Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Sept. 18, 2008). PDF text: 75 p. ; 408 K. UMI publication number: AAT 3303784. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (Ph. D.)--University of Michigan, 1935. / Thesis note on p. 62. "Reprinted from the Annals of mathematical statistics, vol. VII, no. 2, June, 1936."

Thesis (Ph. D.)--University of Washington, 1996. / Vita. Includes bibliographical references (leaves [58]-60).

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La chicorée produit et accumule une panoplie originale d’esters d’acide caféique : les acides caftarique (CTA), chicorique (diCTA), isochlorogénique (diCQA) et chlorogénique (CQA). En plus de leurs multiples rôles physiologiques et écologiques pour la plante, ces composés phénoliques sont dotés de nombreuses propriétés nutritionnelles et thérapeutiques. La valorisation de ces composés nécessite, au préalable, une connaissance approfondie de leur métabolisme. Si la biosynthèse du CQA est bien documentée, celles des autres molécules ne sont que partiellement décrites. L’objectif de ce travail de thèse consistait en la caractérisation de la voie de biosynthèse du CQA et du diCQA. L’analyse détaillée des contenus en polyphénols a révélé une distribution tissulaire originale. Le CTA et le diCTA sont les composés majeurs dans les feuilles alors que le diCQA est le composé majeur dans les racines. Les contenus en CQA ne permettent pas de différencier ces organes. En vue d’une analyse transcriptomique, plusieurs systèmes expérimentaux ont été testés de manière à induire la production et l’accumulation des composés ciblés. Par une approche de génétique inverse, deux gènes codant des HCTs et trois des HQTs ont été identifiés et caractérisés. Ces protéines interviennent dans la synthèse du CQA. Une approche de biochimie a permis d’identifier une séquence protéique potentiellement impliquée dans la synthèse de diCQA chez la patate douce. Par homologie de séquence, un gène candidat a été identifié chez la chicorée. Les travaux présentés dans ce mémoire constituent une contribution significative au décryptage des voies de biosynthèse de ces molécules au fort potentiel. / Chicory synthesizes and accumulates an original combination of caffeic acid i.e. caftaric (CTA), chicoric (diCTA), isochlorogenic (diCQA) and chlorogenic (CQA) acids. In addition to their multiple physiological and ecological roles in plants, these compounds have many pharmaceutical and nutritional properties. A complete understanding of their biochemical pathways is required for optimization of their production. If CQA biosynthesis is well documented, the pathways involved in the synthesis of the other molecules are far to be fully understood. The goal of this PhD thesis was to characterize the pathways involved in CQA and diCQA synthesis.Detailed analysis of phenolic contents revealed an original tissue distribution. CTA and diCTA are mainly accumulated in shoots whereas diCQA was the main compound in roots. CQA is uniformly distributed. To anticipate a transcriptomic analysis, several experimental models have been used in order to modulate the synthesis and the accumulation of the compounds of interest. Through a reverse genetic approach we identified and characterized 2 genes encoding HCTs and 3 genes encoding HQTs. These proteins are involved in the synthesis of CQA. By a biochemical approach, we identify a peptide sequence putatively involved in diCQA synthesis in sweet potato. An homologous gene has been identified in chicory. Data reported here contribute to a better understanding of the biosynthesis of these high-value compounds.

