RUI: Extremal Combinatorics of Patterns, Correlation, and Structure

RUI:模式、相关性和结构的极值组合

基本信息

  • 批准号:
    1500856
  • 负责人:
  • 金额:
    $ 15万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2015
  • 资助国家:
    美国
  • 起止时间:
    2015-09-15 至 2019-08-31
  • 项目状态:
    已结题

项目摘要

Combinatorics considers finite structures, many of which play a crucial role in problems that arise in science and technology. Preeminent among these structures are finite binary sequences (strings of zeroes and ones) that are used in the communications networks, cryptographic systems, remote sensing, acoustic design, and efficient operation of scientific instrumentation. Other finite structures arising from polynomials, sets, and graphs also find use in a wide variety of technological and scientific endeavors. To achieve an engineering goal or understand a natural process, one must often find the structures that are extremal (minimal or maximal) with respect to a certain feature. For example, we might seek a family of binary sequences that resemble each other as little as possible in order avoid mutual interference in a multi-user communications network: this is the problem of low correlation. The solutions to such extremal problems often involve mathematical objects with a large amount of structure. This research project aims to investigate some problems in extremal combinatorics and the mathematical structures involved in these extremal problems.The organizing principle of this project is to investigate important problems in pure mathematics involving highly structured discrete objects, many of which are of great interest in science and technology. For example, the problem of minimizing aperiodic autocorrelation of binary sequences is of vital importance in engineering applications like remote sensing and communication. Later, physicists noted that the minima describe the ground states of certain systems in statistical physics. Yet the problem is also related to questions in harmonic analysis raised by Littlewood in 1966 and still actively researched, with recent contributions from the principal investigator that are being further developed. Problems such as this are rich in connections to other branches of mathematics, because the optimal or best known discrete structures for them often come from fields like number theory, algebra, or geometry. For example, the sequences with lowest known asymptotic aperiodic autocorrelation derive from the Fekete polynomials in analytic number theory. The Weil sums studied in this project originate in number theory and arithmetic algebraic geometry: they provide a method for counting points on curves over finite fields. In technology, they determine the nonlinearity of functions used in cryptography, the weight distribution of error-correcting codes, and the cross-correlation properties of linear recursive sequences over finite fields. New techniques to bound the maximum number of instances of a pattern in a finite set of points in the plane utilize diverse techniques that range from order relations to topological arguments. The interplay of all these ideas, pure and applied, leads to a mutual enrichment of mathematics, engineering, and science.
组合学考虑有限结构,其中许多结构在科学技术中出现的问题中起着至关重要的作用。这些结构中最突出的是有限二进制序列(0和1的字符串),用于通信网络、密码系统、遥感、声学设计和科学仪器的有效操作。由多项式、集合和图产生的其他有限结构也在各种各样的技术和科学努力中得到广泛的应用。为了实现一个工程目标或理解一个自然过程,人们必须经常找到与某个特征相关的极端(最小或最大)的结构。例如,为了避免多用户通信网络中的相互干扰,我们可能会寻找一组彼此尽可能不相似的二进制序列:这是低相关性的问题。这类极端问题的解决方案往往涉及具有大量结构的数学对象。本研究项目旨在探讨极值组合中的一些问题以及这些极值问题所涉及的数学结构。该项目的组织原则是研究涉及高度结构化离散对象的纯数学中的重要问题,其中许多问题在科学和技术中具有很大的兴趣。例如,最小化二值序列的非周期自相关问题在遥感和通信等工程应用中至关重要。后来,物理学家注意到,在统计物理学中,极小值描述了某些系统的基态。然而,这个问题也与利特尔伍德在1966年提出的谐波分析问题有关,目前仍在积极研究中,首席研究员最近的贡献正在进一步发展。诸如此类的问题与数学的其他分支有着丰富的联系,因为它们的最优或最知名的离散结构通常来自数论、代数或几何等领域。例如,已知的最小渐近非周期自相关序列,是由解析数论中的Fekete多项式推导出来的。本项目研究的Weil和起源于数论和算术代数几何:它们提供了一种计算有限域上曲线上点的方法。在技术上,它们决定了密码学中使用的函数的非线性,纠错码的权重分布,以及有限域上线性递归序列的互相关性质。在平面上的有限点集合中绑定模式实例的最大数量的新技术利用了从顺序关系到拓扑参数的各种技术。所有这些思想的相互作用,无论是纯粹的还是应用的,都导致了数学、工程和科学的相互丰富。

