The Kalman-Yakubovich-Popov (KYP) lemma is a useful tool in control and signal processing that allows an important family of computationally intractable semi-infinite programs in the entire frequency range to be characterized by computationally tractable semidefinite programs. The first part of this thesis presents a new variation of the frequency selective Kalman-Yakubovich-Popov (FS-KYP) lemma for single input single output systems, which generalizes the conventional KYP lemma on given frequency intervals. Based on the transfer function representation of single input single output systems, the proposed FS-KYP lemma provides a unified framework to convert an important family of semi-infinite programs with generic frequency selective constraints that arise from a variety of analysis and synthesis problems for infinite impulse response systems into semidefinite programs. In contrast to existing variations of the FS-KYP lemma, which invariably involves Lyapunov variables of large dimensions, the proposed FS-KYP lemma is free from Lyapunov variables. As a consequence, the proposed semidefinite programs require a minimal number of additional variables, thus can be efficiently solved by general purpose semidefinite programming solvers on a standard personal computer. The second part of this thesis studies several applications of the FS-KYP lemma to control and signal processing. Firstly, we investigate the beam pattern synthesis of an antenna array with bounded sidelobe and mainlobe levels. It is shown that the pattern synthesis problem can be posed as a convex semi-infinite program that is turned into an semidefinite program via the proposed FS-KYP lemma. The attractive feature of the proposed method is that our semidefinite program uses only a minimal number of auxiliary variables. This subsequently enables the design of patterns for arrays with several hundred elements to be achieved on a standard personal computer using existing SDP solvers. Secondly, we develop an efficient method to design several types of digital and analog infinite impulse response filters and filter banks via the new FS-KYP lemma. The proposed method is more flexible than analytical methods in the sense that it allows direct control of more design parameters, which in turn enables more requirements such as degree of flatness to be incorporated into the design process. Finally, we examine some applications of the new FS-KYP to robustness analysis of continuous control systems. Specifically, we introduce a new bisection method to compute the H∞ gain of uncertain polytopic systems.

El principal objetivo de este trabajo de memoria es definir, especificar requerimientos y modelar todos los elementos, componentes, relaciones y dependencias que dan forma a una arquitectura SOA, para la capa VAS de una empresa de telefonía móvil. Sobre esta arquitectura, se definirá y planteará la estructura y organización necesaria para la implantación de un sistema BAM, de manera de cubrir las necesidades técnicas y de negocio que la arquitectura SOA no logra cubrir.

The distance to uncontrollability of a controllable linear system is a measure of the degree of perturbation a system can undergo and remain controllable. The definition of the distance to uncontrollability leads to a non-convex optimization problem in two variables. In 2000 Gu proposed the first polynomial time algorithm to compute this distance. This algorithm relies heavily on efficient eigenvalue solvers. In this work we examine two alternative algorithms that result in linear matrix inequalities. For the first algorithm, proposed by Ebihara et. al., a semidefinite programming problem is derived via the Kalman-Yakubovich-Popov (KYP) lemma. The dual formulation is also considered and leads to rank conditions for exactness verification of the approximation. For the second algorithm, by Dumitrescu, Şicleru and Ştefan, a semidefinite programming problem is derived using a sum-of-squares relaxation of an associated matrix-polynomial and the associated Gram matrix parameterization. In both cases the optimization problems are solved using primal-dual-interior point methods that retain positive semidefiniteness at each iteration. Numerical results are presented to compare the three algorithms for a number of benchmark examples. In addition, we also consider a system that results from a finite element discretization of the one-dimensional advection-diffusion equation. Here our objective is to test these algorithms for larger problems that originate in PDE-control. / Master of Science

