Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaves [86]-88).

Alors que les études effectuées sur la biosynthèse de l’amidon ont permis,depuis une vingtaine d’années, une compréhension approfondie de ce mécanisme,les travaux sur la dégradation sont aujourd’hui assez peu développés et restreintsessentiellement au modèle de l’amidon transitoire chez Arabidopsis thaliana chez quiune approche de génétique inverse est mise en oeuvre. Dans ce contexte, nousavons entrepris une démarche complémentaire de génétique formelle chezChlamydomonas reinhardtii, organisme modèle permettant l’étude du métabolismede l’amidon transitoire et de réserve, dans le but d’identifier de nouvelles fonctionsnotamment impliquées dans la régulation du processus catabolique. L’applicationd’un crible à l’iode en deux étapes a permis l’isolement de 62 souchespotentiellement déficientes pour la dégradation de l’amidon parmi plus de 32000transformants. L’identification des gènes touchés a mis en évidence des fonctionsdéjà caractérisées chez le modèle Arabidopsis, telles que les protéines Mex, Bam1et Dpe2, confirmant ainsi la force du crible et validant la démarche entreprise. Lacaractérisation d’autres mutants nous permet d’envisager l’identification de nouvellesfonctions impliquées dans la dégradation de l’amidon ou dans la régulation de ceprocessus chez les végétaux. En parallèle, la caractérisation de la granulométrie desamidons produits par nos mutants augure également de la découverte de fonctionsimpliquées dans le déterminisme de la taille des grains d’amidon. / Starch biosynthesis has been widely studied for more than twenty years andthe understanding of this process is now quite complete. Meanwhile, studies onstarch catabolism have mainly been restricted to one single organism, Arabidopsisthaliana, a plant model for transitory starch metabolism studies through reversegenetics. We then decided to apply a complementary forward genetics approach inthe unicellular microalga Chlamydomonas reinhardtii in order to decipher thecatabolism of both transitory and storage starches. Using random mutagenesis and atwo-step iodine screening, we were able to isolate 62 putative catabolic mutantsamong more than 32000 insertional transformants. The localization of the foreignDNA insertion sites allowed the identification of mutations for key catabolic activitiessuch as Mex, Bam1 and Dpe2, which were already described in Arabidopsis,revealing the strength of our phenotypic screening procedure. The preliminarycharacterizations performed on the other mutants defective for previouslyuncharacterized functions may define new functions affecting starch catabolism orregulation of this process in microalgae. . Some of these mutants are also harboringaltered size distributions of their starch granules and may represent a valuablematerial for understanding the mechanisms controlling the starch granule sizesdetermination in Chlamydomonas reinhardtii.

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M/EEG mechanisms allow determining changes in the brain activity, which is useful in diagnosing brain disorders such as epilepsy. They consist of measuring the electric potential at the scalp and the magnetic field around the head. The measurements are related to the underlying brain activity by a linear model that depends on the lead-field matrix. Localizing the sources, or dipoles, of M/EEG measurements consists of inverting this linear model. However, the non-uniqueness of the solution (due to the fundamental law of physics) and the low number of dipoles make the inverse problem ill-posed. Solving such problem requires some sort of regularization to reduce the search space. The literature abounds of methods and techniques to solve this problem, especially with variational approaches. This thesis develops Bayesian methods to solve ill-posed inverse problems, with application to M/EEG. The main idea underlying this work is to constrain sources to be sparse. This hypothesis is valid in many applications such as certain types of epilepsy. We develop different hierarchical models to account for the sparsity of the sources. Theoretically, enforcing sparsity is equivalent to minimizing a cost function penalized by an l0 pseudo norm of the solution. However, since the l0 regularization leads to NP-hard problems, the l1 approximation is usually preferred. Our first contribution consists of combining the two norms in a Bayesian framework, using a Bernoulli-Laplace prior. A Markov chain Monte Carlo (MCMC) algorithm is used to estimate the parameters of the model jointly with the source location and intensity. Comparing the results, in several scenarios, with those obtained with sLoreta and the weighted l1 norm regularization shows interesting performance, at the price of a higher computational complexity. Our Bernoulli-Laplace model solves the source localization problem at one instant of time. However, it is biophysically well-known that the brain activity follows spatiotemporal patterns. Exploiting the temporal dimension is therefore interesting to further constrain the problem. Our second contribution consists of formulating a structured sparsity model to exploit this biophysical phenomenon. Precisely, a multivariate Bernoulli-Laplacian distribution is proposed as an a priori distribution for the dipole locations. A latent variable is introduced to handle the resulting complex posterior and an original Metropolis-Hastings sampling algorithm is developed. The results show that the proposed sampling technique improves significantly the convergence. A comparative analysis of the results is performed between the proposed model, an l21 mixed norm regularization and the Multiple Sparse Priors (MSP) algorithm. Various experiments are conducted with synthetic and real data. Results show that our model has several advantages including a better recovery of the dipole locations. The previous two algorithms consider a fully known leadfield matrix. However, this is seldom the case in practical applications. Instead, this matrix is the result of approximation methods that lead to significant uncertainties. Our third contribution consists of handling the uncertainty of the lead-field matrix. The proposed method consists in expressing this matrix as a function of the skull conductivity using a polynomial matrix interpolation technique. The conductivity is considered as the main source of uncertainty of the lead-field matrix. Our multivariate Bernoulli-Laplacian model is then extended to estimate the skull conductivity jointly with the brain activity. The resulting model is compared to other methods including the techniques of Vallaghé et al and Guttierez et al. Our method provides results of better quality without requiring knowledge of the active dipole positions and is not limited to a single dipole activation.

