Variações ambientais e de processo representam um grande desafio a ser vencido pelas redes de distribuição de relógio. O efeito das variações nos atrasos da rede de distribuição de relógio não pode ser previsto com precisão e portanto não podem ser diretamente considerados no projeto das redes de distribuição de relógio. Estruturas baseadas em clock meshes (i.e. clock mesh, clock spines e crosslinks) são a maneira mais eficiente de proteger a rede de relógio do efeito das variações nos atrasos. Clock meshes tem sido utilizados por bastante tempo no projeto de microprocessadores e recentemente foram incluídos no fluxo de síntese de ASICs. Embora o uso de clock meshes esteja aumentando há uma grande necessidade por métodos de analise e otimização dos mesmos. Essa tese propõe soluções para ambos os problemas. Uma metodologia para permitir a simulação elétrica de clock meshes grandes é proposta. O método proposto permite que a simulação dos clock meshes seja paralelizada com um erro menor que 1%. Duas metodologias de otimização também são propostas nessa tese. A primeira consiste em um algoritmo para dimensionamento para os mesh buffers. Esse algoritmo permite que o clock skew e o consumo de potência sejam reduzidos ao custo de aumentar o clock slew. O segundo método de otimização proposto consiste em um novo projeto para os mesh buffers. O novo mesh buffer é capaz de reduzir o clock skew em 22% e o consumo de potencia em 59%. / Process and environmental variations are a great challenge to clock network designers. Variations effect on the clock network delays can not be predicted, hence it can not be directly accounted in the design stage. Clock mesh-based structures (i.e. clock mesh, clock spines and crosslinks) are the most effective way to tolerate variation effects on delays. Clock meshes have been used for a long time in microprocessor designs and recently became supported by commercial tools in the ASIC design flow. Although clock meshes have been known for some time and its use in ASIC design is increasing, there is a lack of good analysis and optimization strategies for clock meshes. This thesis tackles both problems. Chapter 1 presents a basic introduction to clock distribution and important definitions. A review of existent clock dsitribution design strategies is presented in chapter 2. A study about the clock distribution architecture used in several microprocessor and a comparison between mesh-based and pure tree clock distribution architectures is shown in chapter 3.2. A methodology for enabling and speeding up the simulation of large clock meshes is presented in chapter 4. The proposed analysis methodology was shown to enable the parallel evaluation of large clock meshes with an error smaller than 1%. Chapter 5 presents two optimization strategies, a new mesh buffer design and a mesh buffer sizing algorithm. The new mesh buffer design was proposed improving clock skew by 22% and clock power by 59%. The mesh buffer sizing algorithm can reduce clock skew by 33%, power consumption by 20% with at the cost of a 26% slew increase. At last conclusions are presented on chapter 6.

Involutions and fixed-point-free involutions arise naturally as representatives for certain Borel orbits in invertible matrices. Similarly, partial involutions and partial fixed-point-free involutions represent certain Borel orbits in matrices which are not necessarily invertible. Inclusion relations among Borel orbit closures induce a partial order on these discrete parameterizing sets. In this dissertation we investigate the associated order complex of these posets. In particular, we prove that the order complex of the Bruhat poset of Borel orbit closures is shellable in symmetric as well as skew-symmetric matrices. / acase@tulane.edu

