arXiv subjects

Moritz Schubotz

Publications and source records attributed to Moritz Schubotz.

At least 55 records · Page 3Linked to original sources

arXiv2021

10 Years Later: The Mathematics Subject Classification and Linked Open Data

Ten years ago, the Mathematics Subject Classification MSC 2010 was released, and a corresponding machine-readable Linked Open Data collection was published using the Simple Knowledge Organization System (SKOS). Now, the new MSC 2020 is out. This paper recaps the last ten years of working on machine-readable MSC data and presents the new machine-readable MSC 2020. We describe the processing required to convert the version of record, as agreed by the editors of zbMATH and Mathematical Reviews, into the Linked Open Data form we call MSC2020-SKOS. The new form includes explicit marking of the changes from 2010 to 2020, some translations of English code descriptions into Chinese, Italian, and Russian, and extra material relating MSC to other mathematics classification efforts. We also outline future potential uses for MSC2020-SKOS in semantic indexing and sketch its embedding in a larger vision of scientific research data.

cs.DL↗

arXiv2021

zbMATH Open: API Solutions and Research Challenges

We present zbMATH Open, the most comprehensive collection of reviews and bibliographic metadata of scholarly literature in mathematics. Besides our website https://zbMATH.org which is openly accessible since the beginning of this year, we provide API endpoints to offer our data. The API improves interoperability with others, i.e., digital libraries, and allows using our data for research purposes. In this article, we (1) illustrate the current and future overview of the services offered by zbMATH; (2) present the initial version of the zbMATH links API; (3) analyze potentials and limitations of the links API based on the example of the NIST Digital Library of Mathematical Functions; (4) and finally, present the zbMATH Open dataset as a research resource and discuss connected open research problems.

cs.DL↗

arXiv2021

Discovering Mathematical Objects of Interest -- A Study of Mathematical Notations

Mathematical notation, i.e., the writing system used to communicate concepts in mathematics, encodes valuable information for a variety of information search and retrieval systems. Yet, mathematical notations remain mostly unutilized by today's systems. In this paper, we present the first in-depth study on the distributions of mathematical notation in two large scientific corpora: the open access arXiv (2.5B mathematical objects) and the mathematical reviewing service for pure and applied mathematics zbMATH (61M mathematical objects). Our study lays a foundation for future research projects on mathematical information retrieval for large scientific corpora. Further, we demonstrate the relevance of our results to a variety of use-cases. For example, to assist semantic extraction systems, to improve scientific search engines, and to facilitate specialized math recommendation systems. The contributions of our presented research are as follows: (1) we present the first distributional analysis of mathematical formulae on arXiv and zbMATH; (2) we retrieve relevant mathematical objects for given textual search queries (e.g., linking $P_{n}^{(α, β)}\!\left(x\right)$ with `Jacobi polynomial'); (3) we extend zbMATH's search engine by providing relevant mathematical formulae; and (4) we exemplify the applicability of the results by presenting auto-completion for math inputs as the first contribution to math recommendation systems. To expedite future research projects, we have made available our source code and data.

cs.DL↗

arXiv2021

Fast Linking of Mathematical Wikidata Entities in Wikipedia Articles Using Annotation Recommendation

Mathematical information retrieval (MathIR) applications such as semantic formula search and question answering systems rely on knowledge-bases that link mathematical expressions to their natural language names. For database population, mathematical formulae need to be annotated and linked to semantic concepts, which is very time-consuming. In this paper, we present our approach to structure and speed up this process by supporting annotators with a system that suggests formula names and meanings of mathematical identifiers. We test our approach annotating 25 articles on https://en.wikipedia.org. We evaluate the quality and time-savings of the annotation recommendations. Moreover, we watch editor reverts and comments on Wikipedia formula entity links and Wikidata item creation and population to ground the formula semantics. Our evaluation shows that the AI guidance was able to significantly speed up the annotation process by a factor of 1.4 for formulae and 2.4 for identifiers. Our contributions were reverted in 12% of the edited Wikipedia articles and 33% of the Wikidata items within a test window of one month. The >>AnnoMathTeX<< annotation recommender system is hosted by Wikimedia at https://annomathtex.wmflabs.org. In the future, our data refinement pipeline is ready to be integrated seamlessly into the Wikipedia user interface.

cs.DL↗

arXiv2020

ARQMath Lab: An Incubator for Semantic Formula Search in zbMATH Open?

