On s'intéresse dans cette thèse à la complexité bilinéaire de la multiplication dans toute extension de degré $n$ d'un corps $F_{q}$ à $q$ éléments, qui est étroitement liée au rang de tenseur de la multiplication dans $F_{q^n}$. L'algorithme de type évaluation-interpolation, introduit par D.V et G.V Chudnovsky en 1987, est à la base des techniques algorithmiques fournissant actuellement les meilleures bornes uniformes et asymptotiques de la complexité bilinéaire. Pour obtenir ces meilleures bornes, la stratégie adoptée jusqu'à présent consistait à fixer le degré des places en augmentant le genre du corps de fonctions algébriques.Néanmoins, l'étude de la construction effective associée à ce type de stratégie fut jusqu'à présent négligée en raison d'un obstacle, lié à la construction du point de degré $n$, relevé par Shparlinski, Tsfasman et Vladut en 1992.On présente dans cette thèse une nouvelle stratégie qui consiste à fixer le genre du corps de fonctions algébriques tout en augmentant le degré des places.En appliquant cette stratégie aux corps de fonctions elliptiques, on montre d'une part que le rang de tenseur de la multiplication dans $F_{q^n}$ est quasi-linéaire en $n$, et d'autre part que la construction des algorithmes de multiplications bilinéaires issus de cette stratégie est réalisable en temps polynomial. On montre également comment construire explicitement ces algorithmes sur $F_{q^n}$, en les illustrant par un exemple. Enfin, on établit la première construction asymétrique de l'algorithme de type Chudnovsky. / In this thesis, we focus on the bilinear complexity of multiplication in any degree $n$ extension of the finite field $ F_{q}$, which is closely related to the tensor rank of multiplication in $ F_{q^n} $. The evaluation-interpolation type algorithm introduced by D.V and G.V Chudnovsky in 1987, is the basis of all algorithmic technique providing for now, the lower asymptotic and uniform bounds for the bilinear complexity.So far, the strategy to obtain these lower bounds was to fix the degree of places while increasing the genus of algebraic function fields. However, the study of the effective construction associated with this kind of strategy was until now neglected because of an obstacle related to the construction of a degree $n$ point, identified par Shparlinski, Tsfasman and Vladut in 1992. We present a new strategy which consists in fixing the genus of algebraic function fields while increasing the degree of places. Applying this strategy to the elliptic function fields, we show on the one hand that the tensor rank of multiplication in $ F_{q^n} $ is quasi-linear in $ n $, and on the other hand we prove that the construction of bilinear multiplication algorithms with this strategy is feasible in polynomial time. We also show how to construct explicitly these algorithms over $ F_{q^n} $ for large $n$ by illustrating the construction with an example. Finally, we establish the first asymmetric construction of the Chudnovsky type algorithm.

The Growth Curve Model is a bilinear statistical model which can be used to analyse several groups of repeated measurements. Normally the Growth Curve Model is defined in such a way that the permitted sampling frequency of the repeated measurement is limited by the number of observed individuals in the data set.In this thesis, we examine the possibilities of utilizing highly frequently sampled measurements to increase classification accuracy for real world data. That is, we look at the case where the regular Growth Curve Model is not defined due to the relationship between the sampling frequency and the number of observed individuals. When working with this high frequency data, we develop a new method of basis selection for the regression analysis which yields what we call a Bilinear Gaussian Radial Basis Function Network (BGRBFN), which we then compare to more conventional polynomial and trigonometrical functional bases. Finally, we examine if Tikhonov regularization can be used to further increase the classification accuracy in the high frequency data case.Our findings suggest that the BGRBFN performs better than the conventional methods in both classification accuracy and functional approximability. The results also suggest that both high frequency data and furthermore Tikhonov regularization can be used to increase classification accuracy.

No description available.

