Y_i-\bar Y_n)^2}$ ou, quand les espérances sont connues, $\tilde r_n=\sum_{i=1}^n(X_i-\mathbb E(X))(Y_i-\mathbb E(Y))/\sqrt{\sum_{i=1}(X_i-\mathbb E(X))^2 \sum_{i=1}(Y_i-\mathbb E(Y))^2} \, .$. Notre cadre est celui d’échantillons (Xi, Yi) ayant une distribution sphérique ou une distribution gaussienne. Dans chaque cas, le schéma de preuve suit celui de Bercu et al.Par la suite, nous considérons la statistique de Moran $T_n=\frac{1}{n}\sum_{k=1}^n\log\frac{X_i}{\bar X_n}+\gamma \, ,$o\`u $\gamma$, où γ est la constante d’ Euler. Enfin l’appendice est consacré aux preuves de résultats techniques. / This thesis focuses on the study of Sharp large deviations (SLD) for two test statistics:the Pearson’s empirical correlation coefficient and the Moran statistic.The two first chapters aim to recall general results on SLD principles and Laplace’s methodsused in the sequel. Then we study the SLD of empirical Pearson coefficients, name $r_n=\sum_{i=1}^n(X_i-\bar X_n)(Y_i-\bar Y_n)/\sqrt{\sum_{i=1}(X_i-\bar X_n)^2 \sum_{i=1}(Y_i-\bar Y_n)^2}$ and when the meansare known,$\tilde r_n=\sum_{i=1}^n(X_i-\mathbb E(X))(Y_i-\mathbb E(Y))/\sqrt{\sum_{i=1}(X_i-\mathbb E(X))^2 \sum_{i=1}(Y_i-\mathbb E(Y))^2} \, .$ .Our framework takes place in two cases of random sample (Xi, Yi): spherical distributionand Gaussian distribution. In each case, we follow the scheme of Bercu et al. Next, westate SLD for the Moran statistic $T_n=\frac{1}{n}\sum_{k=1}^n\log\frac{X_i}{\bar X_n}+\gamma \, ,$o\`u $\gamma$ , where γ is the Euler constant.Finally the appendix is devoted to some technical results.

In my thesis, I will answer question of what is sharp power, how China use sharp power and then on 4 cases illustrate that China has different strategies of influence operations. In Japan, respectively Okinawa, China is focusing on their common history and trying to lure Okinawans away from Japan. In South Korea, China exploit Korean economic dependence during the THAAD dispute to their advantage. In Taiwan, thanks to common cultural ties China wants to change everybody mind about Taiwanese "status-quo". In New Zealand, China utilize overseas Chinese community to spread Chinese propaganda. In the end, I will compare each country situation and find out where China's sharp power was effective and where it wasn't.

Text in English / Submitted in partial fulfillment of a Master's Degree at the University of South Africa / Our main goal is to collate into a single document what is presently known regarding pointfree convergence. This will be done by exposing some well-known results on pointfree convergence in a much more simpler way. We will start to study the convergence and clustering of filters in frames in terms of covers and use this to characterise compact frames and some type of uniform frames. We will extend this study to a more general type of filters. We will then discuss convergence and clustering of filters on a locale, where a filter on a locale L is just a filter in the sublattice of all the sublocales of L. This convergence has many applications like characterising compact locales and also characterising sharp points which will also be studied. Finally, the latter concepts of convergence and clustering will be reconciled with the previous one. / Mathematical Sciences

Denna studie behandlar fyra individer som kommer från S:t Hans medeltida kyrka i Visby, Gotland. Samtliga av dessa individer uppvisar tydliga indikationer på att de har fallit offer för våldshandlingar av skarpt slag, varav två av dem avrättade. Syftet med studien är att undersöka skadornas natur och orsak, samt att fastställa tidpunkten för dessa händelser och deras motiv. Vidare ägnas uppmärksamhet åt de begravningspraktiker som dessa individer har undergått, och hur dessa kan bidra till vår förståelse av deras identitet. Slutligen diskuteras de avrättades straff i relation till de rättsliga normer som var rådande under medeltiden i Sverige. / This study examines four individuals originating from St. Hans Medieval Church in Visby, Gotland. All individuals exhibit clear indications of having fallen victim to acts of sharp force trauma, two of whom were executed. The purpose of this study is to investigate the nature and cause of these injuries, as well as to determine the timing and motives behind these events. Furthermore, attention is devoted to the burial rituals these individuals have undergone and how they can contribute to our understanding of their identity. Finally, the punishments inflicted upon the executed individuals are discussed in relation to the legal norms during the medieval period in Sweden.

