交互空间：迈向复杂系统的通用数学理论
Interaction spaces: towards a universal mathematical theory of complex systems
AI总结：
本文提出交互空间理论的初步框架，用统一数学概念涵盖元胞自动机、智能体模型、神经网络等多种复杂系统建模方法。
摘要：
我们介绍了交互空间理论的初步步骤，这是一种关于复杂系统的通用数学理论，能够将元胞自动机、基于智能体的模型、基于主方程的模型、随机或确定性、连续或离散动力系统、网络化动力学模型、人工神经网络以及遗传算法嵌入到单一概念中。因此，交互空间代表了一种共同的数学语言，可用于描述多种复杂系统建模范式。这是开启复杂系统数学理论的第一步。每个概念都通过列举大量示例进行直观描述，并同时使用现代数学语言加以引入。
英文摘要：
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous or discrete dynamical systems, networked dynamical models, artificial neural networks and genetic algorithms in a single notion. Therefore, interaction spaces represent a common mathematical language that can be used to describe several complex systems modeling frameworks. This is the first step to start a mathematical theory of complex systems. Every notion is introduced both using an intuitive description by listing lots of examples, and using a modern mathematical language.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
