Experimental Mathematics for Constitution and Computation in Complex Systems

发展了复杂系统构造与计算的实验数学方法。复杂系统是指不能用还原论的方法，即古罗马皇帝采用的“分而同”的方法进行分析，而只能通过系统的构成或过程来理解的系统。来自各个研究领域的研究者们聚集在札幌，围绕中心方法展开了广泛而深入的讨论。阐明了几种方法. 1.耦合映象格子对于寻求隐藏在微观和宏观两个层次的中间层次的普遍性是有用的.一种新型的随机理论是分析高维混沌所必需的.几何和变分的方法是有用的高维时空模式的机制.逻辑和范畴理论是研究网络系统并发过程的工具.逻辑和动力学之间的转换对于不同层次的动力学重叠的系统是有效的。面向对象的理论是为复杂系统构建适当语言的必要条件。

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.