The Vagus nerve has shown to play an important role regarding inflammatory diseases, regulating the production of proteins that mediate inflammation. Two important such proteins are the pro-inflammatory cytokines, TNF and IL-1β. This thesis makes use of Vagus nerve recordings, where TNF and IL-1β are subsequently injected in mice, with the aim to see if cytokine-specific information can be extracted. To this end, a type of semi-supervised learning approach is applied, where the observed waveform-data are modeled using a conditional probability distribution. The conditioning is done based on an estimate of how often each observed waveform occurs and local maxima of the conditional distribution are interpreted as candidate-waveforms to encode cytokine information. The methodology yields varying, but promising results. The occurrence of several candidate waveforms are found to increase substantially after exposure to cytokine. Difficulties obtaining coherent results are discussed, as well as different approaches for future work. / Vagusnerven har visat sig spela en viktig roll beträffande inflammatoriska sjukdomar. Denna nerv reglerar produktionen av inflammatoriska protein, som de inflammationsfrämjande cytokinerna TNF och IL-1β. Detta arbete använder sig av elektroniska mätningar av Vagusnerven i möss som under tiden blir injicerade med de två cytokinerna TNF och IL-1β. Syftet med arbetet är att undersöka om det är möjligt att extrahera information om de specifika cytokinerna från Vagusnervmätningarna. För att uppnå detta designar vi en semi-vägledd lärandemetod som modellerar dem observerade vågformerna med en betingad sannolikhetsfunktion. Betingandet baseras på en uppskattning av hur ofta varje enskild vågform förekommer och lokala maximum av den betingade sannolikhetsfunktionen tolkas som möjliga kandidat-vågformer att innehålla cytokin-information. Metodiken ger varierande, men lovande resultat. Förekomsten av flertalet kandidat-vågformer har en tydlig ökning efter tidpunkten för cytokin-injektion. Vidare så diskuteras svårigheter i att uppnå konsekventa resultat för alla mätningar, samt olika möjligheter för framtida arbete inom området.

This dissertation addresses the problem of adaptive image filtering. Although the topic has a long history in the image processing community, researchers continuously present novel methods to obtain ever better image restoration results. With an expanding market for individuals who wish to share their everyday life on social media, imaging techniques such as compact cameras and smart phones are important factors. Naturally, every producer of imaging equipment desires to exploit cheap camera components while supplying high quality images. One step in this pipeline is to use sophisticated imaging software including, e.g., noise reduction to reduce manufacturing costs, while maintaining image quality. This thesis is based on traditional formulations such as isotropic and tensor-based anisotropic diffusion for image denoising. The difference from main-stream denoising methods is that this thesis explores the effects of introducing contextual information as prior knowledge for image denoising into the filtering schemes. To achieve this, the adaptive filtering theory is formulated from an energy minimization standpoint. The core contributions of this work is the introduction of a novel tensor-based functional which unifies and generalises standard diffusion methods. Additionally, the explicit Euler-Lagrange equation is derived which, if solved, yield the stationary point for the minimization problem. Several aspects of the functional are presented in detail which include, but are not limited to, tensor symmetry constraints and convexity. Also, the classical problem of finding a variational formulation to a given tensor-based partial differential equation is studied. The presented framework is applied in problem formulation that includes non-linear domain transformation, e.g., visualization of medical images. Additionally, the framework is also used to exploit locally estimated probability density functions or the channel representation to drive the filtering process. Furthermore, one of the first truly tensor-based formulations of total variation is presented. The key to the formulation is the gradient energy tensor, which does not require spatial regularization of its tensor components. It is shown empirically in several computer vision applications, such as corner detection and optical flow, that the gradient energy tensor is a viable replacement for the commonly used structure tensor. Moreover, the gradient energy tensor is used in the traditional tensor-based anisotropic diffusion scheme. This approach results in significant improvements in computational speed when the scheme is implemented on a graphical processing unit compared to using the commonly used structure tensor. / VIDI / NACIP / GARNICS / EMC^2

Recently there has been a surge in interest in coupling ensemble-based data assimilation methods with variational methods (commonly referred to as 4DVar). Here we discuss a number of important differences between ensemble-based and variational methods that ought to be considered when attempting to fuse these methods. We note that the Best Linear Unbiased Estimate (BLUE) of the posterior mean over a data assimilation window can only be delivered by data assimilation schemes that utilise the 4-dimensional (4D) forecast covariance of a prior distribution of non-linear forecasts across the data assimilation window. An ensemble Kalman smoother (EnKS) may be viewed as a BLUE approximating data assimilation scheme. In contrast, we use the dual form of 4DVar to show that the most likely non-linear trajectory corresponding to the posterior mode across a data assimilation window can only be delivered by data assimilation schemes that create counterparts of the 4D prior forecast covariance using a tangent linear model. Since 4DVar schemes have the required structural framework to identify posterior modes, in contrast to the EnKS, they may be viewed as mode approximating data assimilation schemes. Hence, when aspects of the EnKS and 4DVar data assimilation schemes are blended together in a hybrid, one would like to be able to understand how such changes would affect the mode-or mean-finding abilities of the data assimilation schemes. This article helps build such understanding using a series of simple examples. We argue that this understanding has important implications to both the interpretation of the hybrid state estimates and to their design.

