The coding and feedback inaccuracies of the channel state information (CSI) in limited feedback multiple-input multiple-output (MIMO) wireless systems can severely impact the achievable data rate and reliability. The CSI is mathematically represented as a Grassmann manifold or manifold of unitary matrices. These are non-Euclidean spaces with special constraints that makes efficient and high fidelity coding especially challenging. In addition, the CSI inaccuracies may occur due to digital representation, time variation, and delayed feedback of the CSI. To overcome these inaccuracies, the manifold structure of the CSI can be exploited. The objective of this dissertation is to develop a new signal processing techniques on the manifolds to harvest the benefits of MIMO wireless systems. First, this dissertation presents the Kerdock codebook design to represent the CSI on the Grassmann manifold. The CSI inaccuracy due to digital representation is addressed by the finite alphabet structure of the Kerdock codebook. In addition, systematic codebook construction is identified which reduces the resource requirement in MIMO wireless systems. Distance properties on the Grassmann manifold are derived showing the applicability of the Kerdock codebook to beam-forming and spatial multiplexing systems. Next, manifold-constrained algorithms to predict and encode the CSI with high fidelity are presented. Two prominent manifolds are considered; the Grassmann manifold and the manifold of unitary matrices. The Grassmann manifold is a class of manifold used to represent the CSI in MIMO wireless systems using specific transmission strategies. The manifold of unitary matrices appears as a collection of all spatial information available in the MIMO wireless systems independent of specific transmission strategies. On these manifolds, signal processing building blocks such as differencing and prediction are derived. Using the proposed signal processing tools on the manifold, this dissertation addresses the CSI coding accuracy, tracking of the CSI under time variation, and compensation techniques for delayed CSI feedback. Applications of the proposed algorithms in single-user and multiuser systems show that most of the spatial benefits of MIMO wireless systems can be harvested. / text

La robotique chirurgicale vise à rendre les gestes du chirurgien plus précis et moins invasifs. La complexité d'une salle d'opération conduit à rechercher des dispositifs robotiques aussi compacts que possible et pouvant être facilement stérilisés. Une conception robotique basée sur l'emploi de mécanismes compliants à structures monolithiques et d'actionneurs piézoélectriques est particulièrement intéressante sur ce point. Des travaux précédents conduits au laboratoire ont permis de proposer un dispositif robotique pour le pontage coronarien qui facilite la réalisation des gestes minimalement invasifs sur cœur battant. Ce dispositif répond au besoin médical mais manque aujourd'hui de la compacité souhaitée pour une intégration optimale. À partir du cas d'application où nous cherchons à réduire la taille du dispositif de compensation, nous nous intéressons, dans cette thèse, aux problématiques de conception de mécanismes compliants à fortes contraintes d'intégration. Nous étudions d'abord la possibilité d'intégrer le dispositif de compensation directement dans la tige du stabilisateur cardiaque passif. Puis, nous étudions la possibilité de réduire la taille du dispositif de compensation en amont, en explorant les possibilités de réaliser des mécanismes dans un plan. Nous avons notamment proposé une méthode originale de conception de mécanismes compliants plans à partir de l'analyse des singularités de mécanismes à architectures parallèles en configuration plane. Afin d'optimiser les différents mécanismes très contraints par les volumes imposés, une méthode originale d'optimisation à base d'un algorithme de colonie de fourmis est employée.