This thesis deals with several statistical and probabilistic aspects of symmetry and asymmetry, both in a univariate and multivariate context, and is divided into three distinct parts. The first part, composed of Chapters 1, 2 and 3 of the thesis, solves two conjectures associated with multivariate skew-symmetric distributions. Since the introduction in 1985 by Adelchi Azzalini of the most famous representative of that class of distributions, namely the skew-normal distribution, it is well-known that, in the vicinity of symmetry, the Fisher information matrix is singular and the profile log-likelihood function for skewness admits a stationary point whatever the sample under consideration. Since that moment, researchers have tried to determine the subclasses of skew-symmetric distributions who suffer from each of those problems, which has led to the aforementioned two conjectures. This thesis completely solves these two problems. The second part of the thesis, namely Chapters 4 and 5, aims at applying and constructing extremely general skewing mechanisms. As such, in Chapter 4, we make use of the univariate mechanism of Ferreira and Steel (2006) to build optimal (in the Le Cam sense) tests for univariate symmetry which are very flexible. Actually, their mechanism allowing to turn a given symmetric distribution into any asymmetric distribution, the alternatives to the null hypothesis of symmetry can take any possible shape. These univariate mechanisms, besides that surjectivity property, enjoy numerous good properties, but cannot be extended to higher dimensions in a satisfactory way. For this reason, we propose in Chapter 5 different general mechanisms, sharing all the nice properties of their competitors in Ferreira and Steel (2006), but which moreover can be extended to any dimension. We formally prove that the surjectivity property holds in dimensions k>1 and we study the principal characteristics of these new multivariate mechanisms. Finally, the third part of this thesis, composed of Chapter 6, proposes a test for multivariate central symmetry by having recourse to the concepts of statistical depth and runs. This test extends the celebrated univariate runs test of McWilliams (1990) to higher dimensions. We analyze its asymptotic behavior (especially in dimension k=2) under the null hypothesis and its invariance and robustness properties. We conclude by an overview of possible modifications of these new tests./ Cette thèse traite de différents aspects statistiques et probabilistes de symétrie et asymétrie univariées et multivariées, et est subdivisée en trois parties distinctes. La première partie, qui comprend les chapitres 1, 2 et 3 de la thèse, est destinée à la résolution de deux conjectures associées aux lois skew-symétriques multivariées. Depuis l'introduction en 1985 par Adelchi Azzalini du plus célèbre représentant de cette classe de lois, à savoir la loi skew-normale, il est bien connu qu'en un voisinage de la situation symétrique la matrice d'information de Fisher est singulière et la fonction de vraisemblance profile pour le paramètre d'asymétrie admet un point stationnaire quel que soit l'échantillon considéré. Dès lors, des chercheurs ont essayé de déterminer les sous-classes de lois skew-symétriques qui souffrent de chacune de ces problématiques, ce qui a mené aux deux conjectures précitées. Cette thèse résoud complètement ces deux problèmes. La deuxième partie, constituée des chapitres 4 et 5, poursuit le but d'appliquer et de proposer des méchanismes d'asymétrisation très généraux. Ainsi, au chapitre 4, nous utilisons le méchanisme univarié de Ferreira and Steel (2006) pour construire des tests de symétrie univariée optimaux (au sens de Le Cam) qui sont très flexibles. En effet, leur méchanisme permettant de transformer une loi symétrique donnée en n'importe quelle loi asymétrique, les contre-hypothèses à la symétrie peuvent prendre toute forme imaginable. Ces méchanismes univariés, outre cette propriété de surjectivité, possèdent de nombreux autres attraits, mais ne permettent pas une extension satisfaisante aux dimensions supérieures. Pour cette raison, nous proposons au chapitre 5 des méchanismes généraux alternatifs, qui partagent toutes les propriétés de leurs compétiteurs de Ferreira and Steel (2006), mais qui en plus sont généralisables à n'importe quelle dimension. Nous démontrons formellement que la surjectivité tient en dimension k > 1 et étudions les caractéristiques principales de ces nouveaux méchanismes multivariés. Finalement, la troisième partie de cette thèse, composée du chapitre 6, propose un test de symétrie centrale multivariée en ayant recours aux concepts de profondeur statistique et de runs. Ce test étend le célèbre test de runs univarié de McWilliams (1990) aux dimensions supérieures. Nous en analysons le comportement asymptotique (surtout en dimension k = 2) sous l'hypothèse nulle et les propriétés d'invariance et de robustesse. Nous concluons par un aperçu sur des modifications possibles de ces nouveaux tests.