Šiame darbe yra aprašomas optimizavimo paketas SeDuMi Interface ir jam priklausantis skaičiavimo paketas SeDuMi 1.05. Išvardintos paketo savybės, kurios išskiria jį iš kitų optimizavimo paketų. Aprašytos paketo funkcijų reikšmės. Supažindinama su optimizavimo paketų įvairove. Palyginamas pusiau apibrėžtas programavimas su tiesiniu programavimu, kadangi pakete SeDuMi interface realizuoti pusiau apibrėžto programavimo algoritmai. Taip pat lyginami programų skaičiavimų laikai: programų naudojančių SeDuMi paketo funkcijas ir programų su MATLAB funkcijomis. Palyginimui realizuoti, naudojamas klasikinis optimizavimo uždavinys –mažiausių reikšmių elipsoido uždavinys. / The optimization software SeDuMi Interface and it‘s calculation packet SeDuMi 1.05 is described in this work. Distinctive software features are listed. and values of packet’s functions are described. Variety of optimization packets is presented. Semidefinite programming is compared with linear programming, since semidefinite programming algorithms are implemented in the SeDuMi interface. Time of execution of the programs has been also compared: programs using SeDuMi software functions has been compared with programs using MATLAB functions. For the comparison classical optimization problem is used – the minimum volume ellipsoid problem.

[pt] O principal objetivo deste trabalho é desenvolver um sistema computacional, denominado SDP, para auxiliar a elaboração de programas baseados no Método dos Elementos Finitos (MEF). É dividido em três partes: primeiramente é apresentado o SDP, que compreende um sistema de gerenciamento de dados (memória principal, arquivos em disco e fita), uma padronização para a documentação e facilidades para testes e depuração de programas; em uma segunda parte, utilizando-se este sistema, é desenvolvida uma organização para os programas e para as bibliotecas de rotinas; finalmente, são apresentadas aplicações mostrando as principais características do sistema e sua potencialidade. Os problemas de elasticidade infinitesinal linear, condução de calor e elasto-plasticidade incremental são descritos através de uma formulação variacional, a partir da qual são desenvolvidas soluções aproximadas utilizando-se o MEF. Por último, tomando-se por base as soluções encontradas por meio desta abordagem, são elaborados os programas aplicativos. / [en] The main purpose of this work is to develop a computational system, denominated SDP, to aid the elaboration of Finite Element Method (FEM) programs. This work is divided in three parts: initially is presented the SDP that comprises a data management system (main memory, disc file and tapes), a standardization for the documentation and facilities for program testing and debugging. In the second part, a program and a routines library organization are developed using this computational system. Finally, applications showing the main characteristics and capacity of the SDP are presented. The problems of Linear Infinitesimal Elasticity, Heat Transfer and Incremental Elastic Plasticity are described by a variational formulation. Based on the variational theory approximated solutions are developed by means of the FEM. The last step is the applicative program elaboration using the solutions achieved by this approach.

