Due to their ability to provide high data rates, Multiple-Input Multiple-Output (MIMO) wireless communication systems have become increasingly popular. Decoding of these systems with acceptable error performance is computationally very demanding. In the case of large overdetermined MIMO systems, we employ the Sequential Decoder using the Fano Algorithm. A parameter called the bias is varied to attain different performance-complexity trade-offs. Low values of the bias result in excellent performance but at the expense of high complexity and vice versa for higher bias values. We attempt to bound the error by bounding the bias, using the minimum distance of a lattice. Also, a particular trend is observed with increasing SNR: a region of low complexity and high error, followed by a region of high complexity and error falling, and finally a region of low complexity and low error. For lower bias values, the stages of the trend are incurred at lower SNR than for higher bias values. This has the important implication that a low enough bias value, at low to moderate SNR, can result in low error and low complexity even for large MIMO systems. Our work is compared against Lattice Reduction (LR) aided Linear Decoders (LDs). Another impressive observation for low bias values that satisfy the error bound is that the Sequential Decoder's error is seen to fall with increasing system size, while it grows for the LR-aided LDs. For the case of large underdetermined MIMO systems, Sequential Decoding with two preprocessing schemes is proposed – 1) Minimum Mean Square Error Generalized Decision Feedback Equalization (MMSE-GDFE) preprocessing 2) MMSE-GDFE preprocessing, followed by Lattice Reduction and Greedy Ordering. Our work is compared against previous work which employs Sphere Decoding preprocessed using MMSE-GDFE, Lattice Reduction and Greedy Ordering. For the case of large systems, this results in high complexity and difficulty in choosing the sphere radius. Our schemes, particularly 2), perform better in terms of complexity and are able to achieve almost the same error curves, depending on the bias used.

<p>Methodologies for the analysis and computer simulations of active optimal vibration control of complex elastic structures are considered. The structures, generally represented by a large number of degrees of freedom (DOF), are to be controlled by a comparatively small number of actuators.</p><p>Various techniques presently available to solve the optimal control problems are briefly discussed. A Parametric optimization technique that is versatile enough to solve almost any type of optimization problems is found to give poor accuracy and is time consuming. More promising is the optimality equations approach, which is based on Pontryagins principle. Several new numerical procedures are developed using this approach. Most of the problems in this thesis are analysed in the modal space. Even complex structures can be approximated accurately in the modal space by using only few modes. Different techniques have been first applied to the cases where the number of modes to control was the same as the number of actuators (determined optimal control problems), then to cases in which the number of modes to control is larger than the number of actuators (overdetermined optimal control problems). </p><p>The determined optimal control problems can be solved by applying the Independent Modal Space Control (IMSC) approach. Such an approach is implemented in the Beam Analogy (BA) method that solves the problem numerically by applying the Finite Element Method (FEM). The BA, which uses the ANSYS program, is numerically very efficient. The effects of particular optimization parameters involved in BA are discussed in detail. Unsuccessful attempts have been made to modify this method in order to make it applicable for solving overdetermined or underactuated problems. </p><p>Instead, a new methodology is proposed that uses modified optimality equations. The modifications are due to the extra constraints present in the overdetermined problems. These constraints are handled by time dependent Lagrange multipliers. The modified optimality equations are solved by using symbolic differential operators. The corresponding procedure uses the MAPLE programming, which solves overdetermined problems effectively despite of the high order of differential equations involved.</p><p>The new methodology is also applied to the closed loop control problems, in which constant optimal gains are determined without using Riccatis equations.</p>

