发现感兴趣的数学对象--数学符号研究
Discovering Mathematical Objects of Interest -- A Study of Mathematical Notations
摘要：
数学符号，即，书写系统用于交流数学概念，为各种信息搜索和检索系统编码有价值的信息。然而，数学符号仍然大多未被今天的系统使用。在本文中，我们提出了第一次深入研究的分布在两个大型科学语料库：开放获取arXiv（2.5 B数学对象）和数学评论服务的纯数学和应用数学zbMATH（61 M数学对象）的数学符号。本文的研究为今后大型科学语料库数学信息检索的研究奠定了基础。此外，我们证明了我们的结果的相关性，以各种用例。例如，帮助语义提取系统，改进科学搜索引擎，以及促进专门的数学推荐系统。我们所提出的研究的贡献如下：（1）我们提出了arXiv和zbMATH上数学公式的第一分布分析;（2）我们为给定的文本搜索查询检索相关的数学对象（例如，链接$P_{n}^{(α, β)}\!\left(x\right)$与“雅可比多项式”）;（3）我们通过提供相关的数学公式来扩展zbMATH的搜索引擎;以及（4）我们通过将数学输入的自动完成作为对数学推荐系统的第一贡献来验证结果的适用性。为了加快未来的研究项目，我们提供了我们的源代码和数据。
英文摘要：
Mathematical notation, i.e., the writing system used to communicate concepts in mathematics, encodes valuable information for a variety of information search and retrieval systems. Yet, mathematical notations remain mostly unutilized by today's systems. In this paper, we present the first in-depth study on the distributions of mathematical notation in two large scientific corpora: the open access arXiv (2.5B mathematical objects) and the mathematical reviewing service for pure and applied mathematics zbMATH (61M mathematical objects). Our study lays a foundation for future research projects on mathematical information retrieval for large scientific corpora. Further, we demonstrate the relevance of our results to a variety of use-cases. For example, to assist semantic extraction systems, to improve scientific search engines, and to facilitate specialized math recommendation systems. The contributions of our presented research are as follows: (1) we present the first distributional analysis of mathematical formulae on arXiv and zbMATH; (2) we retrieve relevant mathematical objects for given textual search queries (e.g., linking $P_{n}^{(α, β)}\!\left(x\right)$ with `Jacobi polynomial'); (3) we extend zbMATH's search engine by providing relevant mathematical formulae; and (4) we exemplify the applicability of the results by presenting auto-completion for math inputs as the first contribution to math recommendation systems. To expedite future research projects, we have made available our source code and data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
