Partant du constat que dans plus en plus d'applications, la taille des données à traiter augmente, il semble pertinent d'utiliser des outils appropriés tels que la théorie des matrices aléatoires dans le régime en grandes dimensions. Plus particulièrement, dans les applications de traitement d'antenne et radar spécifiques STAP et MIMO-STAP, nous nous sommes intéressés au traitement d'un signal d'intérêt corrompu par un bruit additif composé d'une partie dite rang faible et d'un bruit blanc gaussien. Ainsi l'objet de cette thèse est d'étudier dans le régime en grandes dimensions la détection et le filtrage dit rang faible (fonction de projecteurs) pour le traitement d'antenne en utilisant la théorie des matrices aléatoires.La thèse propose alors trois contributions principales, dans le cadre de l'analyse asymptotique de fonctionnelles de projecteurs. Ainsi, premièrement, le régime en grandes dimensions permet ici de déterminer une approximation/prédiction des performances théoriques non asymptotiques, plus précise que ce qui existe actuellement en régime asymptotique classique (le nombre de données d'estimation tends vers l'infini à taille des données fixe). Deuxièmement, deux nouveaux filtres et deux nouveaux détecteurs adaptatifs rang faible ont été proposés et il a été montré qu'ils présentaient de meilleures performances en fonction des paramètres du système en terme de perte en RSB, probabilité de fausse alarme et probabilité de détection. Enfin, les résultats ont été validés sur une application de brouillage, puis appliqués aux traitements radar STAP et MIMO-STAP sparse. L'étude a alors mis en évidence une différence notable avec l'application de brouillage liée aux modèles de matrice de covariance traités dans cette thèse. / Nowadays, more and more applications deal with increasing dimensions. Thus, it seems relevant to exploit the appropriated tools as the random matrix theory in the large dimensional regime. More particularly, in the specific array processing applications as the STAP and MIMO-STAP radar applications, we were interested in the treatment of a signal of interest corrupted by an additive noise composed of a low rang noise and a white Gaussian. Therefore, the aim of this thesis is to study the low rank filtering and detection (function of projectors) in the large dimensional regime for array processing with random matrix theory tools.This thesis has three main contributions in the context of asymptotic analysis of projector functionals. Thus, the large dimensional regime first allows to determine an approximation/prediction of theoretical non asymptotic performance, much more precise than the literature in the classical asymptotic regime (when the number of estimation data tends to infinity at a fixed dimension). Secondly, two new low rank adaptive filters and detectors have been proposed and it has been shown that they have better performance as a function of the system parameters, in terms of SINR loss, false alarm probability and detection probability. Finally, the results have been validated on a jamming application and have been secondly applied to the STAP and sparse MIMO-STAP processings. Hence, the study highlighted a noticeable difference with the jamming application, related to the covariance matrix models concerned by this thesis.

There have been a number of computational modelling studies that aim to replicate the cerebellar Purkinje cell, though these typically use the morphology of rodent cells. While many species, including rodents, display intricate dendritic branching, it is not a universal feature among Purkinje cells. This study uses morphological reconstructions of 24 Purkinje cells from seven species to explore the changes that occur to the cell through evolution and examine whether this has an effect on the processing capacity of the cell. This is achieved by combining several modes of study in order to gain a comprehensive overview of the variations between the cells in both morphology and behaviour. Passive and active computational models of the cells were created, using the same electrophysiological parameters and ion channels for all models, to characterise the voltage attenuation and electrophysiological behaviour of the cells. These results and several measures of branching and size were then used to look for clusters in the data set using machine learning techniques. They were also used to visualise the differences within each species group. Information theory methods were also employed to compare the estimated information transfer from input to output across each cell. Along with a literature review into what is known about Purkinje cells and the cerebellum across the phylogenetic tree, these results show that while there are some obvious differences in morphology, the variation within species groups in electrophysiological behaviour is often as high as between them. This suggests that morphological changes may occur in order to conserve behaviour in the face of other changes to the cerebellum.