[pt] À medida que o processo de digitalização avança em diversos setores, a criação de modelos digitais 3D torna-se cada vez mais necessária. Normalmente, esses modelos são construídos por designers 3D, exigindo um esforço manual considerável quando o objeto modelado é complexo. Além disso, como o designer não tem uma referência precisa na maioria dos casos, o modelo resultante está sujeito a erros de medição. No entanto, é possível minimizar o esforço de construção e o erro de medição usando técnicas de aquisição 3D e modelos CAD previamente construídos. A saída típica de uma técnica de aquisição 3D é uma nuvem de pontos 3D bruta, que precisa de processamento para reduzir o ruído inerente e a falta de informações topológicas. Os modelos CAD são normalmente usados para documentar um processo de projeto de engenharia, apresentando alta complexidade e muitos detalhes irrelevantes para muitos processos de visualização. Portanto, dependendo da aplicação, devemos simplificar bastante o modelo CAD para atender aos seus requisitos. Nesta tese, nos concentramos na construção de modelos digitais 3D a partir dessas fontes. Mais precisamente, apresentamos um conjunto de algoritmos de processamento de geometria para automatizar diferentes etapas de um fluxo de trabalho típico usado para esta construção. Primeiro, apresentamos um algoritmo de redução de ruído de nuvem de pontos que visa preservar as feições nítidas da superfície subjacente. Este algoritmo inclui soluções para a estimativa normal e problemas de detecção de feições nítidas. Em segundo lugar, apresentamos uma extensão do algoritmo de redução de ruído de nuvem de pontos para processar malhas triangulares, onde tiramos proveito da topologia explícita definida pela malha. Por fim, apresentamos um algoritmo para a simplificação extrema de modelos CAD complexos, que tendem a se aproximar da superfície externa do objeto modelado. Os algoritmos propostos são comparados com métodos de última geração, apresentando resultados competitivos e superando-os na maioria dos casos de teste. / [en] As the digitalization process advances in several industries, the creation of 3D digital models is becoming more and more required. Commonly, these models are constructed by 3D designers, requiring considerable manual effort when the modeled object is complex. In addition, since the designer does not have an accurate reference in most cases, the resulting model is prone to measurement errors. However, it is possible to minimize the construction effort and the measurement error by using 3D acquisition techniques and previously constructed CAD models. The typical output of a 3D acquisition technique is a raw 3D point cloud, which needs processing to reduce the inherent noise and lack of topological information. CAD models are typically used to document an engineering design process, presenting high complexity and too many details irrelevant to many visualization processes. So, depending on the application, we must severely simplify the CAD model to meet its requirements. In this thesis, we focus on the construction of 3D digital models from these sources. More precisely, we present a set of geometry processing algorithms to automatize different stages of a typical workflow used for this construction. First, we present a point cloud denoising algorithm that seeks to preserve the sharp features of the underlying surface. This algorithm includes solutions for the normal estimation and sharp feature detection problems. Second, we present an extension of the point cloud denoising algorithm to process triangle meshes, where we take advantage of the explicit topology defined by the mesh. Finally, we present an algorithm for the extreme simplification of complex CAD models, which tends to approximate the outer surface of the modeled object. The proposed algorithms are compared with state-of-the-art methods, showing competitive results and outperforming them in most test cases.

In this thesis we derive various generalizations and refinements of some classical inequalities in different function spaces. We consider some of the most important inequalities namely the Hardy, Pólya-Knopp, Jensen, Minkowski and Beckenbach-Dresher inequalities. The main focus is put on the Hardy and their limit Pólya-Knopp inequalities. Indeed, we derive such inequalities even in a general Banach functionsetting. The thesis consists of three papers (A, B and C) and an introduction, which put these papers into a more general frame. This introduction has also independent interest since it shortly describe the dramatic more than 100 years of development of Hardy-type inequalities. It contains both well-known and very new ideas and results. In paper A we prove and discuss some new Hardy-type inequalities in Banach function space settings. In particular, such a result is proved and applied for a new general Hardy operator, which is introduced in this paper (this operator generalizes the usualHardy kernel operator). These results generalize and unify several classical Hardy-type inequalities. In paper B we prove some new refined Hardy-type inequalities again in Banach function space settings. The used (super quadraticity) technique is also illustrated by making refinements of some generalized forms of the Jensen, Minkowski and Beckenbach-Dresher inequalities. These results both generalize and unify several results of this type. In paper C for the case 0<p≤q<∞ we prove some new Pólya-Knopp inequalities in two and higher dimensions with good two-sided estimates of the sharp constants. By using this result and complementary ideas it is also proved a new multidimensional weighted Pólya-Knopp inequality with sharp constant. / In this thesis we derive various generalizations and refinements of some classical inequalities in different function spaces. We consider some of the most important inequalities namely the Hardy, Pólya-Knopp, Jensen, Minkowski and Beckenbach-Dresher inequalities. The main focus is put on the Hardy and their limit, Pólya-Knopp inequalities. Indeed, we derive such inequalities even in a general Banach function setting.  We prove and discuss some new Hardy-type inequalities in Banach function space settings. In particular, such a result is proved and applied for a new general Hardy operator. These results generalize and unify several classical Hardy-type inequalities. Next, we prove some new refined Hardy-type inequalities again in Banach function space settings. We used superquadraticity technique to prove refinements of some classical inequalities. Finally, for the case 0<p≤q<∞, we prove some new Pólya-Knopp inequalities in two and higher dimensions with good two-sided estimates of the sharp constants. By using this result and complementary ideas it is also proved a new multidimensional weighted Pólya-Knopp inequality with sharp constant.

