28 research outputs found
Making Presentation Math Computable
This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book
Making Presentation Math Computable
This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book
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
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
Performance evaluation of random forest algorithm for automating classification of mathematics question items
Automated classification of mathematics question items based on the Table of Specifications is crucial in developing well-defined assessment content, significantly reducing teachers’ workload. This study presents a performance evaluation of a Random Forest model designed to classify mathematics question items based on the content standards of the first quarter of tenth grade stipulated by the Philippines’ Department of Education Curriculum Guide. The model uses an algorithm that extracts mathematical expressions as tokens for the Bag-of-words Model. The evaluation was conducted using precision, recall, F-1 score, and overall accuracy metrics, and the confusion matrix was used to assess the Random Forest model’s performance. The results showed that the Random Forest model achieved 95% in precision, 95% in recall, 95% in F-1 score, and 95% in overall accuracy, demonstrating its effectiveness in classifying mathematics question items
Improving Academic Plagiarism Detection for STEM Documents by Analyzing Mathematical Content and Citations
Identifying academic plagiarism is a pressing task for educational and
research institutions, publishers, and funding agencies. Current plagiarism
detection systems reliably find instances of copied and moderately reworded
text. However, reliably detecting concealed plagiarism, such as strong
paraphrases, translations, and the reuse of nontextual content and ideas is an
open research problem. In this paper, we extend our prior research on analyzing
mathematical content and academic citations. Both are promising approaches for
improving the detection of concealed academic plagiarism primarily in Science,
Technology, Engineering and Mathematics (STEM). We make the following
contributions: i) We present a two-stage detection process that combines
similarity assessments of mathematical content, academic citations, and text.
ii) We introduce new similarity measures that consider the order of
mathematical features and outperform the measures in our prior research. iii)
We compare the effectiveness of the math-based, citation-based, and text-based
detection approaches using confirmed cases of academic plagiarism. iv) We
demonstrate that the combined analysis of math-based and citation-based content
features allows identifying potentially suspicious cases in a collection of
102K STEM documents. Overall, we show that analyzing the similarity of
mathematical content and academic citations is a striking supplement for
conventional text-based detection approaches for academic literature in the
STEM disciplines.Comment: Proceedings of the ACM/IEEE-CS Joint Conference on Digital Libraries
(JCDL) 2019. The data and code of our study are openly available at
https://purl.org/hybridP