Computing Science and Complex systems

计算科学与复杂系统

• 批准号: 02452010
• 负责人: TANAKA Syunichi
• 金额: $ 4.1万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1990
• 资助国家: 日本
• 起止时间: 1990 至 1991
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-02452010/
• 关键词: Complex Systems; Formal Methods; Axiomatic Set Theory; Concurrency; Nonstandard Analysis; 並行プロセス; 述語論理

The purpose of this project is to study possible relations between computing science and complex systems such as brain and market. As yet no secure theoretical foundation for studying these systems is available, we tried to search the one. The candidate is Formal Mathematics and Science based on the axiomatic set theory. Nonstandard Analysis is an important example in mathematics. In information and languages, Milner's Process Calculus and Barwise's Situation Theory (for natural languages) are formalized on non-well-founded set theory (developed by Aczel). These independent developments suggest the unity of various formal methods.Neural network theory is a dynamical aspects of a complex system. Infinitesimals and hyperfinite integers of nonstandard analysis may give us new perspective on large finite dynamical systems.Details of above observations are contained in the accompanying report.

该项目的目的是研究计算科学与复杂系统（如大脑和市场）之间可能的关系。到目前为止，还没有可靠的理论基础来研究这些系统，我们试图寻找一个。候选人是基于公理化集合论的形式数学与科学。非标准分析是数学中的一个重要例子。在信息和语言方面，Milner的过程演算和Barwise的情境理论（用于自然语言）是在非良好基础的集合理论（由Aczel开发）上形式化的。这些独立的发展表明了各种形式方法的统一性。神经网络理论是一个动态方面的复杂系统。非标准分析的无穷小和超有限整数为我们研究大型有限动力系统提供了新的视角。上述意见的详细情况载于所附报告。

项目成果

T. Yanagawa, Y. Kikuchi, K. G. Brown: "Statistical Issues on the Non-Observed-Adverse-Effect level in a Categorical Response" Enviromental Health Perspectives.

T. Yanakawa、Y. Kikuchi、K. G. Brown：“分类响应中未观察到的不利影响水平的统计问题”环境健康观点。

T.Yanagawa;Y.Kikuchi;K.G.Brown: "Statistical Issues on the NonーObservedーAdverseーEffect level in a Categorical Response" Environmental Health Perspectives.

T.Yanakawa；Y.Kikuchi；K.G.Brown：“分类响应中未观察到的不利影响水平的统计问题”环境健康观点。

T.Yanagawa: "Homogeneity test with a generalized MantelーHaenszel es timator for L_<2×K> contigency tables" J.Amer.Stat.Assoc.85. 744-748 (1990)

T. Yanakawa：“使用广义 Mante-Haenszel es 刺激器对 L_<2×K> 列联表进行均匀性检验”J.Amer.Stat.Assoc.85 (1990)。

M.Furukawa: "A Second-order Extension of Ljusternik's Theorem without Twice Frechet Differentiability Condition" Bull.Informatics and Cybernetics.

M.Furukawa：“没有两次 Frechet 可微性条件的 Ljusternik 定理的二阶扩展”Bull.Informatics and Cyber​​netics。

M.Nakao: "Solving nonlinear parabolic problems with result verification I" Journal of Comutational and Applied Mathematics. 38. 323-334 (1991)

M.Nakao：“通过结果验证解决非线性抛物线问题 I”《计算与应用数学杂志》。