Esta tesis constituye un estudio detallado y exhaustivo de las propiedades de una variedad específica de ondas ópticas solitarias. Observadas experimentalmente por primera vez en 1995, estas ondas estan formadas por un haz óptico a frecuencia fundamental y su segundo armónico que están ligados entre sí y viajan juntos en el material cuadrático; y son debidas al equilibrio entre la difracción lineal que sufre el haz al propagarse y un término no lineal de segundo orden en la susceptibilidad del medio. Las llamamos por eso solitones ópticos en medios cuadráticos o simplemente 'solitones cuadráticos'. También se les conoce como 'Solitones Multicolor' aludiendo al hecho de que requieren de haces a diferentes frecuencias para formarse.Un medio no-lineal cuadrático tiene por fuerza que ser no-centrosimétrico, lo cual es una variedad de anisotropía. Una gran parte de los materiales no-lineales cuadráticos (los que tienen mayor interés para la industria) son uniaxiales lo que significa que presentan un eje de simetría que suele llamarse eje óptico. De la dirección de un haz relativa a ese eje óptico dependen las características de la propagación del haz en el medio cuadrático no-lineal. Una consecuencia de eso en configuraciones de interés es un desvío ('walk-off') sufrido por el haz respecto a su dirección de propagación inicial al entrar en el material no-lineal.Las propiedades de los solitones cuadráticos 'caminantes' son también estudiadas en la tesis, estableciendo que existe una relación entre la potencia inyectada en el medio y el ángulo de desvío (walking angle).Una parte importante de la tesis está dedicada al estudio a través de exhaustivos experimentos numéricos del potencial de estas ondas solitarias para constituir la base de dispositivos de conmutación y encaminamiento totalmente ópticos que puedan hacer realidad la promesa de la red transparente totalmente óptica. Los experimentos han permitido identificar varias configuraciones de interés con niveles de potencia y dimensiones que permiten plantearse el diseño y construcción de dispositivos comerciales de conmutación y encaminamiento totalmente ópticos basados en solitones ópticos cuadráticos. / This thesis is a comprehensive study of the fundamental properties of a specific kind of optical spatial solitary waves. First observed experimentally in 1995, these solitary waves are formed by an optical beam at a fundamental frequency and its second harmonic which propagate together and are mutually entangled; and are due to a balanced interplay between the beams' linear diffraction and a second-order nonlinear susceptibility of the medium. They are thereby referred as 'Optical Solitons in Quadratic Nonlinear Media' or simply 'Quadratic Solitons', They are also known as 'Multicolor Solitons' recalling that they are formed by beams at different frequencies.A quadratic nonlinear media needs to be non centrosymmetric which is a special kind of anisotropy. A great deal of quadratic nonlinear materials (the most used by industry such as lithim niobate, KTP, etc.) are uniaxial meaning that they feature a symmetry axis known as 'optical axis'. The direction of propagation of an optical beam relative to that axis determines the characteristics of the beam's propagation through the quadratic nonlinear material. A main result of that in some configurations of interest is a walk-off suffered by the beam as it enters the quadratic material.The properties of the families of quadratic solitons in the presence of a linear walk-off (quadratic walking solitons) are studied as well in the thesis stating that there is a relationship between the power injected into the medium and the walking angle, suitable to applications of all-optical switching and routing.An important last part of the thesis is devoted to the study from a practical viewpoint and through extensive numerical experiments of the potential of these solitary waves as the basis of practical all-optical switches and routers which could take the all-optical transparent network to a reality. The experiments have allowed to identify several configurations of interest with power level and dimensions suited to practical applications which could allow the production of commercial all-optical switching and routing devices based on quadratic solitons.

