208 research outputs found
A Survey on Retrieval of Mathematical Knowledge
We present a short survey of the literature on indexing and retrieval of
mathematical knowledge, with pointers to 72 papers and tentative taxonomies of
both retrieval problems and recurring techniques.Comment: CICM 2015, 20 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
Bravo MaRDI: A Wikibase Powered Knowledge Graph on Mathematics
Mathematical world knowledge is a fundamental component of Wikidata. However,
to date, no expertly curated knowledge graph has focused specifically on
contemporary mathematics. Addressing this gap, the Mathematical Research Data
Initiative (MaRDI) has developed a comprehensive knowledge graph that links
multimodal research data in mathematics. This encompasses traditional research
data items like datasets, software, and publications and includes semantically
advanced objects such as mathematical formulas and hypotheses. This paper
details the abilities of the MaRDI knowledge graph, which is based on Wikibase,
leading up to its inaugural public release, codenamed Bravo, available on
https://portal.mardi4nfdi.de.Comment: Accepted at Wikidata'23: Wikidata workshop at ISWC 202
Querying Geometric Figures Using a Controlled Language, Ontological Graphs and Dependency Lattices
Dynamic geometry systems (DGS) have become basic tools in many areas of
geometry as, for example, in education. Geometry Automated Theorem Provers
(GATP) are an active area of research and are considered as being basic tools
in future enhanced educational software as well as in a next generation of
mechanized mathematics assistants. Recently emerged Web repositories of
geometric knowledge, like TGTP and Intergeo, are an attempt to make the already
vast data set of geometric knowledge widely available. Considering the large
amount of geometric information already available, we face the need of a query
mechanism for descriptions of geometric constructions.
In this paper we discuss two approaches for describing geometric figures
(declarative and procedural), and present algorithms for querying geometric
figures in declaratively and procedurally described corpora, by using a DGS or
a dedicated controlled natural language for queries.Comment: 14 pages, 5 figures, accepted at CICM 201
Leveraging Mathematical Subject Information to Enhance Bibliometric Data
The field of mathematics is known to be especially challenging from a bibliometric point of view. Its bibliographic metrics are especially sensitive to distortions and are heavily influenced by the subject and its popularity. Therefore, quantitative methods are prone to misrepresentations, and need to take subject information into account. In this paper we investigate how the mathematical bibliography of the abstracting and reviewing service Zentralblatt MATH (zbMATH) could further benefit from the inclusion of mathematical subject information MSC2010. Furthermore, the mappings of MSC2010 to Linked Open Data resources have been upgraded and extended to also benefit from semantic information provided by DBpedia
Performance Evaluation and Optimization of Math-Similarity Search
Similarity search in math is to find mathematical expressions that are
similar to a user's query. We conceptualized the similarity factors between
mathematical expressions, and proposed an approach to math similarity search
(MSS) by defining metrics based on those similarity factors [11]. Our
preliminary implementation indicated the advantage of MSS compared to
non-similarity based search. In order to more effectively and efficiently
search similar math expressions, MSS is further optimized. This paper focuses
on performance evaluation and optimization of MSS. Our results show that the
proposed optimization process significantly improved the performance of MSS
with respect to both relevance ranking and recall.Comment: 15 pages, 8 figure
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