La robotique chirurgicale vise à rendre les gestes du chirurgien plus précis et moins invasifs. La complexité d’une salle d’opération conduit à rechercher des dispositifs robotiques aussi compacts que possible et pouvant être facilement stérilisés. Une conception robotique basée sur l’emploi de mécanismes compliants à structures monolithiques et d’actionneurs piézoélectriques est particulièrement intéressante sur ce point. Des travaux précédents conduits au laboratoire ont permis de proposer un dispositif robotique pour le pontage coronarien qui facilite la réalisation des gestes minimalement invasifs sur cœur battant. Ce dispositif répond au besoin médical mais manque aujourd’hui de la compacité souhaitée pour une intégration optimale. À partir du cas d’application où nous cherchons à réduire la taille du dispositif de compensation, nous nous intéressons, dans cette thèse, aux problématiques de conception de mécanismes compliants à fortes contraintes d’intégration. Nous étudions d’abord la possibilité d’intégrer le dispositif de compensation directement dans la tige du stabilisateur cardiaque passif. Puis, nous étudions la possibilité de réduire la taille du dispositif de compensation en amont, en explorant les possibilités de réaliser des mécanismes dans un plan. Nous avons notamment proposé une méthode originale de conception de mécanismes compliants plans à partir de l‘analyse des singularités de mécanismes à architectures parallèles en configuration plane. Afin d’optimiser les différents mécanismes très contraints par les volumes imposés, une méthode originale d’optimisation à base d’un algorithme de colonie de fourmis est employée. / Surgical robotics helps to increase the surgeon’s accuracy and limits the invasiveness of the surgery. The complexity of an operation room implies to design surgical devices that are as compact as possible and that can be easily sterilized. One interesting design approach is to combine compliant mechanisms, which have a monolithic structure, and piezoelectric actuators. Based on this approach, a robotic device for minimally invasive coronary artery bypass grafting has been proposed previously in our laboratory. This device successfully helps to increase the stabilization of the heart surface during the surgery but its compactness needs to be increased for an optimal integration in the operation room. Based on the need to reduce the compensation mechanism of this device, the problem of the design of compliant mechanisms with strong integration constrains is studied in this PhD thesis. First, the possibility to integrate the compensation mechanism directly in the shaft is considered. Then, the possibility to reduce the compensation mechanism at the end of the shaft by considering an assembly of planar manufactured structures is considered. Among the contributions, we propose an original design method based on the analysis of singularities of parallel manipulators in planar configuration. We also propose an original optimization method based on ant colony optimization in order to optimize the compliant architectures proposed in this work.

The concept of a propagator is useful and is a well-known object in diffusion NMR experiments. Here, we investigate the related concept; the propagator for the magnetization or the Green’s function of the Torrey-Bloch equations. The magnetization propagator is constructed by defining functions such as the Hamiltonian and Lagrangian and using these to define a path integral. It is shown that the equations of motion derived from the Lagrangian produce complex-valued trajectories (classical paths) and it is conjectured that the end-points of these trajectories are real-valued. The complex nature of the trajectories also suggests that the spin degrees of freedom are also encoded into the trajectories and this idea is explored by explicitly modeling the spin or precessing magnetization by anticommuting Grassmann variables. A pseudoclassical Lagrangian is constructed by combining the diffusive (bosonic) Lagrangian with the Grassmann (fermionic) Lagrangian, and performing the path integral over the Grassmann variables recovers the original Lagrangian that was used in the construction of the propagator for the magnetization. The trajectories of the pseudoclassical model also provide some insight into the nature of the end-points.

No description available.

With the increasing number of wireless devices and the phenomenal amount of data that is being generated by them, there is a growing interest in the wireless communications community to complement the traditional model-driven design approaches with data-driven machine learning (ML)-based solutions. However, managing the large-scale multi-dimensional data to maintain the efficiency and scalability of the ML algorithms has obviously been a challenge. Tensors provide a useful framework to represent multi-dimensional data in an integrated manner by preserving relationships in data across different dimensions. This thesis studies two new applications of tensors to ML for wireless communications where the tensor structure of the concerned data is exploited in novel ways. The first contribution of this thesis is a tensor learning-based low-complexity precoder codebook design technique for a full-dimension multiple-input multiple-output (FD-MIMO) system with a uniform planar antenna (UPA) array at the transmitter (Tx) whose channel distribution is available through a dataset. Represented as a tensor, the FD-MIMO channel is further decomposed using a tensor decomposition technique to obtain an optimal precoder which is a function of Kronecker-Product (KP) of two low-dimensional precoders, each corresponding to the horizontal and vertical dimensions of the FD-MIMO channel. From the design perspective, we have made contributions in deriving a criterion for optimal product precoder codebooks using the obtained low-dimensional precoders. We show that this product codebook design problem is an unsupervised clustering problem on a Cartesian Product Grassmann Manifold (CPM), where the optimal cluster centroids form the desired codebook. We further simplify this clustering problem to a $K$-means algorithm on the low-dimensional factor Grassmann manifolds (GMs) of the CPM which correspond to the horizontal and vertical dimensions of the UPA, thus significantly reducing the complexity of precoder codebook construction when compared to the existing codebook learning techniques. The second contribution of this thesis is a tensor-based bandwidth-efficient gradient communication technique for federated learning (FL) with convolutional neural networks (CNNs). Concisely, FL is a decentralized ML approach that allows to jointly train an ML model at the server using the data generated by the distributed users coordinated by a server, by sharing only the local gradients with the server and not the raw data. Here, we focus on efficient compression and reconstruction of convolutional gradients at the users and the server, respectively. To reduce the gradient communication overhead, we compress the sparse gradients at the users to obtain their low-dimensional estimates using compressive sensing (CS)-based technique and transmit to the server for joint training of the CNN. We exploit a natural tensor structure offered by the convolutional gradients to demonstrate the correlation of a gradient element with its neighbors. We propose a novel prior for the convolutional gradients that captures the described spatial consistency along with its sparse nature in an appropriate way. We further propose a novel Bayesian reconstruction algorithm based on the Generalized Approximate Message Passing (GAMP) framework that exploits this prior information about the gradients. Through the numerical simulations, we demonstrate that the developed gradient reconstruction method improves the convergence of the CNN model. / Master of Science / The increase in the number of wireless and mobile devices have led to the generation of massive amounts of multi-modal data at the users in various real-world applications including wireless communications. This has led to an increasing interest in machine learning (ML)-based data-driven techniques for communication system design. The native setting of ML is {em centralized} where all the data is available on a single device. However, the distributed nature of the users and their data has also motivated the development of distributed ML techniques. Since the success of ML techniques is grounded in their data-based nature, there is a need to maintain the efficiency and scalability of the algorithms to manage the large-scale data. Tensors are multi-dimensional arrays that provide an integrated way of representing multi-modal data. Tensor algebra and tensor decompositions have enabled the extension of several classical ML techniques to tensors-based ML techniques in various application domains such as computer vision, data-mining, image processing, and wireless communications. Tensors-based ML techniques have shown to improve the performance of the ML models because of their ability to leverage the underlying structural information in the data. In this thesis, we present two new applications of tensors to ML for wireless applications and show how the tensor structure of the concerned data can be exploited and incorporated in different ways. The first contribution is a tensor learning-based precoder codebook design technique for full-dimension multiple-input multiple-output (FD-MIMO) systems where we develop a scheme for designing low-complexity product precoder codebooks by identifying and leveraging a tensor representation of the FD-MIMO channel. The second contribution is a tensor-based gradient communication scheme for a decentralized ML technique known as federated learning (FL) with convolutional neural networks (CNNs), where we design a novel bandwidth-efficient gradient compression-reconstruction algorithm that leverages a tensor structure of the convolutional gradients. The numerical simulations in both applications demonstrate that exploiting the underlying tensor structure in the data provides significant gains in their respective performance criteria.