The zbMATH database contains more than 4 million bibliographic entries. We aim to provide easy access to these entries. Therefore, we maintain different index structures, including a formula index. To optimize the findability of the entries in our database, we continuously investigate new approaches to satisfy the information needs of our users. We believe that the findings from the ARQMath evaluation will generate new insights into which index structures are most suitable to satisfy mathematical information needs. Search engines, recommender systems, plagiarism checking software, and many other added-value services acting on databases such as the arXiv and zbMATH need to combine natural and formula language. One initial approach to address this challenge is to enrich the mostly unstructured document data via Entity Linking. The ARQMath Task at CLEF 2020 aims to tackle the problem of linking newly posted questions from Math Stack Exchange (MSE) to existing ones that were already answered by the community. To deeply understand MSE information needs, answer-, and formula types, we performed manual runs for tasks 1 and 2. Furthermore, we explored several formula retrieval methods: For task 2, such as fuzzy string search, k-nearest neighbors, and our recently introduced approach to retrieve Mathematical Objects of Interest (MOI) with textual search queries. The task results show that neither our automated methods nor our manual runs archived good scores in the competition. However, the perceived quality of the hits returned by the MOI search particularly motivates us to conduct further research about MOI.

cs.DL↗

arXiv2020

AutoMSC: Automatic Assignment of Mathematics Subject Classification Labels

Authors of research papers in the fields of mathematics, and other math-heavy disciplines commonly employ the Mathematics Subject Classification (MSC) scheme to search for relevant literature. The MSC is a hierarchical alphanumerical classification scheme that allows librarians to specify one or multiple codes for publications. Digital Libraries in Mathematics, as well as reviewing services, such as zbMATH and Mathematical Reviews (MR) rely on these MSC labels in their workflows to organize the abstracting and reviewing process. Especially, the coarse-grained classification determines the subject editor who is responsible for the actual reviewing process. In this paper, we investigate the feasibility of automatically assigning a coarse-grained primary classification using the MSC scheme, by regarding the problem as a multi-class classification machine learning task. We find that our method achieves an (F_1)-score of over 77%, which is remarkably close to the agreement of zbMATH and MR ((F_1)-score of 81%). Moreover, we find that the method's confidence score allows for reducing the effort by 86% compared to the manual coarse-grained classification effort while maintaining a precision of 81% for automatically classified articles.

cs.DL↗

arXiv2020

A First Step Towards Content Protecting Plagiarism Detection

Plagiarism detection systems are essential tools for safeguarding academic and educational integrity. However, today's systems require disclosing the full content of the input documents and the document collection to which the input documents are compared. Moreover, the systems are centralized and under the control of individual, typically commercial providers. This situation raises procedural and legal concerns regarding the confidentiality of sensitive data, which can limit or prohibit the use of plagiarism detection services. To eliminate these weaknesses of current systems, we seek to devise a plagiarism detection approach that does not require a centralized provider nor exposing any content as cleartext. This paper presents the initial results of our research. Specifically, we employ Private Set Intersection to devise a content-protecting variant of the citation-based similarity measure Bibliographic Coupling implemented in our plagiarism detection system HyPlag. Our evaluation shows that the content-protecting method achieves the same detection effectiveness as the original method while making common attacks to disclose the protected content practically infeasible. Our future work will extend this successful proof-of-concept by devising plagiarism detection methods that can analyze the entire content of documents without disclosing it as cleartext.

cs.CR↗

arXiv2020

Classification and Clustering of arXiv Documents, Sections, and Abstracts, Comparing Encodings of Natural and Mathematical Language

In this paper, we show how selecting and combining encodings of natural and mathematical language affect classification and clustering of documents with mathematical content. We demonstrate this by using sets of documents, sections, and abstracts from the arXiv preprint server that are labeled by their subject class (mathematics, computer science, physics, etc.) to compare different encodings of text and formulae and evaluate the performance and runtimes of selected classification and clustering algorithms. Our encodings achieve classification accuracies up to $82.8\%$ and cluster purities up to $69.4\%$ (number of clusters equals number of classes), and $99.9\%$ (unspecified number of clusters) respectively. We observe a relatively low correlation between text and math similarity, which indicates the independence of text and formulae and motivates treating them as separate features of a document. The classification and clustering can be employed, e.g., for document search and recommendation. Furthermore, we show that the computer outperforms a human expert when classifying documents. Finally, we evaluate and discuss multi-label classification and formula semantification.

