Thesis (doctoral)--Justus Liebig-Universität Giessen, 2005. / "Teil 1 der Arbeit mit dem Literaturverzeichnis ist in Heft 255 erschienen."

Dissertation (Ph.D.)--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references.

This dissertation proposes a family of algorithms for deriving signatures of mutually associated features, to which we refer as attractor metafeatures, or simply attractors. Specifically, we present multi-cancer attractor derivation algorithms, identifying correlated features in signatures from multiple biological data sets in one analysis, as well as the groups of samples or cells that exclusively express these signatures. Our results demonstrate that these signatures can be used, in proper combinations, as biomarkers that predict a patient’s survival rate, based on the transcriptome of the tumor sample. They can also be used as features to analyze the composition of the tumor. Through analyzing large data sets of 18 cancer types and three high-throughput platforms from The Cancer Genome Atlas (TCGA) PanCanAtlas Project and multiple single-cell RNA-seq data sets, we identified novel cancer attractor signatures and elucidated the identity of the cells that express these signatures. Using these signatures, we developed a prognostic biomarker for breast cancer called the Breast Cancer Attractor Metagenes (BCAM) biomarker as well as a software platform to analyze the tumor sample, called Analysis of the Single-Cell Omics for Tumor (ASCOT).

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, 2016 / An investigation and analysis of a collection of different techniques, for estimating the states of nonlinear systems, was undertaken. It was found that most of the existing literature on the topic could be organized into several groups of nonlinear observer design techniques, of which each group follows a specific concept and slight variations thereof. From out of this investigation it was discovered that a variation of the adaptive observer could be successfully applied to numerous nonlinear systems, given only limited output information. This particular technique formed the foundation on which a design procedure was developed in order to asymptotically estimate the states of nonlinear systems of a certain form, using only partial state information available. Lyapunov stability theory was used to prove the validity of this technique, given that certain conditions and assumptions are satisfied. A heuristic procedure was then developed to get a linearized model of the error transient behaviour that could form the upper bounds of the transient times of the observer. The technique above, characterized by a design algorithm, was then applied to three well-known nonlinear systems; namely the Lorenz attractor, the Rössler attractor, and the Van Der Pol oscillator. The results, illustrated through numerical simulation, clearly indicate that the technique developed is successful, provided all assumptions and conditions are satisfied. / MT2017

A geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to show that for suitable parameters the flow contains a strange attractor. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

In this work, we develop an extension of the generalized Fourier transform for exterior domains due to T. Ikebe and A. Ramm for all dimensions n>2 to study the Laplacian, and fractional Laplacian operators in such a domain. Using the harmonic extension approach due to L. Caffarelli and L. Silvestre, we can obtain a localized version of the operator, so that it is precisely the square root of the Laplacian as a self-adjoint operator in L2 with DIrichlet boundary conditions. In turn, this allowed us to obtain a maximum principle for solutions of the dissipative two-dimensional quasi-geostrophic equation the exterior domain, which we apply to prove decay results using an adaptation of the Fourier Splitting method of M.E. Schonbek. / by Leonardo Kosloff. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

This dissertation can be essentially divided into two parts. The first, consisting of Chapters I, II, and III, studies the graph theoretic nature of complex systems. This includes the spectral properties of such systems and in particular their influence on the systems dynamics. In the second part of this dissertation, or Chapter IV, we consider a new class of one-dimensional dynamical systems or functions with an eventual negative Schwarzian derivative motivated by some maps arising in neuroscience. To aid in understanding the interplay between the graph structure of a network and its dynamics we first introduce the concept of an isospectral graph reduction in Chapter I. Mathematically, an isospectral graph transformation is a graph operation (equivalently matrix operation) that modifies the structure of a graph while preserving the eigenvalues of the graphs weighted adjacency matrix. Because of their properties such reductions can be used to study graphs (networks) modulo any specific graph structure e.g. cycles of length n, cliques of size k, nodes of minimal/maximal degree, centrality, betweenness, etc. The theory of isospectral graph reductions has also lead to improvements in the general theory of eigenvalue approximation. Specifically, such reductions can be used to improved the classical eigenvalue estimates of Gershgorin, Brauer, Brualdi, and Varga for a complex valued matrix. The details of these specific results are found in Chapter II. The theory of isospectral graph transformations is then used in Chapter III to study time-delayed dynamical systems and develop the notion of a dynamical network expansion and reduction which can be used to determine whether a network of interacting dynamical systems has a unique global attractor. In Chapter IV we consider one-dimensional dynamical systems of an interval. In the study of such systems it is often assumed that the functions involved have a negative Schwarzian derivative. Here we consider a generalization of this condition. Specifically, we consider the functions which have some iterate with a negative Schwarzian derivative and show that many known results generalize to this larger class of functions. This includes both systems with regular as well as chaotic dynamic properties.

Thesis (Ph. D.)--University of Notre Dame, 2006. / Thesis directed by Steven M. Boker for the Department of Psychology. "December 2006." Includes bibliographical references (leaves 99-102).

Thesis (Honors)--College of William and Mary, 2009. / Includes bibliographical references (leaves 56-57). Also available via the World Wide Web.

Made available in DSpace on 2014-11-10T11:09:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-08-02Bitstream added on 2014-11-10T11:57:46Z : No. of bitstreams: 1 000788290.pdf: 1350300 bytes, checksum: efc63ae2b101504d42d2745bc5a4a3c9 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho estudaremos a aproximaçãoo de equações diferenciais parabólicas semilineares através de sua discretização via o método de elementos finitos. Vamos provar que os atratores da discretizaçãoao se comportam continuamente quando o tamanho do passo tende a zero estendendo os resultados de [17]. Vamos também calcular a taxa de convergência dos atratores em termos do passo da discretização / In this work we study the approximation of semilinear parabolic di erential equations through their discretization via the nite element method. We prove that the attractors of discretization behave continuously when the step size tends to zero extending the results of [17]. We also calculate the rate of convergence of attractors in terms of step of discretization