Unfortunately nowadays, research lacks a clear comparison of the scalability and performance for database technologies that store and query documents in XML versus the more modern JSON format. However, we believe that XML-based solutions can still deliver performance in executing complex queries on heterogeneous collections. Currently, the majority of these solutions have been replaced with the more modern JSON based Database Management Systems. Thus, Native XML Databases, which were initially designed to manipulate XML data using standardized querying languages, i.e., XQuery and XPath, were rebranded as NoSQL Document-Oriented Databases Systems.
As current data generated by different sources and devices, especially from IoT sensors and actuators, use either XML or JSON format, depending on the application, database technologies that store and query semi-structured data in XML format are needed. These solutions were developed to relieve the issue of rigid data structures present in relational databases, by introducing semi-structured and flexible schema design. In the current context of Big Data, a multitude of new NoSQL solutions for storing, managing, and extracting information and patterns from semi-structured data have been proposed and implemented.
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To expedite future research projects, we have made available our source code and data. 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 $P_\!\left(x\right)$ 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. For example, to assist semantic extraction systems, to improve scientific search engines, and to facilitate specialized math recommendation systems. Further, we demonstrate the relevance of our results to a variety of use-cases.
Our study lays a foundation for future research projects on mathematical information retrieval for large scientific corpora. 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). Yet, mathematical notations remain mostly unutilized by today's systems.
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.
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