cs.DL↗

arXiv2020

Mathematical Formulae in Wikimedia Projects 2020

This poster summarizes our contributions to Wikimedia's processing pipeline for mathematical formulae. We describe how we have supported the transition from rendering formulae as course-grained PNG images in 2001 to providing modern semantically enriched language-independent MathML formulae in 2020. Additionally, we describe our plans to improve the accessibility and discoverability of mathematical knowledge in Wikimedia projects further.

cs.DL↗

arXiv2020

Pairwise Multi-Class Document Classification for Semantic Relations between Wikipedia Articles

Many digital libraries recommend literature to their users considering the similarity between a query document and their repository. However, they often fail to distinguish what is the relationship that makes two documents alike. In this paper, we model the problem of finding the relationship between two documents as a pairwise document classification task. To find the semantic relation between documents, we apply a series of techniques, such as GloVe, Paragraph-Vectors, BERT, and XLNet under different configurations (e.g., sequence length, vector concatenation scheme), including a Siamese architecture for the Transformer-based systems. We perform our experiments on a newly proposed dataset of 32,168 Wikipedia article pairs and Wikidata properties that define the semantic document relations. Our results show vanilla BERT as the best performing system with an F1-score of 0.93, which we manually examine to better understand its applicability to other domains. Our findings suggest that classifying semantic relations between documents is a solvable task and motivates the development of recommender systems based on the evaluated techniques. The discussions in this paper serve as first steps in the exploration of documents through SPARQL-like queries such that one could find documents that are similar in one aspect but dissimilar in another.

cs.DL↗

arXiv2019

NewsDeps: Visualizing the Origin of Information in News Articles

In scientific publications, citations allow readers to assess the authenticity of the presented information and verify it in the original context. News articles, however, do not contain citations and only rarely refer readers to further sources. Readers often cannot assess the authenticity of the presented information as its origin is unclear. We present NewsDeps, the first approach that analyzes and visualizes where information in news articles stems from. NewsDeps employs methods from natural language processing and plagiarism detection to measure article similarity. We devise a temporal-force-directed graph that places articles as nodes chronologically. The graph connects articles by edges varying in width depending on the articles' similarity. We demonstrate our approach in a case study with two real-world scenarios. We find that NewsDeps increases efficiency and transparency in news consumption by revealing which previously published articles are the primary sources of each given article.

cs.IR↗

arXiv2019

Forms of Plagiarism in Digital Mathematical Libraries

We report on an exploratory analysis of the forms of plagiarism observable in mathematical publications, which we identified by investigating editorial notes from zbMATH. While most cases we encountered were simple copies of earlier work, we also identified several forms of disguised plagiarism. We investigated 11 cases in detail and evaluate how current plagiarism detection systems perform in identifying these cases. Moreover, we describe the steps required to discover these and potentially undiscovered cases in the future.

cs.DL↗

arXiv2019

Introducing MathQA -- A Math-Aware Question Answering System

We present an open source math-aware Question Answering System based on Ask Platypus. Our system returns as a single mathematical formula for a natural language question in English or Hindi. This formulae originate from the knowledge-base Wikidata. We translate these formulae to computable data by integrating the calculation engine sympy into our system. This way, users can enter numeric values for the variables occurring in the formula. Moreover, the system loads numeric values for constants occurring in the formula from Wikidata. In a user study, our system outperformed a commercial computational mathematical knowledge engine by 13%. However, the performance of our system heavily depends on the size and quality of the formula data available in Wikidata. Since only a few items in Wikidata contained formulae when we started the project, we facilitated the import process by suggesting formula edits to Wikidata editors. With the simple heuristic that the first formula is significant for the article, 80% of the suggestions were correct.

cs.IR↗

arXiv2019

Semantic Preserving Bijective Mappings for Expressions involving Special Functions in Computer Algebra Systems and Document Preparation Systems

