Conference Proposal: Theory and Applications of Benford's Law

本福德定律描述了许多数据集的前导有效位数的分布；第一个数字等于d的概率通常是log_10(1 + 1/d)，而不是均匀分布的。满足本福德定律的系统数量是惊人的，而且极其多样化，包括预算和所得税数据、股票市场表、人口普查数据、图像中的dct域系数、水文数据、标准数学函数（如n!）、动态映射的迭代、l函数的值和随机矩阵集合的特征多项式、递归关系的解和3x+1问题，仅举几例。我们认为，我们提议的研讨会是第一次尝试聚集大量具有代表性的样本，这些样本来自本福德定律理论和应用的无数学科。人们将一个领域的工具和技术应用于另一个领域，从而在科学和数学领域取得重大进步的例子数不胜数。我们希望在这里也能取得类似的成功。具体来说，我们计划通过收集研究本福德定律的所有不同领域的专家，将问题和技术传播到不同的学科。参与者很可能会相互提供有用的建议（或者对提出的问题感兴趣并参与联合研究）。课程主题包括数学基础、口译、信息取证和欺诈检测、信号和数据处理、动力系统、复杂网络和系统设计。由于我们的主要目标之一是在整个社区传播与本福德定律相关的工具、技术和问题的知识，我们计划出版研讨会的会议记录。我们正在研究通过SIAM或AMS出版一本基于研讨会演讲的书，以及可能的一些说明性文章。研讨会的直接交付成果将是一份报告，以及电子会议记录。较长期的可交付成果是发表的会议记录以及获得大笔资助的团队提案。

Benford's Law describes the distribution of the leading significant digit of many data sets; rather than being uniformly distributed, the probability the first digit equals d is often log_10(1 + 1/d). The number of systems satisfying Benford's Law is astounding, and extremely diverse, including budget and income tax data, stock market tables, census figures, DCT-domain coefficients in images, hydrology data, standard mathematical functions (such as n!), iterates of dynamical maps, values of L-functions and characteristic polynomials of random matrix ensembles, solutions of recurrence relations, and the 3x+1 problem, to name just a few. We believe that our proposed workshop is the first attempt to assemble a large, representative sample of people in the myriad of disciplines working on the theory and applications of Benford's law. There are numerous examples of major advances in science and mathematics arising from people applying the tools and techniques of one field in another. We hope to have similar success here. Specifically, by gathering experts from all the different fields studying Benford's law, we plan on disseminating the problems and techniques across the different disciplines. It is likely that participants will be able to provide helpful suggestions to each other (or be intrigued by proposed questions and participate in joint research).The list of topics include mathematical foundations, interpretation, information forensics and fraud detection, signal and data processing, dynamical systems, complex networks and system design. As one of our primary goals is to disseminate knowledge of tools, techniques and problems related to Benford's Law throughout the community, we plan on publishing proceedings of the workshop. We are investigating the publication through SIAM or AMS of a book based on the workshop talks, as well as possibly some expository articles. The immediate deliverables of the workshop will be a report, as well as electronic proceedings. The longer term deliverables are published proceedings as well as a team proposal for a large grant.