DIMACS/Georgia Tech Special Focus on Discrete Random Systems

在过去的十年里，离散数学、理论计算机科学、概率理论和统计物理之间存在着巨大的相互作用。这个项目聚集了来自不同领域的研究人员，探索他们界面上的主题，这个领域被称为离散随机系统。重点是物理系统和组合结构研究中出现的概率算法和模型，主要主题贯穿于这些交互作用中，包括：相变；概率组合学；马尔可夫链蒙特卡罗和其他随机游动；随机结构和随机化算法。一系列的研讨会将讨论大型图的性质，复杂网络和应用，马尔可夫链抽样(理论与实践)，以及随机结构中的相变。研究人员的重点工作组将专注于马尔可夫链和相变之间的界面，启发式和严格的方法来识别和分析算法中的相变。离散随机系统是一个相对较新的领域，十年前在DIMACS中心和高级研究所举行的一系列跨学科研讨会中固化了这个领域。从那时起，它已经相当成熟，一方面是离散数学家和理论计算机科学家与另一方面是概率学家和统计物理学家之间真正的双边交流，从根本上影响了所有这些领域的研究方向和理解。该领域探索在组合学和理论计算机科学领域中出现的物理系统和数学结构的研究中出现的算法和模型，重点是类似的行为，如相移。目前的项目力求促进和加快这一跨学科领域的发展，使其协调一致，并促进科学的快速发展。该项目将围绕一系列研讨会、教程、研究工作组和访客计划进行组织，所有这些都旨在促进新的互动。研讨会允许来自不同学科的思想和技术的交叉滋养。不太正式的研究人员小组将聚集在一起，就专业主题进行集中的合作研究，在项目期间将形成更多的工作组。离散随机系统的新应用领域的探索将通过在生物学、流行病学、社会科学和国土安全方面的并行DIMACS计划而得到加强。在这个项目中形成的想法将对无数领域产生影响，并建立许多新的跨学科联系。访客计划将鼓励资深和初级研究人员，包括学生，参与由研讨会产生的合作研究和工作组的工作。每个工作坊将有一个研究生支持基金，博士后和工作坊将有一个通过重要的教程组成部分的实体教育部分。这一主题很适合本科生的研究，参与的教职员工将与已经存在的本科生研究计划(REU计划)协调主题。预计该项目的长期影响将远远超过其两年的持续时间，因为该项目的研讨会、工作组、参观者和传播部分将使所形成的想法接触到全国和世界各地的数百人。该项目将对一大批杰出的初级研究人员的职业生涯产生重大影响，并将在培养和发展准备好成为离散随机系统领域领导者的科学家方面发挥重要作用。

During the past decade there has been tremendous interplay amongdiscrete mathematics, theoretical computer science, probabilitytheory, and statistical physics. This project brings togetherresearchers from these various fields to explore topics at theirinterface, the field coming to be called Discrete Random Systems.The focus is on probabilistic algorithms and models that arise inthe study of physical systems and combinatorial structures, with strongthemes running through these interactions including: phase transitions;probabilistic combinatorics; Markov-Chain Monte Carlo and otherrandom walks; and random structures and randomized algorithms.A series of workshops will address properties of large graphs, complexnetworks and applications, Markov chain sampling (theory vs. practice),and phase transitions in random structures. Focused working groups ofresearchers will concentrate on the interface between Markov chainsand phase transitions, on heuristic and rigorous approaches to identifyingand analyzing phase transitions in algorithms.Discrete Random Systems is a relatively new field that solidifiedduring an interdisciplinary series of workshops held at the DIMACSCenter and the Institute for Advanced Study ten years ago. Since thenit has matured considerably, and the truly bilateral exchange betweendiscrete mathematicians and theoretical computer scientists on the onehand, and probabilists and statistical physicists on the other, hasradically impacted research directions and understanding in all ofthese fields. The field explores algorithms and models that arise inboth the study of physical systems and the mathematical structuresarising from the fields of combinatorics and theoretical computerscience, with an emphasis on analogous behavior such as phasetransitions. The current project seeks to foster and speed thedevelopment of this interdisciplinary field and to bring to itcoherence as well as rapid scientific development. The project willbe organized around a series of workshops, tutorials, research workinggroups, and a visitor program, all intended to facilitate newinteractions. Workshops allow a cross-fertilization of ideas andtechniques from the disparate disciplines. Less formal groups ofresearchers will convene for concentrated collaborative research onspecialized topics, and additional working groups will evolve duringthe project. Exploration of new areas of application of Discrete RandomSystems will be enhanced by parallel DIMACS programs in Biology,Epidemiology, the Social Sciences, and Homeland Security. The ideasdeveloped in this project will have impact on a myriad of fields andcreate many new cross-disciplinary connections. A visitor program willencourage senior and junior researchers, including students, toparticipate in collaborative research spawned by the workshops and inthe work of the working groups. Each workshop will have a fund forsupport of graduate students and postdocs and workshops will have asubstantial educational component through significant tutorialcomponents. The topic lends itself well to undergraduate research andparticipating faculty will coordinate topics with an undergraduateresearch program (REU program) already in existence. The project isexpected to have a long-term impact well beyond its two year durationsince the workshop, working group, visitor, and disseminationcomponents of the project will allow the ideas developed to reachhundreds of people nationwide and worldwide. The project shouldsignificantly influence the careers of a large number of outstandingjunior researchers and it should play an important role in thetraining and development of scientists who are well-prepared to becomeleaders in the field of Discrete Random Systems.