The application of polymers in robust engineering designs is on the rise due to their excellent mechanical properties such as high fracture toughness, specific strength, durability, as well as, thermal and chemical resistances. Implementation of some advanced polymeric solids is limited due to the lack of available mechanical properties. In order for these materials to endure strenuous engineering designs it is vital to investigate their response in multiple loading rates and conditions. In this thesis, the mechanical response of polyethermide (PEI) is characterized under quasi-static, high strain rate, and multiple impact conditions. Standard tension, torsion, and compression experiments are performed in order to distinguish the multi-regime response of PEI. The effects of physical ageing and rejuvenation on the quasi-static mechanical response are investigated. The strain softening regime resulting from strain localization is eliminated by thermal and mechanical rejuvenation, and the advantages of these processes are discussed. The dynamic fracture toughness of the material in response to notched impact via Charpy impact test is evaluated. The high strain-rate response of PEI to uniaxial compression is evaluated at rates exceeding 104/s via miniaturized Split Hopkinson Pressure Bar (MSHPB), and compared to the quasi-static case to determine strain-rate sensitivity. The elastic response of the aged material to multiple loading conditions are correlated using the Ramberg-Osgood equation, while the elastoplastic response of rejuvenated PEI is correlated using a both the Ramberg-Osgood equation and a novel model. The strain-rate sensitivity of the strength is found to be nominally bilinear and transition strains are modeled using the Ree-Erying formulation. Finally, multiple impact experiments are performed on PEI using the MSHPB and a model is proposed to quantify damage as a result of collision.

<p> Within recent years, there has been a renewed interest in developing data-driven learning based algorithms for solving longstanding challenging control problems. This interest is primarily motivated by the availability of ubiquitous data and an increase in computational resources of modern machines.  However, there is a prevailing concern on the lack of provable performance guarantees on data-driven/model-free learning based control algorithms. This dissertation focuses the following key aspects: i) with what facility can state-of-the-art learning-based control methods eke out successful performance for challenging flight control applications such as aerobatic maneuvering?; and ii) can we leverage well-established tools and techniques in control theory to provide some provable guarantees for different types of learning-based algorithms?  </p> <p>To these ends, a deep RL-based controller is implemented, via high-fidelity simulations, for Fixed-Wing aerobatic maneuvering. which shows the facility with which learning-control methods can eke out successful performances and further encourages the development of learning-based control algorithms with an eye towards providing provable guarantees.<br> </p> <p>Two learning-based algorithms are also developed: i) a model-free algorithm which learns a stabilizing optimal control policy for the bilinear biquadratic regulator (BBR) which solves the regulator problem with a biquadratic performance index given an unknown bilinear system; and ii) a model-free inverse reinforcement learning algorithm, called the Model-Free Stochastic inverse LQR (iLQR) algorithm, which solves a well-posed semidefinite programming optimization problem to obtain unique solutions on the linear control gain and the parameters of the quadratic performance index given zero-mean noisy optimal trajectories generated by a linear time-invariant dynamical system. Theoretical analysis and numerical results are provided to validate the effectiveness of all proposed algorithms.</p>

At many American colleges and universities, efforts to enhance the retention of a diverse group of students have become a priority. This study represents part of this effort at the University of Central Florida, a large public suburban state university in the South. Specifically, this investigation evaluated Pegasus '95 and the Academic Mentoring Program offered in the Summer and Fall Semesters of 1995 to specially-admitted students who fell short of regular admissions requirements. During the summer, Pegasus '95 provided testing, orientation, guided course work, study skills workshops, and mentoring, both individually and in the context of cohesive socialization groups of approximately 15 students each. In the Fall 1995 Semester, students were highly encouraged to participate in one-on-one mentoring in the Academic Mentoring Program (AMP) available through the Student Academic Resource Center (SARC), a university-based office which provides a variety of academic assistance services. A multiple regression analysis was conducted using the following independent predictor variables: gender, SAT/ACT scores, Pegasus participation, use of the AMP in the Fall 1995 semester, four summary scores from the College Student Inventory (CSI), and eight scaled scores from the Noncognitive Questionnaire (NCQ). Dependent variables were individual student GPA in the Summer and Fall 1995 semesters, cumulative GPA after two semesters, and enrolled credit hours into the Spring 1996 academic term. Overall, it was expected that a combination of predictor variables, including both traditional cognitive factors (SAT/ACT scores and high school GPA) and noncognitive factors (NCQ scores and CSI scores, Pegasus participation, and mentoring by the SARC) would significantly predict GP A and retention. The study found that a regression equation including gender, high school GPA, overall SAT scores and the eight NCQ scale scores significantly predicted Fall 1995 and cumulative GPA after two semesters but not Summer 1995 GPA or credit hours enrolled in Spring 1996. Attendance at Pegasus meetings was also shown to be significantly and positively associated with Fall 1995 GPA and cumulative GPA after two semesters but not of Summer 1995 GPA or credit hours enrolled in Spring 1996. Gender, high school GP A, the ACT score and the CSI Dropout Proneness scale significantly predicted credit hours enrolled in Spring 1996, as did use of the AMP program provided by the SARC. Of particular interest was the finding that including noncognitive factors in significant equations led to a greater explanation of the variance than could be obtained with any of the traditional cognitive measurements alone, suggesting that with academically disadvantaged students noncognitive measures must be considered in predicting who can succeed and persist in college.