Im Rahmen des Funktionalintegralzugangs zur Quanteneichfeldtheorie wird in der vorliegenden Arbeit eine Quantisierungsprozedur in Termen eichinvarianter Felder vorgeschlagen und am Beispiel zwei- und vierdimensionaler abelscher Modelle (Thirring-Modell und QED) sowie der One-Flavour QCD konkret realisiert. Dazu wird die Algebra der aus der eichabhängigen Feldkonfiguration der zugrunde liegenden Quantenfeldtheorie gebildeten eichinvarianten Grassmann-Algebra-wertigen Differentialformen, welche die Struktur einer Z_2-graduierten Differentialalgebra trägt, näher untersucht. Danach erfolgt die Implementierung eines geeignet gewählten Satzes eichinvarianter Felder sowie bestimmter algebraischer Relationen in das Funktionalintegral, wodurch die ursprüngliche eichabhängige Feldkonfiguration ausintegriert werden kann. Diese als "Reduktion des Funktionalintegrals" bezeichnete Prozedur führt schließlich auf eine effektive bosonisierte (Quanten-) Theorie wechselwirkender eichinvarianter, und damit physikalischer Felder. Die vorgestellte Prozedur kann als allgemeines Bosonisierungsschema für Quantenfeldtheorien in beliebigen Raum-Zeit-Dimensionen angesehen werden. Die physikalische Auswertung der erhaltenen effektiven Theorien wird am Beispiel der Berechnung der chiralen Anomalie sowie bestimmter Vakuum-Erwartungswerte im Rahmen der untersuchten abelschen Modelle demonstriert. Wie sich dabei zeigt, wird man mit einer Reihe neuartiger Phänomene und Probleme konfrontiert, die bei geeigneter Behandlung tiefere Einblicke in nichtperturbative Fragestellungen erlauben. / Within the thesis a new procedure, called "reduction of the functional integral", is developed for formulating quantum field theories in terms of gauge invariant quantities (physical observable fields). It provides a new way for the construction and analysis of effective field theoretical models. Starting with a detailed mathematical analysis of the algebra of Grassmann--algebra valued gauge invariants, the procedure is applied to the two--dimensional Thirring--model, the four--dimensional spinor QED and the one--flavor QCD in four dimensions. For each of these three models an effective theory of interacting bosonic gauge invariant fields was deduced on the quantum level. Apart from this more theoretical considerations, first steps on the way to an analysis of the obtained effective models towards their application in various physical problems are performed. In the case of the two Abelian models a new approach to the bosonisation scheme and the calculation of the chiral anomaly in two and four dimensions were obtained, giving some deeper insight into the nature of the bosonisation phenomenon as well as the nature of anomalies, respectively. Moreover, the investigation of current--current expectation values shows that the suggested procedure can be viewed as a new way towards a non--perturbative formulation and understanding of quantum field theories.