The Gram positive soil dwelling bacteria Bacillus subtilis produces spores when encountered with a low nutrient environment. However, B. subtilis can delay spore production by a mechanism known as cannibalism. Cannibalism is a process by which B. subtilis delays commitment to sporulation by killing a subpopulation of its cells. This process involves production of two toxins, SDP and SKF. SDP is a 42 amino acid peptide with a disulfide bond derived from the internal cleavage of its precursor protein pro-SdpC. pro-SdpC is part of the sdpABC operon. Production of extracellular SDP induces expression of the sdpRI operon. Encoded in this operon is the negative regulator SdpR and SdpI. SdpI is a dual function protein which acts both as a signal transduction protein and the immunity factor against SDP. The current model states that production of SDP is sensed via SdpI. SdpI will sequester SdpR to the membrane in response and allow for sdpRI expression. The aims of this dissertation are to establish the requirements for SDP production and its response via SdpI/SdpR during cannibalism. Studies in Chapter II were carried out to determine the factors required for production of the antimicrobial peptide SDP. Site directed mutagenesis of the leader signal peptide sequence in pro-SdpC demonstrated that proper signal peptide cleavage was required for SDP production. Additional site directed mutants of the cysteine residues in pro-SdpC revealed that these are not required for SDP toxic activity. These studies also included deletions within the sdpABC operon and revealed that the two proteins of unknown function, SdpA and SdpB are required for SDP production. Using mass spectrometry analysis, we found that SdpA and SdpB together are required to produce the active 42 amino acid peptide SDP. Taken together we concluded that SDP production was a multi step process which required proteins encoded within the operon and additional processing supplemented in the cell. In Chapter III we investigated the role of SdpI, specifically what residues were required for the signaling and immunity functions observed. Our initial screen, included site directed mutagenesis of highly conserved residues between the 4th and 5th transmembrane domains of SdpI. These resulted in over 20 SdpI mutants generated. From these, only two SdpI mutants had defects in either signal transduction or SDP immunity. Additional localized mutagenesis was used to isolate two other mutants in SdpI which only affected signal transduction or SDP immunity. SdpI signaling-immunity+ mutants presented a defect in SdpR membrane sequestration and sdpRIinduction. Our findings suggest these types of SdpI mutants may be important for the downstream effect of SdpR membrane sequestration. SdpI signaling+ immunity- mutants revealed defects in SDP protection. Some of the residues mutated were conserved in other SdpI homologs. Site directed mutagenesis of these conserved residues in the SdpI ortholog YfhL showed these are also required for SDP resistance. For the first time, we were able to identify mutations which affected only SDP immunity and gained further insight into how SdpI signaling-immunity+ mutants play a role during signal transduction. In Chapter IV we initiated studies to define what regions of the negative regulator SdpR are important for its function during cannibalism. We employed localized mutagenesis to identify SdpR mutants which decreased sdpRIexpression even in the presence of inducing signal. We isolated three such SdpR mutants, referred to as super repressors. We expect these SdpR super repressors are unable to be sequestered to the membrane in the presence of SDP.

In this thesis, we consider a wireless network consisting of d source-destination pairs and R relaying nodes. Each source wishes to communicate to its corresponding destination. By exploiting the spatial multiplexing capability of the wireless medium, we develop two cooperative beamforming schemes in order to establish wireless connections between multiple source-destination pairs through a collaborative relay network. Our first communication scheme consists of two steps. In the first step, all sources transmit their signals simultaneously to the relay network. As a result, each relay receives a noisy faded mixture of all source signals. In the second step, each relay transmits an amplitude- and phase-adjusted version of its received signal, i.e., the relay received signals are multiplied by a set of complex coefficients and are retransmitted. Our goal is to obtain these complex coefficients (beamforming weights) through minimization of the total relay transmit power while the signal-to-interference-plus-noise ratio at the destinations are guaranteed to be above certain pre-defined thresholds. Our second scheme is a distributed downlink beamforming technique which is performed in d + 1 successive time slots. In the first d time slots, the d sources transmit their data to the relay network successively. The relay nodes receive and store the noisy faded versions of the source signals. In the (d + 1)th time slot, the relays aim to collectively provide downlink connections to all d destinations. To do so, each relay transmits a linear combination of the stored signals received during the first d time slots. Again, our goal is to determine the complex weights (used at the relaying nodes to linearly combine the source signals) by minimizing the total relay transmit power while satisfying certain quality of services at the destinations. We use semi-definite relaxation to turn both problems into semi-definite programming (SDP) problems. Therefore, they can be efficiently solved using interior point methods. We showed that our proposed schemes significantly outperform orthogonal multiplexing schemes, such as time-division multiple access schemes, in a large range of network data rates. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2008-09-17 13:07:21.505