Purpose: Modern mathematicians and scientists of math-related disciplines often use Document Preparation Systems (DPS) to write and Computer Algebra Systems (CAS) to calculate mathematical expressions. Usually, they translate the expressions manually between DPS and CAS. This process is time-consuming and error-prone. Our goal is to automate this translation. This paper uses Maple and Mathematica as the CAS, and LaTeX as our DPS. Design/methodology/approach: Bruce Miller at the National Institute of Standards and Technology (NIST) developed a collection of special LaTeX macros that create links from mathematical symbols to their definitions in the NIST Digital Library of Mathematical Functions (DLMF). We are using these macros to perform rule-based translations between the formulae in the DLMF and CAS. Moreover, we develop software to ease the creation of new rules and to discover inconsistencies. Findings: We created 396 mappings and translated 58.8% of DLMF formulae (2,405 expressions) successfully between Maple and DLMF. For a significant percentage, the special function definitions in Maple and the DLMF were different. Therefore, an atomic symbol in one system maps to a composite expression in the other system. The translator was also successfully used for automatic verification of mathematical online compendia and CAS. Our evaluation techniques discovered two errors in the DLMF and one defect in Maple. Originality: This paper introduces the first translation tool for special functions between LaTeX and CAS. The approach improves error-prone manual translations and can be used to verify mathematical online compendia and CAS.

cs.DL↗

arXiv2019

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.

cs.DL↗

arXiv2019

Why Machines Cannot Learn Mathematics, Yet

Nowadays, Machine Learning (ML) is seen as the universal solution to improve the effectiveness of information retrieval (IR) methods. However, while mathematics is a precise and accurate science, it is usually expressed by less accurate and imprecise descriptions, contributing to the relative dearth of machine learning applications for IR in this domain. Generally, mathematical documents communicate their knowledge with an ambiguous, context-dependent, and non-formal language. Given recent advances in ML, it seems canonical to apply ML techniques to represent and retrieve mathematics semantically. In this work, we apply popular text embedding techniques to the arXiv collection of STEM documents and explore how these are unable to properly understand mathematics from that corpus. In addition, we also investigate the missing aspects that would allow mathematics to be learned by computers.

cs.DL↗

arXiv2019

A decentralized method for making sensor measurements tamper-proof to support open science applications

Open science has become a synonym for modern, digital and inclusive science. Inclusion does not stop at open access. Inclusion also requires transparency through open datasets and the right and ability to take part in the knowledge creation process. This implies new challenges for digital libraries. Citizens should be able to contribute data in a curatable form to advance science. At the same time, this data should be verifiable and attributable to its owner. Our research project focusses on securing and attributing incoming data streams from sensors. Our contribution is twofold. First, we analyze the promises of open science measurement data and point out how Blockchain technology changed the circumstances for data measurement in science projects using sensors. Second, we present an open hardware project capable of securing the integrity of data directly from the source using cryptographic methods. By using inexpensive modular components and open source software, we lower the barrier for participation in open science projects. We show how time series of measurement values using sensors, e.g., temperature, current, and vibration measurements, can be verifiably and immutably stored. The approach we propose enables time series data to be stored in a tamper-proof manner and securely timestamped on a blockchain to prevent any subsequent modification.

cs.CY↗

arXiv2018

Towards Formula Translation using Recursive Neural Networks

While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural networks because mathematical formulae inherently include a structural encoding. In our implementation, we developed new techniques and topologies for recursive tree-to-tree neural networks based on multi-variate multi-valued Long Short-Term Memory cells. We propose a novel approach for mini-batch training that utilizes clustering and tree traversal. We evaluate our translator and analyze the behavior of our proposed topologies and techniques based on a translation from generic LaTeX to the semantic LaTeX notation. We use the semantic LaTeX notation from the Digital Library for Mathematical Formulae and the Digital Repository for Mathematical Formulae at the National Institute for Standards and Technology. We find that a simple heuristics-based clustering algorithm outperforms the conventional clustering algorithms on the task of clustering binary trees of mathematical formulae with respect to their topology. Furthermore, we find a mask for the loss function, which can prevent the neural network from finding a local minimum of the loss function. Given our preliminary results, a complete translation from formula to formula is not yet possible. However, we achieved a prediction accuracy of 47.05% for predicting symbols at the correct position and an accuracy of 92.3% when ignoring the predicted position. Concluding, our work advances the field of recursive neural networks by improving the training speed and quality of training. In the future, we will work towards a complete translation allowing a machine-interpretation of LaTeX formulae.

cs.LG↗