京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20893号 / 理博第4345号 / 新制||理||1624(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 篠本 滋, 教授 佐々 真一, 教授 川上 則雄 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

In a network, the components of a given system are represented as nodes, the interactions are abstracted as links between the nodes. Boolean networks refer to a class of dynamics on networks, in fact it is the simplest possible dynamics where each node has a value 0 or 1. This allows to investigate extensively the dynamics both analytically and by numerical experiments. The present article focuses on the theoretical concept of relevant components and their immediate application in plant biology. References for more in-depth treatment of the mathematical details are also given.

Moore and Shannon's reliability polynomial can be used as a global statistic to explore the behavior of diffusive processes on a graph dynamical system representing a finite sized interacting system. It depends on both the network topology and the dynamics of the process and gives the probability that the system has a particular desired property. Due to the complexity involved in evaluating the exact network reliability, the problem has been classified as a NP-hard problem. The estimation of the reliability polynomials for large graphs is feasible using Monte Carlo simulations. However, the number of samples required for an accurate estimate increases with system size. Instead, an adaptive method using Bernstein polynomials as kernel density estimators proves useful. Network reliability has a wide range of applications ranging from epidemiology to statistical physics, depending on the description of the functionality. For example, it serves as a measure to study the sensitivity of the outbreak of an infectious disease on a network to the structure of the network. It can also be used to identify important dynamics-induced contagion clusters in international food trade networks. Further, it is analogous to the partition function of the Ising model which provides insights to the interpolation between the low and high temperature limits. / Ph. D. / The research presented here explores the effects of the structural properties of an interacting system on the outcomes of a diffusive process using Moore-Shannon network reliability. The network reliability is a finite degree polynomial which provides the probability of observing a certain configuration for a diffusive process on networks. Examples of such processes analyzed here are outbreak of an epidemic in a population, spread of an invasive species through international trade of commodities and spread of a perturbation in a physical system with discrete magnetic spins. Network reliability is a novel tool which can be used to compare the efficiency of network models with the observed data, to find important components of the system as well as to estimate the functions of thermodynamic state variables.