Digital Repository of Mathematical Formulae

The purpose of the NIST Digital Repository of Mathematical Formulae (DRMF) is to create a digital compendium of mathematical formulae for orthogonal polynomials and special functions (OPSF) and of associated mathematical data. The DRMF addresses needs of working mathematicians, physicists and engineers: providing a platform for publication and interaction with OPSF formulae on the web. Using MediaWiki extensions and other existing technology (such as software and macro collections developed for the NIST Digital Library of Mathematical Functions), the DRMF acts as an interactive web domain for OPSF formulae. Whereas Wikipedia and other web authoring tools manifest notions or descriptions as first class objects, the DRMF does that with mathematical formulae. See http://gw32.iu.xsede.org/index.php/Main_Page

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

Making Math Searchable in Wikipedia

Wikipedia, the world largest encyclopedia contains a lot of knowledge that is expressed as formulae exclusively. Unfortunately, this knowledge is currently not fully accessible by intelligent information retrieval systems. This immense body of knowledge is hidden form value-added services, such as search. In this paper, we present our MathSearch implementation for Wikipedia that enables users to perform a combined text and fully unlock the potential benefits.Comment: 7 pages, 2 figures, Conference on Intelligent Computer Mathematics, July 9-14 2012, Bremen, Germany. To be published in Lecture Notes, Artificial Intelligence, Springe

VMEXT: A Visualization Tool for Mathematical Expression Trees

Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). Expression trees are an important mechanism for storing and processing mathematical expressions as well as the most frequently used visualization of the structure of mathematical expressions. Typically, researchers and practitioners manually visualize expression trees using general-purpose tools. This approach is laborious, redundant, and error-prone. Manual visualizations represent a user's notion of what the markup of an expression should be, but not necessarily what the actual markup is. This paper presents VMEXT - a free and open source tool to directly visualize expression trees from parallel MathML. VMEXT simultaneously visualizes the presentation elements and the semantic structure of mathematical expressions to enable users to quickly spot deficiencies in the Content MathML markup that does not affect the presentation of the expression. Identifying such discrepancies previously required reading the verbose and complex MathML markup. VMEXT also allows one to visualize similar and identical elements of two expressions. Visualizing expression similarity can support support developers in designing retrieval approaches and enable improved interaction concepts for users of mathematical information retrieval systems. We demonstrate VMEXT's visualizations in two web-based applications. The first application presents the visualizations alone. The second application shows a possible integration of the visualizations in systems for mathematical knowledge management and mathematical information retrieval. The application converts LaTeX input to parallel MathML, computes basic similarity measures for mathematical expressions, and visualizes the results using VMEXT.Comment: 15 pages, 4 figures, Intelligent Computer Mathematics - 10th International Conference CICM 2017, Edinburgh, UK, July 17-21, 2017, Proceeding

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

A Cartesian co-ordinate system for representing the second to fifth metacarpals in the human hand

Description: This is tha authors' PDF version of an article published in Radiography© 2004. The definitive version is available at www.elsevierhealth.comPurpose The use of hand radiographs has both clinical and anthropometric applications. However, a method for converting standard bony points within the metacarpus to Cartesian co-ordinates does not exist. Methods A simple method for converting standard bony points of the second to fifth metacarpals to Cartesian co-ordinates is described for the first time. Results Using a small set of measurements and treating these with equations of known voracity, this method is accurate and allows the metacarpus to be interro¬gated via a much wider range of geometrical techniques than has so far been available. Conclusions This method allows naked-eye assessments to be supported or re¬placed by metrical evaluations. It is likely to have both clinical and anthropometric uses.University of Liverpool research development grant