Une nouvelle borne supérieure sur le cardinal des codes de sous-espaces d'un espace vectoriel fini est établie grâce à la méthode de la programmation semidéfinie positive. Ces codes sont d'intérêt dans le cadre du codage de réseau (network coding). Ensuite, par la même méthode, l'on démontre une borne sur le cardinal des ensembles qui évitent une distance donnée dans l'espace de Johnson et qui est obtenue par une variante d'un programme de Schrijver. Les résultats numériques permettent d'améliorer les bornes existantes sur le nombre chromatique mesurable de l'espace Euclidien. Une hiérarchie de programmes semidéfinis positifs est construite à partir de certaines matrices issues des complexes simpliciaux. Ces programmes permettent d'obtenir une borne supérieure sur le nombre d'indépendance d'un graphe. Aussi, cette hiérarchie partage certaines propriétés importantes avec d'autres hiérarchies classiques. A titre d'exemple, le problème de déterminer le nombre d'indépendance des graphes de Paley est analysé. / We apply the semidefinite programming method to obtain a new upper bound on the cardinality of codes made of subspaces of a linear vector space over a finite field. Such codes are of interest in network coding.Next, with the same method, we prove an upper bound on the cardinality of sets avoiding one distance in the Johnson space, which is essentially Schrijver semidefinite program. This bound is used to improve existing results on the measurable chromatic number of the Euclidean space.We build a new hierarchy of semidefinite programs whose optimal values give upper bounds on the independence number of a graph. This hierarchy is based on matrices arising from simplicial complexes. We show some properties that our hierarchy shares with other classical ones. As an example, we show its application to the problem of determining the independence number of Paley graphs.

The master's thesis "Development of the Sudeten German political movements in the years 1933 - 1938" is focusing on the formation and development of Sudetenland German political movements in the Czechoslovak Republic. It deals with the situation of German minority group, it analyses the assumptions and also attempts for unification of German (negativistic) political field in the process being aimed at establishment and forming Sudetenland German Patriotic Front (SHF) in 1933. The thesis subsequently follows up the chronological development of Henlein Movement (SHF), the relation to other German political parties and the state, and also the transformation in Sudetenland German Party (SdP) in 1935. Afterwards, the thesis include the analysis of its election programme, the ways of campaigning and the election results in the parliamentary elections in 1935 (the voter turnout in municipal election in 1934 and 1938 is also mentioned). The internal party crisis belongs among other milestones of SdP that are dealt in this thesis just as Carlsbad Programme (with the demands against Czechoslovakia), the dissolving of SdP and the changeover of former members to German National Socialist Labour Party (NSDAP) in 1938.

This master thesis studies the problem of parameter identification for system biology. Two methods have been studied. The method of interval analysis uses subpaving as a class of objects to manipulate and store inner and outer approximations of compact sets. This method works well with the model given as a system of differential equations, but has its limitations, since the analytical expression for the solution to the ODE is not always obtainable, which is needed for constructing the inclusion function. The other method, studied, is SDP-relaxation of a nonlinear and non-convex feasibility problem. This method, implemented in the toolbox bio.SDP, works with system of difference equations, obtained using the Euler discretization method. The discretization method is not exact, raising the need of bounding this discretization error. Several methods for bounding this error has been studied. The method of ∞-norm optimization, also called worst-case-∞-norm is applied on the one-step error estimation method. The methods have been illustrated solving two system biological problems and the resulting SCP have been compared. / Det här examensarbetet studerar problemet med parameteridentifiering för systembiologi. Två metoder har studerats. Metoden med intervallanalys använder union av intervallvektorer som klass av objekt för att manipulera och bilda inre och yttre approximationer av kompakta mängder. Denna metod fungerar väl för modeller givna som ett system av differentialekvationer, men har sina begränsningar, eftersom det analytiska uttrycket för lösningen till differentialekvationen som är nödvändigt att känna till för att kunna formulera inkluderande funktioner, inte alltid är tillgängliga. Den andra studerade metoden, använder SDP-relaxering, som ett sätt att komma runt problemet med olinjäritet och icke-konvexitet i systemet. Denna metod, implementerad i toolboxen bio.SDP, utgår från system av differensekvationer, framtagna via Eulers diskretiserings metod. Diskretiseringsmetoden innehåller fel och osäkerhet, vilket gör det nödvändigt att estimera en gräns för felets storlek. Några felestimeringsmetoder har studerats. Metoden med ∞-norm optimering, också kallat worst-case-∞-norm är tillämpat på ett-stegs felestimerings metoder. Metoderna har illustrerats genom att lösa två system biologiska problem och de accepterade parametermängderna, benämnt SCP, har jämförts och diskuterats.