<div>The recent advances in articial neural networks have demonstrated competitive performance of deep neural networks (and it is comparable with humans) on tasks like image classication, natural language processing and time series classication. These large scale networks pose an enormous computational challenge, especially in resource constrained devices. The current work proposes a targeted-rank based framework for accelerated computation of wide neural networks. It investigates the problem of rank-selection for tensor ring nets to achieve optimal network compression. When applied to a state of the art wide residual network, namely WideResnet, the framework yielded a signicant reduction in computational time. The optimally compressed non-parallel WideResnet is faster to compute on a CPU by almost 2x with only 5% degradation in accuracy when compared to a non-parallel implementation of uncompressed WideResnet.</div>

Identifying the causes and consequences of intra-specific variation in cognitive abilities is fundamental to our understanding of the evolution of cognition. The social environment and cognitive abilities appear inextricably linked, yet evidence for how the social environment affects cognitive performances and further, how cognitive performances influence the social environment, has seldom been explored. Using the pheasant, Phasianus colchicus, I explore the relationships between individual variation in cognitive performances in relation to broad and fine-scale structure of the social environment and endeavour to separate cause and consequence. I demonstrate a positive causal effect of the broad-scale social environment on cognitive performances by observing increases in the accuracy of spatial discrimination performances when individuals are in larger groups (Chapter Two and Chapter Four). I show that the positive effects of larger group size occur over a relatively short period (less than one week), suggesting that cognitive performances are flexible in response to the social environment and I suggest four potential mechanisms. I show that while males are part of a social hierarchy, spatial discrimination performances are related to this fine-scale social structure and higher-ranking males outperform lower ranking males (Chapter Three). When attempting to determine cause and consequence, I found that spatial learning performances early in life did not predict adult cognitive performances on the same task or predict their adult social rank (Chapter Four). Hence, my results do not support that social rank is a consequence of spatial learning abilities in male pheasants. The relationship between spatial learning performances and social rank was found in adult males that had their social rank artificially elevated, suggesting that cognitive performances were not simply the result of the current social environment but remain closely related to past agonistic relationships. I did not find a relationship between early life aggression with performances on either a spatial or a non-spatial task in females or males (Chapter Five). This highlights the importance of investigating early life relationships and suggests that the relationship between spatial learning and aggression in adult males may become associated over time as a consequence of further spatial learning experiences, and, or, aggressive interactions. I then demonstrate a consequence of individual variation in cognitive abilities and show that adult foraging associations in the wild disassort by early life cognitive performances (Chapter Six). Individuals with good inhibitory control performance and poor visual discrimination performances were more central in social networks. I propose that differences in cognitive abilities manifest in foraging strategy and influence the resulting social structure. The implications of this predictable social structure remain to be explored. Finally, I discuss these results and how they contribute to our understanding of how the social environment causes individual differences in cognitive performances, as well as how variation in cognitive performances may shape the social environment. I suggest the potential implications of these findings and ideas for future work.