This dissertation presents results for two separate problems, both in the context of variational fracture models. The first problem involved developing and analyzing models of fracture in which we modeled the energy dissipated by crack growth as concentrated on the front of the crack. While many engineering models of fracture are based on a notion of crack front, there had not been a rigorous definition. We present the first work in this area, which includes a natural weak definition of crack front and front speed, a model of fracture whose evolution is described at the crack front, and a relaxation result that shows that these front based dissipations are all effectively equivalent to a Griffith-type dissipation. The second problem involved the computation of stationary points for Mumford-Shah and fracture using a level set method. Our method improves on existing techniques in that it can handle tips in the singular set and can find minimizers that previous techniques are unable to resolve.

Li Guo-Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 105-107). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Examples for the variational inequality problem --- p.2 / Chapter 1.2 --- Approaches for variational inequality problem --- p.7 / Chapter 1.3 --- Error bounds results for variational inequality problem --- p.8 / Chapter 1.4 --- Organization --- p.9 / Chapter 2 --- Solution Theory --- p.11 / Chapter 2.1 --- "Elementary Convex Analysis, Nonsmooth Analysis and Degree theory" --- p.11 / Chapter 2.1.1 --- Elementary Convex Analysis --- p.11 / Chapter 2.1.2 --- Elementary Nonsmooth Analysis --- p.16 / Chapter 2.1.3 --- Degree Theory --- p.18 / Chapter 2.2 --- Existence and Uniqueness Theory --- p.24 / Chapter 3 --- Merit Functions for variational inequalities problem --- p.36 / Chapter 3.1 --- Regularized gap function --- p.38 / Chapter 3.2 --- D-gap function --- p.44 / Chapter 3.3 --- Generalized Regularize gap function and Generalized D-gap function --- p.61 / Chapter 4 --- Error bound results for the merit functions --- p.74 / Chapter 4.1 --- Error bound results for Regularized gap function --- p.77 / Chapter 4.2 --- Error bound results for D-gap function --- p.78 / Chapter 4.3 --- Error bound results for Generalized Regularized gap function --- p.92 / Chapter 4.4 --- Error bound results for Generalized D-gap function --- p.93 / Bibliography --- p.105

During the past two decades, numerous recurrent neural networks (RNNs) have been proposed for solving VIs and related problems. However, first, the theories of many emerging RNNs have not been well founded yet; and their capabilities have been underestimated. Second, these RNNs have limitations in handling some types of problems. Third, it is certainly not true that these RNNs are best choices for solving all problems, and new network models with more favorable characteristics could be devised for solving specific problems. / In the research, the above issues are extensively explored from dynamic system perspective, which leads to the following major contributions. On one hand, many new capabilities of some existing RNNs have been revealed for solving VIs and related problems. On the other hand, several new RNNs have been invented for solving some types of these problems. The contributions are established on the following facts. First, two existing RNNs, called TLPNN and PNN, are found to be capable of solving pseudomonotone VIs and related problems with simple bound constraints. Second, many more stability results are revealed for an existing RNN, called GPNN, for solving GVIs with simple bound constraints, and it is then extended to solve linear VIs (LVIs) and generalized linear VIs (GLVIs) with polyhedron constraints. Third, a new RNN, called IDNN, is proposed for solving a special class of quadratic programming problems which features lower structural complexity compared with existing RNNs. Fourth, some local convergence results of an existing RNN, called EPNN, for nonconvex optimization are obtained, and two variants of the network by incorporating two augmented Lagrangian function techniques are proposed for seeking Karush-Kuhn-Tucker (KKT) points, especially local optima, of the problems. / Variational inequality (VI) can be viewed as a natural framework for unifying the treatment of equilibrium problems, and hence has applications across many disciplines. In addition, many typical problems are closely related to VI, including general VI (GVI), complementarity problem (CP), generalized CP (GCP) and optimization problem (OP). / Hu, Xiaolin. / "July 2007." / Adviser: Jun Wang. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1102. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 193-207). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

Thesis (Ph. D.)--Oregon State University, 2002. / Printout. Includes bibliographical references (leaves 58-61). Also available on the World Wide Web.

In this thesis, a pursuit-evasion game, in which the pursuer moves with simple motion whereas the evader moves at a fixed speed but with a curvature constraint, is investigated. The game is the inverse of the usual homicidal chauffeur game. Square of the distance between the pursuer and the evader when the game is terminated is selected as the cost function. To solve such a zero-sum game, the variational approach will be employed to solve the problem. An algorithm will be proposed to determine a saddle point and the value of the game under consideration

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

The research described in this dissertation concerns two fields of theoretical chemistry: Part I concerns applications of Density Functional Theory, and part II high accuracy calculations within the Born-Oppenheimer approximation using explicitly correlated Gaussian functions.In the first part, after a brief introduction to Density Functional Theory and Hartree Fock methods, the candidate's research in Density Functional Theory is described in two chapters. One treats the charge transport in B-DNA, specifically (GC)$_N$ oligomers solvated by water. The second chapter treats the charge transfer between the Lithium atom and Fullerene-C$_{60}$ in the endohedral complex Li@C$_{60}$. In both applications Density Functional Theory was the central quantum mechanical technique that allowed the approaching of such large molecular systems.In the second part of this dissertation, the candidate's development of a FORTRAN code using explicitly correlated Gaussian functions within the Born-Oppenheimer approximation is presented.Every item of the author's research during his graduate studies has been published in co-authorship with the author's scientific advisor and other collaborators in peer-reviewed journals. A total of 8 scientific articles and one letter have been published by the author while at The University of Arizona.