Bayesian inverse modelling provides a top-down technique of verifying emissions and uptake of carbon dioxide (CO₂) from both natural and anthropogenic sources. It relies on accurate measurements of CO₂ concentrations at appropriately placed sites and "best-guess" initial estimates of the biogenic and anthropogenic emissions, together with uncertainty estimates. The Bayesian framework improves current estimates of CO₂ fluxes based on independent measurements of CO₂ concentrations while being constrained by the initial estimates of these fluxes. Monitoring, reporting and verification (MRV) is critical for establishing whether emission reducing activities to mitigate the effects of climate change are being effective, and the Bayesian inverse modelling approach of correcting CO₂ flux estimates provides one of the tools regulators and researchers can use to refine these emission estimates. South Africa is known to be the largest emitter of CO₂ on the African continent. The first major objective of this research project was to carry out such an optimal network design for South Africa. This study used fossil fuel emission estimates from a satellite product based on observations of night-time lights and locations of power stations (Fossil Fuel Data Assimilations System (FFDAS)), and biogenic productivity estimates from a carbon assessment carried out for South Africa to provide the initial CO₂ flux estimates and their uncertainties. Sensitivity analyses considered changes to the covariance matrix and spatial scale of the inversion, as well as different optimisation algorithms, to assess the impact of these specifications on the optimal network solution. This question was addressed in Chapters 2 and 3. The second major objective of this project was to use the Bayesian inverse modelling approach to obtain estimates of CO₂ fluxes over Cape Town and surrounding area. I collected measurements of atmospheric CO₂ concentrations from March 2012 until July 2013 at Robben Island and Hangklip lighthouses. CABLE (Community Atmosphere Biosphere Land Exchange), a land-atmosphere exchange model, provided the biogenic estimates of CO₂ fluxes and their uncertainties. Fossil fuel estimates and uncertainties were obtained by means of an inventory analysis for Cape Town. As an inventory analysis was not available for Cape Town, this exercise formed an additional objective of the project, presented in Chapter 4. A spatially and temporally explicit, high resolution surface of fossil fuel emission estimates was derived from road vehicle, aviation and shipping vessel count data, population census data, and industrial fuel use statistics, making use of well-established emission factors. The city-scale inversion for Cape Town solved for weekly fluxes of CO₂ emissions on a 1 km × 1 km grid, keeping fossil fuel and biogenic emissions as separate sources. I present these results for the Cape Town inversion under the proposed best available configuration of the Bayesian inversion framework in Chapter 5. Due to the large number of CO₂ sources at this spatial and temporal resolution, the reference inversion solved for weekly fluxes in blocks of four weeks at a time. As the uncertainties around the biogenic flux estimates were large, the inversion corrected the prior fluxes predominantly through changes to the biogenic fluxes. I demonstrated the benefit of using a control vector with separate terms for fossil fuel and biogenic flux components. Sensitivity analyses, solving for average weekly fluxes within a monthly inversion, as well as solving for separate weekly fluxes (i.e. solving in one week blocks) were considered. Sensitivity analyses were performed which focused on how changes to the prior information and prior uncertainty estimates and the error correlations of the fluxes would impact on the Bayesian inversion solution. The sensitivity tests are presented in Chapter 6. These sensitivity analyses indicated that refining the estimates of biogenic fluxes and reducing their uncertainties, as well as taking advantage of spatial correlation between areas of homogeneous biota would lead to the greatest improvement in the accuracy and precision of the posterior fluxes from the Cape Town metropolitan area.

Recent advancements in inverse rendering have exhibited promising results for 3D representation, novel view synthesis, scene parameter reconstruction, and direct graphical asset generation and editing. Inverse rendering attempts to recover the scene parameters of interest from a set of camera observations by optimizing the photometric error between rendering model output and the true observation with appropriate regularization. The objective of this dissertation is to study inverse problems from several perspectives: (1) Software Framework: the general differentiable pipeline for solving physically-based or neural-based rendering problems, (2) Closed-Form: efficient and closed-form solutions in specific condition in inverse problems, (3) Representation Structure: hybrid 3D scene representation for efficient training and adaptive resource allocation, and (4) Robustness: enhanced robustness and accuracy from controlled lighting aspect. We aim to solve the following tasks: 1. How to address the challenge of rendering and optimizing scene parameters such as geometry, texture, and lighting, while considering multiple viewpoints from physically-based or neural 3D representations. To this end, we present a comprehensive software toolkit that provides support for diverse ray-based sampling and tracing schemes that enable the optimization of a wide range of targeting scene parameters. Our approach emphasizes the importance of maintaining differentiability throughout the entire pipeline to ensure efficient and effective optimization of the desired parameters. 2. Is there a 3D representation that has a fixed computational complexity or closed-form solution for forward rendering when the target has specific geometry or simplified lighting cases for better relaxing computational problems or reducing complexity. We consider multi-bounce reflection inside the plane transparent medium, and design differentiable polarization simulation engine that jointly optimize medium's parameters as well as the polarization state of reflection and transmission light. 3. How can we use our hybrid, learned 3D scene representation to solve inverse rendering problems for scene reconstruction and novel view synthesis, with a particular interest in several scientific fields, including density, radiance field, signed distance function, etc. 4. Unknown lighting condition significantly influence object appearance, to enhance the robustness of inverse rendering, we adopt invisible co-located lighting to further control lighting and suppress unknown lighting by jointly optimize separated channels of RGB and near infrared light, and enable accurate all scene parameters reconstruction from wider application environment. We also demonstrate the visually and quantitatively improved results for the aforementioned tasks and make comparisons with other state-of-the-art methods to demonstrate superior performance on representation and reconstruction tasks.

