Gegenstand dieser Arbeit ist die Untersuchung von statistischen Eigenschaften der ungeordneten Metallen im Rahmen des Anderson-Modells der Lokalisierung. Betrachtet wird ein Elektron auf einem Gitter mit "Nächste-Nachbarn-Hüpfen" und zufälligen potentiellen Gitterplatzenergien. Wegen der Zufälligkeit zeigen die Elektroneigenschaften, zum Beispiel die Eigenenergien und -zustände, irreguläre Fluktuationen, deren Statistik von der Amplitude der Potentialenergie abhängt. Mit steigender Amplitude wird das Elektron immer mehr lokalisiert, was schliesslich zum Metall-Isolator-Übergang führt. In dieser Arbeit wird die Statistik insbesondere im metallischen Bereich untersucht, und dadurch der Einfluss der Lokalisierung an den Eigenschaften des Systems betrachtet. Zuerst wird die Statistik der Matrixelemente des Dipoloperators untersucht. Die numerischen Ergebnisse für das Anderson-Modell werden mit Vorhersagen der semiklassischen Näherung verglichen. Dann wird der spektrale Strukturfaktor betrachtet, der als Fourier-Transformation der zwei-Punkt Zustandsdichtekorrelationsfunktion definiert wird. Dabei werden besonders die nichtuniversellen Abweichungen von den Vorhersagen der Zufallsmatrixtheorie untersucht. Die Abweichungen werden numerisch ermittelt, und danach mit den analytischen Vorhersagen verglichen. Die Statistik der Wellenfunktionen zeigt ebenfalls Abweichungen von der Zufallsmatrixtheorie. Die Abweichungen sind am größten für Statistik der großen Wellenfunktionsamplituden, die sogenannte seltene Ereignisse darstellen. Die analytischen Vorhersagen für diese Statistik sind teilweise widersprüchlich, und deshalb ist es interessant, sie auch numerisch zu untersuchen.

Les chambres réverbérantes à brassage de modes (CRBM) utilisées dans l'industrie pour tester l'immunité ou la susceptibilité des systèmes électroniques embarqués (avion, automobile , smartphone,...) vis-à-vis des ondes électromagnétiques (EM) présentes dans leur environnement. Les CRBM doivent toutes répondre à un certain nombre de critères statistiques fixés par une norme internationale. Le critère principale étant l'obtention d'un champ statistiquement uniforme et isotrope autour de l'objet sous test. Afin améliorer et de mieux maîtriser les propriétés statistiques de ces systèmes pour des fréquences proches de leur fréquence minimale d'utilisation, nous proposons de les rendre chaotiques afin de profiter des propriétés statistiques universelles des résonances des cavités chaotiques. Nous commencerons par montrer comment rendre chaotique, par des modifications simples, des chambres réverbérantes conventionnelles, et comment étendre les prédictions de la théorie des matrices aléatoire appliquée (TMA) à l'hamiltonien effectif, permettant de décrire les systèmes chaotiques ouverts, au cas de systèmes décrits par des champs vectoriels. Ensuite, nous comparerons, au moyen de simulations et d’expériences, les distributions d'intensité et les fluctuations des maxima du champ EM dans une CRBM conventionnelle et dans une CR chaotique au voisinage de la fréquence minimale d’utilisation. Ce travail illustre que les propriétés statistiques spectrales et spatiales universelles des CR chaotiques permettent de mieux répondre aux critères exigés par la norme internationale pour réaliser des tests de compatibilité électromagnétiques. / Mode-stirred reverberation chambers (RC) are used in the industry to test the immunity or the susceptibility of on-board electronic systems (plane, automobile, smartphone) towards the electromagnetic waves present in their environment. Mode-stirred RCs have to comply with a number of statistical criteria fixed by international standards. The chief criterion relies on a statistically uniform and isotropic field around the object under test. In order to improve and master the statistical properties of these systems for frequencies close to their lowest useable frequency, we suggest making them chaotic to take advantage of universal statistical properties of the resonances of chaotic cavities. We first show how to make chaotic RCs by simple modifications of a conventional RC and how to extend the predictions of the random matrix theory applied to the effective hamiltonien describing the open chaotic systems, to the case of vectorial fields. Then, we compare, by means of simulations and experiments, the distributions of intensity and the fluctuations of the maxima of the field in a conventional RC and in a chaotic RC close to the lowest useable frequency. This work illustrates that the universal spectral and spatial statistical properties of chaotic RCs allow to better comply with the criteria required by the international standards.

