Evolving Combinatorial Structures

不断发展的组合结构

• 批准号: 1308899
• 负责人: Harry Crane
• 金额: $ 13.04万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-01 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1308899&HistoricalAwards=false
• 关键词: Evolving; Combinatorial; Structures

The project studies probability models for evolving combinatorial structures, particularly partition, tree and graph-valued stochastic processes. Specific topics to be studied include representation and characterization theorems of combinatorial Markov processes, continuum tree and interval graph scaling limits, consistent systems of partition, tree and graph-valued processes, and connections to random matrices and Levy processes. The dominant theme of the research will be the effect of probabilistic symmetries, especially exchangeability, on the structural properties of evolving large combinatorial objects, as these structural properties impact various practical aspects of these processes. As a result of this project, we should gain further understanding of models for time-varying discrete structures, especially partitions, trees and networks. Such processes arise as natural models in various disciplines, including genetics, physics, biology, computer science and statistics. In particular, understanding graph-valued processes has potentially far-reaching applications in the diverse and burgeoning field of complex networks. Effective models for real-world networks are relevant to problems in national security, public health, sociology, computer science and physical sciences. Other areas in which combinatorial models can be useful include phylogenetics, machine learning, statistics and Bayesian inference.

该项目研究演化组合结构的概率模型，特别是分区、树和图值随机过程。 要研究的具体主题包括组合马尔可夫过程的表示和表征定理、连续树和区间图缩放限制、分区一致系统、树和图值过程以及与随机矩阵和 Levy 过程的连接。 该研究的主题将是概率对称性（尤其是可交换性）对不断演化的大型组合对象的结构特性的影响，因为这些结构特性影响这些过程的各个实际方面。 通过这个项目，我们应该进一步了解时变离散结构的模型，特别是分区、树和网络。 这些过程作为自然模型出现在各个学科中，包括遗传学、物理学、生物学、计算机科学和统计学。 特别是，理解图值过程在复杂网络的多样化和新兴领域具有潜在深远的应用。 现实世界网络的有效模型与国家安全、公共卫生、社会学、计算机科学和物理科学等问题相关。组合模型有用的其他领域包括系统发育学、机器学习、统计学和贝叶斯推理。