This thesis considers the development of a Hammerstein-bilinear approach to non-linear systems modelling, analysis and control systems design, which builds on and extends the applicability of an existing bilinear approach. The underlying idea of the Hammerstein-bilinear approach is to use the Hammerstein-bilinear system models to capture various physical phenomena of interest and subsequently use these for model based control system designs with the premise being that of achieving enhanced control performance. The advantage of the Hammerstein-bilinear approach is that the well-structured system models allow techniques that have been originally developed for linear systems to be extended and applied, while retaining moderate complexity of the corresponding system identification schemes and nonlinear model based control designs. In recognition of the need to be able to identify the Hammerstein-bilinear models a unified suite of algorithms, being the extensions to the simplified refined instrumental variable method for parameter estimation of linear transfer function models is proposed. These algorithms are able to operate in both the continuous-time and discrete-time domains to reflect the requirements of the intended purposes of the identified models with the emphasis being placed on straightforward applicability of the developed algorithms and recognising the need to be able to operate under realistic practical system identification scenarios. Moreover, the proposed algorithms are also applicable to parameter estimation of Hammerstein and bilinear models, which are special cases of the wider Hammerstein-bilinear model class. The Hammerstein-bilinear approach has been applied to an industrial heating, ventilation and air conditioning (HVAC) system, which has also been the underlying application addressed in this thesis. A unique set of dynamic control design purpose oriented air temperature and humidity Hammerstein-bilinear models of an environmentally controlled clear room manufacturing zone has been identified. The greater insights afforded by the knowledge of the system nonlinearities then allow for enhanced control tuning of the associated commercial HVAC control system leading to an improved overall control performance.

On s'intéresse dans cette thèse à la détermination du rang de tenseur de la multiplication dans $mathbb{F}_{q^n}$, l'extension de degré $n$ du corps fini $mathbb{F}_q$ ; ce rang de tenseur correspond en particulier à la complexité bilinéaire de la multiplication dans $mathbb{F}_{q^n}$ sur $mathbb{F}_q$. Dans cette optique, on présente les différentes évolutions de l'algorithme de type évaluation-interpolation introduit en 1987 par D.V. et G.V. Chudnovsky et qui a permis d'établir que le rang de tenseur de la multiplication dans $mathbb{F}_{q^n}$ était linéaire en~$n$. Cet algorithme en fournit désormais les meilleures bornes connues dans le cas d'extensions de degré grand relativement au cardinal du corps de base — le cas des petites extensions étant bien connu. Afin d'obtenir des bornes uniformes en le degré de l'extension, il est nécessaire, pour chaque $n$, de déterminer un corps de fonctions algébriques qui convienne pour appliquer l'algorithme pour $mathbb{F}_{q^n}$, c'est-à-dire qui ait suffisamment de places de petit degré relativement à son genre $g$ et pour lequel on puisse établir l'existence de diviseurs ayant certaines propriétés, notamment des diviseurs non-spéciaux de degré ${g-1}$ ou de dimension nulle et de degré aussi près de ${g-1}$ que possible ; c'est pourquoi les tours de corps de fonctions sont d'un intérêt considérable. En particulier, on s'intéresse ici à l'étude des tours de Garcia-Stichtenoth d'extensions d'Artin-Schreier et de Kummer qui atteignent la borne de Drinfeld-Vlu{a}duc{t}. / In this thesis, we focus on the determination of the tensor rank of multiplication in $mathbb{F}_{q^n}$, the degree $n$ extension of the finite field $mathbb{F}_q$, which corresponds to the bilinear complexity of multiplication in $mathbb{F}_{q^n}$ over $mathbb{F}_q$. To this end, we describe the various successive improvements to the evaluation-interpolation algorithm introduced in 1987 by D.V. and G.V. Chudnovsky which shows the linearity of the tensor rank of multiplication in $mathbb{F}_{q^n}$ with respect to $n$. This algorithm gives the best known bounds for large degree extensions relative to the cardinality of the base field (the case when the degree of the extension is small is well known). In order to obtain uniform bounds, we need to determine, for each $n$, a suitable algebraic function field for the algorithm on $mathbb{F}_{q^n}$, namely a function field with sufficiently many places of small degree relative to its genus $g$ and for which we can prove the existence of divisors with some good properties such as non-special divisors of degree ${g-1}$ or zero-dimensional divisors with degree as close to ${g-1}$ as possiblestring; these conditions lead us to consider towers of algebraic function fields. In particular, we are interested in the study of Garcia-Stichtenoth towers of Artin-Schreier and Kummer extensions which attain the Drinfeld-Vlu{a}duc{t} bound.