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Encoding and consolidation of memories are two processes within the hippocampus, and connected cortical networks, that recruit different circuit level dynamics to effectively process and pass information from brain region to brain region. In the hippocampal CA1 pyramidal layer local field potential (LFP), these processes take the form of theta and sharp wave ripples (SPW-Rs) for encoding and consolidation, respectively. As an animal runs through an environment, neurons become active at specific locations in the environment (place cells) increasing their firing rate, functionally representing these specific locations. These firing rate increases are organized within the local theta oscillations and sequential activation of many place cells creates a map of the environment. Once the animal stops moving and begins consummatory behaviors, such as eating, drinking, or grooming, theta activity diminishes, and large irregular activity (LIA) begins to dominate the LFP. Spontaneously, with the LIA, the place cells active during the experience are replayed during SPW-Rs in the same spatial order they were encountered in the environment. Both theta and SPW-R oscillations and their associated neuronal firing are necessary for effective place recognition as well as learning and memory. As such, interruption or termination of SPW-R events results in decreased learning performance over days. During exploration, the associated theta and sequential place cell activity is thought to encode the experience. During quiet restfulness or slow wave sleep (SWS), SPW-R events, that replay experience specific place sequences, are thought to be the signal by which systems consolidation progresses and the hippocampus guides cortical synaptic reorganization. The granular retrosplenial cortex (gRSC) is an associational area that exhibits high frequency oscillations (HFOs) during both hippocampal theta and SPW-Rs, and is potentially a period when the gRSC interprets incoming content from the hippocampus during encoding and systems consolidation. However, the precise laminar organization of synaptic currents supporting HFOs, whether the local gRSC circuitry can support HFOs without patterned input, and the precise coupling of hippocmapla oscillations to gRSC HFOs across brain states remains unknown. We aimed to answer these questions using in vivo, awake electrophysiological recordings in head-fixed mice that were trained to run for water rewards in a 1D virtual environment. We show that gRSC synaptic currents supporting HFOs, across all awake brain states, are exclusively localized to layer 2/3 (L2/3), even when events are detected within layer 5 (L5). Using focal optogenetics, both L2/3 and L5 can generate induced HFOs given a strong enough broad stimulation. Spontaneous gRSC HFOs occurring outside of SPW-Rs are highly comodulated with medial entorhinal cortex (MEC) generated high gamma in hippocampal stratum lacunosum moleculare. gRSC HFOs may serve a necessary role in communication between the hippocampus during SPW-Rs states and between the hippocampus, gRSC, and MEC during theta states to support memory consolidation and memory encoding, respectively. / Doctor of Philosophy / As an animal moves through an environment, individual neurons in the hippocampus, known as place cells, increase and decrease their firing rate as the animal enters and exits specific locations in the environment. Within an environment, multiple neurons become active in different locations, this cooperation of spiking in various locations creates a place map of the environment. Now let's say when the animal moved from one corner of the environment to another, place cells 'A', 'C', 'B', 'E', and 'D' became active in that order. This means, at any given point in the environment, the animal is standing in a venn-diagram-esque overlap of place fields, or locations individual place cells represent. A key question that entranced researchers for many years was how do these neurons know when to be active to not impinge on their neighbor's locations? The answer to this question rested with population electrical activity, known as the local field potential (LFP), that place cell activity is paced to. During active navigation through an environment, place cells activity is coupled to the phase of a slow ~8 hertz (Hz) theta oscillation. Within one theta cycle, or peak to peak, multiple place cells are active, representing the venn diagram of location the animal is in. Importantly, this theta activity and encoding of place cell activity is largely seen during active running or rapid eye movement (REM) sleep. During slow wave sleep (SWS), after an animal has experienced a specific environment and has created a place map, place cells are reactivated in the same order the animal experienced them in. From our previous example, the content of this reactivation would be the place cells 'A', 'C', 'B', 'E', and 'D' which all would be reactivated in that same order. These reactivations or replays occur during highly synchronous and fast LFP oscillations known as sharp wave-ripples (SPW-Rs). SPW-Rs are thought to be a key LFP event that drives memory consolidation and the eventual conversion of short-term memory into long-term memory. However, for consolidation to occur, connected cortical regions need to be able to receive and interpret the information within SPW-Rs. The granular retrosplenial cortex (gRSC) is one proposed region that serves this role. During SPW-Rs the superficial gRSC has been shown to exhibit high frequency oscillations (HFOs), which potentially serve the purpose for interpreting SPW-R content. However, HFOs have been reported during hippocampal theta, suggesting HFOs serve multiple purposes in interregional communication across different states. In this study, we found that naturally occurring gRSC HFOs occur exclusively in layer 2/3 across all awake brain states. Using focal optogenetic excitation we were able to evoke HFOs in both layer 2/3 and 5. Spontaneous gRSC HFOs occurring without SPW-Rs were highly comodulated with medial entorhinal cortex (MEC) generated high gamma in hippocampal stratum lacunosum moleculare. gRSC HFOs may serve a general role in supporting hippocampo-cortical dialogue during SPW-R and theta brain states to support memory consolidation and encoding, respectively.