Gegenstand dieser Arbeit ist die Untersuchung von statistischen Eigenschaften der ungeordneten Metallen im Rahmen des Anderson-Modells der Lokalisierung. Betrachtet wird ein Elektron auf einem Gitter mit "Nächste-Nachbarn-Hüpfen" und zufälligen potentiellen Gitterplatzenergien. Wegen der Zufälligkeit zeigen die Elektroneigenschaften, zum Beispiel die Eigenenergien und -zustände, irreguläre Fluktuationen, deren Statistik von der Amplitude der Potentialenergie abhängt. Mit steigender Amplitude wird das Elektron immer mehr lokalisiert, was schliesslich zum Metall-Isolator-Übergang führt. In dieser Arbeit wird die Statistik insbesondere im metallischen Bereich untersucht, und dadurch der Einfluss der Lokalisierung an den Eigenschaften des Systems betrachtet. Zuerst wird die Statistik der Matrixelemente des Dipoloperators untersucht. Die numerischen Ergebnisse für das Anderson-Modell werden mit Vorhersagen der semiklassischen Näherung verglichen. Dann wird der spektrale Strukturfaktor betrachtet, der als Fourier-Transformation der zwei-Punkt Zustandsdichtekorrelationsfunktion definiert wird. Dabei werden besonders die nichtuniversellen Abweichungen von den Vorhersagen der Zufallsmatrixtheorie untersucht. Die Abweichungen werden numerisch ermittelt, und danach mit den analytischen Vorhersagen verglichen. Die Statistik der Wellenfunktionen zeigt ebenfalls Abweichungen von der Zufallsmatrixtheorie. Die Abweichungen sind am größten für Statistik der großen Wellenfunktionsamplituden, die sogenannte seltene Ereignisse darstellen. Die analytischen Vorhersagen für diese Statistik sind teilweise widersprüchlich, und deshalb ist es interessant, sie auch numerisch zu untersuchen.

The interest in sustainable investing has increased significantly during recent years. Asset managers and institutional investors are urged to invest more sustainable from their stakeholders, reducing their investment universe. This thesis has found that sustainable investments have a different linear dependence structure compared to the regional markets in Europe and North America, but not in Asia-Pacific. However, the largest drawdowns of an sustainable compliant portfolio has historically been lower compared to the a random market portfolio, especially in Europe and North America. / Intresset för hållbara investeringar har ökat avsevärt de senaste åren. Fondförvaltare och institutionella investerare är, från deras intressenter, manade att investera mer hållbart vilket minskar förvaltarnas investeringsuniversum. Denna uppsats har funnit att hållbara investeringar har en beroendestruktur som är skild från de regionala marknaderna i Europa och Nordamerika, men inte för Asien-Stillahavsregionen. De största värdeminskningarna i en hållbar portfölj har historiskt varit mindre än värdeminskningarna från en slumpmässig marknadsportfölj, framförallt i Europa och Nordamerika.

Random matrix theory (RMT) is a mathematical framework that has found profound applications in physics, particularly in the study of many-body systems. Its success lies in its ability to predict universal statistical properties of complex systems, independent of the specific details. This thesis explores the application of RMT to two classes of many-body systems: quantum and stochastic many-body systems. Within the quantum framework, this work focuses on the Bose-Hubbard system, which is paradigmatic for modeling ultracold atoms in optical traps. According to RMT and the Eigenstate Thermalization Hypothesis (ETH), eigenstate-to-eigenstate fluctuations of expectation values of local observables decay rapidly with the system size in the thermodynamic limit at sufficiently large temperatures. Here, we study these fluctuations in the classical limit of fixed lattice size and increasing boson number. We find that the fluctuations follow the RMT prediction for large system sizes but deviate substantially for small lattices. Partly motivated by these results, the Bose-Hubbard model on three sites is studied in more detail. On few sites, the Bose-Hubbard model is known to be a mixed system, being neither fully chaotic nor integrable. We compare energy-resolved classical and quantum measures of chaos, which show a strong agreement. Deviations from RMT predictions are attributed to the mixed nature of the few-site model. In the context of stochastic systems, generators of Markov processes are studied. The focus is on the spectrum. We present results from two investigations of Markov spectra. First, we investigate the effect of sparsity on the spectrum of random generators. Dense random matrices previously used as a model for generic generators led to very large spectral gaps and therefore to unphysically short relaxation times. In this work, a model of random generators with adjustable sparsity — number of zero matrix elements — is presented, extending the dense framework. It is shown that sparsity leads to longer, more physically realistic relaxation times. Second, the generator spectrum of the Asymmetric Simple Exclusion Process (ASEP), a quintessential model in non-equilibrium statistical mechanics, is analyzed. We investigate the spectral boundary, which is characterized by pronounced spikes. The emergence of these spikes is analyzed from several points of view, including RMT. The results presented in this thesis contribute to the understanding of the applicability of RMT to many-body systems. This thesis highlights successes such as the explanation of “ETH fluctuations” in Bose-Hubbard models, the improvement of random matrix descriptions by introducing sparsity, and the emergence of spikes in the spectral boundary of the ASEP. The latter is a notable case where RMT provides insights even though the ASEP is a Bethe-integrable system. Furthermore, this thesis shows examples of the limits of RMT, exemplified by the results presented for the Bose-Hubbard model with a few sites.