The automotive industry is required to deal with increasingly stringent legislationfor greenhouse gases. Hybrid Electric Vehicles, HEV, are gaining acceptance as thefuture path of lower emissions and fuel consumption. The increased complexityof multiple prime movers demand more advanced control systems, where futuredriving conditions also becomes interesting. For a plug-in Hybrid Electric Vehicle,PIHEV, it is important to utilize the comparatively inexpensive electric energybefore the driving cycle is complete, this for minimize the cost of the driving cycle,since the battery in a PIHEV can be charged from the grid. A strategy with lengthinformation of the driving cycle from a global positioning system, GPS, couldreduce the cost of driving. This by starting to blend the electric energy with fuelearlier, a strategy called blended driving accomplish this by distribute the electricenergy, that is charged externally, with fuel over the driving cycle, and also ensurethat the battery’s minimum level reaches before the driving cycle is finished. Astrategy called Charge Depleting Charge Sustaining, CDCS, does not need lengthinformation. This strategy first depletes the battery to a minimum State of Charge,SOC, and after this engages the engine to maintain the SOC at this level. In thisthesis, a variable SOC reference is developed, which is dependent on knowledgeabout the cycle’s length and the current length the vehicle has driven in the cycle.With assistance of a variable SOC reference, is a blended strategy realized. Thisis used to minimize the cost of a driving cycle. A comparison between the blendedstrategy and the CDCS strategy was done, where the CDCS strategy uses a fixedSOC reference. During simulation is the usage of fuel minimized; and the blendedstrategy decreases the cost of the driving missions compared to the CDCS strategy.To solve the energy management problem is a model predictive control used. Thedesigned control system follows the driving cycles, is charge sustaining and solvesthe energy management problem during simulation. The system also handlesmoderate model errors. / Fordonsindustrin måste hantera allt strängare lagkrav mot utsläpp av emissioneroch växthusgaser. Hybridfordon har börjat betraktas som den framtida vägenför att ytterligare minska utsläpp och användning av fossila bränslen. Den ökadekomplexiteten från flera olika motorer kräver mera avancerade styrsystem. Begränsningarfrån motorernas energikällor gör att framtida förhållanden är viktigaatt estimera. För plug-in hybridfordon, PIHEV, är det viktigt att använda denvvijämförelsevis billiga elektriska energin innan fordonet har nått fram till slutdestinationen.Batteriets nuvarande energimängd mäts i dess State of Charge, SOC.Genom att utnyttja information om hur långt det är till slutdestinationen från ettGlobal Positioning System, GPS, blandar styrsystemet den elektriska energin medbränsle från början, detta kallas för blandad körning. En strategi som inte hartillgång till hur långt fordonet ska köras kallas Charge Depleting Charge Sustaining,CDCS. Denna strategi använder först energin från batteriet, för att sedanbörja använda förbränningsmotorn när SOC:s miniminivå har nåtts. Strategin attanvända GPS informationen är jämförd med en strategi som inte har tillgång tillinformation om körcykelns längd. Blandad körning använder en variabel SOC referens,till skillnad från CDCS strategin som använder sig av en konstant referenspå SOC:s miniminivå. Den variabla SOC referensen beror på hur långt fordonethar kört av den totala körsträckan, med hjälp av denna realiseras en blandad körning.Från simuleringarna visade det sig att blandad körning gav minskad kostnadför de simulerade körcyklerna jämfört med en CDCS strategi. En modellbaseradprediktionsreglering används för att lösa energifördelningsproblemet. Styrsystemetföljer körcykler och löser energifördelningsproblemet för de olika drivkällorna undersimuleringarna. Styrsystemet hanterar även måttliga modellfel.

Analytic and force-directed placement methods that simultaneously minimize wire length and spread cells are receiving renewed attention from both academia and industry. However, these methods are by no means trivial to implement---to date, published works have failed to provide sufficient engineering details to replicate results. This dissertation addresses the implementation of a generic force-directed placer entitled FDP. Specifically, this thesis provides (1) a description of efficient force computation for spreading cells, (2) an illustration of numerical instability in this method and a means to avoid the instability, (3) metrics for measuring cell distribution throughout the placement area, and (4) a complementary technique that aids in minimizing wire length. FDP is compared to Kraftwerk and other leading academic tools including Capo, Dragon, and mPG for both standard cell and mixed-size circuits. Wire lengths produced by FDP are found to be, on average, up to 9% and 3% better than Kraftwerk and Capo, respectively. All told, this thesis confirms the validity and applicability of the approach, and provides clarifying details of the intricacies surrounding the implementation of a force-directed global placer.

