BIOCOMPLEXITY--INCUBATION ACTIVITY: The Mathematics of Network Dynamics in Biological, Social, and Economic Systems

LaubenbacherDMS-0083595摘要：这个生物复杂性孵化活动提案将通过应用代数组合学的新技术以及数理逻辑和统计物理学的方法来研究生态系统的涌现特性。 基于这些方法，我们将开发一个完整的概念框架来分析物种之间的连接结构及其约束所产生的全局属性。 在这个框架内，研究人员将通过采用一套正式的数学/组合工具来分析特定的生态系统。 为了实现这些目标，该项目包括以下活动：项目人员和来访者定期举行会议，以合作和建立一个共同的知识库;为期四天的关于"生物、社会和经济系统中网络动态的数学"的国际研讨会;以及特定系统的模拟和分析。这些模拟的结果将用于改进我们的理论方法。

LaubenbacherDMS-0083595Abstract:This Biocomplexity incubation activity proposal will study the emergent properties of ecological systems by applying new techniques from algebraic combinatorics, as well as methods from mathematical logic and statistical physics. Based on these methods, we will develop an integrated conceptual framework to analyze global properties arising from the connectivity structure among species and their constraints. Within this framework, the researchers will analyze specific ecosystems, by employing a set of formal mathematical/combinatorial tools. To accomplish these goals the project includes the following activities: regular meetings of project personnel and visitors to collaborate and create a common knowledge base; a four-day international workshop hall on "The mathematics of network dynamics in biological, social, and economic systems;" and simulation and analysis of specific systems. The results of these simulations will be used to refine our theoretical approach.