<p>Methodologies for the analysis and computer simulations of active optimal vibration control of complex elastic structures are considered. The structures, generally represented by a large number of degrees of freedom (DOF), are to be controlled by a comparatively small number of actuators.</p><p>Various techniques presently available to solve the optimal control problems are briefly discussed. A Parametric optimization technique that is versatile enough to solve almost any type of optimization problems is found to give poor accuracy and is time consuming. More promising is the optimality equations approach, which is based on Pontryagins principle. Several new numerical procedures are developed using this approach. Most of the problems in this thesis are analysed in the modal space. Even complex structures can be approximated accurately in the modal space by using only few modes. Different techniques have been first applied to the cases where the number of modes to control was the same as the number of actuators (determined optimal control problems), then to cases in which the number of modes to control is larger than the number of actuators (overdetermined optimal control problems). </p><p>The determined optimal control problems can be solved by applying the Independent Modal Space Control (IMSC) approach. Such an approach is implemented in the Beam Analogy (BA) method that solves the problem numerically by applying the Finite Element Method (FEM). The BA, which uses the ANSYS program, is numerically very efficient. The effects of particular optimization parameters involved in BA are discussed in detail. Unsuccessful attempts have been made to modify this method in order to make it applicable for solving overdetermined or underactuated problems. </p><p>Instead, a new methodology is proposed that uses modified optimality equations. The modifications are due to the extra constraints present in the overdetermined problems. These constraints are handled by time dependent Lagrange multipliers. The modified optimality equations are solved by using symbolic differential operators. The corresponding procedure uses the MAPLE programming, which solves overdetermined problems effectively despite of the high order of differential equations involved.</p><p>The new methodology is also applied to the closed loop control problems, in which constant optimal gains are determined without using Riccatis equations.</p>

This work is focused on overdetermined systems of interval linear equati- ons. First part consists of introduction to interval arithmetics and interval linear algebra and basic theory of interval linear systems. In the second part various methods for solving overdetermined interval linear systems are de- scribed. By solution of overdetermined interval system we mean union of all solutions of all subsystems. Known and our variants of algorithms are discussed. We introduce our subsquare method. All mentioned methods are implemented in one toolbox for Matlab. Methods are tested on solvable and unsolvable overdetermined systems. For solvable systems we test solution enclosure, time and special features of methods. For unsolvable systems we test detection of unsolvability. At the end of this work we provide basic in- troduction to Intlab. 1

Medical imaging is critical for the detection and diagnosis of disease, guided biopsies, assessment of therapies, and administration of treatment. While computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), and ultra-sound (US) are the more familiar modalities, interest in yet other modalities continues to grow. Among the motivations are reduction of cost, avoidance of ionizing radiation, and the search for new information, including biochemical and molecular processes. Fluorescence Molecular Tomography (FMT) is one such emerging technique and, like other techniques, has its advantages and limitations. FMT can reconstruct the distribution of fluorescent molecules in vivo using near-infrared radiation or visible band light to illuminate the subject. FMT is very safe since non-ionizing radiation is used, and inexpensive due to the comparatively low cost of the imaging system. This should make it particularly well suited for small animal studies for research. A broad range of cell activity can be identified by FMT, making it a potentially valuable tool for cancer screening, drug discovery and gene therapy. Since FMT imaging is scattering dominated, reconstruction of volume images is significantly more computationally intensive than for CT. For instance, to reconstruct a 32x32x32 image, a flattened matrix with approximately 10¹°, or 10 billion, elements must be dealt with in the inverse problem, while requiring more than 100 GB of memory. To reduce the error introduced by noisy measurements, significantly more measurements are needed, leading to a proportionally larger matrix. The computational complexity of reconstructing FMT images, along with inaccuracies in photon propagation models, has heretofore limited the resolution and accuracy of FMT. To surmount the problems stated above, we decompose the forward problem into a Khatri-Rao product. Inversion of this model is shown to lead to a novel reconstruction method that significantly reduces the computational complexity and memory requirements for overdetermined datasets. Compared to the well known SVD approach, this new reconstruction method decreases computation time by a factor of up to 25, while simultaneously reducing the memory requirement by up to three orders of magnitude. Using this method, we have reconstructed images up to 32x32x32. Also outlined is a two step approach which would enable imaging larger volumes. However, it remains a topic for future research. In achieving the above, the author studied the physics of FMT, developed an extensive set of original computer programs, performed COMSOL simulations on photon diffusion, and unavoidably, developed visual displays.

