EAGER: Computational Models, Topological Games, and Classical Information
EAGER:计算模型、拓扑博弈和经典信息
基本信息
- 批准号:1258595
- 负责人:
- 金额:$ 29.24万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2012
- 资助国家:美国
- 起止时间:2012-10-01 至 2015-09-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Modern computer systems are too complex to be analyzed directly, and often mathematical models are employed to analyze such computer systems to understand how well they function and whether they operate correctly. The area of computational models is devoted to constructing such models, and to their application to solve problems in computing, such as specifying computational devices designed to solve specific problems. Quite distinct from this, the area of Diophantine approximation from number theory studies how well real numbers can be approximated by rational numbers - ones that can be expressed a quotient of two integers. Despite dating back to the time of Diophantus of Alexandria, there are many deep questions here that remain unsolved. Finally, the study of classical communication channels forms the basis for the area of classical information theory that plays a fundamental role in many aspects of everyday life. This project will explore relationships between emerging techniques for building computational models, and research in classical information and in Diophantine approximation. These represent very diverse areas of mathematics, computer science and information theory, and a goal of the project is to develop links between them that reveal common underlying principles that can be applied to solve problems in each area. Such principles will lead to methods that can be used from one area to solve problems in the other areas. The proposed work spans a number of research areas: domain theory and computational models; topological games; classical information and families of classical channels; analysis of complex systems; and applications to Schmidt games and Diophantine approximation. Recent results on channel capacity that underpin the work are based on a topological view of channels and their capacity that offers a unique way to analyze related families of channels. The proposed analysis of existing approaches to constructing domain models of spaces - the co-algebraic approach as opposed to one based on Choquet games - will explore the relationship between these approaches, and will provide insights into their applicability to new and interesting problems in the range of areas listed above. Using domain-theoretic approaches to analyze Schmidt games is a novel idea that should prove useful in understanding these games and how they differ from ones such as Choquet games.
现代计算机系统过于复杂,无法直接分析,通常采用数学模型来分析这些计算机系统,以了解它们的功能以及它们是否正确运行。计算模型领域致力于构建这样的模型,并将其应用于解决计算中的问题,例如指定设计用于解决特定问题的计算设备。与此截然不同的是,数论中的丢番图逼近领域研究了如何用有理数来逼近真实的数--有理数可以表示为两个整数的商。尽管可以追溯到亚历山大的丢番图时代,但这里仍有许多深层次的问题尚未解决。最后,经典通信渠道的研究形成了经典信息理论领域的基础,在日常生活的许多方面发挥着根本性的作用。这个项目将探讨新兴技术之间的关系,建立计算模型,并在经典信息和丢番图近似研究。这些代表了数学,计算机科学和信息理论的不同领域,该项目的目标是在它们之间建立联系,揭示可用于解决每个领域问题的共同基本原则。这些原则将导致可以从一个领域使用的方法来解决其他领域的问题。拟议的工作跨越了一些研究领域:域理论和计算模型;拓扑游戏;经典信息和家庭的经典渠道;复杂系统的分析;和应用程序的施密特游戏和丢番图逼近。最近的结果通道容量的基础上的工作是基于通道和他们的能力,提供了一种独特的方式来分析相关的家庭通道的拓扑视图。建议的分析现有的方法来构建域模型的空间-共代数的方法,而不是一个基于Choquet游戏-将探讨这些方法之间的关系,并将提供深入了解其适用于新的和有趣的问题,在上述领域的范围内列出。使用域理论的方法来分析施密特游戏是一个新的想法,应该证明有助于理解这些游戏,以及它们与Choquet游戏的区别。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Michael Mislove其他文献
Erratum to: Articles by A.H. Clifford
- DOI:
10.1007/s00233-013-9494-7 - 发表时间:
2013-06-06 - 期刊:
- 影响因子:0.700
- 作者:
Michael Mislove - 通讯作者:
Michael Mislove
Dimension raising maps in topological algebra
- DOI:
10.1007/bf01214302 - 发表时间:
1973-03-01 - 期刊:
- 影响因子:1.000
- 作者:
Karl Heinrich Hofmann;Michael Mislove;Albert Stralka - 通讯作者:
Albert Stralka
Semilattices which must contain a copy of 2n
- DOI:
10.1007/bf02575524 - 发表时间:
1985-12-01 - 期刊:
- 影响因子:0.700
- 作者:
Jimmie D. Lawson;Michael Mislove - 通讯作者:
Michael Mislove
Amalgamation in categories with concrete duals
- DOI:
10.1007/bf02485840 - 发表时间:
1976-12-01 - 期刊:
- 影响因子:0.600
- 作者:
Karl Heinrich Hofmann;Michael Mislove - 通讯作者:
Michael Mislove
The centralizing theorem for left normal groups of units in compact monoids
- DOI:
10.1007/bf02572939 - 发表时间:
1971-12-01 - 期刊:
- 影响因子:0.700
- 作者:
Karl Heinrich Hofmann;Michael Mislove - 通讯作者:
Michael Mislove
Michael Mislove的其他文献
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{{ truncateString('Michael Mislove', 18)}}的其他基金
Collaborative Research: A Coalgebraic Framework for Development and Composition of Hybrid Systems
协作研究:混合系统开发和组合的代数框架
- 批准号:
0208743 - 财政年份:2002
- 资助金额:
$ 29.24万 - 项目类别:
Continuing Grant
Support for Mathematical Foundations of Programming Semantics Special Session on Hybrid Systems
支持混合系统编程语义特别会议的数学基础
- 批准号:
0211217 - 财政年份:2002
- 资助金额:
$ 29.24万 - 项目类别:
Standard Grant
Probabilistic Analysis of Hybrid Systems
混合系统的概率分析
- 批准号:
0130550 - 财政年份:2001
- 资助金额:
$ 29.24万 - 项目类别:
Standard Grant
US-Brazil Workshop on Formal Foundations of Software Systems: Tulane University, New Orleans, LA, November 1997
美国-巴西软件系统形式基础研讨会:杜兰大学,路易斯安那州新奥尔良,1997 年 11 月
- 批准号:
9727866 - 财政年份:1997
- 资助金额:
$ 29.24万 - 项目类别:
Standard Grant
The 11th Conference on Mathematical Foundations of Programming Semantics, Tulane University, New Orleans, Louisiana
第 11 届编程语义数学基础会议,杜兰大学,路易斯安那州新奥尔良
- 批准号:
9503096 - 财政年份:1995
- 资助金额:
$ 29.24万 - 项目类别:
Standard Grant
Conference on Semigroup Theory & Its Applications
半群理论会议
- 批准号:
9402118 - 财政年份:1994
- 资助金额:
$ 29.24万 - 项目类别:
Standard Grant
5th WORKSHOP ON MATHEMATICAL FOUNDATION OF PROGRAMMING SEMANTICS
第五届编程语义数学基础研讨会
- 批准号:
8820516 - 财政年份:1989
- 资助金额:
$ 29.24万 - 项目类别:
Standard Grant
U.S.-United Kingdom Cooperative Research: Continuous Lattices, their Structure, Theory and Applications (Mathematics)
美英合作研究:连续格子、其结构、理论与应用(数学)
- 批准号:
8402236 - 财政年份:1984
- 资助金额:
$ 29.24万 - 项目类别:
Standard Grant
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