1,133 research outputs found
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
Ensuring Query Compatibility with Evolving XML Schemas
During the life cycle of an XML application, both schemas and queries may
change from one version to another. Schema evolutions may affect query results
and potentially the validity of produced data. Nowadays, a challenge is to
assess and accommodate the impact of theses changes in rapidly evolving XML
applications.
This article proposes a logical framework and tool for verifying
forward/backward compatibility issues involving schemas and queries. First, it
allows analyzing relations between schemas. Second, it allows XML designers to
identify queries that must be reformulated in order to produce the expected
results across successive schema versions. Third, it allows examining more
precisely the impact of schema changes over queries, therefore facilitating
their reformulation
Threshold copulas and positive dependence
Starting with a notion of positive dependence View the MathML source and with the family of the lower threshold copulas Ct associated with a bivariate distribution having copula C, we define different notions of positive dependence for C, reflecting the dependence properties of the copulas Ct for some t.
Then, we analyze some structural aspects of lower threshold copulas and of the given definitions. Furthermore we consider several specific cases arising from relevant special choices of View the MathML source (e.g., PQD, LTD, TP2 and PLR). Our analysis, in particular, allows us to present a number of relevant examples and counter-examples, which can be useful in the study of the tail dependence for a bivariate distribution
SBML models and MathSBML
MathSBML is an open-source, freely-downloadable Mathematica package that facilitates working with Systems Biology Markup Language (SBML) models. SBML is a toolneutral,computer-readable format for representing models of biochemical reaction networks, applicable to metabolic networks, cell-signaling pathways, genomic regulatory networks, and other modeling problems in systems biology that is widely supported by the systems biology community. SBML is based on XML, a standard medium for representing and transporting data that is widely supported on the internet as well as in computational biology and bioinformatics. Because SBML is tool-independent, it enables model transportability, reuse, publication and survival. In addition to MathSBML, a number of other tools that support SBML model examination and manipulation are provided on the sbml.org website, including libSBML, a C/C++ library for reading SBML models; an SBML Toolbox for MatLab; file conversion programs; an SBML model validator and visualizer; and SBML specifications and schemas. MathSBML enables SBML file import to and export from Mathematica as well as providing an API for model manipulation and simulation
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
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