Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context

Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate information, e.g., in scientific papers, and to perform computations using computer algebra systems. Enabling computers to access the information encoded in mathematical formulae requires machine-readable formats that can represent both the presentation and content, i.e., the semantics, of formulae. Exchanging such information between systems additionally requires conversion methods for mathematical representation formats. We analyze how the semantic enrichment of formulae improves the format conversion process and show that considering the textual context of formulae reduces the error rate of such conversions. Our main contributions are: (1) providing an openly available benchmark dataset for the mathematical format conversion task consisting of a newly created test collection, an extensive, manually curated gold standard and task-specific evaluation metrics; (2) performing a quantitative evaluation of state-of-the-art tools for mathematical format conversions; (3) presenting a new approach that considers the textual context of formulae to reduce the error rate for mathematical format conversions. Our benchmark dataset facilitates future research on mathematical format conversions as well as research on many problems in mathematical information retrieval. Because we annotated and linked all components of formulae, e.g., identifiers, operators and other entities, to Wikidata entries, the gold standard can, for instance, be used to train methods for formula concept discovery and recognition. Such methods can then be applied to improve mathematical information retrieval systems, e.g., for semantic formula search, recommendation of mathematical content, or detection of mathematical plagiarism.Comment: 10 pages, 4 figure

Strategies for Parallel Markup

Cross-referenced parallel markup for mathematics allows the combination of both presentation and content representations while associating the components of each. Interesting applications are enabled by such an arrangement, such as interaction with parts of the presentation to manipulate and querying the corresponding content, and enhanced search indexing. Although the idea of such markup is hardly new, effective techniques for creating and manipulating it are more difficult than it appears. Since the structures and tokens in the two formats often do not correspond one-to-one, decisions and heuristics must be developed to determine in which way each component refers to and is referred to by components of the other representation. Conversion between fine and coarse grained parallel markup complicates ID assignments. In this paper, we will describe the techniques developed for \LaTeXML, a \TeX/\LaTeX to XML converter, to create cross-referenced parallel MathML. While we do not yet consider \LaTeXML's content MathML to be useful, the current effort is a step towards that continuing goal

Three Steps to Heaven: Semantic Publishing in a Real World Workflow

Semantic publishing offers the promise of computable papers, enriched visualisation and a realisation of the linked data ideal. In reality, however, the publication process contrives to prevent richer semantics while culminating in a `lumpen' PDF. In this paper, we discuss a web-first approach to publication, and describe a three-tiered approach which integrates with the existing authoring tooling. Critically, although it adds limited semantics, it does provide value to all the participants in the process: the author, the reader and the machine.Comment: Published as part of SePublica 201

The NASA Astrophysics Data System: Data Holdings

Since its inception in 1993, the ADS Abstract Service has become an indispensable research tool for astronomers and astrophysicists worldwide. In those seven years, much effort has been directed toward improving both the quantity and the quality of references in the database. From the original database of approximately 160,000 astronomy abstracts, our dataset has grown almost tenfold to approximately 1.5 million references covering astronomy, astrophysics, planetary sciences, physics, optics, and engineering. We collect and standardize data from approximately 200 journals and present the resulting information in a uniform, coherent manner. With the cooperation of journal publishers worldwide, we have been able to place scans of full journal articles on-line back to the first volumes of many astronomical journals, and we are able to link to current version of articles, abstracts, and datasets for essentially all of the current astronomy literature. The trend toward electronic publishing in the field, the use of electronic submission of abstracts for journal articles and conference proceedings, and the increasingly prominent use of the World Wide Web to disseminate information have enabled the ADS to build a database unparalleled in other disciplines. The ADS can be accessed at http://adswww.harvard.eduComment: 24 pages, 1 figure, 6 tables, 3 appendice

Drawing Feynman Diagrams with LaTeX and Metafont

Feynmf is a LaTeX package for easy drawing of professional quality Feynman diagrams with Metafont (or Metapost). Feynmf lays out most diagrams satisfactorily from the structure of the graph without any need for manual intervention. Nevertheless all the power of Metafont (or Metapost) is available for the most complicated cases.Comment: 19 pages, standard LaTeX2e with recent graphics and amstex packages, 45 figures (EPS), preformatted PostScript (300dpi) in ftp://crunch.ikp.physik.th-darmstadt.de/pub/preprints/IKDA-95-20.ps.g