In this paper we study through iterative methods the minimization problem min_{x∈C} £K(x) (P) where the set C of constraints is the set of fixed points of a nonexpansive mapping T in a real Hilbert space H, and the objective function £K:H¡÷R is supposed to be continuously Gateaux dierentiable. The gradient projection method for solving problem (P) involves with the projection P_{C}. When C = Fix(T), we provide a so-called hybrid iterative method for solving (P) and the method involves with the mapping T only. Two special cases are included: (1) £K(x)=(1/2)||x-u||^2 and (2) £K(x)=<Ax,x> - <x,b>. The first case corresponds to finding a fixed point of T which is closest to u from the fixed point set Fix(T). Both cases have received a lot of investigations recently.

Most of the cardiac structural abnormalities will be examined by echocardiography. With more understanding of heart diseases, it is commonly recognized that heart failures are closely related to left ventricular systolic and diastolic functions. This work discusses the association between gray-scale differences and the risk of heart disease from the changes in left ventricular systole and diastole of ultrasound image. Owing to the large dimension of data matrix, following Chen (2011), we also simplify the influence factors by factor analysis and calculate factor scores to present the characteristics of subjects. Two kinds of classification criteria are used in this work, namely logistic model with distance indicator and discriminant function. According to Guo et al. (2001), we calculate the Mahalanobis distance from each subject to the center of normal and abnormal group, then use logistic model to fit the distances for classification later. This is called logistic model with distance indicator. For the discriminant analysis, the regularized method by Friedman (1989) for estimation of covariance matrix is used, which is more flexible and can improve the covariance matrix estimates when the sample size is small. As far as the cut-point of ROC curve, following the approach as in Hanley et al. (1982), we find the most appropriate cut-point which has good performances for both sensitivity and specificity under the same classification criteria. Then the regularized method and the cut-point of ROC curve are combined to be a new classification criterion. The results under the new classification criterion are presented to classify normal and abnormal groups.

Technology scaling has been the most obvious choice of designers and chip manufacturing companies to improve the performance of analog and digital circuits. With the ever shrinking technological node, process variations can no longer be ignored and play a significant role in determining the performance of nanoscaled devices. By choosing a worst case design methodology, circuit designers have been very munificent with the design parameters chosen, often manifesting in pessimistic designs with significant area overheads. Significant work has been done in estimating the impact of intra-die process variations on circuit performance, pertinently, noise margin and standby leakage power, for fixed transistor channel dimensions. However, for an optimal, high yield, SRAM cell design, it is absolutely imperative to analyze the impact of process variations at every design point, especially, since the distribution of process variations is a statistically varying parameter and has an inverse correlation with the area of the MOS transistor. Furthermore, the first order analytical models used for optimization of SRAM memories are not as accurate and the impact of voltage and its inclusion as an input, along with other design parameters, is often ignored. In this thesis, the performance parameters of a nano-scaled 6-T SRAM cell are modeled as an accurate, yield aware, empirical polynomial predictor, in the presence of intra-die process variations. The estimated empirical models are used in a constrained non-linear, robust optimization framework to design an SRAM cell, for a 45 nm CMOS technology, having optimal performance, according to bounds specified for the circuit performance parameters, with the objective of minimizing on-chip area. This statistically aware technique provides a more realistic design methodology to study the trade off between performance parameters of the SRAM. Furthermore, a dual optimization approach is followed by considering SRAM power supply and wordline voltages as additional input parameters, to simultaneously tune the design parameters, ensuring a high yield and considerable area reduction. In addition, the cell level optimization framework is extended to the system level optimization of caches, under both cell level and system level performance constraints.