项目成果

期刊论文数量(7)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Sequences with Low Correlation
  • DOI:
    10.1007/978-3-030-05153-2_8
  • 发表时间:
    2018-06
  • 期刊:
  • 影响因子:
    0
  • 作者:
    D. Katz
  • 通讯作者:
    D. Katz
Peak Sidelobe Level and Peak Crosscorrelation of Golay–Rudin–Shapiro Sequences
Golay-Rudin-Shapiro 序列的峰值旁瓣电平和峰值互相关
  • DOI:
    10.1109/tit.2021.3135564
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    2.5
  • 作者:
    Katz, Daniel J.;Van der Linden, Courtney M.
  • 通讯作者:
    Van der Linden, Courtney M.
An improved uncertainty principle for functions with symmetry
对称函数的改进不确定性原理
  • DOI:
    10.1016/j.jalgebra.2021.07.017
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    0.9
  • 作者:
    Garcia, Stephan Ramon;Karaali, Gizem;Katz, Daniel J.
  • 通讯作者:
    Katz, Daniel J.
The Resolution of Niho’s Last Conjecture Concerning Sequences, Codes, and Boolean Functions
  • DOI:
    10.1109/tit.2021.3098342
  • 发表时间:
    2020-06
  • 期刊:
  • 影响因子:
    2.5
  • 作者:
    T. Helleseth;D. Katz;Chunlei Li
  • 通讯作者:
    T. Helleseth;D. Katz;Chunlei Li
Sequence Pairs with Lowest Combined Autocorrelation and Crosscorrelation
具有最低组合自相关和互相关的序列对
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Daniel Katz其他文献

HCV recurrence and death after viral clearance in HCV-viremic donor to HCV-negative kidney recipient - a case report
HCV 病毒清除后 HCV 复发和死亡在 HCV 病毒血症供体到 HCV 阴性肾受体中 - 病例报告
  • DOI:
    10.1016/j.ajt.2024.12.180
  • 发表时间:
    2025-01-01
  • 期刊:
  • 影响因子:
    8.200
  • 作者:
    Shengliang He;Sung-Hoon Kim;Tomohiro Tanaka;David Thomsen;Christie Thomas;Daniel Katz;Hassan Aziz;Alan Reed
  • 通讯作者:
    Alan Reed
Validation of Remote Administration of Social Cognitive Assessments in Pregnant Women
  • DOI:
    10.1016/j.biopsych.2021.02.558
  • 发表时间:
    2021-05-01
  • 期刊:
  • 影响因子:
  • 作者:
    Emma Smith;Danielle Torres;Deborah Li;Vignesh Rajasekaran;Margaret McClure;Daniel Katz;Julie Spicer;Nicole Derish;Antonia S. New;Erin A. Hazlett;Harold W. Koenigsberg;Maria de las Mercedes Perez-Rodriguez
  • 通讯作者:
    Maria de las Mercedes Perez-Rodriguez
375. Social Cognition in Pregnancy and Postpartum and an Association With Maternal Caregiving
  • DOI:
    10.1016/j.biopsych.2023.02.615
  • 发表时间:
    2023-05-01
  • 期刊:
  • 影响因子:
  • 作者:
    Emma Smith;Matina Kakalis;Juliana Camacho Castro;Kendall Moore;Samantha Miyares;Cristela Lopez;Sarah Garikana;Madeleine Carter;Leif Alino;Maeve McClure;Marie Balemian;Harold W. Koenigsberg;Nakiyah Knibbs;Luciana Vieira;Rebecca H. Jessel;Andres Ramirez-Zamudio;Anna Rommel;Robert Pietrzak;Veerle Bergink;Daniel Katz
  • 通讯作者:
    Daniel Katz
Quantifying Pollen Forecast Accuracy: An Assessment Of Private Sector Predictions In New York
量化花粉预报准确性:对纽约私营部门预测的评估
  • DOI:
    10.1016/j.jaci.2023.11.355
  • 发表时间:
    2024-02-01
  • 期刊:
  • 影响因子:
    11.200
  • 作者:
    Daniel Katz;Kyle Edwards;Sida Huang;Guy Robinson
  • 通讯作者:
    Guy Robinson
Ezra Pound’s Provincial Provence: Arnaut Daniel, Gavin Douglas, and the Vulgar Tongue
埃兹拉·庞德的普罗旺斯省:阿诺特·丹尼尔、加文·道格拉斯和粗俗的舌头
  • DOI:
    10.1215/00267929-1589167
  • 发表时间:
    2012
  • 期刊:
  • 影响因子:
    0.4
  • 作者:
    Daniel Katz
  • 通讯作者:
    Daniel Katz

Daniel Katz的其他文献

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{{ truncateString('Daniel Katz', 18)}}的其他基金