Dans cette thèse, on construit un grand nombre de solutions globales pour de nombreuses équations de Schrödinger sur-critiques. Le principe consiste à rendre la donnée initiale aléatoire, selon les mêmes méthodes que Nicolas Burq, Nikolay Tzvetkov et Laurent Thomann afin de gagner de la dérivabilité.On considère d'abord l'équation de Schrödinger cubique en dimension 3. En partant de variables aléatoires gaussiennes et de la base de L^2(R^3) formée des fonctions d'Hermite tensorielles, on construit des ensembles de solutions globales pour des données initiales qui sont moralement dans L^2(R^3). Les points clefs de la démonstration sont l'existence d'une estimée bilinéaire de type Bourgain pour l'oscillateur harmonique et la transformation de lentille qui permet de se ramener à prouver l'existence locale de solutions à l'équation de Schrödinger avec potentiel harmonique.On étudie ensuite l'effet régularisant pour prouver un théorème analogue où le gain de dérivée vaut 1/2-2/(p-1) où p correspond à la non linéarité de l'équation. Le gain est donc plus faible que précédemment mais la base de fonctions propres quelconques. De plus, la méthode s'appuyant sur des estimées linéaires, on établit le résultat pour des variables aléatoires dont la queue de distribution est à décroissance exponentielle.Enfin, on démontre des estimées multilinéaires en dimension 2 pour une base de fonctions propres quelconques ainsi que des inégalités de types chaos de Wiener pour une classe générale de variables aléatoires. Cela nous permet d'établir le théorème pour l'équation de Schrödinger quintique, avec un gain de dérivée égal à 1/3, dans le même cadre que la partie précédente. / In this thesis, we build a large number of global solutions for many supercritical Schrödinger equations. The method is to make the random initial data, using the same methods that Nicolas Burq, Nikolay Tzvetkov and Laurent Thomann in order to obtain differentiability. First, we consider the cubic Schrödinger equation in three dimensional. Using Gaussian random variables and the basis of L^2(R^3) consists of tensorial Hermite functions, we construct sets of solutions for initial data that are morally in L^2(R^3). The main ingredients of the proof are the existence of Bourgain type bilinear estimates for the harmonic oscillator and the lens transform which can be reduced to prove a local existence of solutions for the Schrödinger equation with harmonic potential. Next, we study the smoothing effect to prove an analogous theorem which the gain of differentiability is equalto 1/2-2/(p-1) which p is the nonlinearity of the equation. This gain is lower than previously but the basis of eigenfunctions are general. As the method uses only linear estimates, we establish the result for a general class of random variables.Finally, we prove multilinear estimates in two dimensional for a basis of ordinaries eigenfunctions and Wienerchaos type inequalities for classical random variables. This allows us to establish the theorem for the quinticSchrödinger equation, with a gain of differentiability equals to 1/3, in the same context as the previous chapter.

This master's thesis deals with the design of a differential high-gain transimpedance amplifier in TSMC's 0.18 um mixed signal process that utilizes a DC photodiode current cancellation loop and a switching automatic gain control (AGC) with a bilinear gain curve. The amplifier is designed to satisfy the demands of Optical Coherence Tomography applications where the receiver is expected to measure the envelope power of an amplitude modulated sinusoidal optical signal that incorporates a large DC component. Methods of increasing dynamic range and gain linearity through the use of DC photodiode current cancellation and bilinear gain are explored. Effects of changing DC photodiode current on the overall system response is also demonstrated.