Dans le cadre du traitement statistique du signal, la plupart des algorithmes couramment utilisés reposent sur l'utilisation de la matrice de covariance des signaux étudiés. En pratique, ce sont les versions adaptatives de ces traitements, obtenues en estimant la matrice de covariance à l'aide d'échantillons du signal, qui sont utilisés. Ces algorithmes présentent un inconvénient : ils peuvent nécessiter un nombre d'échantillons important pour obtenir de bons résultats. Lorsque la matrice de covariance possède une structure rang faible, le signal peut alors être décomposé en deux sous-espaces orthogonaux. Les projecteurs orthogonaux sur chacun de ces sous espaces peuvent alors être construits, permettant de développer des méthodes dites rang faible. Les versions adaptatives de ces méthodes atteignent des performances équivalentes à celles des traitements classiques tout en réduisant significativement le nombre d'échantillons nécessaire. Par ailleurs, l'accroissement de la taille des données ne fait que renforcer l'intérêt de ce type de méthode. Cependant, cet accroissement s'accompagne souvent d'un accroissement du nombre de dimensions du système. Deux types d'approches peuvent être envisagées pour traiter ces données : les méthodes vectorielles et les méthodes tensorielles. Les méthodes vectorielles consistent à mettre les données sous forme de vecteurs pour ensuite appliquer les traitements classiques. Cependant, lors de la mise sous forme de vecteur, la structure des données est perdue ce qui peut entraîner une dégradation des performances et/ou un manque de robustesse. Les méthodes tensorielles permettent d'éviter cet écueil. Dans ce cas, la structure est préservée en mettant les données sous forme de tenseurs, qui peuvent ensuite être traités à l'aide de l'algèbre multilinéaire. Ces méthodes sont plus complexes à utiliser puisqu'elles nécessitent d'adapter les algorithmes classiques à ce nouveau contexte. En particulier, l'extension des méthodes rang faible au cas tensoriel nécessite l'utilisation d'une décomposition tensorielle orthogonale. Le but de cette thèse est de proposer et d'étudier des algorithmes rang faible pour des modèles tensoriels. Les contributions de cette thèse se concentrent autour de trois axes. Un premier aspect concerne le calcul des performances théoriques d'un algorithme MUSIC tensoriel basé sur la Higher Order Singular Value Decomposition (HOSVD) et appliqué à un modèle de sources polarisées. La deuxième partie concerne le développement de filtres rang faible et de détecteurs rang faible dans un contexte tensoriel. Ce travail s'appuie sur une nouvelle définition de tenseur rang faible et sur une nouvelle décomposition tensorielle associée : l'Alternative Unfolding HOSVD (AU-HOSVD). La dernière partie de ce travail illustre l'intérêt de l'approche tensorielle basée sur l'AU-HOSVD, en appliquant ces algorithmes à configuration radar particulière: le Traitement Spatio-Temporel Adaptatif ou Space-Time Adaptive Process (STAP). / Most of statistical signal processing algorithms, are based on the use of signal covariance matrix. In practical cases this matrix is unknown and is estimated from samples. The adaptive versions of the algorithms can then be applied, replacing the actual covariance matrix by its estimate. These algorithms present a major drawback: they require a large number of samples in order to obtain good results. If the covariance matrix is low-rank structured, its eigenbasis may be separated in two orthogonal subspaces. Thanks to the LR approximation, orthogonal projectors onto theses subspaces may be used instead of the noise CM in processes, leading to low-rank algorithms. The adaptive versions of these algorithms achieve similar performance to classic classic ones with less samples. Furthermore, the current increase in the size of the data strengthens the relevance of this type of method. However, this increase may often be associated with an increase of the dimension of the system, leading to multidimensional samples. Such multidimensional data may be processed by two approaches: the vectorial one and the tensorial one. The vectorial approach consists in unfolding the data into vectors and applying the traditional algorithms. These operations are not lossless since they involve a loss of structure. Several issues may arise from this loss: decrease of performance and/or lack of robustness. The tensorial approach relies on multilinear algebra, which provides a good framework to exploit these data and preserve their structure information. In this context, data are represented as multidimensional arrays called tensor. Nevertheless, generalizing vectorial-based algorithms to the multilinear algebra framework is not a trivial task. In particular, the extension of low-rank algorithm to tensor context implies to choose a tensor decomposition in order to estimate the signal and noise subspaces. The purpose of this thesis is to derive and study tensor low-rank algorithms. This work is divided into three parts. The first part deals with the derivation of theoretical performance of a tensor MUSIC algorithm based on Higher Order Singular Value Decomposition (HOSVD) and its application to a polarized source model. The second part concerns the derivation of tensor low-rank filters and detectors in a general low-rank tensor context. This work is based on a new definition of tensor rank and a new orthogonal tensor decomposition : the Alternative Unfolding HOSVD (AU-HOSVD). In the last part, these algorithms are applied to a particular radar configuration : the Space-Time Adaptive Process (STAP). This application illustrates the interest of tensor approach and algorithms based on AU-HOSVD.

In this work, the analysis of the computation of the greatest common divisor of univariate and bivariate polynomials is presented. The whole process is split into three stages. In the first stage, data preprocessing is explained and the resulting better numerical behavior is demonstrated. Next stage is concerned with the problem of the computation of the numerical rank of the Sylvester matrix, from which the degree of the greatest common divisor is obtained. The last stage is the actual algorithm for calculating the greatest common divisor of two polynomials. Furthermore, the underlying theory behind the computation of the greatest common divisor is explained and illustrated on many examples. 1

