Dissipative spots are found in physical experiments of many branches of natural science. In this thesis we use three-component reaction-diffusion systems on two-dimensional domains in order to generate these patterns. Using a dynamical system approach we proceed with a Fourier analysis on a linearized reaction-diffusion system in order to provide the bifurcation conditions for a given homogeneous state. We validate our results and establish it's limitations through numerical experiments. We report very interesting behavior during these simulations, notably hysteresis and multi-stability. We will then turn our attention to the relatively unexplored phenomenon of rotating spots. Based on previous work done for spiral waves, we investigate the effect of translational symmetry-breaking on a rotating spot mainly through careful numerical analysis.

Managing large-scale dynamical systems (e.g., transportation systems, complex information systems, and power networks, etc.) in real-time is very challenging considering their complicated system dynamics, intricate network interactions, large scale, and especially the existence of various uncertainties. To address this issue, intelligent techniques which can quickly design decision-making strategies that are robust to uncertainties are needed. This dissertation aims to conquer these challenges by exploring a data-driven decision-making framework, which leverages big-data techniques and scalable uncertainty evaluation approaches to quickly solve optimal control problems. In particular, following techniques have been developed along this direction: 1) system modeling approaches to simplify the system analysis and design procedures for multiple applications; 2) effective simulation and analytical based approaches to efficiently evaluate system performance and design control strategies under uncertainty; and 3) big-data techniques that allow some computations of control strategies to be completed offline. These techniques and tools for analysis, design and control contribute to a wide range of applications including air traffic flow management, complex information systems, and airborne networks.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第22842号 / 工博第4782号 / 新制||工||1748(附属図書館) / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 引原 隆士, 教授 土居 伸二, 教授 木本 恒暢 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The thesis deals with physical and numerical modelling of downsized model of chimney and its demolition. The properties of downsized physical model, which is made of wooden cubes, are being researched and experimentally tested. The physical experiments are then designed using software FyDiK. Numerical Model is simplified to 2D problem, whereas the problem includes dynamic effects. Conformity of designed software model and physical experiment is tested. The aim of this thesis is to achive the best possible conformity of physical and numerical models.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18040号 / 理博第3918号 / 新制||理||1566(附属図書館) / 30898 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 國府 寛司, 教授 加藤 毅, 准教授 浅岡 正幸 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24737号 / 情博第825号 / 新制||情||138(附属図書館) / 京都大学大学院情報学研究科先端数理科学専攻 / (主査)教授 青柳 富誌生, 教授 田口 智清, 准教授 寺前 順之介 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Persistence problem of compact invariant manifold under random perturbation is considered in this dissertation. Under uniformly small random perturbation and the condition of normal hyperbolicity, the original invariant manifold persists and becomes a random invariant manifold. The random counterpart has random local stable and unstable manifolds. They could be invariantly foliated thanks to the normal hyperbolicity. Those underlie an extension of the geometric singular perturbation theory to the random case which means the slow manifold persists and becomes a random manifold so that the local global structure near the slow manifold persists under singular perturbation. A normal form for a random differential equation is obtained and this helps to prove a random version of the exchange lemma.

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Systems biology is an interdisciplinary field that focuses on elucidating complex biological processes (systems) by investigating the interactions among its components through an iterative cycle composed of data generation, data analysis and mathematical modeling. Our contributions to systems biology revolve around the following two axes: - Data analysis: Two data analysis projects, which were initiated when I was a co-op at GlaxoSmithKline, are discussed in this thesis. First, next generation sequencing data generated for a phase I clinical trial is analyzed to determine the altered microbial community in human gut before and after antibiotic usage (Chapter 2). To our knowledge, there have not been similar comparative studies in humans on the impacts on the gut microbiome of an antibiotic when administered by different modes. Second, publicly available gene expression data is analyzed to investigate human immune response to tuberculosis (TB) infection (Chapter 3). The novel feature of this study is systematic drug repositioning for the prevention, control and treatment of TB using the Connectivity map. - Mathematical modeling: Polynomial dynamical systems, a state- and time- discrete logical modeling framework, is used to model two biological processes. First, a denitrification pathway in Pseudomonas aeruginosa is modeled to shed light on the reason of greenhouse gas nitrous oxide accumulation (Chapter 4). It is the first mathematical model of denitrification that can predict the effect of phosphate on the denitrification performance of this bacterium. Second, an iron homeostasis pathway linked to iron utilization, oxidative stress response and oncogenic pathways is constructed to investigate how normal breast cells become cancerous (Chapter 5). To date, our intracellular model is the only expanded core iron model that can capture a breast cancer phenotype by overexpression and knockout simulations. / Ph. D.

Linking the structure of a system with its dynamics is an important problem in the theory of finite dynamical systems. For monomial dynamical systems, that is, a system that can be described by monomials, information about the limit cycles can be obtained from the monomials themselves. In particular, this work contains sufficient and necessary conditions for a monomial dynamical system to have only fixed points as limit cycles. / Ph. D.