Moritz Schubotz

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 users 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 VMEXTs 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.

Analyzing Semantic Concept Patterns to Detect Academic Plagiarism

Detecting academic plagiarism is a pressing problem, e.g., for educational and research institutions, funding agencies, and academic publishers. Existing plagiarism detection systems reliably identify copied text, or near copies of text, but often fail to detect disguised forms of academic plagiarism, such as paraphrases, translations, and idea plagiarism. We present Semantic Concept Pattern Analysis - an approach that performs an integrated analysis of semantic text relatedness and structural text similarity. Using 25 officially retracted academic plagiarism cases, we demonstrate that our approach can detect plagiarism that established text matching approaches would not identify. We view our approach as a promising addition to improve the detection capabilities for strong paraphrases. We plan to further improve Semantic Concept Pattern Analysis and include the approach as part of an integrated detection process that analyzes heterogeneous similarity features to better identify the many possible forms of plagiarism in academic documents.

Giveme5W : Main Event Retrieval from News Articles by Extraction of the Five Journalistic W Questions

Extraction of event descriptors from news articles is a commonly required task for various tasks, such as clustering related articles, summarization, and news aggregation. Due to the lack of generally usable and publicly available methods optimized for news, many researchers must redundantly implement such methods for their project. Answers to the five journalistic W questions (5Ws) describe the main event of a news article, i.e., who did what, when, where, and why. The main contribution of this paper is Giveme5W, the first open-source, syntax-based 5W extraction system for news articles. The system retrieves an article’s main event by extracting phrases that answer the journalistic 5Ws. In an evaluation with three assessors and 60 articles, we find that the extraction precision of 5W phrases is ( p = 0.7 ).

Semantic Preserving Bijective Mappings of Mathematical Formulae Between Document Preparation Systems and Computer Algebra Systems

Document preparation systems like Open image in new window offer the ability to render mathematical expressions as one would write these on paper. Using Open image in new window , Open image in new window , and tools generated for use in the National Institute of Standards (NIST) Digital Library of Mathematical Functions, semantically enhanced mathematical Open image in new window markup (semantic Open image in new window ) is achieved by using a semantic macro set. Computer algebra systems (CAS) such as Maple and Mathematica use alternative markup to represent mathematical expressions. By taking advantage of Youssef’s Part-of-Math tagger and CAS internal representations, we develop algorithms to translate mathematical expressions represented in semantic Open image in new window to corresponding CAS representations and vice versa. We have also developed tools for translating the entire Wolfram Encoding Continued Fraction Knowledge and University of Antwerp Continued Fractions for Special Functions datasets, for use in the NIST Digital Repository of Mathematical Formulae. The overall goal of these efforts is to provide semantically enriched standard conforming MathML representations to the public for formulae in digital mathematics libraries. These representations include presentation MathML, content MathML, generic Open image in new window , semantic Open image in new window , and now CAS representations as well.

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.

Evaluating and Improving the Extraction of Mathematical Identifier Definitions

Mathematical formulae in academic texts significantly contribute to the overall semantic content of such texts, especially in the fields of Science, Technology, Engineering and Mathematics. Knowing the definitions of the identifiers in mathematical formulae is essential to understand the semantics of the formulae. Similar to the sense-making process of human readers, mathematical information retrieval systems can analyze the text that surrounds formulae to extract the definitions of identifiers occurring in the formulae. Several approaches for extracting the definitions of mathematical identifiers from documents have been proposed in recent years. So far, these approaches have been evaluated using different collections and gold standard datasets, which prevented comparative performance assessments. To facilitate future research on the task of identifier definition extraction, we make three contributions. First, we provide an automated evaluation framework, which uses the dataset and gold standard of the NTCIR-11 Math Retrieval Wikipedia task. Second, we compare existing identifier extraction approaches using the developed evaluation framework. Third, we present a new identifier extraction approach that uses machine learning to combine the well-performing features of previous approaches. The new approach increases the precision of extracting identifier definitions from 17.85% to 48.60%, and increases the recall from 22.58% to 28.06%. The evaluation framework, the dataset and our source code are openly available at: https://ident.formulasearchengine.com.

HyPlag: A Hybrid Approach to Academic Plagiarism Detection

Current plagiarism detection systems reliably find instances of copied and moderately altered text, but often fail to detect strong paraphrases, translations, and the reuse of non-textual content and ideas. To improve upon the detection capabilities for such concealed content reuse in academic publications, we make four contributions: i) We present the first plagiarism detection approach that combines the analysis of mathematical expressions, images, citations and text. ii) We describe the implementation of this hybrid detection approach in the research prototype HyPlag. iii) We present novel visualization and interaction concepts to aid users in reviewing content similarities identified by the hybrid detection approach. iv) We demonstrate the usefulness of the hybrid detection and result visualization approaches by using HyPlag to analyze a confirmed case of content reuse present in a retracted research publication.

Extraction of Main Event Descriptors from News Articles by Answering the Journalistic Five W and One H Questions

The identification and extraction of the events that news articles report on is a commonly performed task in the analysis workflow of various projects that analyze news articles. However, due to the lack of universally usable and publicly available methods for news articles, many researchers must redundantly implement methods for event extraction to be used within their projects. Answers to the journalistic five W and one H questions (5W1H) describe the main event of a news story, i.e., who did what, when, where, why, and how. We propose Giveme5W1H, an open-source system that uses syntactic and domain-specific rules to extract phrases answering the 5W1H. In our evaluation, we find that the extraction precision of 5W1H phrases is p=0.64, and p=0.79 for the first four W questions, which discretely describe an event.

Random backaction in tunneling of single electrons through nanostructures

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Automated Symbolic and Numerical Testing of DLMF Formulae Using Computer Algebra Systems

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