This thesis focuses on the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the affect of the deformation on the diffusion process, and the effect of the transport of an inert chemical species on the deformation of the solid. A robust computational framework is presented for solving the proposed mathematical model, which consists of coupled non-linear partial differential equations. It should be noted that many popular numerical formulations may produce unphysical negative values for the concentration, particularly, when the diffusion process is anisotropic. The violation of the non-negative constraint by these numerical formulations is not mere numerical noise. In the proposed computational framework we employ a novel numerical formulation that will ensure that the concentration of the diffusant be always non-negative, which is one of the main contributions of this thesis. Representative numerical examples are presented to show the robustness, convergence, and performance of the proposed computational framework. Another contribution is to systematically study the affect of transport of the diffusant on the deformation of the solid and vice-versa, and their implication in modeling degradation/healing of materials. It is shown that the coupled response is both qualitatively and quantitatively different from the uncoupled response.

In the literature, many methods are proposed to value American options. However, due to computational difficulty, there are only approximate solution or numerical method to evaluate American options. It is not easy for general investors either to understand nor to apply. In this thesis, we build up an option pricing and virtual asset model system, which provides a friendly environment for general public to calculate early exercise boundary of an American option. This system modularize the well-handled pricing models to provide the investors an easy way to value American options without learning difficult financial theories. The system consists two parts: the first one is an option pricing system, the other one is an asset model simulation system. The option pricing system provides various option pricing methods to the users; the virtual asset model system generates virtual asset prices for different underlying models.

In the thesis, the Wilcoxon approach to linear regression problems is combined with the fractal image compression to form a novel Wilcoxon fractal image compression. When the original image is corrupted by noise, we argue that the fractal image compression scheme should be insensitive to those outliers present in the corrupted image. This leads to the new concept of robust fractal image compression. The proposed Wilcoxon fractal image compression is the first attempt toward the design of robust fractal image compression. Four different numerical methods, i.e., steepest decent, line minimization based on quadratic interpolation, line minimization based on cubic interpolation, and least absolute deviation, will be proposed to solve the associated linear Wilcoxon regression problem. From the simulation results, it will be seen that, compared with the traditional fractal image compression, Wilcoxon fractal image compression has very good robustness against outliers caused by salt-and-pepper noise. However, it does not show great improvement of the robustness against outliers caused by Gaussian noise.

<p>This thesis consists of four independent papers concerningdifferent aspects of interior methods for optimization. Threeof the papers focus on theoretical aspects while the fourth oneconcerns some computational experiments.</p><p>The systems of equations solved within an interior methodapplied to a convex quadratic program can be viewed as weightedlinear least-squares problems. In the first paper, it is shownthat the sequence of solutions to such problems is uniformlybounded. Further, boundedness of the solution to weightedlinear least-squares problems for more general classes ofweight matrices than the one in the convex quadraticprogramming application are obtained as a byproduct.</p><p>In many linesearch interior methods for nonconvex nonlinearprogramming, the iterates can "falsely" converge to theboundary of the region defined by the inequality constraints insuch a way that the search directions do not converge to zero,but the step lengths do. In the sec ond paper, it is shown thatthe multiplier search directions then diverge. Furthermore, thedirection of divergence is characterized in terms of thegradients of the equality constraints along with theasymptotically active inequality constraints.</p><p>The third paper gives a modification of the analytic centerproblem for the set of optimal solutions in linear semidefiniteprogramming. Unlike the normal analytic center problem, thesolution of the modified problem is the limit point of thecentral path, without any strict complementarity assumption.For the strict complementarity case, the modified problem isshown to coincide with the normal analytic center problem,which is known to give a correct characterization of the limitpoint of the central path in that case.</p><p>The final paper describes of some computational experimentsconcerning possibilities of reusing previous information whensolving system of equations arising in interior methods forlinear programming.</p><p><b>Keywords:</b>Interior method, primal-dual interior method,linear programming, quadratic programming, nonlinearprogramming, semidefinite programming, weighted least-squaresproblems, central path.</p><p><b>Mathematics Subject Classification (2000):</b>Primary90C51, 90C22, 65F20, 90C26, 90C05; Secondary 65K05, 90C20,90C25, 90C30.</p>