O uso de provas elaboradas na forma de itens, em processos de avaliação para classificação, é uma herança histórica dos séculos XVI e XVII, ainda em uso nos dias atuais tanto na educação formal quanto em processos seletivos, a exemplo dos exames vestibulares. Elaboradas para mensurar conhecimentos, traços latentes que não podem ser medidos diretamente, as provas costumam ser corrigidas considerando unicamente o escore obtido pelo sujeito avaliado, sem contemplar informações importantes relacionadas aos itens das mesmas. O presente trabalho teve como objetivos: (i) utilizar a modelagem baseada na teoria da resposta ao item unidimensional - TRI e multidimensional - TRIM para construir escalas do conhecimento para a prova da FUVEST e (ii) classificar os candidatos aos seis cursos de graduação oferecidos pela Escola Superior de Agricultura \"Luiz de Queiroz\", unidade da Universidade de São Paulo, com base na escala construída. A hipótese imbutida no corpo do trabalho admitiu que o uso da TRIM classifica de forma diferente os candidatos que os atuais métodos utilizados pela FUVEST. Foram utilizados os padrões de respostas dos 2326 candidatos submetidos à prova, para que uma análise unidimensional fosse realizada, sob o enfoque da TRI, gerando uma escala de proficiências . Quatro traços latentes foram diagnosticados no processo avaliativo, por meio da modelagem multidimensional da TRIM, gerando uma escala das quatro dimensões. Uma proposta para classificação dos candidatos é apresentada, baseada na média das proficiências individuais ponderada pelas cargas fatoriais diagnosticadas pela modelagem. Análise comparativa entre os critérios de classificação utilizados pela FUVEST e pela TRIM foram realizados, identificando discordância entre os mesmos. O trabalho apresenta propostas de interpretação pedagógica para as escalas unidimensional e multidimensional e indica a TRIM como o critério complementar para classificação dos candidatos, valorizando informações individuais dos itens e, portanto, utilizando uma avaliação classificatória mais abrangente. / The use of elaborate exams in the form of items, in evaluation procedures for classification, is a historical legacy of the 16th and 17th centuries, still in use today both in formal education and in selective cases such as entrance examinations. Designed to measure knowledge, latent trait that can not be measured directly, the exams are usually corrected considering only the score obtained by the subject, without including important information related to the items of it. This study aimed to: (i) use the modeling approach unidimensional and multidimensional item response theory (IRT and MIRT, respectively), to build knowledge scales of the entrance examination FUVEST/2012; (ii) classifing candidates for the 6 undergraduate courses offered by the \"Luiz de Queiroz\" College of Agriculture , unit of the University of São Paulo, based on the scale then. The hypothesis supposes that the use of MIRT ranked candidates differently than current methods used by FUVEST. We used the patterns of responses of 2326 candidates submitted to the test, so that a one-dimensional analysis was performed under the IRT approach, generating a range of proficiencies. Four latent traits were diagnosed in the evaluation process by means of multidimensional modeling MIRT, generating a scale of four dimensions. A proposal for classification of the candidates is presented, based on the weighted average of the individual proficiencies by the factor loadings diagnosed by modeling. Comparative analysis of the classification criteria used by FUVEST and MIRT were performed by identifying discrepancies between them. This work presents the proposals of the pedagogical interpretation for one-dimensional and multidimensional scales and indicates the MIRT as additional criteria for the candidates, to valorize individual information of the items and therefore using a more comprehensive classification review.

Modern big data often emerge as tensors. Standard statistical methods are inadequate to deal with datasets of large volume, high dimensionality, and complex structure. Therefore, it is important to develop algorithms such as low-rank tensor decomposition for data compression, dimensionality reduction, and approximation. With the advancement in technology, high-dimensional images are becoming ubiquitous in the medical field. In lung radiation therapy, the respiratory motion of the lung introduces variabilities during treatment as the tumor inside the lung is moving, which brings challenges to the precise delivery of radiation to the tumor. Several approaches to quantifying this uncertainty propose using a model to formulate the motion through a mathematical function over time. [Li et al., 2011] uses principal component analysis (PCA) to propose one such model using each image as a long vector. However, the images come in a multidimensional arrays, and vectorization breaks the spatial structure. Driven by the needs to develop low-rank tensor decomposition and provided the 4DCT and Displacement Vector Field (DVF), we introduce two tensor decompositions, Population Value Decomposition (PVD) and Population Tucker Decomposition (PTD), to estimate the respiratory lung motion with high levels of accuracy and data compression. The first algorithm is a generalization of PVD [Crainiceanu et al., 2011] to higher order tensor. The second algorithm generalizes the concept of PVD using Tucker decomposition. Both algorithms are tested on clinical and phantom DVFs. New metrics for measuring the model performance are developed in our research. Results of the two new algorithms are compared to the result of the PCA algorithm.