Inverse systems, inverse limit spaces, and bonding maps are defined. An investigation of the properties that an inverse limit space inherits, depending on the conditions placed on the factor spaces and bonding maps is made. Conditions necessary to ensure that the inverse limit space is compact, connected, locally connected, and semi-locally connected are examined. A mapping from one inverse system to another is defined and the nature of the function between the respective inverse limits, induced by this mapping, is investigated. Certain restrictions guarantee that the induced function is continuous, onto, monotone, periodic, or open. It is also shown that any compact metric space is the continuous image of the cantor set. Finally, any compact Hausdorff space is characterized as the inverse limit of an inverse system of polyhedra.

Convolution and, as a special case, autoconvolution of functions are important in many branches of mathematics and have found lots of applications, such as in physics, statistics, image processing and others. While it is a relatively easy task to determine the autoconvolution of a function (at least from the numerical point of view), the inverse problem, which consists in reconstructing a function from its autoconvolution is an ill-posed problem. Hence there is no possibility to solve such an inverse autoconvolution problem with a simple algebraic operation. Instead the problem has to be regularized, which means that it is replaced by a well-posed problem, which is close to the original problem in a certain sense. The outline of this thesis is as follows: In the first chapter we give an introduction to the type of inverse problems we consider, including some basic definitions and some important examples of regularization methods for these problems. At the end of the introduction we shortly present some general results about the convergence theory of Tikhonov-regularization. The second chapter is concerned with the autoconvolution of square integrable functions defined on the interval [0, 1]. This will lead us to the classical autoconvolution problems, where the term “classical” means that no kernel function is involved in the autoconvolution operator. For the data situation we distinguish two cases, namely data on [0, 1] and data on [0, 2]. We present some well-known properties of the classical autoconvolution operators. Moreover, we investigate nonlinearity conditions, which are required to show applicability of certain regularization approaches or which lead convergence rates for the Tikhonov regularization. For the inverse autoconvolution problem with data on the interval [0, 1] we show that a convergence rate cannot be shown using the standard convergence rate theory. If the data are given on the interval [0, 2], we can show a convergence rate for Tikhonov regularization if the exact solution satisfies a sparsity assumption. After these theoretical investigations we present various approaches to solve inverse autoconvolution problems. Here we focus on a discretized Lavrentiev regularization approach, for which even a convergence rate can be shown. Finally, we present numerical examples for the regularization methods we presented. In the third chapter we describe a physical measurement technique, the so-called SD-Spider, which leads to an inverse problem of autoconvolution type. The SD-Spider method is an approach to measure ultrashort laser pulses (laser pulses with time duration in the range of femtoseconds). Therefor we first present some very basic concepts of nonlinear optics and after that we describe the method in detail. Then we show how this approach, starting from the wave equation, leads to a kernel-based equation of autoconvolution type. The aim of chapter four is to investigate the equation and the corresponding problem, which we derived in chapter three. As a generalization of the classical autoconvolution we define the kernel-based autoconvolution operator and show that many properties of the classical autoconvolution operator can also be shown in this new situation. Moreover, we will consider inverse problems with kernel-based autoconvolution operator, which reflect the data situation of the physical problem. It turns out that these inverse problems may be locally well-posed, if all possible data are taken into account and they are locally ill-posed if one special part of the data is not available. Finally, we introduce reconstruction approaches for solving these inverse problems numerically and test them on real and artificial data.