Collaborative Research: EAGER: Characterizing Research Software from NSF Awards
协作研究:EAGER:获得 NSF 奖项的研究软件特征
  • 批准号:
    2211279
  • 财政年份:
    2022
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
CIF: Small: RUI: Highly Nonlinear and Pseudorandom Structures for Communications and Sensing
CIF:小:RUI:用于通信和传感的高度非线性和伪随机结构
  • 批准号:
    2206454
  • 财政年份:
    2022
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
Collaborative Research: Sustainability: A Community-Centered Approach for Supporting and Sustaining Parsl
合作研究:可持续性:以社区为中心的支持和维持 Parsl 的方法
  • 批准号:
    2209920
  • 财政年份:
    2022
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
Collaborative Research: Frameworks: funcX: A Function Execution Service for Portability and Performance
协作研究:框架:funcX:可移植性和性能的函数执行服务
  • 批准号:
    2004932
  • 财政年份:
    2020
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
Collaborative Research: OAC Core: Small: Efficient and Policy-driven Burst Buffer Sharing
合作研究:OAC Core:小型:高效且策略驱动的突发缓冲区共享
  • 批准号:
    2008286
  • 财政年份:
    2020
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
CIF: Small: RUI: Low Correlation and Highly Nonlinear Structures for Communications and Sensing
CIF:小型:RUI:用于通信和传感的低相关性和高度非线性结构
  • 批准号:
    1815487
  • 财政年份:
    2018
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
REU Site: INCLUSION - Incubating a New Community of Leaders Using Software, Inclusion, Innovation, Interdisciplinary and OpeN-Science
REU 网站:包容性 - 利用软件、包容性、创新、跨学科和开放科学孵化新的领导者社区
  • 批准号:
    1659702
  • 财政年份:
    2017
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
Kansas-Missouri-Nebraska Commutative Algebra Conference (KUMUNU 2016)
堪萨斯州-密苏里州-内布拉斯加州交换代数会议 (KUMUNU 2016)
  • 批准号:
    1645050
  • 财政年份:
    2016
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
The 4th Workshop on Sustainable Software for Science: Best Practices and Experiences (WSSSPE4)
第四届科学可持续软件研讨会:最佳实践和经验(WSSSPE4)
  • 批准号:
    1648293
  • 财政年份:
    2016
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
Promoting Action to Build Research Communities in the Age of Open Science
促进开放科学时代建设研究社区的行动
  • 批准号:
    1645571
  • 财政年份:
    2016
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant

相似国自然基金

带奇点的extremal度量和toric流形上的extremal度量
  • 批准号:
    10901160
  • 批准年份:
    2009
  • 资助金额:
    10.0 万元
  • 项目类别:
    青年科学基金项目

相似海外基金

Extremal Combinatorics: Themes and Challenging Problems
极值组合学:主题和挑战性问题
  • 批准号:
    2401414
  • 财政年份:
    2023
  • 资助金额:
    $ 15万
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Discrete Geometry and Extremal Combinatorics
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  • 批准号:
    2246659
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    2023
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    $ 15万
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Extremal Combinatorics: Themes and Challenging Problems
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  • 批准号:
    2246641
  • 财政年份:
    2023
  • 资助金额:
    $ 15万
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Probabilistic and Extremal Combinatorics
概率和极值组合学
  • 批准号:
    2246907
  • 财政年份:
    2023
  • 资助金额:
    $ 15万
  • 项目类别:
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Extremal Combinatorics Exact Bounds
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  • 批准号:
    574168-2022
  • 财政年份:
    2022
  • 资助金额:
    $ 15万
  • 项目类别:
    University Undergraduate Student Research Awards
FRG: Collaborative Research: Extremal Combinatorics and Flag Algebras
FRG:协作研究:极值组合学和标志代数
  • 批准号:
    2152488
  • 财政年份:
    2022
  • 资助金额:
    $ 15万
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Extremal Combinatorics Asymptotics
极值组合渐近学
  • 批准号:
    574167-2022
  • 财政年份:
    2022
  • 资助金额:
    $ 15万
  • 项目类别:
    University Undergraduate Student Research Awards
Extremal Combinatorics: Problems and Algorithmic Aspects
极值组合学:问题和算法方面
  • 批准号:
    2154082
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    2022
  • 资助金额:
    $ 15万
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    Continuing Grant
Graph Theory and Extremal Combinatorics
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  • 批准号:
    576024-2022
  • 财政年份:
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  • 资助金额:
    $ 15万
  • 项目类别:
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FRG: Collaborative Research: Extremal Combinatorics and Flag Algebras
FRG:协作研究:极值组合学和标志代数
  • 批准号:
    2152490
  • 财政年份:
    2022
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
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