Submitted by Etelvina Domingos (etelvina.domingos@ufpe.br) on 2015-03-10T17:09:30Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) HLAG.pdf: 1126552 bytes, checksum: 1e1ac46e79a77b1688e9cb1f88285609 (MD5) / Made available in DSpace on 2015-03-10T17:09:30Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) HLAG.pdf: 1126552 bytes, checksum: 1e1ac46e79a77b1688e9cb1f88285609 (MD5) Previous issue date: 2012-01 / O objetivo desse trabalho é mostrar que os Top Intersection Numbers das Grassmannianas de retas G(2,n+2) satisfazem a relação de recorrência apresentada no artigo "Catalan Traffic at the Beach" e a conexão desses dois com os números de Catalan. Tudo isso será feito com a teoria das Derivações de Schubert e sua conexão com as Grassmannianas de retas.

Made available in DSpace on 2014-06-12T18:33:54Z (GMT). No. of bitstreams: 2 arquivo9589_1.pdf: 1126552 bytes, checksum: 1e1ac46e79a77b1688e9cb1f88285609 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2012 / O objetivo desse trabalho é mostrar que os Top Intersection Numbers das Grassmannianas de retas G(2,n+2) satisfazem a relação de recorrência apresentada no artigo "Catalan Traffic at the Beach" e a conexão desses dois com os números de Catalan. Tudo isso será feito com a teoria das Derivações de Schubert e sua conexão com as Grassmannianas de retas

Im Rahmen des Funktionalintegralzugangs zur Quanteneichfeldtheorie wird in der vorliegenden Arbeit eine Quantisierungsprozedur in Termen eichinvarianter Felder vorgeschlagen und am Beispiel zwei- und vierdimensionaler abelscher Modelle (Thirring-Modell und QED) sowie der One-Flavour QCD konkret realisiert. Dazu wird die Algebra der aus der eichabhängigen Feldkonfiguration der zugrunde liegenden Quantenfeldtheorie gebildeten eichinvarianten Grassmann-Algebra-wertigen Differentialformen, welche die Struktur einer Z_2-graduierten Differentialalgebra trägt, näher untersucht. Danach erfolgt die Implementierung eines geeignet gewählten Satzes eichinvarianter Felder sowie bestimmter algebraischer Relationen in das Funktionalintegral, wodurch die ursprüngliche eichabhängige Feldkonfiguration ausintegriert werden kann. Diese als "Reduktion des Funktionalintegrals" bezeichnete Prozedur führt schließlich auf eine effektive bosonisierte (Quanten-) Theorie wechselwirkender eichinvarianter, und damit physikalischer Felder. Die vorgestellte Prozedur kann als allgemeines Bosonisierungsschema für Quantenfeldtheorien in beliebigen Raum-Zeit-Dimensionen angesehen werden. Die physikalische Auswertung der erhaltenen effektiven Theorien wird am Beispiel der Berechnung der chiralen Anomalie sowie bestimmter Vakuum-Erwartungswerte im Rahmen der untersuchten abelschen Modelle demonstriert. Wie sich dabei zeigt, wird man mit einer Reihe neuartiger Phänomene und Probleme konfrontiert, die bei geeigneter Behandlung tiefere Einblicke in nichtperturbative Fragestellungen erlauben. / Within the thesis a new procedure, called "reduction of the functional integral", is developed for formulating quantum field theories in terms of gauge invariant quantities (physical observable fields). It provides a new way for the construction and analysis of effective field theoretical models. Starting with a detailed mathematical analysis of the algebra of Grassmann--algebra valued gauge invariants, the procedure is applied to the two--dimensional Thirring--model, the four--dimensional spinor QED and the one--flavor QCD in four dimensions. For each of these three models an effective theory of interacting bosonic gauge invariant fields was deduced on the quantum level. Apart from this more theoretical considerations, first steps on the way to an analysis of the obtained effective models towards their application in various physical problems are performed. In the case of the two Abelian models a new approach to the bosonisation scheme and the calculation of the chiral anomaly in two and four dimensions were obtained, giving some deeper insight into the nature of the bosonisation phenomenon as well as the nature of anomalies, respectively. Moreover, the investigation of current--current expectation values shows that the suggested procedure can be viewed as a new way towards a non--perturbative formulation and understanding of quantum field theories.