Experimental Mathematics for Constitution and Computation in Complex Systems

发展了复杂系统组成和计算的实验数学方法。复杂系统被定义为不能用简化论者的方法来分析的系统，即古罗马皇帝采用的一种“分而治之”的方法，而是很容易通过这种系统的构成或其过程来理解的。来自不同研究领域的许多研究人员齐聚札幌，深入而广泛地讨论了什么是中心方法。阐明了几种方法。耦合映象格子对于寻求中间水平的普适性是有用的，这是隐藏在微观和宏观水平上的。分析高维混沌需要一种新型的随机理论。几何和变分方法对于高维时空图样的机制是有用的。逻辑范畴理论是网络系统并发处理的工具。对于不同级别的动力学干扰的系统，逻辑和动力学之间的转换是有效的。面向观察者的理论对于为复杂系统构建适当的语言是必不可少的。

Experimental mathematics method for constitution and computation in complex systems were developed. Complex systems are defined as systems which cannot be analyzed by reductionist's method, that is, a method of "divide-and-concur" that ancient Roman emperors adopted, but rather be easily understood via constitution or its process of such systems.Many researchers from various kinds of research fields gathered together in Sapporo, and discussed intensively and extensively what a central method should be. Several methods were clarified.1. Coupled map lattices are useful for the purpose of seeking a universality at intermediate levles which is hidden at both microscopic and macroscopic levels.2. A new type of stochastic theory is necessary for analysing a high dimensional chaos.3. A geometric and variational method is useful for a mechanism of high-dimensional spatio-temporal patterns.4. Logics and category theory is a tool for concurrent process of network systems.5. A transformation between logics and dynamics is effective for a system where a different levels of dynamics interfere.6. An observer-oriented theory is essential for constructing an adequate language for complex systems.