Face recognition is a field of biometrics that deals with identification of subjects based on features present in the images of their faces. The factors that make face recognition popular and favorite as compared to other biometric methods are easier operation and ability to identify subjects without their knowledge. With these features, face recognition has become an integral part of the present day security systems, targeting a smart and secure world. There are various factors that de ne the performance of a face recognition system. The most important among them are recognition accuracy of algorithm used and time taken for recognition. Recognition accuracy of the face recognition algorithm gets affected by changes in pose, facial expression and illumination along with occlusions in the images. There have been a number of algorithms proposed to enable recognition under these ambient changes. However, it has been hard to and a single algorithm that can efficiently recognize faces in all the above mentioned conditions. Moreover, achieving real time performance for most of the complex face recognition algorithms on embedded platforms has been a challenge. Real-time performance is highly preferred in critical applications such as identification of crime suspects in public. As available software solutions for FR have significantly large latency in recognizing individuals, they are not suitable for such critical real-time applications. This thesis focuses on real-time aspect of FR, where acceleration of the algorithms is achieved by means of parallel hardware architectures. The major contributions of this work are as follows. We target to design a face recognition system that can identify at most 30 faces in each frame of video at 15 frames per second, which amounts to 450 recognitions per second. In addition, we target to achieve good recognition accuracy along with scalability in terms of database size and input image resolutions. To design a system with these specifications, as a first step, we explore algorithms in literature and come up with a hybrid face recognition algorithm. This hybrid algorithm shows good recognition accuracy on face images with changes in illumination, pose and expressions, and also with occlusions. In addition the computations in the algorithm are modular in nature which are suitable for real-time realizations through parallel processing. The face recognition system consists of a face detection module to detect faces in the input image, which is followed by a face recognition module to identify the detected faces. There are well established algorithms and architectures for face detection in literature which can perform detection at 15 frames per second on video frames. Detected faces of different sizes need to be scaled to the size specified by the face recognition module. To meet the real-time constraints, we propose a hardware architecture for real-time bi-cubic convolution interpolation with dynamic scaling factors. To recognize the resized faces in real-time, a scalable parallel pipelined architecture is designed for the hybrid algorithm which can perform 450 recognitions per second on a database containing grayscale images of at most 450 classes on Virtex 6 FPGA. To provide flexibility and programmability, we extend this design to REDEFINE, a multi-core massively parallel reconfigurable architecture. In this design, we come up with FR specific programmable cores termed Scalable Unit for Region Evaluation (SURE) capable of performing modular computations in the hybrid face recognition algorithm. We replicate SUREs in each tile of REDEFINE to construct a face recognition module termed REDEFINE for Face Recognition using SURE Homogeneous Cores (REFRESH). There is a need to learn new unseen faces on-line in practical face recognition systems. Considering this, for real-time on-line learning of unseen face images, we design tiny processors termed VOP, Processor for Vector Operations. VOPs function as coprocessors to process elements under each tile of REDEFINE to accelerate micro vector operations appearing in the synaptic weight computations. We also explore deep neural networks which operate similar to the processing in human brain and capable of working on very large face databases. We explore the field of Random matrix theory to come up with a solution for synaptic weight initialization in deep neural networks for better classification . In addition, we perform design space exploration of hardware architecture for deep convolution networks and conclude with directions for future work.