The mechanics of paper is a difficult subject because paper is a unique material. It is very thin, flexible at bending, unstable in compression and stiff at tension. Dealing with paper we have to account for orthotropy and heterogeneities created during the manufacturing process. This thesis addresses two topics in mechanics of paper webs in printing press applications. First is the dynamic behaviour of the travelling webs. Second is so-called “fluting” after heat-set web-fed offset printing. There are a number of challenges in simulating the dynamics of the paper web. It is necessary to include the influence of the paper web transport velocity. Due to initial sag or vibrations, gyroscopic forces affect the dynamics of the webs. Furthermore, the transport velocity reduces the stress stiffening of the web. A good theoretical model should account for large displacements and should be capable of simulating wrinkles, which is essentially a post-buckling phenomenon. Finally, the paper web is surrounded with air which reduces the natural frequencies substantially by “adding" mass to the paper. A non-linear finite element formulation has been developed in this study for simulation of travelling webs. The results of the studies shows that for the tension magnitudes used in the printing industry the critical web speed lies far above those used today. Speed limitations are rather caused by ink setting and tension control problems. If the web tension profile is skew, however, edge vibrations are inevitable even at small external excitations. Fluting is a permanent wavy distortion of the paper web after heat-set web offset printing. It is often seen in high quality printing products, especially in areas covered with ink. It is generally accepted that tension and heat are required to create fluting. However, there have been certain disputes as to the mechanism of fluting formation, retention and key factors affecting this phenomenon. Most of the existing studies related to fluting are based on linear buckling theories. A finite element model, capable of simulating a post-buckling behaviour has been developed and experimentally verified. Studies show that none of the existing theories can consistently explain fluting. A new basic mechanism of fluting formation has been proposed and numerically demonstrated. Fluting was explained as a post-buckling phenomenon due to small scale moisture variations developing during through-air drying. It was concluded that air permeability variation is the key factor affecting fluting tendency. Fluting is retained due to inelastic deformations promoted by high drying temperatures. / QC 20100906

This thesis incorporates an array of Contact Potential Difference (CPD) sensors to measure and monitor the degree of skew in the rolling elements of a spherical roller bearing. Skewing is the motion of a roller as it turns about an axis normal to the roller race interface. Roller skew is generated as part of the kinematic effects of roller bearings. Skew monitoring is important for bearing design as it is an indirect measure of bearing life. For the purpose of this thesis, roller skew was measured utilizing multiple pairs of CPD probes located around the bearings outer raceway at varying points of the loading zone. These CPD probes are not in direct contact with the rollers, but in close proximity to their surface (through the bearing outer ring). The skew angle measured is related to different operating conditions such as applied load, shaft speed, and lubrication. The pair of CPD probes detected a signal as the roller surface passed by and the phase difference between the two distinct signals measured the skew angles in the range of 0.016 to 1.10. The shaft is rotated both clockwise and counterclockwise to capture any probe misalignment which was in the range of 0.5 up to 2.0 . This thesis also provides a model for the probe signal as a spherical roller surface passes the probe surface.

Circuit optimization is extremely important in order to design today's high performance integrated circuits. As systems become more and more complex, traditional optimization techniques are no longer viable due to the complex and simulation intensive nature of the optimization problem. Two examples of such problems include clock mesh skew reduction and optimization of large analog systems, for example Phase locked loops. Mesh-based clock distribution has been employed in many high-performance microprocessor designs due to its favorable properties such as low clock skew and robustness. However, such clock distributions can become quite complex and may consist of hundreds of nonlinear drivers strongly coupled via a large passive network. While the simulation of clock meshes is already very time consuming, tuning such networks under tight performance constraints is an even daunting task. Same is the case with the phase locked loop. Being composed of multiple individual analog blocks, it is an extremely challenging task to optimize the entire system considering all block level trade-offs. In this work, we address these two challenging optimization problems i.e.; clock mesh skew optimization and PLL locking time reduction. The expensive objective function evaluations and difficulty in getting explicit sensitivity information make these problems intractable to standard optimization methods. We propose to explore the recently developed asynchronous parallel pattern search (APPS) method for efficient driver size tuning. While being a search-based method, APPS not only provides the desirable derivative-free optimization capability, but also is amenable to parallelization and possesses appealing theoretically rigorous convergence properties. In this work it is shown how such a method can lead to powerful parallel optimization of these complex problems with significant runtime and quality advantages over the traditional sequential quadratic programming (SQP) method. It is also shown how design-specific properties and speeding-up techniques can be exploited to make the optimization even more efficient while maintaining the convergence of APPS in a practical sense. In addition, the optimization technique is further enhanced by introducing the feature to handle non-linear constraints through the use of penalty functions. The enhanced method is used for optimizing phase locked loops at the system level.