Cette thèse s’inscrit dans le domaine des mathématiques appelé optimisation de formes. Plus précisément, nous étudions ici un problème inverse de détection à l’aide du calcul de forme et de l’analyse asymptotique. L’objectif est de localiser un objet immergé dans un fluide visqueux, incompressible et stationnaire. Les questions principales qui ont motivé ce travail sont les suivantes :– peut-on détecter un objet immergé dans un fluide à partir d’une mesure effectuée à la surface ?– peut-on reconstruire numériquement cet objet, i.e. approcher sa position et sa forme, à partir de cette mesure ?– peut-on connaître le nombre d’objets présents dans le fluide en utilisant cette mesure ?Les résultats obtenus sont décrits dans les cinq chapitres de cette thèse :– le premier met en place un cadre mathématique pour démontrer l’existence des dérivées de forme d’ordre un et deux pour les problèmes de détection d’inclusions ;– le deuxième analyse le problème de détection à l’aide de l’optimisation géométrique de forme : un résultat d’identifiabilité est montré, le gradient de forme de plusieurs types de fonctionnelles de forme est caractérisé et l’instabilité de ce problème inverse est enfin démontrée ;– le chapitre 3 utilise nos résultats théoriques pour reconstruire numériquement des objets immergés dans un fluide à l’aide d’un algorithme de gradient de forme ;– le chapitre 4 analyse la localisation de petites inclusions dans un fluide à l’aide de l’optimisation topologique de forme : le gradient topologique d’une fonctionnelle de forme de Kohn-Vogelius est caractérisé ;– le dernier chapitre utilise cette dernière expression théorique pour déterminer numériquement le nombre et la localisation de petits obstacles immergés dans un fluide à l’aide d’un algorithme de gradient topologique. / This dissertation takes place in the mathematic field called shape optimization. More precisely, we focus on a detecting inverse problem using shape calculus and asymptotic analysis. The aim is to localize an object immersed in a viscous, incompressible and stationary fluid. This work was motivated by the following main questions:– can we localize an obstacle immersed in a fluid from a boundary measurement?– can we reconstruct numerically this object, i.e. be close to its localization and its shape, from this measure?– can we know how many objects are included in the fluid using this measure?The results are described in the five chapters of the thesis:– the first one gives a mathematical framework in order to prove the existence of the shape derivatives oforder one and two in the frame of the detection of inclusions;– the second one analyzes the detection problem using geometric shape optimization: an identifiabilityresult is proved, the shape gradient of several shape functionals is characterized and the instability of thisinverse problem is proved;– the chapter 3 uses our theoretical results in order to reconstruct numerically some objets immersed in a fluid using a shape gradient algorithm;– the fourth chapter analyzes the detection of small inclusions in a fluid using the topological shape optimization : the topological gradient of a Kohn-Vogelius shape functional is characterized;– the last chapter uses this theoretical expression in order to determine numerically the number and the location of some small obstacles immersed in a fluid using a topological gradient algorithm.

Práce se zabývá metodami pro testování lineárních analogových obvodů v kmitočtové oblasti. Cílem je navrhnout efektivní metody pro automatické generování testovacího plánu. Snížením počtu měření a výpočetní náročnosti lze výrazně snížit náklady za testování. Práce se zabývá multifrekveční parametrickou poruchovou analýzou, která byla plně implementována do programu Matlab. Vhodnou volbou testovacích kmitočtů lze potlačit chyby měření a chyby způsobené výrobními tolerancemi obvodových prvků. Navržené metody pro optimální volbu kmitočtů byly statisticky ověřeny metodou MonteCarlo. Pro zvýšení přesnosti a snížení výpočetní náročnosti poruchové analýzy byly vyvinuty postupy založené na metodě nejmenších čtverců a přibližné symbolické analýze.