A geostatistical inverse method of estimating hydraulic parameters of a heterogeneous porous medium at discrete points in space, called pilot points, is presented. In this inverse method the parameter estimation problem is posed as a nonlinear optimization problem with a likelihood based objective function. The likelihood based objective function is expressed in terms of head residuals at head measurement locations in the flow domain, where head residuals are the differences between measured and model-predicted head values. Model predictions of head at each iteration of the optimization problem are obtained by solving a forward problem that is based on nonlocal conditional ensemble mean flow equations. Nonlocal moment equations make possible optimal deterministic predictions of fluid flow in randomly heterogenous porous media as well as assessment of the associated predictive uncertainty. In this work, the nonlocal moment equations are approximated to second order in the standard deviation of log-transformed hydraulic conductivity, and are solved using the finite element method. To enhance computational efficiency, computations are carried out in the complex Laplace-transform space, after which the results are inverted numerically to the real temporal domain for analysis and presentation. Whereas a forward solution can be conditioned on known values of hydraulic parameters, inversion allows further conditioning of the solution on measurements of system state variables, as well as for the estimation of unknown hydraulic parameters. The Levenberg-Marquardt algorithm is used to solve the optimization problem. The inverse method is illustrated through two numerical examples where parameter estimates and the corresponding predictions of system state are conditioned on measurements of head only, and on measurements of head and log-transformed hydraulic conductivity with prior information. An example in which predictions of system state are conditioned only on measurements of log-conductivity is also included for comparison. A fourth example is included in which the estimation of spatially constant specific storage is demonstrated. In all the examples, a superimposed mean uniform and convergent transient flow field through a bounded square domain is used. The examples show that conditioning on measurements of both head and hydraulic parameters with prior information yields more reliable (low uncertainty and good fit) predictions of system state, than when such information is not incorporated into the estimation process.

This thesis reports on the research carried out in the area of Microwave Tomography (MWT) where the study aims to develop inversion algorithms to obtain cheap and stable solutions of MWT inverse scattering problems which are mathematically formulated as nonlinear ill posed problems. The study develops two algorithms namely Inexact Newton Backtracking Method (INBM) and Newton Iterative-Conjugate Gradient on Normal Equation (NI-CGNE) which are based on Newton method. These algorithms apply implicit solutions of the Newton equations with unspecific manner functioning as the regularized step size of the Newton iterative. The two developed methods were tested by the use of numerical examples and experimental data gained by the MWT system of the University of Manchester. The numerical experiments were done on samples with dielectric contrast objects containing different kinds of materials and lossy materials. Meanwhile, the quality of the methods is evaluated by comparingthem with the Levenberg Marquardt method (LM). Under the natural assumption that the INBM is a regularized method and the CGNE is a semi regularized method, the results of experiments show that INBM and NI-CGNE improve the speed, the spatial resolutions and the quality of direct regularization method by means of the LM method. The experiments also show that the developed algorithms are more flexible to theeffect of noise and lossy materials compared with the LM algorithm.

Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients) and the source of PDE models are often unknown and are estimated from available measurements. Despite its importance, solving the estimation problem is mathematically and numerically challenging and especially when the measurements are corrupted by noise, which is often the case. Various methods have been proposed to solve estimation problems in PDEs which can be classified into optimization methods and recursive methods. The optimization methods are usually heavy computationally, especially when the number of unknowns is large. In addition, they are sensitive to the initial guess and stop condition, and they suffer from the lack of robustness to noise. Recursive methods, such as observer-based approaches, are limited by their dependence on some structural properties such as observability and identifiability which might be lost when approximating the PDE numerically. Moreover, most of these methods provide asymptotic estimates which might not be useful for control applications for example. An alternative non-asymptotic approach with less computational burden has been proposed in engineering fields based on the so-called modulating functions. In this dissertation, we propose to mathematically and numerically analyze the modulating functions based approaches. We also propose to extend these approaches to different situations. The contributions of this thesis are as follows. (i) Provide a mathematical analysis of the modulating function-based method (MFBM) which includes: its well-posedness, statistical properties, and estimation errors. (ii) Provide a numerical analysis of the MFBM through some estimation problems, and study the sensitivity of the method to the modulating functions' parameters. (iii) Propose an effective algorithm for selecting the method's design parameters. (iv) Develop a two-dimensional MFBM to estimate space-time dependent unknowns which is illustrated in estimating the source term in the damped wave equation describing the physiological characterization of brain activity. (v) Introduce a moving horizon strategy in the MFBM for on-line estimation and examine its effectiveness on estimating the source term of a first order hyperbolic equation which describes the heat transfer in distributed solar collector systems.

>Magister Scientiae - MSc / In this study a complete set of exclusive (~p; 2p) polarization transfer observables of closed-shell oxygen isotopes are calculated using both direct and inverse kinematics using the relativistic plane wave impulse approximation. The interaction matrix is written in terms of the SPVAT (scalar, pseudoscalar, vector axial vector, tensor) covariants where each amplitude is obtained directly from experimental phase shifts. A relativistic mean eld theory approximation is used to compute boundstate wave functions of the nucleons. We study the evolution of polarization transfer observables within oxygen isotopes and identify observables which may discriminate between these isotopes. The same kinematical conditions are considered for both direct and inverse kinematics: the incident energy is set at 504 MeV and coplanar angles are xed at (22:12 ;􀀀40:30 ). The results indicate that only three spin observables, namely, Ay, P and Dnn distinguish di erent oxygen isotopes at these kinematical conditions in the inverse kinematics.

The problem under consideration is that of obtaining a representation of the permeability of a porous medium which is heterogeneous and anisotropic from limited information. To solve this inverse problem we propose the use of two different pieces that work together. A simulated annealing algorithm is presented and coupled with an homogenization technique; together these solve the problem which was posed. Further, numerical simulation results are presented illustrating the use of the simulated annealing algorithm as well as a coupling with the homoginization technique. This study illustrates that the performance of the annealing algorithm is enhanced with usage of homogenization.

Shock wave interactions such as those that occur during atmospheric re-entry, can produce extreme thermal loads on aerospace structures. These interactions are reproduced experimentally in hypersonic wind tunnels to study how the flow structures relate to the deleterious heat fluxes. In these studies, localized fluid jets created by shock interactions impinge on a test cylinder, where the temperature due to the heat flux is measured. These measurements are used to estimate the heat flux on the surface as a result of the shock interactions. The nature of the incident flux usually involves dynamic transients and severe nonuniformities. Finding this boundary flux from discrete unsteady temperature measurements is characterized by instabilities in the solution. The purpose of this work is to evaluate existing methodologies for the determination of the unsteady heat flux and to introduce a new approach based on an inverse technique. The performance of these methods was measured first in terms of accuracy and their ability to handle inherently ``unstable'' or highly dynamic data such as step fluxes and high frequency oscillating fluxes. Then the method was expanded to estimate unsteady and nonuniform heat fluxes. The inverse methods proved to be the most accurate and stable of the methods examined, with the proposed method being preferable. / Ph. D.