Investigation of more than seventy highway bridges revealed that multisimple-span skew bridges with expansion joints were very common in Turkish practice. The expansion joints, used to provide deck expansion against shrinkage, creep and thermal effects, create costly maintenance problems due to leaked water, impact loads and accumulated debris in the joints. Therefore, elimination of expansion joints decreases the maintenance cost for the bridges. Reinforced concrete link slabs provide continuity at the deck level with the elimination of expansion joints. This thesis focuses on evaluating the seismic behavior of the skew multisimple-span bridges in Turkey and also discusses the use of reinforced concrete link slabs as a seismic retrofit option. The effects of addition of link slab and varying skew angle on the performance of the bridges were investigated. The use of link slabs can provide a better seismic displacement control, can decrease the member forces and can prevent or reduce deterioration of the top of the piers and ends of the girders from the water and chemical leakage by abandoning or minimizing number of expansion joints.

The Multiplicative Ergodic Theorem is a powerful tool for studying certain types of dynamical systems, involving real matrix cocycles. It gives a block diagonalization of these cocycles, according to the Lyapunov exponents. We ask if it is always possible to refine the diagonalization to a block upper-triangularization, and if not over the real numbers, then over the complex numbers. After building up to the posing of the question, we prove that there are counterexamples to this statement, and give concrete examples of matrix cocycles which cannot be block upper-triangularized. / Graduate / 0405 / jahoran@uvic.ca

Groebner-Shirshov bases, introduced independently by Shirshov in 1962 and Buchberger in 1965, are powerful computational tools in mathematics, science, engineering, and computer science. This thesis focuses on the theories, algorithms, and applications of Groebner-Shirshov bases for two classes of noncommutative algebras: differential difference algebras and skew solvable polynomial rings. This thesis consists of three manuscripts (Chapters 2--4), an introductory chapter (Chapter 1) and a concluding chapter (Chapter 5). In Chapter 1, we introduce the background and the goals of the thesis. In Chapter 2, we investigate the Gelfand-Kirillov dimension of differential difference algebras. We find lower and upper bounds of the Gelfand-Kirillov dimension of a differential difference algebra under some conditions. We also give examples to demonstrate that our bounds are sharp. In Chapter 3, we generalize the Groebner-Shirshov basis theory to differential difference algebras with respect to any left admissible ordering and develop the Groebner-Shirshov basis theory of finitely generated free modules over differential difference algebras. By using the theory we develop, we present an algorithm to compute the Gelfand-Kirillov dimensions of finitely generated modules over differential difference algebras. In Chapter 4, we first define skew solvable polynomial rings, which are generalizations of solvable polynomial algebras and (skew) PBW extensions. Then we present a signature-based algorithm for computing Groebner-Shirshov bases in skew solvable polynomial rings over fields. Our algorithm can detect redundant reductions and therefore it is more efficient than the traditional Buchberger algorithm. Finally, in Chapter 5, we summarize our results and propose possible future work.

Time-interleaved analog-to-digital converters are an attractive architecture for achieving a high speed, high resolution ADC in a power efficient manner. However, due to process and manufacturing variations, timing skews occur between the sampling clocks of the sub ADCs within the TI-ADC. These timing skews compromise the spurious free dynamic range of the converter. In addition, jitter on the sampling clocks, degrades the signal-to-noise ratio of the TI-ADC. Therefore, in order to maintain an acceptable spurious free dynamic range and signal to noise ratio, it is necessary to correct the timing skews while adding minimal jitter. Two analog-based architectures for correcting timing skews were investigated, with one being selected for implementation. The selected architecture and additional test circuitry were designed and fabricated in a 0.18??m CMOS process and tested using a 125 MSPS 16 bit ADC. The circuit achieves a correction precision on the order of 10???s of femtoseconds for timing skews as large as approximately 180 picoseconds, while adding less than 200 femtoseconds of rms jitter.