本論文系以中共所謂「建國」以來，所事實統治之中國大陸為研究地區，其自課為一「社會主義國家」，並將國家工作人員統稱為幹部，涵蓋黨、政、軍、群、企、事等各部門，此等幹部管理迥異一般民主國家，不僅概念籠統，而且缺乏科學分類，自文革後其黨十一屆三中全會(一九七八年)決定推動改革開放政策以來，幹部體制為應需要而不斷調整，尤其自黨十三大(一九八七年)確立推行國家公務員制度，並將其行政部門人員分離出來，嗣後不斷研議相關法規，而黨十四大則決定加速推行此種制度，一九九三年八月因其國務院發布「國家公務員暫行條例」的總體性法規，業已確定其幹部邁向現代化的競爭實績、科學管理取向，稚在總結經驗，配合實際管理需要而作調整之外，意識形態，黨政關係仍然貫穿整個管理體制及運作之中；因此，本文為便於分析，幾經斟酌，乃以其黨十三大以來的國家行政機關工作人員(不含工勤人員)為分析對象(中共過去因概念含混，是以本文仍以幹部稱之)。 全文共分七章，二十二節，其實容要旨如次： 第一章「緒論」，說明研究動機與目的、研究範圍與方法，並就一般性了解，提出研究架構、假設與限制，同時對本研究重要概念予以界定與區分，以為本文探討之準據。 第二章「中共幹部制度之發展與改革」，說明中共體制現代化與理性，意識形態的關係，牌瞭解改革之特殊性，其次再析述其幹部建構理念與制度發展，以及改革背景與發展要求格局，然後再就改革運作原則，國家公務員制度之建立過程、取向加以敘述，以掌握改革動態。 第三章「人事管理體制宏觀分析」，就中共幹部管理體制而言，其宏觀層次的人事體制傳統與現行模式架構予以解析，次就其管理機構等設置及其原則，監察管理予以析述，然後再就人員的行為規範之權利義務，迴避、申訴控告等予以解析，牌期瞭解其體制總體運作。 第四章「人力引進與調節」，政府體系運作涉及人力配置、運用，中共隨改革發展、計畫體制走向市場經濟而變革，茲就其法規等歸納，得知其人力甄補的考試錄用、人員任免，以及人力流動的升降遷調與交流等制度設計，特再述明並分析其人力培訓發展之情勢。 第五章「人員少勵與維護」，激勵維護措施，在維護現有人力運作暨未來人力投入之誘因，經由考核獎懲汰劣獎優，確保工作品質與人力素質，而以工資福利維持其生活與地位，並激發工作意願（勞動積極性），而退離辭卸則促使人力有效代謝與雙向交流。 第六章「幹部體系轉化的檢視與調適」，經由前述各章分析，總結其幹部改革戰略與檢視發展走向，並先釐出其改革議題，再研析發展模式與中國特色，牌期瞭解國家公務員制度發展建構；然後再分析其改革論爭、具體問題，並說明其改革調適與影響。 第七章「結論」，就前述各章所發現問題及獲致之研究結論，參照本論文研究架構與假設，提出研究發現與發展評估，並說明其高制改革之發展前景。

Les études épidémiologiques longitudinales sur la qualité de vie (QdV) connaissent un essor depuis quelques années, surtout pour les maladies chroniques où aucun traitement curatif n'existe. L'objectif de ces études est la surveillance de la santé incluant la QdV et la survie. Une telle surveillance repose sur la comparaison de l'évolution longitudinale de QdV entre groupes de patients. Aussi, avons nous élaboré un test global de type log-rank pour l'évolution longitudinale de QdV par rapport à un taux de dégradation de QdV pour deux groupes de patients. <br />Généralement lors de ces études, des questionnaires de QdV sont donnés à remplir aux patients permettant de calculer leur score de QdV. L'évolution de QdV se traduit par le concept de dégradation de QdV. Un taux critique x de dégradation de QdV peut être fixé. Les patients sont considérés comme dégradés si leur score de QdV est supérieur à x. Nous étendons la statistique du score de vraisemblance partielle afin de prendre en compte un taux x de dégradation de QdV préalablement fixé et montrons que le vecteur du processus de score normalisé converge vers un processus gaussien centré. Le taux x de dégradation de QdV est ensuite supposé variable. A l'aide de la théorie des processus empiriques nous prouvons la convergence en distribution de la statistique du score normalisé vers un processus gaussien. Ces travaux ont permis de construire, lorsque le taux x de dégradation de QdV est variable, un test de type log-rank permettant de comparer l'évolution longitudinale de la dégradation de QdV pour deux goupes de patients.<br />Des simulations et une application à une cohorte de patients infectés par le VIH sont présentées.